Solutions Manual
FINANCIAL MANAGEMENT Principles and Practice Fourth Edition
Timothy J. Gallagher Colorado State University
Joseph D. Andrew, Jr. Webster University
2006 Freeload Press, Madison Wisconsin
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Solutions Manual to accompany
Financial Management: Principles and Practice 4rd Edition by Timothy J. Gallagher and Joseph D. Andrew, Jr.
This solutions manual provides the answers to all the review questions and end-of-chapter problems in Financial Management: Principles and Practice, by Gallagher and Andrew. The answers and the steps taken to obtain the answers are shown. We remind our readers that in finance there is often more than one answer to a question or to a problem, depending on one‘s viewpoint and assumptions. We provide one answer to each question and show one approach to solving each problem. Other answers and approaches may be equally valid, or judged even better according to each individual‘s preference.
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TABLE OF CONTENTS Chapter 1 Solutions ...................................................................................................................5 Chapter 2 Solutions ...................................................................................................................9 Chapter 3 Solutions .................................................................................................................13 Chapter 4 Solutions .................................................................................................................16 Chapter 5 Solutions .................................................................................................................24 Chapter 6 Solutions .................................................................................................................34 Chapter 7 Solutions .................................................................................................................41 Chapter 8 Solutions .................................................................................................................53 Chapter 9 Solutions .................................................................................................................61 Chapter 10 Solutions ...............................................................................................................67 Chapter 11 Solutions ...............................................................................................................79 Chapter 12 Solutions ...............................................................................................................93 Chapter 13 Solutions .............................................................................................................103 Chapter 14 Solutions .............................................................................................................113 Chapter 15 Solutions .............................................................................................................120 Chapter 16 Solutions .............................................................................................................124 Chapter 17 Solutions .............................................................................................................131 Chapter 18 Solutions .............................................................................................................138 Chapter 19 Solutions .............................................................................................................147 Chapter 20 Solutions .............................................................................................................163 Chapter 21 Solutions .............................................................................................................167
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Chapter 1 Solutions Answers to Review Questions 1.
How is finance related to the disciplines of accounting and economics? Financial management is essentially a combination of accounting and economics. First, financial managers use accounting information—balance sheets, income statements, and so on—to analyze, plan, and allocate financial resources for business firms. Second, financial managers use economic principles to guide them in making financial decisions that are in the best interest of the firm. In other words, finance is an applied area of economics that relies on accounting for input.
2.
List and describe the three career opportunities in the field of finance. Finance has three main career paths: financial management, financial markets and institutions, and investments. Financial management involves managing the finances of a business. Financial managers—people who manage a business firm's finances—perform a number of tasks. They analyze and forecast a firm's finances; assess risk, evaluate investment opportunities, decide when and where to find money sources and how much money to raise, and decide how much money to return to the firm's investors. Bankers, stockbrokers, and others who work in financial markets and institutions focus on the flow of money through financial institutions and the markets in which financial assets are exchanged. They track the impact of interest rates on the flow of that money. People who work in the field of investments locate, select, and manage income-producing assets. For instance, security analysts and mutual fund managers both operate in the investment field.
3.
Describe the duties of the financial manager in a business firm. Financial managers measure the firm's performance, determine what the financial consequences will be if the firm maintains its present course or changes it, and recommend how the firm should use its assets. Financial managers also locate external financing sources and recommend the most beneficial mix of financing sources, and they determine the financial expectations of the firm's owners. All financial managers must be able to communicate, analyze, and make decisions based on information from many sources. To do this, they need to be able to analyze financial statements, forecast and plan, and determine the effect of size, risk, and timing of cash flows.
4.
What is the basic goal of a business? The primary financial goal of the business firm is to maximize the wealth of the firm's owners. Wealth, in turn, refers to value. If a group of people owns a business firm, the contribution that firm makes to that group's wealth is determined by the market value of that firm. 5
5.
List and explain the three financial factors that influence the value of a business. The three factors that affect the value of a firm's stock price are cash flow, timing, and risk. The Importance of Cash Flow: In business, cash is what pays the bills. It is also what the firm receives in exchange for its products and services. Cash is therefore of ultimate importance, and the expectation that the firm will generate cash in the future is one of the factors that gives the firm its value. The Effect of Timing on Cash Flows: Owners and potential investors look at when firms can expect to receive cash and when they can expect to pay out cash. All other factors being equal, the sooner companies expect to receive cash and the later they expect to pay out cash, the more valuable the firm and the higher its stock price will be. The Influence of Risk: Risk affects value because the less certain owners and investors are about a firm's expected future cash flows, the lower they will value the company. The more certain owners and investors are about a firm's expected future cash flows, the higher they will value the company. In short, companies whose expected future cash flows are doubtful will have lower values than companies whose expected future cash flows are virtually certain.
6.
Explain why accounting profits and cash flows are not the same thing. Stock value depends on future cash flows, their timing, and their riskiness. Profit calculations do not consider these three factors. Profit, as defined in accounting, is simply the difference between sales revenue and expenses. It is true that more profits are generally better than less profits, but when the pursuit of short-term profits adversely affects the size of future cash flows, their timing, or their riskiness, then these profit maximization efforts are detrimental to the firm.
7.
What is an agent? What are the responsibilities of an agent? An agent is a person who has the implied or actual authority to act on behalf of another. The owners whom the agents represent are the principals. Agents have a legal and ethical responsibility to make decisions that further the interests of the principals.
8.
Describe how society's interests can influence financial managers. Sometimes the interests of a business firm's owners are not the same as the interests of society. For instance, the cost of properly disposing of toxic waste can be so high that companies may be tempted to simply dump their waste in nearby rivers. In so doing, the companies can keep costs low and profits high, and drive their stock prices higher (if they are not caught). However, many people suffer from the polluted environment. This is why we have environmental and other similar laws: So that society's best interests take precedence over the interests of individual company owners. When businesses take a long-term view, the interests of the owners and society often (but not always) coincide. When companies encourage recycling, sponsor programs for disadvantaged young people,
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run media campaigns promoting the responsible use of alcohol, and contribute money to worthwhile civic causes, the goodwill generated as a result of these activities causes long-term increases in the firm's sales and cash flows, which translate into additional wealth for the firm's owners.
9.
Briefly define the terms proprietorship, partnership, and corporation. A proprietorship is a business owned by one person. Two or more people who join together to form a business make up a partnership. This can be done on an informal basis without a written partnership agreement, or a contract can spell out the rights and responsibilities of each partner. A limited liability company is a hybrid between a partnership and a corporation. Profits and losses pass through to the members. Members generally enjoy limited liability. Corporations are legal entities separate from their owners. To form a corporation, the owners specify the governing rules for the running of the business in a contract known as the articles of incorporation. They submit the articles to the government of the state in which the corporation is formed, and the state issues a charter that creates the separate legal entity.
10.
Compare and contrast the potential liability of owners of proprietorships, partnerships (general partners), and corporations. The sole proprietor has unlimited liability for matters relating to the business. This means that the sole proprietor is responsible for all the obligations of the business, even if those obligations exceed the amount the proprietor has invested in the business. Each partner in a partnership is usually liable for the activities of the partnership as a whole. Even if there are a hundred partners, each one is technically responsible for all the debts of the partnership. If ninety-nine partners declare personal bankruptcy, the hundredth partner still is responsible for all the partnership's debts. A corporation is a legal entity that is liable for its own activities. Stockholders, the corporation's owners, have limited liability for the corporation's activities. They cannot lose more than the amount they paid to buy the corporation‘s stock.
Answers to End-of-Chapter Problems 1.
An accountant prepares financial statements while a financial analyst interprets them.
2.
A financial manager‘s role in a publicly traded company is to make financial decisions so as to best serve the principal stockholders.
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3.
a. The value of the firm would go down due to the increase in the amount of time it takes to receive the cash inflows. b. The value of the firm would go up due to the increase in expected cash inflows. c. If expected future cash flows do not change the value of the firm would go down due to the increased riskiness of the firm.
4.
This practice obviously takes advantage of people who are in a difficult financial situation. This transaction is voluntary, however, and high risk loans have high interest rates.
5.
LLCs have a small number of members like partnerships and each of these members is likely to have an active voice in the company like a partnership. The LLC is taxed like a partnership. Unlike a partnership, and more like a corporation, the owners generally enjoy limited liability.
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Chapter 2 Solutions
Answers to Review Questions 1.
What are financial markets? Why do they exist? Financial markets are where financial securities are bought and sold. They exist primarily to bring deficit economic units (those needing money) and surplus economic units (those having extra money) together.
2.
What is a security? Securities are claims on financial assets. They can be described as “claim checks‖ that give their owners the right to receive funds in the future. Securities are traded in both the money and capital markets. Money market securities include Treasury bills, negotiable certificates of deposit, commercial paper, and banker’s acceptances. Capital market securities include bonds and stock.
3.
What are the characteristics of an efficient market? The term market efficiency refers to the ease, speed, and cost of trading securities. In an efficient market, securities can be traded easily, quickly, and at low cost. Markets lacking these qualities are considered to be inefficient.
4.
How are financial trades made on an organized exchange? Each exchange-listed security is traded at a specified location on the trading floor called the post. The trading is supervised by specialists who act either as brokers (bringing together buyers and sellers) or as dealers (buying or selling the stock themselves). Prominent international securities exchanges include the New York Stock Exchange (NYSE) and major exchanges in Tokyo, London, Amsterdam, Frankfurt, Paris, Hong Kong, and Mexico.
5.
How are financial trades made in an over-the-counter market? Discuss the role of a dealer in the OTC market. In contrast to the organized exchanges, which have physical locations, the over-the-counter market has no fixed location,or more correctly, it is everywhere. The over-the-counter market, or OTC, is a network of dealers around the world who maintain inventories of securities for sale. If you wanted to buy a security that is traded OTC, you would call your broker, who would then shop among competing dealers who have the security in their inventory. After locating the dealer with the best price, your broker would buy the security on your behalf.
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The role of dealers: Dealers make their living buying securities and reselling them to others. They operate just like car dealers who buy cars from manufacturers for resale to others. Dealers make money by buying securities for one price (called the bid price) and selling them for a higher price, (called the ask price). The difference, or spread, between the bid price and the ask price represents the dealer’s fee.
6.
What is the role of a broker in security transactions? How are brokers compensated? Brokers handle orders to buy or sell securities. Brokers are agents who work on behalf of an investor. When investors call with an order, brokers work on their behalf to find someone to take the other side of the proposed trade. If investors want to buy, brokers find sellers. If investors want to sell, brokers find buyers. Brokers are compensated for their services when the person whom they represent, the investor, pays them a commission on the sale or purchase of securities.
7.
What is a Treasury bill? How risky is it? Treasury bills are short-term debt instruments issued by the U.S. Treasury that are sold at a discount and pay face value at maturity. They are very nearly risk-free as they are backed by the U.S. Government which could, if need by, print money to pay their holders at maturity.
8.
Would there be positive interest rates on bonds in a world with absolutely no risk (no default risk, maturity risk, and so on)? Why would a lender demand, and a borrower be willing to pay, a positive interest rate in such a no-risk world? Yes, there would be a positive rate of interest in a risk-free world. This is because regardless of risk, lenders of money must postpone spending during the time the money is loaned. Lenders, then, lose the opportunity to invest their money for that period of time. To compensate for the cost of losing investment opportunities while they postpone their spending, lenders demand, and borrowers pay, a basic rate of return, the real rate of interest.
Answers to End of Chapter Problems 2-1.
a. Surplus economic units have income that exceeds their expenditures. Wealthy families in the household sector and most states (which have balanced budget requirements) are surplus economic units. b. Deficit economic units have expenditures that exceed their incomes. Home buyers and college students are likely to be deficit economic units.
2.2.
a. false b. false c. false d. false
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2-3.
a. 2 3 4 1 b. The money market is dominated by large institutional traders and there is much competition. The New York Stock Exchange tends to have larger more actively traded stocks. The over-the-counter market tends to have smaller less actively traded securities. The real estate market has very high transaction costs and trades take months.
2.4.
a. A money market security is short term and actively traded. b. Treasury bills and commercial paper are both traded in the money market.
2-5.
$66.25/$1,000 = 6 5/8 % coupon rate
2-6. The yield on a Bonds-R-Us bond: Real rate of interest...................... Inflation premium........................ Default risk premium................... Liquidity risk premium................ Maturity risk premium.................
2% 3% 1% 1% 1%
Total yield on Bonds-R-Us Bond: 8% (reference figure 2-2) 2-7. Treasury Yield Curve: Given: Treasury Security Yields: Three-month T-bills Six-month T-bills One-year T-notes Two-year T-notes Three-year T-bonds Five-year T-bonds Ten-year T-bonds Thirty-year T-bonds
4.50% 4.75% 5.00% 5.25% 5.50% 5.75% 6.00% 6.50%
Chart: (see next page)
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Maturity in Years (for Chart) 0.25 0.5 1 2 3 5 10 30
Implications: a. For borrowers: Borrowers tend to look for the low point of the curve, which indicates the least expensive loan maturity. In this case the low point is 3 months, leading the borrower to seek a shortterm loan. However, if a firm borrows long-term and obtains the higher interest rate, that rate is locked in for the life of the loan (30 years in this case). If interest rates rise the borrower may be glad he/she locked in the long-term rate. b. Lenders face the opposite situation. Granting short-term-term loans at relatively low interest rates may look unattractive now; but if short-term rates rise, the lenders will be able to roll over investments at higher and higher rates.
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Chapter 3 Solutions
Answers to Review Questions 1.
Define intermediation. The financial system makes it possible for surplus and deficit economic units to come together, exchanging funds for securities, to their mutual benefit. When funds flow from surplus economic units to a financial institution to a deficit economic unit, the process is known as intermediation. The financial institution acts as an intermediary between the two economic units.
2.
What can a financial institution often do for a surplus economic unit that it would have difficulty doing for itself if the surplus economic unit (SEU) were to deal directly with a deficit economic unit (DEU)? Surplus economic units do not usually have the expertise to determine whether deficit economic units can and will make good on their obligations, so it is difficult for them to predict when a would-be deficit economic unit will fail to pay what it owes. Such a failure is likely to be devastating to a surplus economic unit that has lent a proportionately large amount of money. In contrast, a financial institution is in a better position to predict who will pay and who won't. It is also in a better position, having greater financial resources, to occasionally absorb a loss when someone fails to pay. (This is just one example of the beneficial things financial institutions do for SEUs)
3.
What can a financial institution often do for a deficit economic unit (DEU)that it would have difficulty doing for itself if the DEU were to deal directly with an SEU? SEUs typically want to supply a small amount of funds, while DEUs typically want to obtain a large amount of funds. Thus it is often difficult for surplus and deficit economic units to come together on their own to arrange a mutually beneficial exchange of funds for securities. A financial institution can step in and save the day. A bank, savings and loan, or insurance company can take in small amounts of funds from many individuals, form a large pool of funds, and then use that large pool to purchase securities from individual businesses and governments. (This is just one example of the beneficial things financial institutions do for DEUs)
4.
What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary goal? Vault cash and deposits in the bank's account at the Fed are used to satisfy these reserve requirements; they are called primary reserves. These primary reserves are non-interest-earning assets held by financial institutions. The Federal Reserve requires all commercial banks to keep a minimum amount of reserves on hand to meet the withdrawal demands of its depositors and to pay other obligations as they come due.
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Many would argue, however, that the reserve requirement is set more with monetary policy in mind than to ensure that banks meet their depositors' withdrawal requests.
5.
Compare and contrast mutual and stockholder-owned savings and loan associations. Some savings and loan associations are owned by stockholders, just as commercial banks and other corporations are owned by their stockholders. Other S&Ls, called mutuals, are owned by their depositors. When a person deposits money in an account at a mutual S&L, that person becomes a part owner of the firm. The mutual S&L's profits (if any) are put into a special reserve account from which dividends are paid from time to time to the owner/depositors.
6.
Who owns a credit union? Explain. Credit unions are owned by their members. When credit union members put money in their credit union, they are not technically "depositing" the money. Instead, they are purchasing shares of the credit union. In general, credit unions exist to pay interest on shares bought by, and collect interest on loans made to, the members.
7.
Which type of insurance company generally takes on the greater risks: a life insurance company or a property and casualty insurance company? The risks protected against by property and casualty companies are much less predictable than are the risks insured by life insurance companies. Hurricanes, fires, floods, and trial judgments are all much more difficult to predict than the number of sixty-year-old females who will die this year among a large number in this risk class. This means that property and casualty insurance companies must keep more liquid assets than do life insurance companies.
8.
Compare and contrast a defined benefit and a defined contribution pension plan. In a defined benefit plan, retirement benefits are determined by a formula that usually considers the worker's age, salary, and years of service. The employee and/or the firm contribute the amounts necessary to reach the goal. In a defined contribution plan, the contributions to be made by the employee and/or employer are spelled out, but retirement benefits depend on the total accumulation in the individual's account at the retirement date.
9.
Special security software is used such that customers who enter their identification and password information can keep sensitive information out of the hands of hackers.
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Answers to End-of-Chapter Problems 3-1.
a) If there were no financial institutions the SEUs and the DEUs would find that the amount of money needed by a given DEU did not match the amount of money available by a given SEU. The money available would not be put to work and the economic activity that would have otherwise taken place would not. b) If financial institutions were available in this society they could position themselves between the SEUs and DEUs. The financial institution could pool the $1,000 available (100 SEUs times $10 each) and pass that money along in $100 increments to the DEUs. This could be done via either a debt or equity claim that the financial institution would accept from the DEU in return for the money.
3-2.
a) .10 rate on loans made - .05 rate paid to depositors = .05 = 5% interest rate spread b) (.5 x .10) + (.5 x .12) = .11 = 11% weighted average loan rate (.5 x .05) + (.5 x .07) = .06 = 6% weighted average deposit rate 11% - 6% = 5% interest rate spread
3-3.
($48,300,000 - $7,800,000) x .03) + (($60,000,000 - $48,300,000) x .10) + ($20,000,000 x 0) + ($10,000,000 x 0) = $6,732,000
3-4.
a) The FOMC should buy government securities in the open market. This would increase the reserves of the banking system and would put downward pressure on the federal funds rate. b) The Fed‘s trader at the New York Federal Reserve Bank would contact various government securities dealers and would buy the Treasury securities from them. Payment would be made by crediting the accounts at the Fed of these dealers. This would make more funds available and would tend to put downward pressure on the cost of these funds, the federal funds rate.
3-5.
a) ($1,000,000 x .08) – ($1,000,000 x .07) = $10,000 a profit of $10,000 b) ($1,000,000 x .08) – ($1,000,000 x .09) = -$10,000 a loss of $10,000
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Chapter 4 Solutions
Answers to Review Questions 1.
Why do total assets equal the sum of total liabilities and equity? Explain. Assets = Liabilities + Equity Assets are the items of value a business owns. Liabilities are claims on the business by non-owners, and equity is the owners' claim on the business. The sum of the liabilities and equity is the total capital contributed to the business, which, by definition, equals the total value of the assets.
2.
What are the time dimensions of the income statement, the balance sheet, and the statement of cash flows? Hint: Are they videos or still pictures? Explain. The income statement is like a video: It measures a firm's profitability over a period of time (which can be a week, a month, a year, or any other time period). The balance sheet is like a still photograph. The balance sheet shows the firm's assets, liabilities, and equity at a given point in time. This cash flow statement like the income statement, can be compared to a video: It shows how cash flows into and out of a company over a given period of time.
3.
Define depreciation expense as it appears on the income statement. How does depreciation affect cash flow? Accounting depreciation is the allocation of an asset's initial cost over time. Depreciation expense on an income statement is the amount of the asset=s initial cost allocated to the period covered by the income statement. Depreciation expense is not a cash flow. Depreciation as an expense category affects cash flow, however, because it is tax-deductible. Depreciation expense lowers a company‘s taxable income and, therefore its income tax liability. In this way depreciation reduces cash outflows..
4.
What are retained earnings? Why are they important? Retained earnings represents the sum of all the earnings available to common stockholders of a business during its entire history, minus the sum of all the common stock dividends which it has ever paid. Those earnings that were not paid out were, by definition, retained. Retained earnings are important because they represent amounts reinvested in a company on behalf of the company’s owners instead of being paid out in the form of dividends.
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5.
Explain how earnings available to common stockholders and common stock dividends paid from the current income statement affect the balance sheet item retained earnings. The change in the retained earnings account from one balance sheet to the next equals net income less preferred stock dividends (which is the amount of earnings available to common stockholders) less common stock dividends.
6.
What is accumulated depreciation? Depreciation is the allocation of an asset's initial cost over time. Accumulated depreciation is the total of all the depreciation expense that has been recognized to date.
7.
What are the three major sections of the statement of cash flows? Cash flows from Operations Cash flows from investing activities Cash flows from financing activities Net change in cash balance Cash balance at beginning of period Cash balance at end of period
8.
How do financial managers calculate the average tax rate? Average tax rates are calculated by dividing tax dollars paid by earnings before taxes (EBT).
9.
Why do financial managers calculate the marginal tax rate? Financial managers use marginal tax rates to estimate the future after-tax cash flows from investments. Since they are interested in how much of the next dollar earned from new investments will have to be paid in taxes, they use the marginal tax rate (rather than the average tax rate) to calculate the tax liability.
10.
Identify whether the following items belong on the income statement or the balance sheet. a. Interest Expense IS b. Preferred Stock Dividends Paid IS c. Plant and Equipment BS d. Sales IS e. Notes Payable BS f. Common Stock BS g. Accounts Receivable BS h. Accrued Expenses BS i. Cost of Goods Sold IS j. Preferred Stock BS k. Long-Term Debt BS
l. Cash BS m. Capital in Excess of Par BS n. Operating Income IS o. Depreciation Expense IS p. Marketable Securities BS q. Accounts Payable BS r. Prepaid Expenses BS s. Inventory BS t. Net Income IS u. Retained Earnings BS
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11.
Indicate in which section the following balance items belong (current assets, fixed assets, current liabilities, long-term liabilities, or equity). a. Cash CA b. Notes Payable CL c. Common Stock EQ d. Accounts Receivable CA e. Accrued Expenses CL f. Preferred Stock EQ g. Plant and Equipment FA
h. Capital in Excess of Par EQ i. Marketable Securities CA j. Accounts Payable CL k. Prepaid Expenses CA l. Inventory CA m. Retained Earnings EQ
Answers to End-of-Chapter Problems 4-1. Revenues Expenses Net Income Retained Earnings, Jan 1 Dividends Declared Retained Earnings, Dec 31 Current Assets, Dec 31 Non-current Assets, Dec 31 Total Assets, Dec 31 Current Liabilities, Dec 31 Non-current Liabilities, Dec 31 Total Liabilities, Dec 31 CS & Cap. in Excess of Par, Dec 31 Total Stockholders‘ Equity, Dec 31
CASE A 200,000 160,000 40,000 300,000 70,000 270,000 80,000 850,000 930,000 40,000 100,000 140,000 520,000 790,000
CASE B 110,000 70,000 40,000 100,000 30,000 110,000 230,000 180,000 410,000 60,000 140,000 200,000 100,000 210,000
Sales COGS Gross Profit Operating Expenses Operating Income (EBIT) Interest Expense Earnings Before Taxes (EBT) Tax Expense (40%) Net Income
CASE A 500,000 200,000 300,000 60,000 240,000 10,000 230,000 92,000 138,000
CASE B 250,000 100,000 150,000 60,000 90,000 10,000 80,000 32,000 48,000
4-2.
4-3.
a) 15%; $48,000 X 0.15 = $7,200 b) $7,200/$48,000 = 0.15 or 15%
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4-4.
a) Tax = $50,000 X 0.15 + $25,000 X 0.25 + $25,000 X 0.34 + $50,000 X 0.39 = $41,750 b) Effective tax rate = $41,750/$150,000 = 0.2783 or 27.83%
4-5.
The marginal tax rate is the tax rate applied to the next dollar of income. Therefore, the marginal tax rate is 34%. The average tax rate is 34% 50,000 * .15 = 7,500 25,000 * .25 = 6,250 25,000 * .34 = 8,500 235,000 * .39 = 91,650 2,865,000 * .34 = 974,100 $1,088,000 $1,088,000/$3,200,000 = 34%
4-6.
$1 + $400,000/200,000 = $3.00 per share
4-7.
Sales $10,000,000 - Operating Costs 5,200,000 - Interest Expense 200,000 = EBT $4,600,000 - Taxes (40%) 1,840,000 Net after-tax income $2,760,000 Simon‘s net after-tax income was $2,760,000 for the year.
4-8.
Depreciation expense in 2006 = $70,000 - $60,000 = $10,000.
4-9 a) Cash + Marketable Securities + Inventory + Accounts Receivable + Prepaid expenses. (11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) = 35,000,000 Current Assets = $35,000,000 b) Fixed assets – depreciation 30,000,000 – 8,000,000 = 22,000,000 Net Fixed Assets = $22,000,000 c) Notes Payable + Accrued Expenses 4,000,000 + 2,000,000 = 6,000,000 Current Liabilities = $6,000,000
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d) Current Assets – Current Liabilities (11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) – (4,000,000 + 2,000,000) 35,000,000 – 6,000,000 = 29,000,000 Net Working Capital = $29,000,000
4-10.
a) b) c) d) e)
Gross Profit $440,000 - $200,000 = $240,000 Operating Income (EBIT) $240,000 - $40,000 - 85,000 = $115,000 Earning Before Taxes (EBT) $ 115,000 - $40,000 = $75,000 Income Taxes $ 75,000 X 0.4 = $30,000 Net Income $75,000 - $30,000 = $45,000
4-11
$1,500,000 – $200,000 = $1,300,000 Simon and Pieman had a net worth of $1,300,000 at the end of the year.
4-12
a ) 2006 Depreciation Expense for this process line ($131,000 + $12,000) X (0.245) = $35,035 b ) Amount of tax savings due to this investment. $35,035 X 0.4 = $14,014
4-13.
Operating Income (EBIT) = $768,000 + Depreciation = $42,000 + Amortization = $15,000 $825,000 Target Telecom‘s EBITDA = $825,000.
4-14
a ) The company's 2006 taxable income =
($400,000 - $130,000 X 0.2)
=
$374,000
b ) Income tax = $374,000 X 0.34 = $127,160
4-15.
a) Earnings = [($600,000 - 50,000) X (1 - .34) - $63,000] = $300,000 Earnings per share = $300,000 / 100,000 = $3 per share b) Addition to Retained Earnings = $300,000 - 100,000 = $200,000
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4-16.
a ) Current Assets: b ) Total Assets: c ) Current Liabilities: d ) Total Liabilities: e ) Total Stockholders' Equity:
4-17.
2005: $5,534 + 14,745 + 10,733 + 952 + 3,234 = $35,198 2006: $9,037 + 15,943 + 11,574 + 1,801 + 2,357=$40,712 2005: $35,198+(57,340 - 29,080)+1,010+2,503 = $66,971 2006: $40,712+(60,374 - 32,478)+1,007+4,743 = $74,358 2005: $3,253 + 6,821 = $10,074 2006: $2,450 + 7,330 = $9,780 2005: $10,074 + 2,389 = $12,463 2006: $9,780 + 2,112 = $11,892 2005: $8,549 + 45,959 = $54,508 2006: $10,879 + 51,587 = $62,466
2005: $12,463 TL + $54,508 EQ = $66,971 TA 2006: $11,892 TL + $62,466 EQ = $74,358 TA
4-18. a ) Accumulated Depreciation b ) Accounts Receivable (net) c ) Inventories d ) Prepaid Expenses e ) Accounts Payable f ) Accrued Expenses g ) Plant and Equipment (gross) h ) Marketable Securities i ) Land j ) Long Term Investments k ) Common Stock l ) Bonds Payable
4-19.
Operations: Add:
(Dollars) Inflow Outflow Outflow Inflow Outflow Inflow Outflow Outflow Inflow Outflow Inflow Outflow
3,398 1,198 841 877 803 509 3,034 849 3 2,240 2,330 277
Pinewood Company and Subsidiaries Statement of Cash Flows For the year 2006
Net Income Depreciation Exp. Decrease in Prepaid Expenses Increase in Accrued Expenses Less: Increase in A/C Receivable Increase in Marketable Securities Increase in Inventories Decrease in A/C Payable Total Cash Flow from Operations Investments: Add: Decrease in Land Less: Increase in Plant and Equipment Increase in Long Term Investment Total Cash Flow from Investments
10,628 3,398 877 509 (1,198) ( 849) ( 841) ( 803) $11,721 3 (3,034) (2,240) ($5,271)
21
Financing: Add: Less:
Increase in Common Stock Common Stock Dividends Decrease in Bonds Payable Cash Flow from Financing
2,330 (5,000) ( 277) ($2,947)
Net Cash Flow
$3,503
4-20. $3,503 = $9,037 end of ‗02 cash - $5,534 end of ‗01 cash Yes, the net cash flow figure from problem #16 gives the same answer as calculating the change in the cash figures from the end of 2005 to the end of 2006 balance sheets.
4-21.
Sales COGS Gross Profit Operating Expenses Operating Income (EBIT) Interest Expense Income before taxes (EBT) Tax Expense (30%) Net Income
900,000 300,000 600,000 200,000 400,000 100,000 300,000 90,000 $210,000
4-22.
Retained Earnings end of 2006 $8,700,000 Retained Earnings end of 2005 8,000,000 Addition to retained earnings 2006 700,000 Earnings Available to Common Stockholders $1,500,000 -Addition to Retained Earnings -700,000 Dividends paid to Common Stockholders 2006 = $ 800,000
4-23.
Year Deprec. % * Depreciable Base = Depreciation 1 10% $385,000 $38,500 2 18% $385,000 $69,300 3 14.4% $385,000 $55,440 4 11.5% $385,000 $44,275 5 9.2% $385,000 $35,420 6 7.4% $385,000 $28,490 7 6.6% $385,000 $25,410 8 6.6% $385,000 $25,410 9 6.5% $385,000 $25,025 10 6.5% $385,000 $25,025 11 3.3% $385,000 $12,705
4-24.
Basis = $1,000,000 + $100,000 + $50,000 = $1,150,000 Year 3 depreciation = $1,150,000 * .148 = $170,200
22
4-25.
Year 1 $7,000,000 * .1 = $700,000 Year 2 $7,000,000 * .18 = $1,260,000 Year 3 $7,000,000 * .144 = $1,008,000 Year 4 $7,000,000 * .115 = $805,000 Year 5 $7,000,000 * .092 = $644,000 Year 6 $7,000,000 *.074 = $518,000 Year 7 $7,000,000 * .066 = $462,000 Year 8 $7,000,000 * .066 = $462,000 Year 9 $7,000,000 * .065 = $455,000 Year 10 $7,000,000 * .065 = $455,000 Year 11 $7,000,000 * .033 = $231,000
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Chapter 5 Solutions
Answers to Review Questions 1.
What is a financial ratio? A financial ratio is a number that expresses the value of one financial variable relative to another. Put more simply, a financial ratio is the result you get when you divide one financial number by another. Calculating an individual ratio is simple, but each ratio must be analyzed carefully to effectively measure a firm's performance.
2.
Why do analysts calculate financial ratios? Ratios are comparative measures. Because the ratios show relative value, they allow financial analysts to compare information that could not be compared in its raw form. For example, ratios may be used to compare one ratio to a related ratio, a firm's performance to management's goals, a firm's past and present performance, or a firm's performance to similar firms
3.
Which ratios would a banker be most interested in when considering whether to approve an application for a short-term business loan? Explain. Bankers and other lenders use liquidity ratios to see whether to extend short-term credit to a firm. Liquidity ratios measure the ability of a firm to meet its short-term obligations. These ratios are important because failure to pay such obligations can lead to bankruptcy. Generally, the higher the liquidity ratio, the more able a firm is to pay its short-term obligations.
4.
Which ratios would a potential long-term bond investor be most interested in? Explain. Current and potential lenders of long-term funds, such as banks and bondholders, are interested in debt ratios. When a business's debt ratios increase significantly, bondholder and lender risk increases because more creditors compete for that firm's resources if the company runs into financial trouble.
5.
Under what circumstances would market to book value ratios be misleading? Explain. The Market to Book ratio is useful, but it is only a rough approximation of how liquidation and going concern values compare. This is because the Market to Book ratio uses accounting-based book values. The actual liquidation value of a firm is likely to be different than the book value. For instance, the assets of a firm may be worth more or less than the value at which they are currently carried on the company's balance sheet. In addition, the current market price of the company's bonds and preferred stock may also differ from the accounting value of these claims.
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6.
Why would an analyst use the Modified Du Pont system to calculate ROE when ROE may be calculated more simply? Explain. Actually, an analyst would not use the Modified Du Pont equation to calculate ROE for precisely the reason stated above. What an analyst would use the Modified Du Pont equation for is to help analyze the factors that contribute to a firm's ROE. In other words, analysts use the Modified Du Pont system to ―take apart‖ ROE to see what factors are influencing it.
7.
Why are trend analysis and industry comparison important to financial ratio analysis? Trend analysis helps financial managers and analysts see whether a company's current financial situation is improving or deteriorating. Cross-sectional analysis, or industry comparison, allows analysts to put the value of a firm's ratios in the context of its industry.
Answers to End-of-Chapter Problems 5-1.
a) Gross Profit Margin = Gross Profit/Sales 20,000,000/35,000,000 = .5714 Gross Profit margin = 57.14% b) Operating Profit Margin = EBIT/Sales 16,000,000/35,000,000 = .4571 Operating Profit Margin = 45.71% c) Net Profit Margin = Net Income/Sales 8,100,000/35,000,000 = .2314 Net Profit Margin = 23.14%
5-2.
Current Ratio = Total Current Assets/Total Current Liabilities (5,000) / (500 +850 + 600) = 2.56 Current Ratio = 2.56 Quick Ratio = (Total Current Assets - Inventory)/Total Current Liabilities (5,000 – 900)/(500 + 850 + 600) = 2.10 Quick Ratio = 2.10
5-3.
Average Daily Credit Sales = Annual credit sales/365 5,000,000/365 = $13,698.63 Average Collection Period = Accounts Receivable/Average Daily Credit Sales $500,000/13,698.63 = 36.5 Average Collection Period = 36.5 days 25
5-4.
Inventory Turnover = Sales/Inventory 35,000,000/2,400,000 = 14.58 Inventory Turnover = 14.58 X Total Asset Turnover = Sales/Total Assets 35,000,000/(15,000,000 + 20,000,000) = 1 Total Asset Turnover = 1 X
5-5.
a) Book value per share Book price per share = Common Stock Equity/Number of shares Outstanding $4,500,000/650,000 =$6.92 BPS = $6.92 b) Market to book value ratio Market to book value ratio = Market price per share/Book value per share $25.00/$6.92 = 3.61 Market to book value ratio = 3.61
5-6.
a) b) c) d) e)
Gross profit margin: Operating profit margin Net profit margin Return on assets Return on equity
$47,378/$94,001 $12,941/$94,001 $8,620/$94,001 $8,620/$66,971 $8,620/$54,508
= = = = =
50.40% 13.77% 9.17% 12.87% 15.81%
While the Net profit margin is higher than the industry average, the Return on assets is lower. may consider increasing its debt to leverage profits.
5-7.
a) Current assets = $5,534 + $14,745 + $10,733 + $952 + $3,234 = $35,198 Current ratio = $35,198/$10,074 = 3.494 b) Quick ratio = ($35,198 - $10,733)/$10,074 = 2.429 Pinewood seems highly capable of paying off short-term debts.
5-8.
a) Total debt = $3,253 + $6,821 + $2,389 = $12,463 Debt to total assets = $12,463/$66,971 = 18.61% b) Times interest earned = $12,941/$48 = 270 times
Pinewood
Yes. The Pinewood has very low debt and its earnings are extremely high compared to its interest expense.
5-9.
a. Average collection period b. Inventory turnover c. Total asset turnover
$14,745/($94,001 / 365) = 57.25 days $94,001/$10,733 = 8.76 $94,001/$66,971 = 1.404
We would need to know the industry averages for these figures, and also know about Pinewood‘s credit and inventory management practices to comment meaningfully on the above figures.
26
5-10. Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity = 0.0917 X 1.404 X $66,971/$54,508 = 15.82%
5-11.
a) EVA = EBIT (1- tax rate) – (invested capital * investor‘s required rate of return) EVA = $12,941,000 * (1 - 0.35) – ($77,389,000 * 0.10) = $672,750 b) Pinewood has a true economic profit of $672,750. This is the amount by which its earnings exceed the returned expected by the firm‘s investors. c) MVA = Total market value – invested capital MVA = ($75,000,000 + $2,389,000) – ($54,508,000 + $2,389,000) = $20,492,000 d) Pinewood has a total market value that is $20,492,000 greater that the amount of capital invested in the firm.
5-12.
a) EVA = EBIT (1 – Tax Rate) – (invested capital * investors required rate of return) EVA = $8,000 (.65) – ($33,000 * .12) = $5,200 – $3,960 EVA = $1,240 b) The economic value is positive; therefore, Eversharp earned a sufficient amount during the year to provide more than the expected rate of return from the investors and lenders who contributed to the capital of the company. c) MVA = Total market value – invested capital MVA = $33,000 - $21,000 = $12,000 d) Eversharp‘s total market value exceeds its invested capital by $12,000.
5-13. EVA & MVA Calculation: Income tax rate Cost of Capital Stock Price (ref) Number of shares outstanding (ref) Market Value of Common Equity (ref) Book Value of Common Equity Debt Capital (ref) Total Invested Capital (ref) EVA MVA a. EVA
35% 12% Ka $9 3,000 $27,000 $15,210 $6,630 (Notes payable + Long-Term Debt ) $33,630 (Debt + Common)
$189
EBIT(1-Tr) - (Invested Capital * Ka)
b. Comment on EVA: This year T & J earned enough to exceed the return expected by the contributors of the firm's capital by $189.
27
5-14.
a. Du Pont:
ROA
Modified Du Pont:
ROE Equity
= Net Profit Margin X Total Asset Turnover = (80/1,000) X (1,000/500) = 16% = Net Profit Margin X Total Asset Turnover X Assets = ($80/$1,000) X ($1,000/$500) X (1/(1-0.5) = 32%
b. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.7) = 53.3% c. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.9) = 160% d. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.1) = 17.78%
5-15. Assets Cash Accounts Receivable Inventory Prepaid Expenses Total Current Assets Fixed Assets Total Assets
$6,000 15,068 6,667 282 28,017 34,483 $62,500
Liabilities + Equity Accounts Payable Notes Payable Accrued Expenses Total Current Liabilities Bonds Payable Common Stock Retained Earnings Total Liabilities + Equity
$6,000 2,739 600 9,339 15,661 16,000 21,500 $62,500
Total Assets = Sales / Total Asset Turnover = $100,000/1.6 = $62,500 Fixed Assets = Sales / Fixed Asset Turnover = $100,000/2.9 = $34,483 Total Current Assets = $62,500 - $34,483 = $28,017 Accounts Receivable = Sales/day X Ave. Collection Period = ($100,000/365) X 55 = $15,068 Inventory = Sales / Inventory Turnover = $100,000/15 = $6,667 Prepaid Expenses = $28,017 - ($15,068 + $6,667 + $6,000) = $282 Total Debt = Total Assets X Debt to Asset Ratio = $62,500 X 0.4 = $25,000 Total Current Liabilities = Total Current Assets / Current Ratio = $28,017/3 = $9,339 Bonds Payable = Total Debt - Total Current Liabilities = $25,000 - $9,339 = $15,661 Retained Earnings = $62,500 - ($16,000 + $25,000) = $21,500 Notes Payable = $9,339 - ($600 + $6,000) = $2,739
5-16.
NI/$5,000 = 0.10 NI = $500 TE = TA - TL = $10,000 - $6,000 = $4,000 ROE = $500/$4,000 = .125 = 12.5%
5-17.
Current Liability = $20,000 - $18,000 = $2,000 Current Ratio = $5,000/$2,000 = 2.5 times
5-18.
Return on Assets = Net Profit Margin X Total Asset Turnover 0.12 = 0.04 X Total Asset Turnover Total Asset Turnover = 0.12/0.04 = 3
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over
5-19.
Gross Profit = 0.50 X $5,000,000 = $2,500,000
5-20.
EBIT = $2,500,000 - $200,000 - $50,000 = $2,250,000 Operating Profit Margin = $2,250,000/$5,000,000 = .45 = 45%
5-21.
Net Income = 0.20 X $5,000,000 = $1,000,000
5-22.
Net Income = 0.20 X $5,000,000 = $1,000,000 ROA = $1,000,000/$20,000,000 = .05 = 5%
5-23.
Net Income = 0.10 X $15,000,000 = $1,500,000
5-24.
Current Ratio = (20,000,000 - 2,000,000)/4,000,000 = 4.5
5-25.
Quick Ratio = ($20,000,000 - $2,000,000 - $3,000,000)/$4,000,000 = 3.75 times
5-26.
Total Debt = 0.30 X $20,000,000 = $6,000,000 Debt to Equity ratio = $6,000,000/$14,000,000 = 0.43
5-27.
Inventory Turnover = 5,000,000/3,000,000 = 1.67
5-28.
Return on Assets = 0.20 X 0.25 = 0.05 = 5%
5-29. a) Du Pont:
ROA
= Net Profit Margin X Total Asset Turnover = ($200/$2,000) X ($2,000/$1,000) = .20 = 20% Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.6)) = .50 = 50%
b)
ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.8)) = 100%
c)
ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.2)) = 25%
5-30.
Notoriously Niagara
Niagara‘s Notions
a)
NPM = $100,000/$500,000 = 0.20
NPM = $10,000/$500,000 = 0.02
b)
TATO = $500,000/$500,0000 = 0.10
TATO = $500,000/$500,000 = 1.0
c)
ROA = 0.20 X 0.10 = 0.02
ROA = 0.02 X 1.0 = 0.02
29
d) Notoriously Niagara must have a higher net profit margin because their asset turnover is low compared to that of Niagara‘s Notions even though they have the same ROA. Niagra‘s Notions has a high asset turnover but a low net profit margin.
5-31.
a) b) c) d) e)
$2,250,000/1,750,000=$1.29 $40/$1.29 = 31 $15,000,000/1,750,000 = $8.57 $40/$8.57 = 4.67 Yes, the market seems to believe that the company has going-concern value as evidenced by the market to book ratio greater than 1.
5-32.
Net Profit Margin Current Ratio NI/Sales CA/CL
Year 2004 2005 2006 Golden Products Industry averages:
Total Asset Turnover Sales/TA
10.00% 9.44% 9.36%
.94 1.02 1.08
1.05 1.15 1.18
9.42%
1.13
2.00
The NPM is about average, although it is deteriorating. The liquidity, as measured by the current ratio, is below average but improving. Asset utilization, as measured by the total asset turnover is way below average. 5-33.
The Industry averages are: Fixed Asset Turnover 1.33 YEAR 2004 2005 2006
Return on Assets
Debt to Assets Ratio
11.00% PM 10.00% 9.44% 9.36%
CR 0.94 1.02 1.08
Return on equity
0.60 TATO 1.05 1.15 1.18
FATO 1.21 1.33 1.36
26% ROA 10.53% 10.90% 11.00%
D/A 0.68 0.64 0.60
ROE 33.33% 30.36% 27.50%
Golden Products has an improving ROA that now equals that of the industry norm. The ROE has slipped a little, but is still above the industry norm in spite of the fact that Golden has a little less debt in its capital structure in 2006. Overall, Johnny should be pleased.
5-34. ( Figures in $ '000) Mining Smelting NPM 3.3% 8.7% ROA 4.2% 10.4%
Rolling Extrusion 11.7% 10.0% 17.9% 13.9%
30
Whole Company 9.7% 13.4%
5-35. National Glass Company Income Statement (in $ 000's) 2006 Sales Cost of Goods Sold Gross Profit Selling and Admin Expenses Depreciation Operating Income Interest Expense Earnings Before Tax Income Taxes Net Income Preferred Dividends Earnings Available to Common
$45,000 23,000 22,000 13,000 3,000 6,000 200 5,800 2,320 $3,480
Ratios: ACP Inventory Turnover Debt to Assets Current Ratio Total Asset turnover Fixed Asset Turnover Return on Equity Return on Assets Operating Profit Margin Gross Profit Margin
48.7 days 9X 40% 1.6250 1.50 2.6471 19.33% 11.6% 13.33% 48.89%
$0 $3,480
Balance Sheet (in $ 000's) As of Dec 31 2006 Assets Current Assets: Cash Accounts Receivable Inventory Total Current Assets Plant & Equipment, Net Land Total Assets Liabilities & Equity Current Liabilities: Accounts Payable Notes Payable Accrued Expenses Total Current Liabilities Bonds Payable Total Liabilities Common Stock Retained Earnings Total Stockholders' Equity Total Liabilities & Equity
5-36. a.)
$2,000 6,000 5,000 13,000 16,000 1,000 $30,000
$2,000 3,000 3,000 8,000 4,000 12,000 4,000 14,000 18,000 $30,000
(Industry) i. ii. iii. iv. v. vi. vii. viii. ix.
Kingston, 2006
Gross Profit Margin (50%) Operating Profit Margin (15%) Net Profit Margin (8%) Return on Assets (10%) Return on Equity (20%) Current Ratio (1.5) Quick Ratio (1.0) Debt to Total Asset (0.5) Times Interest Earned (25)
48.9% 15.1% 8.5% 11.56% 19.3% 1.63 1.00 .4 15.5X
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Kingston, 2007 48.9% 13.3% 7.5% 9.97% 16.3% 1.62 1.04 .39 14.6X
x. xi. xii.
Average Collection Period (45 days) Inventory Turnover (8) Total Asset Turnover (1.6)
53.5days 8.18X 1.4X
61.6days 8.62X 1.3X
b.) Kingston has about the same net profit margin and return on equity as the industry norm. The return on assets ratio for Kingston is about the same as than the industry norm. c.) Determine the sources and uses of funds and prepare a statement of cash flows for 2007. (1) Sources and Uses of Funds: Change, 2006 to 2007 Balance SheetSources Uses Net Income Dividends paid Depreciation Cash Accounts Receivable, Net Inventory Property, Plant & Equipment, Gross Land Accounts Payable Notes Payable Accrued expenses Bonds Payable Common Stock Totals
$3,353 $733 $3,000 ($200) $200 $1,600 $1,600 $220 $220 $5,000 $5,000 $0 $600 $600 $300 $300 $100 $100 $0 $0 $7,553$7,553
(2) Statement of Cash Flows: Kingston Tool Company Statement of Cash Flows for the year 2007 ( in $ 000s) Cash Flows from Operations: Net Income $3,353 Depreciation 3,000 Decrease(Increase) in Accounts Receivable (1,600) Decrease(Increase) in Inventory (220) Increase(Decrease) in Accounts Payable 600 Increase(Decrease) in Notes Payable 300 Increase(Decrease) in Accrued Expenses 100 Total Cash Flows from Operations $5,533 Cash Flows from Investments: New Property, Plant, & Equipment ($5,000) Total Cash Flows from Investments ($5,000) Cash Flows from Financing: Dividends Paid ($733) Total Cash Flows from Financing (733) Net Cash Flow ($200) Beginning Cash Balance Ending Cash Balance
$2,000 $1,800
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d.) Profit margins are eroding and generally a little below the industry norm. Liquidity is about average. Debt is low, but interest coverage is below the industry norm in spite of the low debt load. Inventory turnover is way below average. The negative cash flow of $200,000 came mainly from the buildup of accounts receivable and plant & equipment. e.) The current ratio, quick ratio, and times interest earned would get the most scrutiny from loan officers. 5-36b. EVA = EBIT * (1 – tax rate) – (invested capital * investor‘s required rate of return) EVA = ($4,000 * 0.60) – ($60,000 * 0.10) = -$3,600 EVA = -$3,600 MVA = Total market value – invested capital MVA = $50,000 - $60,000 = -$10,000 MVA = -$10,000
5.37.
a) Accounts Receivable/Average Daily Credit Sales $564,000.00 / ($3,814,000 / 365)= 53.71 = 54 days b) Super Dot Com was more profitable in 2006 than it was in 2004. 2004 $519,000/$2,100,000 Net Profit Margin 24.71%
Return on Assets
2006_________ $1,115,000/$3,814,000 29.23%
$519,000/$2,859,000 18.15%
$1,115,000/$5,316,000 20.97%
Both the NPM and ROA ratios were better in 2006. c) Super Dot Com was less liquid at the end of 2006 than it was at the end of 2004.
Current Ratio
2004 $981,000/$245,000 4.00
2006_________ $1,720,000/$623,000 2.76
Quick Ratio
($981,000 - $307,000)/$245,000 2.75
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($1,720,000 - $960,000)/$623,000 1.22
Chapter 6 Solutions
Answers to Review Questions 1.
Why do businesses spend time, effort, and money to produce forecasts? Explain. Businesses succeed or fail depending on how well prepared they are to deal with the situations they confront in the future. Therefore they expend considerable sums making estimates (forecasts) of what the future situation is likely to be. Businesses develop new products, set production quotas, and select financing sources based on forecasts about the future economic environment and the firm's condition. If economists predict interest rates will be relatively high, for example, firms may plan to limit borrowing and defer expansion plans.
2.
What is the primary assumption behind the experience approach to forecasting? The experience approach to forecasting is based on the assumption that things will happen a certain way in the future because they happened that way in the past. For instance, if it has always taken you fifteen minutes to drive to the grocery store, then you will probably assume that it will take you about fifteen minutes the next time you drive to the store. Similarly, financial managers often assume sales, expenses, or earnings will grow at certain rates in the future because they grew at that rate in the past.
3.
Describe the sales forecasting process. Sales forecasting is a group effort. Sales and marketing personnel usually provide assessments of demand and the competition. Production personnel usually provide estimates of manufacturing capacity and other production constraints. Top management will make strategic decisions affecting the firm as a whole. Financial managers coordinate, collect, and analyze the sales forecasting information. Figure 6-1 in the text shows a diagram of the process.
4.
Explain how the cash budget and the capital budget relate to pro forma financial statements. The cash budget shows the projected flow of cash in and out of the firm for specified time periods. The capital budget shows planned expenditures for major asset acquisitions. Forecasters incorporate data from these budgets into pro forma financial statements under the assumption that the budget figures will, in fact, occur.
5.
Explain how management goals are incorporated into pro forma financial statements. Management sets a target goal, and forecasters produce pro forma financial statements under the assumption that the goal will be reached. For example, if management‘s goal is to pay off all shortterm notes during the coming year, forecasters would incorporate this into the pro forma balance sheet by setting Notes Payable to zero.
34
6.
Explain the significance of the term additional funds needed. When the pro forma balance sheet is completed, total assets and total liabilities and equity will rarely match. The discrepancy between forecasted assets and forecasted liabilities and equity results when either too little or too much financing is projected for the amount of asset growth expected. The discrepancy is called additional funds needed (AFN) when forecast assets exceed forecast liabilities and equity, and excess financing when forecast liabilities and equity exceed forecast assets.
7.
What do financial managers look for when they analyze pro forma financial statements? After the pro forma financial statements are complete, financial managers analyze the forecast to determine (1) what current trends suggest what will happen to the firm in the future, (2) what effect management's current plans and budgets will have on the firm, and (3) what actions to take to avoid problems revealed in the pro forma statements
8.
What action(s) should be taken if analysis of pro forma financial statements reveals positive trends? Negative trends? When analyzing the pro forma statements, managers often see signs of emerging positive or negative conditions. If forecasters discover positive indicators, they will recommend that current plans be continued. If forecasters see negative indicators, they will recommend corrective action.
Answers to End-of-Chapter Problems 6-1. Sales Record for The Miniver Corporation $250,000
$200,000
$150,000
$100,000
$50,000
$0 1997
1998
1999
2000
2001
2002
2003
Sales in 2007 is expected to be approximately $215,000 following the trend of the last six years as shown above.
35
6-2. This year
Next Year
Forecasting Assumption
100 50 40 10
120 60 40 20
5
10
Current Assets Fixed Assets Total Assets
60 100 160
72 100 172
Constant % of sales(120 X 0.6) Remains same (100 + 72)
Current Liabs. Long-term Debt Common Stock Retained Earns. Tot Liabs & Eq
20 20 20 100 160
24 20 20 110 174
Constant % of sales (120 X 0.2) Remains same Remains same (100+20-10)
Sales - Variable Costs - Fixed Costs = Net Income Dividends
Sales will grow 20%(100 X 1.2) Constant % of sales(120 X 0.5) Remains same (120 - 60 - 40) Keep 50% Payout Ratio(20 X 0.5)
AFN = 172-174= -2 (Negative AFN means there are excess funds.)
6-3.
Jolly Joe's Pizza, Inc. Financial Status and Forecast 2006
Est. for 2007
$10,000 4,000 6,000 3,000 3,000 1,000 $2,000
20,000 8,000 12,000 3,000 9,000 3,000 6,000
$0
0
Current Assets Net Fixed Assets Total Assets
$25,000 15,000 $40,000
50,000 15,000 65,000
Current Liabilities Long-term debt Common Stock Retained Earnings Total Liabs & Eq
$17,000 3,000 7,000 13,000 $40,000
34,000 3,000 7,000 19,000 63,000
Sales COGS Gross Profit Fixed Expenses Before-Tax Profit Tax @ 33.33% Net Profit Dividends
Joe will need $2,000 in additional funds in 2007 ($65,000 - $63,000).
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6-4.
Sugar Cane Alley Financial Status and Forecast 2006 Sales $90,000 COGS 48,000 Gross Profit 42,000 Selling and marketing expenses 13,000 General and administrative expenses 5,000 Depreciation Expense 2,000 Operating Income Interest Expense EBT Tax @ 30% Net Profit
Est. for 2007 110,000 58,667 51,333 15,889 5,000 2,000
22,000
28,444 800 27,644 8,293 19,351
Dividends
10,000
Addition to RE
9,351
6-5.
a)
Cash .111111 X $110,000 = $12,222 Accounts Receivable .024667 X $110,000 = $2,713 Inventory .088889 X $110,000 = $9,778
b)
Property and Equipment, gross $25,000 Accumulated Depreciation $6,000 Property and Equipment, net $19,000 Total Assets $19,000 + $12,222 + $2,713 + $9,778 = $43,713
c)
Accounts Payable
d)
Total Liabilities = $8,000 + $1,687 = $9,687
e)
Total Liabilities and Equity = $50,878
f)
Total Assets = $12,222 + $2,713 + $9,778 + $19,000 = $43,713 AFN = $43,713 - $50,878 = -$7,165 There are excess funds of $7,165.
g)
2006: Net Profit Margin = $14,840/$90,000 = 16.49% 2007: Net Profit Margin = $19,351/$110,000 = 17.6%
.015333 X $110,000 = $1,687
= $9,687 + $9,351 + $5,000 + $26,840
37
6-6. Assets
2006
2007
Liabilities
Cash $10,000 $12,500 Acct Rec. 25,000 31,250 Inventory 20,000 25,000 Prepaid Exp 2,000 2,500 Total Current Assets 57,000 71,250 Fixed Assets 32,000 32,000 Depreciation 4,000 4,000 Total Assets 85,000 $99,250
Accounts Payable Notes Payable Accrued Expenses Long Term Debt Common Equity Total Liabilities Equity
2006
2007
$10,500 10,000 11,000 15,000 38,500
$13,125 12,500 13,750 15,000 38,500
85,000
$92,875
*Net Sales for 2007 = $150 million * 1.25 = $187.5 million Additional funds needed = $99,250 - $92,875 = $6,375
6-7. 2006 Sales Variable Costs Fixed Costs Net Income Dividends
6-8.
2007
1,000 500 160 340 136
1,250 562.50 160 527.50 290.13
Pro Forma Balance Sheets End of Year Assets 2006 2007 Cash $4,000 4,400 Accounts Rec 10,000 11,000 Inventory 13,000 14,300 Prepaid Exp 400 440 Current Assets27,400 30,140 Fixed Assets 11,000 11,000
Liabilities + Equity 2006 2007 Accounts Payable $4,400 4,840 Notes Payable 4,000 4,400 Accrued Expenses 5,000 5,500 Tot.Current Liabilities13,400 14,740 Bonds Payable 6,000 6,000 Common Equity 19,000 21,468
Total Assets
Tot.Liab. + Equity
$38,400 $41,140
$38,400 $42,208
In 2007 there would be $1,068 ($42,208-$41,140) in excess funds. This assumes, as the problem states, that notes payable would increase by 10% along with other current liabilities. Notes payable usually does not increase with sales. Year 2007
Total Sales $85,000 X 1.1 = $93,500
PBT NI Addition to RE $93,500 X .11 $10,285 X .6 $6,171 X .40 = $10,285 = $6,171 = $2,468
38
6-9. Compute the following ratios for 2006 and 2007: 2006 2007 Current Ratio 3 3 Debt to Assets Ratio 25% 25.3% Sales to Assets Ratio 62.5% 66.27% Net Profit Margin 10% 13.64% Return on Assets 6.25% 9.04% Return on Equity 8.33% 12.10% Liquidity seems strong and stable. Debt is modest and stable. Asset utilization is improving slightly while all the profit margins calculated show marked improvement.
6-10. BRIGHT FUTURE CORPORATION Historical and Projected Income Statements Historical 2006 Sales Cost of goods Sold Gross Profit Selling & Admin. Expenses Depreciation Expense Operating Income (EBIT) Interest Expenses Earnings Before Tax (EBT) Income Tax (40%) Net Income (NI)
Projected 2007
$10,000,000 $12,000,000 $4,000,000 $4,800,000 $6,000,000 $7,200,000 $800,000 $960,000 $2,000,000 $2,000,000 $3,200,000 $4,240,000 $1,350,000 $1,350,000 $1,850,000 $2,890,000 $740,000 $1,156,000 $1,110,000 $1,734,000
Common Stock Dividends paid Addition to Retained earnings Earnings per Share (1,000,000 shares)
$400,000 $710,000 $1.11
$400,000 $1,334,000 $1.73
BRIGHT FUTURE CORPORATION Historical and Projected Balance Sheets Projection with AFN Historical Projected Excess Financing Dec 31, 2006 Dec 31, 2007 Incorporated ASSETS Current Assets: Cash Marketable Securities Accounts Receivable (gross) Less: Allowance for bad Debts Accounts Receivable (Net) Inventory Prepaid Expenses Total Current Assets Plant and Equipment (gross) Less: Accumulated Depreciation Plant and equipment (net) TOTAL ASSETS
$9,000,000 $8,000,000 $1,200,000 $200,000 $1,000,000 $20,000,000 $1,000,000 $39,000,000 $20,000,000 $9,000,000 $11,000,000 $50,000,000
$10,800,000 $9,600,000 $1,440,000 $240,000 $1,200,000 $24,000,000 $1,200,000 $46,800,000 $20,000,000 $11,000,000 $9,000,000 $55,800,000
$10,800,000 $9,600,000 $1,440,000 $240,000 $1,200,000 $24,000,000 $1,200,000 $46,800,000 $20,000,000 $11,000,000 $9,000,000 $55,800,000
LIABILITIES AND EQUITY Current Liabilities: Accounts payable Notes Payable
$12,000,000 $14,400,000 $5,000,000 $5,000,000
$14,400,000 $5,000,000
39
Accrued Expenses Total Current Liabilities L-T Debt (Bonds Payable, 5%, due 2015) Total Liabilities Common Stock (1,000,000 shares, $1 par) Capital in Excess of Par Retained Earnings Total Equity TOTAL LIABILITIES AND EQUITY
$3,000,000 $20,000,000 $20,000,000 $40,000,000 $1,000,000 $4,000,000 $5,000,000 $10,000,000 $50,000,000
$3,600,000 $23,000,000 $20,000,000 $43,000,000 $1,000,000 $4,000,000 $6,334,000 $11,224,000 $54,224,000
Question 2a. Excess Financing (Additional Funds Needed)
$1,466,000
$3,600,000 $23,000,000 $21,466,000 $44,576,000 $1,000,000 $4,000,000 $6,334,000 $11,224,000 $55,800,000
AFN is incorporated in L-T debt. If $1,466,000 of new L-T debt is issued the financing need will be met. Other financing sources could be used but we chose new L-T debt in this illustration. Question 2, Ratios: 2006
2007
b. Current Ratio
1.95
2.03
c. Total Asset Turnover Inventory Turnover
0.20 0.50
0.22 0.50
d. Total Debt to Assets
0.80
0.77
e. Net Profit Margin Return on Assets Return on Equity
11.10% 14.45% 2.22% 3.11% 11.10% 15.30%
Question 3, Comments on liquidity, asset productivity, debt management, and profitability: Liquidity is improving. Debt is high but stable. Inventory and overall asset utilization are stable. The net profit margin appears healthy. The return on assets ratio is much lower than the net profit margin because of the low asset turnover. The return on equity ratio is much higher than the return on assets because of the high debt load. Question 4, Recommendations: A 20% projected increase in sales is quite impressive. Management should prepare now, however, to raise the $1,466,000 that will be needed in 2007 to support the necessary new investments if the projected sales increase is to be achieved.
40
Chapter 7 Solutions
Answers to Review Questions 1.
What is risk aversion? If common stockholders are risk averse, how do you explain the fact that they often invest in very risky companies? Risk aversion is the tendency to avoid additional risk. Risk-averse people will avoid risk if they can, unless they receive additional compensation for assuming that risk. In finance, the added compensation is a higher expected rate of return. People are not all are equally risk averse. For example, some people are willing to buy risky stocks, while others are not. The ones that do, however, almost always demand an appropriately high expected rate of return for taking on the additional risk.
2.
Explain the risk–return relationship. The relationship between risk and required rate of return is known as the risk–return relationship. It is a positive relationship because the more risk assumed, the higher the required rate of return most people will demand. Risk aversion explains the positive risk–return relationship. It explains why risky junk bonds carry a higher market interest rate than essentially risk-free U.S. Treasury bonds.
3.
Why is the coefficient of variation often a better risk measure when comparing different projects than the standard deviation? Whenever we want to compare the risk of investments that have different means, we use the coefficient of variation (CV). The CV represents the standard deviation's percentage of the mean. Because the CV is a ratio, it adjusts for differences in means, while the standard deviation does not. therefore the CV provides a standardized measure of the degree of risk that can be used to compare alternatives.
4.
What is the difference between business risk and financial risk? Business risk refers to the uncertainty a company has with regard to its operating income (also known as earnings before interest and taxes or EBIT). Business risk is brought on by sales volatility and intensified by the presence of fixed operating costs. Financial risk is the additional volatility of net income caused by the presence of interest expense. Firms that have only equity financing have no financial risk because they have no debt on which to make fixed interest payments. Conversely, firms that operate primarily on borrowed money are exposed to a high degree of financial risk.
41
5.
Why does the riskiness of portfolios have to be looked at differently than the riskiness of individual assets? The riskiness of portfolios has to be looked at differently than the riskiness of individual assets because the weighted average of the standard deviations of returns of individual assets does not result in the standard deviation of a portfolio containing the assets. There is a reduction in the fluctuations of the returns of portfolios which is called the diversification effect.
6.
What happens to the riskiness of a portfolio if assets with very low correlations (even negative correlations) are combined? How successfully diversification reduces risk depends on the degree of correlation between the two variables in question. When assets with very low or negative correlations are combined in portfolios, the riskiness of the portfolios (as measured by the coefficient of variation) is greatly reduced.
7.
What does it mean when we say that the correlation coefficient for two variables is -1? What does it mean if this value were zero? What does it mean if it were +1? Correlation is measured by the correlation coefficient, represented by the letter r. The correlation coefficient can take on values between +1.0 (perfect positive correlation) to -1.0 (perfect negative correlation). The closer r is to +1.0, the more the two variables will tend to move with each other at the same time. The closer r is to -1.0, the more the two variables will tend to move opposite each other at the same time. An r value of zero indicates that the variables‘ values aren't related at all. This is known as statistical independence.
8.
What is nondiversifiable risk? How is it measured? Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the other half—which is extremely unlikely—some risk will remain after assets are combined into a portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk that can't be eliminated by diversifying. Nondiversifiable risk is measured by a term called beta (). The ultimate group of diversified assets, the market, has a beta of 1.0. The betas of portfolios, and individual assets, relate their returns to those of the overall stock market. Portfolios with betas higher than 1.0 are relatively more risky than the market. Portfolios with betas less than 1.0 are relatively less risky than the market. (Risk-free portfolios have a beta of zero.)
9.
Compare diversifiable and nondiversifiable risk. Which do you think is more important to financial managers in business firms? Diversifiable risk can be dealt with by, of course, diversifying. Nondiversifiable risk is generally compensated for by raising one‘s required rate of return. Both types of risk are important to financial managers.
42
10.
How do risk-averse investors compensate for risk when they take on investment projects? Because of risk aversion, people demand higher rates of return for taking on higher-risk projects.
11.
Given that risk-averse investors demand more return for taking on more risk when they invest, how much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury bill? Although we know that the risk–return relationship is positive, the question of much return is appropriate for a given degree of risk is especially difficult. Unfortunately, no one knows the answer for sure. One well-known model used to calculate the required rate of return of an investment, given its degree of risk, is the Capital Asset Pricing Model (CAPM).
12.
Discuss risk from the perspective of the Capital Asset Pricing Model (CAPM). The Capital Asset Pricing Model, or CAPM, can be used to calculate the appropriate required rate of return for an investment project given its degree of risk as measured by beta (). A project's beta represents its degree of risk relative to the overall stock market. In the CAPM, when the beta term is multiplied by the market risk premium term, the result is the additional return over the risk-free rate that investors demand from that individual project. High-risk (high-beta) projects have high required rates of return, and low-risk (low-beta) projects have low required rates of return.
Answers to End-of-Chapter Problems 7-1. Cash Flow
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
$10,000
5.00%
$500
$13,000
10.00%
$16,000
20.00%
$19,000
30.00%
$5,700
$0
$0
$0
$22,000
20.00%
$4,400
$3,000
$9,000,000
$1,800,000
$25,000
10.00%
$2,500
$6,000
$36,000,000
$3,600,000
$28,000
5.00%
$1,400
$9,000
$81,000,000
$4,050,000
Sum of (R x P) = mean:
$19,000
Sum of P x (CF- mean) = variance: Square root of variance = standard deviation of the variance:
$18,900,000 $4,347
2
2
($9,000)
$81,000,000
$4,050,000
$1,300
($6,000)
$36,000,000
$3,600,000
$3,200
($3,000)
$9,000,000
$1,800,000
2
Coefficient of Variation = std.dev./mean =
43
(CF - mean) P x (CF - mean)
22.88%
7-2. EXPECTED VALUE, STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF OPERATING INCOME Operating Sales Variable
Fixed
Estimate Expenses Expenses
Income
Prob.
Estimate
of Occurrence
CF
P
CF x P
CF - mean
2.00%
$0
($350)
$122,500
$2,450
$500
$250
$250
$0
(CF - mean)
2
Px(CF - mean
2
$700
$350
$250
$100
8.00%
$8
($250)
$62,500
$5,000
$1,200
$600
$250
$350
80.00%
$280
$0
$0
$0
$1,700
$850
$250
$600
8.00%
$48
$250
$62,500
$5,000
$1,900
$950
$250
$700
2.00%
$14 $350
$350
$122,500
$2,450
b.
Sum of (CF- mean) x P= variance Square root of variance = standard deviation:
$14,900 $122
c.
Coeff. of Variation = std.dev/mean:
34.88%
a.
Sum of (R x P) = mean:
2
d. New expected value, standard deviation, and coefficient of variation based on revised sales forecast: Operating Sales Variable
Fixed
Estimate Expenses Expenses
Income
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
Px(CF - mean)
2
$500
$250
$250
$0
10.00%
$0
($350)
$122,500
$12,250
$700
$350
$250
$100
15.00%
$15
($250)
$62,500
$9,375
$1,200
$600
$250
$350
50.00%
$175
$0
$0
$0
$1,700
$850
$250
$600
15.00%
$90
$250
$62,500
$9,375
$1,900
$950
$250
$700
10.00%
$70 $350 $350 Sum of (R x P) = mean: 2 Sum of P x (CF - mean) = variance:
$122,500
$12,250
a.
b. Square root of variance = standard deviation: c. e. Comments:
7-3.
Coeff. of Variation = std. dev./mean:
$43,250 $208 59.43%
Note how the increased possibilities that sales will be other than $1,200 caused the standard deviation and coefficient of variation of operating income to nearly double.
Mean: .10(1,000) + .2(5,000) + .45(10,000) + .15(15,000) + .10(20,000) = 100 + 1,000 + 4,500 + 2,250 + 2,000 Mean = $9,850 Standard Deviation: ơ 2 = .1(1,000 – 9,850)2 + .2(5,000 – 9,850)2 + .45(10,000 – 9,850)2 + .15(15,000 – 9,850)2 + .1(20,000 – 9,850)2 ơ 2 = 7,832,250 + 4,704,500 + 10,125 + 3,978,375 + 10,302,250 ơ 2 = 26,827,500 ơ = √ 26,827,500 ơ = 5,179.53 Standard deviation = 5,179.53 44
7-4. I. EQUITY EDDIE'S COMPANY: Operating Income Estimate
Interest
Before-Tax
Expense
Income
Taxes
Net
Probability
Income
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
Px(CF 2 mean)
$100
$0
$100
$28
$72
5.00%
$4
($216)
$46,656
$2,333
$200
$0
$200
$56
$144
10.00%
$14
($144)
$20,736
$2,074
$400
$0
$400
$112
$288
70.00%
$202
$0
$0
$0
$600
$0
$600
$168
$432
10.00%
$43
$144
$20,736
$2,074
$700
$0
$700
$196
$504
5.00%
$25 $288
$216
$46,656
$2,333
a.
Sum of (R x P) = mean: 2
Sum of P x (CF - mean) = variance:
$8,813 $94
b. Square root of variance = standard deviation: c. Coeff. of Variation = std. dev./mean:
32.60%
II. BARRY BORROWER'S COMPANY: Operating Income Estimate
Interest
Before-Tax
Expense
Income
Taxes
Net
Probability
Income
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
Px(CF 2 mean)
$110
$40
$70
$19.6
$50.4
5.00%
$2.52
($237.60)
$56,453.76
$2,822.69
$220
$40
$180
$50.4
$129.6
10.00%
$12.96
($158.40)
$25,090.56
$2,509.06
$440
$40
$400
$112.0
$288.0
70.00%
$201.60
$0.00
$0.00
$0.00
$660
$40
$620
$173.6
$446.4
10.00%
$44.64
$158.40
$25,090.56
$2,509.06
$770
$40
$730
$204.4
$525.6
5.00%
$26.28 $288.00
$237.60
$56,453.76
$2,822.69
a.
Sum of (R x P) = mean: 2
Sum of P x (CF - mean) = variance: b. Square root of variance = standard deviation= c. Coeff. of Variation = std. dev./ mean: e. Comments:
$10,663.49 $103.26 35.86%
Note how Barry Borrower's use of debt financing causes his company to have a higher standard deviation and coefficient of variation of net income than Equity Eddie's.
7-5. STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF CASH FLOWS FOR THE GO-RILLA PROJECT Cash Flow
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
P x (CF - mean)
2
$20,000
1.00%
$200
($6,000)
$36,000,000
$360,000
$22,000
12.00%
$2,640
($4,000)
$16,000,000
$1,920,000
$24,000
23.00%
$5,520
($2,000)
$4,000,000
$920,000
$26,000
28.00%
$7,280
$0
$0
$0
$28,000
23.00%
$6,440
$2,000
$4,000,000
$920,000
45
$30,000
12.00%
$3,600
$4,000
$16,000,000
$1,920,000
$32,000
1.00%
$320 $26,000
$6,000
$36,000,000
$360,000
Sum of (R x P) = mean: 2
Sum of P x (CF - mean) =
variance:
$6,400,000
a. Square root of variance = standard deviation:
$2,530
b. Coefficient of Variation = std. dev./mean:
9.73%
c. Comment:
Given that the average coefficient of variation of George's other product lines is 12%, we would say that the Go-Rilla project is LESS risky than average
7-6. Effect of Adding Asset B to Existing Portfolio A Correlation coefficient r between existing portfolio A and new asset B:
0
Amount invested in Portfolio A:
$700,000
Amount invested in Asset B:
$200,000
Total value of combined portfolio:
$900,000
Weight of existing assets in combined portfolio:
77.8%
Weight of new asset B in combined portfolio:
22.2%
Expected Return of existing portfolio A: Standard deviation of existing portfolio A:
9.00% 3.00%
Coefficient of variation of existing portfolio A:
33.33%
Expected Return of new asset B:
12.00%
Standard deviation of new asset B: Coefficient of variation of new asset B:
4.00% 33.33%
Expected Return of combined portfolio per equation 7-1:
9.67%
Standard deviation of combined portfolio per equation 7-5:
2.50%
Coefficient of Variation of combined portfolio:
25.83%
a. Comparison of standard deviations of existing portfolio A and the new combined portfolio: Standard deviation of existing portfolio A:
3.00%
Standard deviation of combined portfolio:
2.50%
a. Comparison of coefficients of variation of existing portfolio A and the new combined portfolio: Coefficient of variation of existing portfolio A:
33.33%
Coefficient of variation of combined portfolio:
25.83%
46
7-7.
Coefficient of variation (CV) = Standard Deviation/Mean 288/1,200 = .24 CVzazzle = 24%
7-8.
Total Portfolio = $10,000 Weights: Stock A: 4,000/10,000 = .4 Stock B: 6,000/10,000 = .6 .4(13) + .6(9) = 10.6% Expected Rate of Return = 10.6%
7-9.
ơp = √ (0.3)2 * (0.05)2 + (0.7)2 * (0.02)2 + ( 2 * 0.3 * 0.7 * 0.6 * 0.05 * 0.02) ơp = √0.000673 ơp = 0.0259 ơp = 2.59%
7-10. Effect of Adding PROJ1 to Existing Portfolio Expected Return of existing portfolio:
11.00%
Standard deviation of existing portfolio: Coefficient of variation of existing portfolio:
4.00% 36.36%
Expected Return of new PROJ1:
13.00%
Standard deviation of new PROJ1: Coefficient of variation of new PROJ1:
5.00% 38.46%
Amount invested in existing portfolio:
$820,000
Amount invested in PROJ1:
$194,000
Total value of combined portfolio:
$1,014,000
c.
Weight of existing assets in combined portfolio:
80.9%
d.
Weight of new PROJ1 in combined portfolio:
19.1%
Correlation coefficient r between existing portfolio and new PROJ1:
0
Standard deviation of combined portfolio:
3.37%
(lower than existing portfolio) Expected Return of combined portfolio per equation 7-1 f.: Coefficient of Variation of combined portfolio
11.38% 29.63%
a.
b.
e. :
(lower than existing portfolio) g. Firm's risk decreases with the addition of PROJ1 to the portfolio
47
7-11. Required Rate of Return per the CAPM Risk free rate (kRF) Expected rate of return on the market (km)
5.0% 15.0%
Beta Required rate of return on stock per the CAPM:
1.2 17.0%
(equation 7-6)
7-12.
kl = 4.5 + .5(12.5) = 10.75% ka = 4.5 + 1.0(12.5) = 17% kh = 4.5 + 1.6(12.5) = 24.5%
7-13. Effect on CAPM Required Rate of Return of Adding a New Project Risk free rate (kRF)
5.0%
Expected rate of return on the market (km)
15.0%
Existing firm's Beta
1.5
New Project's Beta
0.8
a. Required rate of return on company per the CAPM:
20.0%
b. Required rate of return on new project per the CAPM:
13.0%
c.
Weight of new project in firm's portfolio:
20.0%
Weight of firm's other assets:
80.0% 1.36
Beta of firm with new project
7-14. STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF PSC SALES REVENUE Sales
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
2
2
(CF - mean) P x (CF - mean)
$800
2.00%
$16
($1,200)
$1,440,000
$28,800
$1,000
8.00%
$80
($1,000)
$1,000,000
$80,000
$1,400
20.00%
$280
($600)
$360,000
$72,000
$2,000
40.00%
$800
$0
$0
$0
$2,600
20.00%
$520
$600
$360,000
$72,000
$3,000
8.00%
$240
$1,000
$1,000,000
$80,000
$3,200 2.00% Sum of (R x P) = exp val:
$64 $2,000
$1,200
$1,440,000
$28,800
48
2
Sum of P x (CF - mean) = variance:
$361,600
Square root of variance = standard deviation:
$601
Coefficient of Variation = std. dev./mean:
30.07%
7-15. COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME Operating Sales Variable Estimate
Fixed
Expenses
Expenses
Income
Probability
Estimate
of Occurrence
CF
P
CF x P
2
CF - mean (CF - mean) Px(CF - mean)
2
$800
$480
$0
$320
2.00%
$6
($480)
$230,400
$4,608
$1,000
$600
$0
$400
8.00%
$32
($400)
$160,000
$12,800
$1,400
$840
$0
$560
20.00%
$112
($240)
$57,600
$11,520
$2,000
$1,200
$0
$800
40.00%
$320
$0
$0
$0
$2,600
$1,560
$0
$1,040
20.00%
$208
$240
$57,600
$11,520
$3,000
$1,800
$0
$1,200
8.00%
$96
$400
$160,000
$12,800
$3,200
$1,920
$0
$1,280
2.00%
$26 $800
$480
$230,400
$4,608
Sum of (R x P) = mean: 2
Sum of P x (CF - mean) = variance:
$57,856
Square root of variance = standard deviation:
$241
Coefficient of Variation = std. dev./mean:
30.07%
7-16. COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME Operating Sales Variable Estimate
Fixed
Expenses Expenses
Income
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
2
(CF - mean) Px(CF - mean)
2
$800
$480
$400
($80)
2.00%
($2)
($480)
$230,400
$4,608
$1,000
$600
$400
$0
8.00%
$0
($400)
$160,000
$12,800
$1,400
$840
$400
$160
20.00%
$32
($240)
$57,600
$11,520
$2,000
$1,200
$400
$400
40.00%
$160
$0
$0
$0
$2,600
$1,560
$400
$640
20.00%
$128
$240
$57,600
$11,520
$3,000
$1,800
$400
$800
8.00%
$64
$400
$160,000
$12,800
$3,200
$1,920
$400
$880
2.00%
$18
$480
$230,400
$4,608
Sum of (R x P) = mean:
$400
49
2
Sum of P x (CF - mean) = variance:
$57,856
Square root of variance = standard deviation:
$241
Coefficient of Variation = std. dev./mean:
60.13%
Note how the addition of fixed costs caused the coefficient of variation of PSC's operating income to double from what it was in problem 7-10
Comment:
7-17. MEASURING PSC'S FINANCIAL RISK I. Expected value, standard deviation, and coefficient of variation of PSC's net income when no interest expense is present Sales
Operating Interest BeforeTax Estimate Expenses Expenses Income Expense Income Taxes
$800 $1,000 $1,400 $2,000 $2,600 $3,000 $3,200
Variable
$480 $600 $840 $1,200 $1,560 $1,800 $1,920
Fixed
$400 $400 $400 $400 $400 $400 $400
-$80 $0 $160 $400 $640 $800 $880
$0 $0 $0 $0 $0 $0 $0
Probability of Net Occurrence Income NI P NI X P NI - mean (NI 2 mean)
-$80 -$56 -$24 2% $0 $0 $0 8% $160 $112 $48 20% $400 $280 $120 40% $640 $448 $192 20% $800 $560 $240 8% $880 $616 $264 2% Sum of (NI X P) = mean
$0 $0 $10 $48 $38 $19 $5 $ 120
-$144 -$120 -$72 $0 $72 $120 $144
P X (NI 2 mean)
$20,736 $14,400 $5,184 $0 $5,184 $14,400 $20,736
$415 $1,152 $1,037 $0 $1,037 $1,152 $415
Sum of P X (CF - mean) = variance: Square root of variance = standard deviation: Coefficient of Variation = std. dev./mean:
$5,207 $72 60.1%
2
II. Expected value, standard deviation, and coefficient of variation of PSC's net income when interest expense is present Sales Variable
Operating Interest BeforeTax Estimate Expenses Expenses Income Expense Income
$800 $1,000 $1,400 $2,000 $2,600 $3,000 $3,200
$480 $600 $840 $1,200 $1,560 $1,800 $1,920
Fixed
$400 $400 $400 $400 $400 $400 $400
($80) $0 $160 $400 $640 $800 $880
$60 $60 $60 $60 $60 $60 $60
Probability of Taxes Net Income NI
Occurrence P
($140) ($42) ($98) 2% ($60) ($18) ($42) 8% $100 $30 $70 20% $340 $102 $238 40% $580 $174 $406 20% $740 $222 $518 8% $820 $246 $574 2% Sum of (R X P) = mean =
NI X P NI - mean (NI 2 mean) ($2) ($3) $14 $95 $81 $41 $11 $ 238
($336) $112,896 ($280) $78,400 ($168) $28,224 $0 $0 $168 $28,224 $280 $78,400 $336 $112,896 2
Sum of P X (CF - mean) = variance = Square root of variance = standard deviation = Coefficient of variation equals std. dev./mean =
50
P X (NI 2 mean) $2,258 $6,272 $5,645 $0 $5,645 $6,272 $2,258
$28,349 $168 70.7%
7-18. I. New coefficient of variation of PSC's operating income: Operating Sales Variable Fixed Income Probability of Estimate Expenses Expenses Estimate Occurrence EBIT P EBIT X EBIT - (EBIT 2 P mean mean) $800 $1,000 $1,400 $2,000 $2,600 $3,000 $3,200
$480 $600 $840 $1,200 $1,560 $1,800 $1,920
$250 $70 1% $250 $150 6% $250 $310 13% $250 $550 60% $250 $790 13% $250 $950 6% $250 $1,030 1% Sum of (EBIT X P) = mean =
P X (EBIT - mean)
$0.70 ($480) $230,400 $9.00 ($400) $160,000 $40.30 ($240) $57,600 $330.00 $0 $0 $102.70 $240 $57,600 $57.00 $400 $160,000 $10.30 $480 $230,400 $550.00
2
$2,304 $9,600 $7,488 $0 $7,488 $9,600 $2,304
2
Sum of P X (CF - mean) = variance = Square root of variance = standard deviation = Coefficient of Variation = std. dev./mean =
$38,784 $197 35.8%
II. New coefficient of variation of PSC's net income when no interest expense is present Sales
Variable
Fixed
Operating
Estimate Expenses Expenses Income
$800 $1,000 $1,400 $2,000 $2,600 $3,000 $3,200
$480 $600 $840 $1,200 $1,560 $1,800 $1,920
$250 $250 $250 $250 $250 $250 $250
$70 $150 $310 $550 $790 $950 $1,030
Interest
BeforeTax Expense Income Taxes
$0 $70 $0 $150 $0 $310 $0 $550 $0 $790 $0 $950 $0 $1,030
$21 $45 $93 $165 $237 $285 $309
Net
Probability of
Income Occurrence NI P
$49 1% $105 6% $217 13% $385 60% $553 13% $665 6% $721 1% Sum of (NI X P) = mean =
NI X (NI 2 P mean)
P X (NI 2 mean)
$0 $112,896 $1,129 $6 $78,400 $4,704 $28 $28,224 $3,669 $231 $0 $0 $72 $28,224 $3,669 $40 $78,400 $4,704 $7 $112,896 $1,129 $385 2
Sum of P X (CF - mean) = variance = $19,004 Square root of variance = standard deviation = $138 Coefficient of Variation = std. dev./mean = 35.8% III. New coefficient of variation of PSC's net income when interest expense is present Sales Variable Fixed Operating Interest Estimate Expenses Expenses Income Expense
$800 $1,000 $1,400 $2,000 $2,600 $3,000 $3,200
$480 $600 $840 $1,200 $1,560 $1,800 $1,920
$250 $250 $250 $250 $250 $250 $250
$70 $150 $310 $550 $790 $950 $1,030
$40 $40 $40 $40 $40 $40 $40
B-T Income Taxes
$30 $110 $270 $510 $750 $910 $990
51
$9 $33 $81 $153 $225 $273 $297
Net Probability of Income Occurrence NI P
$21 1% $77 6% $189 13% $357 60% $525 13% $637 6% $693 1% Sum of (NI X P) = mean =
NI X (NI 2 P mean)
P X (NI 2 mean)
$0 $112,896 $1,129 $5 $78,400 $4,704 $25 $28,224 $3,669 $214 $0 $0 $68 $28,224 $3,669 $38 $78,400 $4,704 $7 $112,896 $1,129 $357
2
Sum of P X (CF - mean) = variance = $19,004 Square root of variance = standard deviation = $138 Coefficient of Variation = std. dev./mean = 38.62% Summary: Old Coefficient of variation of operating income (business risk) 60.13% New coefficient of variation of operating income (business risk) 35.81% Old difference between the coefficient of variation of net income with and without interest expense (financial risk) New difference between the coefficient of variation of net income with and without interest expense (financial risk)
-10.6% -2.8%
Comments: The effect of PSC's risk reduction measures was to lower business risk substantially, but financial risk increased slightly. Managers must evaluate this trade-off and proceed accordingly.
52
Chapter 8 Solutions Answers to Review Questions 1.
What is the time value of money? The time value of money means that money you hold in your hand today is worth more than money you expect to receive in the future. Similarly, money you must pay out today is a greater burden than the same amount paid in the future.
2.
Why does money have time value? Positive interest rates indicate that money has time value. When one person lets another borrow money, the first person requires compensation in exchange for reducing current consumption. The person who borrows the money is willing to pay to increase current consumption. The required rate of return on an investment reflects the pure time value of money, an adjustment for expected inflation, and any risk premiums present.
3.
What is compound interest? Compare compound interest to discounting. Compound interest occurs when interest is earned on interest and on the original principal of an investment. Discounting is the inverse of compounding. Compound interest causes the value of a beginning amount to increase at an increasing rate. Discounting causes the present value of a future amount to decrease at an increasing rate.
4.
How is present value affected by a change in the discount rate? Present value is inversely related to the discount rate. In other words, present value moves in the opposite direction of the discount rate. If the discount rate increases, present value decreases. If the discount rate decreases, present value increases.
5.
What is an annuity? An annuity is a series of equal cash flows, spaced evenly over time.
6.
Suppose you are planning to make regular contributions in equal payments to an investment fund for your retirement. Which formula would you use to figure out how much your investments will be worth at retirement time, given an assumed rate of return on your investments?
To figure out how much your investments will be worth at retirement time, given an assumed rate of return on your investments, you would use the future value of an annuity formula:
53
Future Value of an Annuity Formula
(1 k ) n 1 FVA PMT k where:
7.
FVA = Future Value of an Annuity PMT = Amount of each annuity payment k = Interest rate per time period n = Number of annuity payments
How does continuous compounding benefit an investor? The effect of increasing the number of compounding periods per year is to increase the future value of the investment. The more frequently interest is compounded, the greater the future value. The smallest compounding period is used when we do continuous compounding--compounding that occurs every tiny unit of time (the smallest unit of time imaginable).
8.
If you are doing PVA and FVA problems, what difference does it make if the annuities are "ordinary annuities" or "annuities due"? In FVA or a PVA of annuity due problems, annuity payments earning interest one period sooner than in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due problems, each annuity payment occurs one period sooner, so the payments are discounted less severely.
9.
Which formula would you use to solve for the payment required for a car loan if you know the interest rate, length of the loan, and the borrowed amount? Explain. To solve for k when the known values are PVA, n, and PMT, start with the present value of an annuity formula, Equation 8-3b, as follows: Present Value of an Annuity Formula, Table Method PVA = PMT(PVIFA k, n) Next, rearrange terms and solve for (PVIFA k, n) as follows PVA / PMT = (PVIFA k, n) Now refer to the PVIFA values in the text, Table IV. You know n, so find the n row corresponding to the number of periods in your problem on the left hand side of the table. You have also determined the PVIFA, so move across the n row until you find (or come close to) the value of PVIFA that you have solved for. The percent column in which the value is located is the interest rate.
54
Answers to End-of-Chapter Problems 8-1.
$1,000 X (1 + 0.07)5 = $1,402.55
8-2.
a) 0% $50,000 X (1 + 0.00)10 = $50,000.00 b) 5% $50,000 X (1 + 0.05)10 = $81,444.73 c) 10% $50,000 X (1 + 0.10)10 = $129,687.12 d) 20% $50,000 X (1 + 0.20)10 = $309,586.82
8-3.
$5,000 * (1 + 0.08)10 = $10,794.62
8-4.
a) 3% b) 6% c) 9% d) 12%
$100,000 * (1 + 0.03)15 = $155,796.74 $100,000 * (1 + 0.06)15 = $239,655.82 $100,000 * (1 + 0.09)15 = $364,248.25 $100,000 * (1 + 0.12)15 = $547,356.58
8-5
a) 50,000 b) 75,000 c) 100,000 d) 125,000
$50,000 * (1 + 0.10)25 = $541,735.30 $75,000 * (1 + 0.10)25 = $812,602.95 $100,000 * (1 + 0.10)25 = $1,083,470.59 $125,000 * (1 + 0.10)25 = $1,354,338.24
8-6
a) 5 years b) 10 years c) 15 years d) 20 years
$60,000 * (1 + 0.12)5 = $105,740.50 $60,000 * (1 + 0.12)10 = $186,350.89 $60,000 * (1 + 0.12)15 = $328,413.95 $60,000 * (1 + 0.12)20 = $578,777.59
8-7.
PV = $20,000 X [1/(1 + .12)10] = $6,439.46
8-8.
a) 0% $60,000 X [1/(1+0.00)20] = $60,000.00 b) 5% $60,000 X [1/(1+0.05)20] = $22,613.37 c) 10% $60,000 X [1/(1+0.10)20] = $8,918.62 d) 20% $60,000 X [1/(1+0.20)20] = $1,565.04
8-9
$9,000 * [1/(1+0.08)4] = $6,615.27
8-10
a) 3% b) 6% c) 9% d) 12%
$25,000 * [1/(1 + 0.03)10] = $18,602.35 $25,000 * [1/(1 + 0.06)10] = $13,959.87 $25,000 * [1/(1 + 0.09)10] = $10,560.27 $25,000 * [1/(1 + 0.12)10] = $8,049.33
55
8-11.
a)$50,000 b)$75,000 c)$100,000 d)$125,000
$50,000 * [1/(1 + 0.06)15 = $20,863.25 $75,000 * [1/(1 + 0.06)15 = $31,294.88 $100,000 * [1/(1 + 0.06)15 = $41,726.51 $125,000 * [1/(1 + 0.06)15 = $52,158.13
8-12.
a) 5 years b) 10 years c) 15 years d) 20 years
$80,000 * [1/(1 + 0.09)5] = $51,994.51 $80,000 * [1/(1 + 0.09)10] = $33,792.86 $80,000 * [1/(1 + 0.09)15] = $21,963.04 $80,000 * [1/(1 + 0.09)20] = $14,274.47
8-13.
PVA = $500 X [(1-1/1.0610)/0.06] = $3,680.04
8-14.
a) 0% $10,000 X 30 = $300,000 b) 10% $10,000 X [(1-1/1.1030)/0.10] = $94,269.14 c) 20% $10,000 X [(1-1/1.2030)/0.20] = $49,789.36 d) 50% $10,000 X [(1-1/1.5030)/0.50] = $19,999.90
8-15.
$20,000 * [(1-1/1.0710)/0.07] = $140,471.63
8-16.
a) b) c) d)
8-17.
FVA = $500 X [(1.095-1)/.09] = $2,992.36
8-18.
a) 0% $6,000 X 12 = $72,000.00 b) 2% $6,000 X [(1.0212-1)/0.02] = $80,472.54 c) 10% $6,000 X [(1.1012-1)/0.10] = $128,305.70 d) 20% $6,000 X [(1.2012-1)/0.20] = $237,483.01
8-19.
$5,000 * [(1.0610 – 1)/0.06] = $65,903.97
8-20.
$5,000 * [(1.118 – 1)/0.11] = $59,297.17
8-21.
a) $1,000 b) $10,000 c) $75,000 d) $125,000
9% $10,000 * [(1-1/1.095)/0.09] = $38,896.51 13% $10,000 * [(1-1/1.135)/0.13] = $35,173.31 15%$10,000 * [(1-1/1.155)/0.15] = $33,521.55 21% $10,000 * [(1-1/1.215)/0.21] = $29,259.84
$1,000 * [(1.105 – 1)/0.10] = $6,105.10 $10,000 * [(1.105 – 1)/0.10] = $61,051.00 $75,000 * [(1.105 – 1)/0.10] = $457,882.50 $125,000 * [(1.105 – 1)/0.10] = $763,137.50
56
8-22.
$1,200 X [(1.1240 – 1)/.12] X 1.12 = $1,030,970.87
8-23.
$500 * [(1.085 – 1)/0.08] * 1.08 = $3,167.96
8-24.
$56,370.93 * 1.06 = $59,753.19
8-25.
$80 X [(1-1/1.1220)/.12] X 1.12 = $669.26
8-26.
$30,000 * [1-1/1.0925)/0.09] * 1.09 = $321,198.35
8-27.
$1,300 * [1-1/1.00583333180)/0.00583333] * 1.00583 = $144,632.74
8-28.
$185,361 = FVIF10,k% X $50,000 FVIF10,k% = 3.7072; from Table I, k = 14%
8-29.
$1,000 X (1 + k)5 = $773.78 (1 + k)5 = $773.78/$1,000 (1 + k)5 = .77378 1 + k = .95 k = -.05 = -5%
8-30.
$50,000 * (1 + k)10 = $246,795 (1 + k)10 = $246,795/$50,000 (1 + k)10 = 4.9359 1 + k = 1.173104 k = .1731 = 17.31%
8-31.
PV = $50/0.08 = $625
8-32.
$80/0.09 = $888.89
8-33.
$65/0.085 = $764.71
8-34.
FV = $10 X (1.08)200 = $48,389,496
8-35.
PVA = PMT X PVIFA k,n $24,000 = $4,247.62 X PVIFA k,10
57
5.6502 = PVIFA k,10 k = 12%
8-36
PVA = PMT X PVIFA k,n $200,000 = $1,330.61 X PVIFA k,360 150.3070 = PVIFA k,360 k = .5833% per month X 12 = 7% annual rate
8-37.
a ) 5 years? b ) 10 years? c ) 20 years?
8-38.
PV = $16,850.58 X [1/(1+.11)5] PV = $10,000
10,000/(1+.07)5 = 7130 10,000/(1+.07)10 = 5083 10,000/(1+.07)20 = 2584
8-39. a ) FV = $20,000 X (1 + .05)7 = $28,142.01 b ) FV = $20,000 X (1 + .07)10 = $39,343.03
8-40.
$55.00 = $67.73 X [PVIFk%, 12 years ] .8120 = PVIFk%, 12 years; k = 1.75%
8-41.
1,000 = 2653.3 X [PVIF5%, ?]; .3769 = PVIF5%,?; ? = 20 semi-annual periods, so it will take 10 years.
8-42.
PV = 20,000 X [(1-1/1.0615)/0.06] = $194,244.98
8-43.
$4,000 * [(1.0920 –1)/0.09] * 1.09 = $223,058.12
8-44.
$100 * [(1.0220 –1)/0.02] = $2,429.74
8-45.
$2,000 X [((1+.08)10 - 1)/.08] = $2,000 X 14.4866 = $28,973
8-46.
a ) $300 X [((1+.02)120 - 1)/.02] = $146,477 b ) $146,477 = $6,000 X [PVIFA2%, n quarters ] PVIFA2%, n quarters = 24.4128; n = 34 quarters or 8.5 years
58
8-47.
$30,000 = PMT X [(1-1/(1+0.1)7)/0.1]; $30,000 = PMT X 4.86841882; PMT = $6,162.16
8-48.
$10,000/.12 = $83,333.33
8-49.
FV = $500 X e.05 x 23 = $1,579.10
8-50.
FVIF k=8%, n=? = 2 n = 9 years
8-51.
PVA = PMT X PVIFA k,n $4,000 = $200 X PVIFA k=.195/12, n=? 20 = PVIFA k=.01625, n=? n = 24.39 months
8-52.
$14,568.50 = $5,000 X [PVIFAk%,4 years], assuming payments start one year from the date of borrowing [PVIFAk%,4 years] = 2.9137; k = 14%
8-53.
a) FVA = $1,000 X [[(1+.02)60 - 1]/.02] = $114,051.54 b) $114,051.54 = $6,000 X PVIFA.02, n quarters PVIFA.02, n quarters = 19.00859; n = 24 quarters = 6 years
8-54.
Option 1) PV = $5,650 Option 2) PV = $6,750 X [1/1.028] = $5,761.06 Option 3) PV = $800 X [(1-(1/(1+.02)8)/.02] = $5,860.39 Option 4) PV = $1,000 + $5,250 X (1/(1+.02)8) = $5,480.82 Option 4) is the one with lowest cost to Jack.
8-55.
n = 30 X 12 = 360 k = .09/12 =0 .0075 or 0.75% $120,000 = PMT X [(1-1/1.0075360)/0.0075] PMT = $120,000/124.28186568 = $965.55
8-56.
PVA = PMT [(1-1/1.005 180)/.005] $250,000 = PMT X 118.5035147 PMT = $2,109.64
8-57.
a) n = 4 X 12 = 48 k = .06/12 =0 .005 or 0.5%
59
$18,000 = PMT X [(1-1/1.00548)/0.005] PMT = $18,000/42.58031778 = $422.73 b) n = 6 X 12 = 72 k = .06/12 =0 .005 or 0.5% $18,000 = PMT X [(1-1/1.00572)/0.005] PMT = $18,000/60.33951394 = $298.31
8-58, Missing Cash Flow Problem I. Given Information: Discount Rate 10% Known Cash Flows Time 0 Time 1 $100 Time 2 $150 Time 3 Time 4 $100 Total Present Value of all Cash Flows, including the missing cash flow
$320.74
II. Solution: The value of the missing cash flow at Time 3: Known Cash Flows Present Value of Known Cash Flows Time 0 Time 1 $100 $90.9091 Time 2 $150 $123.9669 Time 3 Time 4 $100 $68.3013 Total Present Value of all Cash Flows, including the missing cash flow Total present value of known cash flows only Difference (Present Value of missing cash flow) Future Value of Missing Cash Flow at Time 3
8-59.
a) n = 5*12 = 60 k = .08/12 = .0066666 $22,000 = PMT * [1-1/1.00666666760)/0.006666667] PMT = $22,000/118.5035147 = $446.0806 = $446.08
60
$320.74 (given) $283.1774 $37.5657 $50
Chapter 9 Solutions
Answers to Review Questions 1.
Which is lower for a given company: the cost of debt or the cost of equity? Explain. Ignore taxes in your answer. The cost of debt is always less than the cost of equity for a given firm. This is because the debt investor is taking a lower risk than the equity investor and therefore the required rate of return is lower.
2.
When a company issues new securities, how do flotation costs affect the cost of raising that capital? When a company issues new securities flotation costs increase the cost of raising the capital. The company receives a smaller amount of the proceeds from the new issues, the greater the flotation costs.
3.
What does the ―weight‖ refer to in the weighted average cost of capital? The weight referred to in weighted average cost of capital refers to the portion of the total capital raised by the firm that comes from a given source such as debt, preferred stock or equity.
4.
How do tax considerations affect the cost of debt and the cost of equity? Because interest on debt is tax deductible to the issuing firm, the higher the tax rate the lower the after tax cost of debt financing. Tax considerations do not enter into the cost of equity calculation since dividends paid to stockholders are not tax deductible to the firm.
5.
If dividends paid to common stockholders are not legal obligations of a corporation, is the cost of equity zero? Explain your answer. Although common stockholders do not have a contractual claim on dividends the funds supplied by stockholders definitely have a cost. Equity investors are paid last and so they are taking the greatest risk among all the suppliers of capital. If the company does not earn a higher rate of return on equity funds to compensate for the higher risk taken by equity investors, the price of the stock will fall and therefore the value of the firm.
6.
What is the investment opportunity schedule (IOS)? How does it help financial managers make business decisions?
61
The investment opportunity schedule shows graphically proposed capital budgeting projects depicting the IRR and dollar amount of investment for each project. This helps the financial manager make business decisions since the investment opportunity schedule and the marginal cost of capital schedule can be plotted together, with those projects on the IOS schedule above the MCC being acceptable.
7.
What is a marginal cost of capital schedule (MCC)? Is the schedule always a horizontal line? Explain. The marginal cost of capital schedule is a graphic depiction of the weighted average cost of capital at different levels of financing. The MCC schedule is not always a horizontal line. For many firms the MCC schedule increases, usually at discreet intervals, as the amount of funds to be raised increases.
8.
For a given IOS and MCC, how do financial managers decide which proposed capital budgeting projects to accept, and which to reject? For a given IOS and MCC, all independent projects that plot on the IOS above the MCC are accepted. Those projects on the IOS below the MCC are rejected.
Answers to End-of-Chapter Problems 9-1.
9-2.
9-3.
a)
(i) YTM = 7% (ii) YTM = 11% (iii) YTM = 13%
AT kd = .07(1-.40) = 4.2% AT kd = .11(1-.40) = 6.6% AT kd = .13(1-.40) = 7.8%
b)
(i) YTM = 7% (ii) YTM = 11% (iii) YTM = 13%
AT kd = .07(1-.34) = 4.62% AT kd = .11(1-.34) = 7.26% AT kd = .13(1-.34) = 8.58%
a)
AT kd = .10(1-.00) = 10.0%
b)
AT kd = .10(1-.22) = 7.8%
c)
AT kd = .10(1-.34) = 6.6%
Company A B C
YTM 8% 11% 14%
Tax Rate(%) 34% 40% 30%
AT kd 0.8(1-.34) = 5.28% 0.11(1-.40) = 6.60% 0.14(1-.30) = 9.80%
62
9-4.
YTM
AT kd T=40% 0.08(1-.40) = 4.80% 0.14(1-.40) = 8.40% 0.16(1-.40) = 9.60%
8% 14% 16%
9-5.
a)
kd = 13%
b)
AT kd = .13(1-.40) = 7.8%
9-6.
kd = .095 * (1 - .35) = .06175 = 6.2%
9-7.
kp = $2/($26 - $0.75) = $2/$25.25 = 7.92%
9-8.
kp = $8.00/($61.00 - $1.00) = 13.3% AT kd = .11(1-.40) = 6.6% Leo is correct. The cost of debt is lower.
9-9.
a) b)
9-10.
kp = $100 X 0.12/($89 - ($89 X 0.05)) = $12/($89 - $4.45) = 14.19%
9-11.
kp = $0.75/($27 - $1) = 2.88%
9-12.
a) b)
AT kd T=34% 0.08(1-.34) = 5.28% 0.14(1-.34) = 9.24% 0.16(1-.34) = 10.56%
kp = $6/$50 = 12% kp = $6/($50 - $2.25) = 12.57%
ks = ($7/$143) + 0. 13 = 17.90% kn = ($7/($143 - $4) + 0. 13 = 18.04%
9-13. AT kd = 0.14(1-.30) = 9.80% ks = ($1.50/$39.00) + 0.04 = 7.85% The cost of the company's retained earnings is lower. This would lead you to reevaluate the estimated numbers, or question the applicability of the valuation models used here, since ks cannot be lower than AT kd for a given company. 9-14.
ks = .045 + 1.4(.12 - .045) = 15%
63
9-15.
a) b)
ks = ($7/$65) + 0.10 = 20.77% kn = ($7/($65 - $3)) + 0.10 =21.29%
Yes. Floatation costs make cost of capital from new common stock higher.
9-16.
ks = kRF + (kM - kRF) X = .03 + (.11 - .03) X 1.6 = 15.8%
9-17. a )
9-18.
ks = ($2 X 1.05)/$30 + .05 = 12.0%
b)
kn = ($2 X 1.05)/($30-$2) + .05 = 12.5%
c)
ks = .03 + (.12 - .03) x 1.4 = 15.6%
AT kd = 0.10(1-0.4) = 6% kp = $2/($31 - $1) = 6.67% kn = $4/($100 -$4) + .06 = 10.17% ka = (0.3)(6) + (0.15)(6.67) + (0.55)(10.17) = 8.394%
9-19. AT kd = 0.11(1-0.4) = 6.60% kp = $2/($26 - $0.75) = 7.92% kn = $7/($143 - $4) + .13 = 18.04% ka = (300,000/600,000)(0.066) + (100,000/600,000)(0.0792) + (200,000/600,000)(0.1804) = 10.63%
9-20. ka = (600/1250)(0.12(1-0.04)) + (250/1250)(0.14) + (400/1250)(0.16) = (.48 X .072) + (.20 X .14) + (.32 X .16) = .03456 + .028 + .0512 = 11.38%
9-21. AT kd = .10(1-.35) = 6.5% kp = $2/($25 - $1.00) = $2/$24 = 8.33% kn = ($5/($140 - $4) + 0.10 = 13.68% ka = (300,000/1,000,000)(0.065) + (100,000/1,000,000)(0.0833) +(600,000/1,000,000)(0.1368) = 10.99% = minimum expected rate of return needed to satisfy the suppliers of capital.
9-22.
0.60(0.05) + 0.10(0.08) + 0.30(0.12) = 0.074 = 7.4%
9-23.
kd = .095(1 - 0.35) = .06175 = 6.2% kp = $10/$50 = 0.20 = 20% ks = 0.04 + 1.1(0.12 – 0.04) = 12.8%
64
Weight: Debt = 230,000/430,000 = 0.54 Preferred Stock = 100,000/430,000 = 0.23 Common Equity = 100,000/430,000 = 0.23 WACC = .54(0.062) + .23(0.20) + .23(0.128) = .10892 = 10.892%
9-24. a ) $200,000/0.40 = $500,000 equity break-point b ) $500,000/0.60 = $833,333 debt break-point
9-25. $1,000,000/.4 = $2,500,000 total capital raised before BPd1 is reached. $2,000,000/.4 = $5,000,000 total capital raised before BPd2 is reached. $2,750,000/.5 = $5,500,000 total capital raised before BPe is reached. a)
ka = (0.40)(0.11(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.34%
b)
ka = (0.40)(0.13(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.82%
c)
ka = (0.40)(0.15(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 11.30%
9-26. OPTIMAL CAPITAL STRUCTURE: DEBT 35.00% TAX RATE 40.00% NET INCOME NEXT YEAR: $1,200,000 ADDITION TO RETAINED EARNINGS $1,000,000 LOAN INTEREST RATE 10.00% 12.00% COMMON STOCK PRICE PER SHARE $50 DIVIDEND PER SHARE $5 GROWTH RATE 9.00% FLOATATION COST 8.00% a. COST OF NEW EQUITY COST OF RETAINED EARNINGS AT COST OF DEBT
b. EQUITY BREAK POINT DEBT DEBT BREAK POINT DEBT TOTAL EQUITY
INVESTMENT OPPORTUNITIES PROJECT INVESTMENT RETURN EQUITY 65.00% A $500,000 0.16 B $1,600,000 0.12 C $600,000 0.15 D $1,500,000 0.18 FOR LOAN UPTO $750,000 $4,200,000 FOR LOAN ABOVE $750,000
19.87% 19.00% 6.00% FOR LOAN UPTO $750,000 7.20% FOR LOAN ABOVE $750,000 $1,538,462 $538,462 $2,142,857 $750,000 $1,392,857
c. MCC UPTO TOTAL CAPITAL OF $1,538,462 =
14.45%
MCC BETWEEN $1,538,462 AND $2,142,857 15.02% MCC ABOVE $2,142,857
15.44%
65
d.
INVESTMENT OPPORTUNITY SCHEDULE PROJECT D A C
INVESTMENT $1,500,000 $500,000 $600,000
RETURN 0.18 0.16 0.15
B $1,600,000
0.12
e.
MCC/IOS Schedule
Costs of Capital and IRRs
Stone Wood Products 19.00% 18.00%
Project D
17.00% 16.00% 15.00% 14.00%
A C
13.00% 12.00% 11.00%
B $0
$500
$1,000 $1,500 $2,000 $2,500 $3,000 $3,500 $4,000 $4,500
Capital Budget Size ($000s) MCC
IOS
f. Only Projects D and A would be chosen. They are the ones with IRR values on the IOS schedule that plot above the MCC schedule.
66
Chapter 10 Solutions
Answers to Review Questions 1.
How do we calculate the payback period for a proposed capital budgeting project? What are the main criticisms of the payback method? We calculate the payback period for a proposed project by adding a project‘s positive cash flows, one period at a time, until the sum equals the initial investment. The number of time periods it takes to cover this investment is the payback period. The main criticisms of the payback method are that cash flows after the payback period are ignored and the time value of money is not considered.
2.
How does the net present value relate to the value of the firm? The net present value is the dollar amount of the change to the value of the firm if the project under consideration is accepted.
3.
What are the advantages and disadvantages of the internal rate of return method? The internal rate of return method is a discounted cash flow method and a number expressed as a percentage. These are typically seen as advantages. The main disadvantage of the internal rate of return is that it is somewhat more difficult to calculate, although this is less true with the ready availability of financial calculators.
4.
Provide three examples of mutually exclusive projects. Mutually exclusive projects are projects that compete against each other for our selection. If a firm were considering the purchase of a new computer, needing only one computer, then the proposals made by the sales reps from Hewlett-Packard, Compaq, and Toshiba would be mutually exclusive projects vying for our selection.
5.
What is the decision rule for accepting or rejecting proposed projects when using net present value? When using the net present value decision rule any project with a net present value greater than or equal to zero would be acceptable. Any project with a negative net present value would be rejected.
6.
What is the decision rule for accepting or rejecting proposed projects when using internal rate of return?
67
Whenever the internal rate of return is greater than or equal to the required rate of return, the hurdle rate, the project is accepted. When the internal rate of return is less than this required rate of return, the project is rejected.
7.
What is capital rationing? Should a firm practice capital rationing? Why? Capital rationing is the practice of setting dollar limits on what will be invested in new capital budgeting projects. Proprietorships, partnerships and private corporations are in a position to do whatever the owners wish. It can be argued, however, that for a publicly traded corporation capital rationing may not be consistent with maximizing the value of the firm. This is because some value adding projects may be rejected if they would cause the firm to exceed its self imposed capital rationing limit.
8.
Explain how to resolve a ―ranking conflict‖ between the net present value and the internal rate of return. Why should the conflict be resolved as you explained? Whenever there is a ranking conflict between net present value and internal rate of return we generally suggest that the project with the highest net present value be chosen. This is because the net present value method ties more directly with the primary financial goal of the firm, to maximize firm value.
9.
Explain how to measure the firm risk of a capital budgeting project. The firm risk of a capital budgeting project measures the impact of adding a new project to the existing projects of the firm.
10.
Why is the coefficient of variation a better risk measure to use than the standard deviation when evaluating the risk of capital budgeting projects? The coefficient of variation is a better risk measure than the standard deviation alone because the CV adjusts for the size of the project. The CV measures the standard deviation divided by the mean and therefore puts the standard deviation into context. For example, a standard deviation of .05 may be considered large relative to a mean of .02 but would be considered a small value relative to a mean value of 8.
11.
Explain why we measure a project‘s risk as the change in the CV. We measure a project‘s risk as the change in the coefficient of variation because this focuses on the change in the riskiness of the firm‘s existing portfolio.
12.
Explain how using a risk-adjusted discount rate improves capital budgeting decision making compared to using a single discount rate for all projects?
68
The risk-adjusted discount rate improves capital budgeting decision making compared to the single discount rate approach because the RADR allows us to set a higher hurdle for the high risk project and a lower hurdle for the low risk project thus aligning our capital budgeting decision making process more closely with the goal of maximizing the value of the firm.
Answers to End-of-Chapter Problems 10-1.
a)
Peter: (10,000) + 4,000 + 4,000 + 4,000 ----> 2.5 years Paul: (10,000) + 2,000 +8,000 + 2,000 ----> 2.0 years Mary: (10,000) + 10,000 + 1,000 + 1,000 ----> 1 year
b)
Mary's project is most liquid using payback as the liquidity measure.
10-2.
CF0 = -20,000,000 CF1-25 = $2,000,000 I = 8% NPV = $1,349,552
10-3.
IRR = 8.78%
10-4.
CF0 = -20,000,000 CF25 = 146, 211,879.90 MIRR = 8.28%
10-5. Year 0 1 2 3 4
Expected Cash Flows Weights Cum. CF -$200,000 (200,000) 100,000 (100,000) 75,000 (25,000) 50,000 25,000 100,000 125,000
Waters Cum. CF -$300,000 (300,000) 200,000 (100,000) 150,000 50,000 150,000 200,000 150,000 350,000
Project Weights: 2.5 years Project Waters: 1.67 years Project Waters is the better project according to payback because it recoups its investment in a shorter time.
69
10-6. Year 0 1 2 3 4
Expected Cash Flows Weights Waters -$200,000 -$300,000 100,000 200,000 75,000 150,000 50,000 150,000 100,000 150,000
k= 10% NPVweights (k = 10%) = $58,759.65 NPVwaters (k= 10%) = $220,934.36 10-7.
10-8.
a)
NPV = (17,291.42) + 5,000[1/1.121] + 8,000[1/1.122] + 10,000[1/1.123] = $668.22
b)
NPV = (17,291.42) + 5,000[1/(1+k)1] + 8,000[1/(1+k)2] + 10,000[1/(1+k)3] = $0 IRR = k = 14%
c)
Yes. NPV is positive and IRR > Cost of capital
a)
Rifle Stock: NPV = -9,000 + 2,000 X .8850 + 5,000 X .7831 + 1,000 X .6931 + 4,000 X .6133 = -168.20 Fork Lift: NPV = -12,000 +5,000 X .8850 + 4,000 X .7831 +6,000 X .6931 + 2,000 X .6133 = +942.60 Packaging Equip. NPV = -18,200 + 5,000 X .7831 + 10,000 X .6931 + 12,000 X .6133 = +6.10
b)
Fork Lift and Packaging; both have positive NPVs.
10-9. a )
Cal's Project: NPV = -100,000 + 22,611 X (4.5638) = $3,192.08 Aron's Project:NPV = -300,000 + 63,655 X (4.5638) = -$9,491.31
b)
Cal's Project: 100,000/22,611 = PVIFAk,7 year; k = 13% = IRR Aron's Project:300,000/63,655 = PVIFAk,7 year; k = 11% = IRR
c)
Cal's Project; NPV is positive and IRR > Cost of Capital.
d)
No.
70
10-10.
Time
Cash Flow
Initial investment T- 1 T- 2 T- 3 T- 4 T- 5 T- 6 T- 7 T- 8 T- 9 T- 10
10-11. a )
FV of Cash Flow at T10 if reinvested @ 15% cost of capital (per Years Equation 8-1a) to go
($10,000) $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000
$14,072 $12,236 $10,640 $9,252 $8,045 $6,996 $6,084 $5,290 $4,600 $4,000
Terminal Value
$81,215
a.) IRR
38%
b.) MIRR
23.3%
9 8 7 6 5 4 3 2 1 0
Printer #1: Payback = 2 years Printer #2: Payback = 1.77 years
b)
Printer #1: NPV Printer #2: NPV
= -2,000 +900 X .9091 + 1,100 X .8264 + 1,300 X .7513 = +703.92 = -2,500 + 1,500 X .9091 + 1,300 X .8264 + 800 X .7513 = +539.01
c)
Printer #1: NPV = 0 = -2,000 + 900 X [1/(1+k)1] + 1,100 X [1/(1+k)2] + 1,300 X [1/(1+k)3] IRR = k = .2782 = 27.82% = -2,500 + 1,500 X [1/(1+k)1] + 1,300 X [1/(1+k)2] + 800 X [1/(1+k)3] IRR = k = .2325 = 23.25%
Printer #2: NPV = 0
d)
Printer #1 with higher NPV and higher IRR
e ) Printer #1: NPV = -2,000 + 900 X .8621 + 1,100 X .7432 + 1,300 X .6407 = +426.32 Printer #2: NPV = -2,500 + 1,500 X .8621 + 1,300 X .7,432 + 800 X .6407 = +271.87 No. NPV of Printer #1 is still higher.
71
10-12. Expected Cash Flows Year 0 1 2 3 4 5 6 7 8 9 10
Program -20,000,000 1,000,000 2,000,000 5,000,000 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000
I = 15% NPV = $2,082,694.77 IRR = 17.14% MIRR = 16.14% TV = $89,336,820
10-13. a )
Project A: Project B: Project A.
NPV = -11,000 + 4,000 X (3.9975) = $4,990.00 NPV = -17,000 + 4,500 X (3.9975) = $988.75 Project A should be selected because it has the higher NPV
b)
Both. Both the NPVs are positive.
c)
Project A: Project B:
d)
Mutually exclusive: Independent:
e)
Project C: Project C.
IRR : 11000/4000 = PVIFAk,6 year; k =28.16 % IRR : 17000/4500 = PVIFAk,6 year; k = 15.07% Project A has the higher IRR and would be selected. Select both. (IRR > Cost of Capital for both the projects)
NPV = -17,000 + 37,500X(PVIF13%,6 year) = -17,000 + 37,500 X .4803 = $1,011.25 NPV of Project C > NPV of Project B Project C would be chosen of Project B if these projects were mutually exclusive.
f)
Project C:
IRR: 17,000/37,500 = .4533 = PVIFk,6 year; k = 14.09 % IRR of Project C < IRR of Project B Project B would be chosen because it has the higher IRR value.
g)
Selections based on NPV and IRR method contradict each other. Since NPV method is generally preferred, select Project C.
72
10-14. a ) NPV = -5M + 1.85M(2.7982) -.25M(.4761) = $57,645 b ) Multiple IRRs are possible because of two sign changes in the cash flow series. In this case there is only one IRR, however. Do an NPV profile if you don‘t believe us. The IRR is 16.59%. TI BAII PLUS Financial Calculator Solution IRR Keystrokes
Display
[CF]
CF0 = old contents
[2nd][CLR Work]
CF0 = 0.00
5000000[+/-][ENTER]
CF0 = -5,000,000.00 C01 = 1,850,000.00 F01 = 4.00
[
-][ENTER]
C02 = -250,000.00 F02 = 1.00
[IRR]
IRR = 0.00
[CPT]
IRR = 16.59
c ) The IRR of 16.59% is greater than the required rate of return of 16%, so the project would get a positive recommendation.
10-15. a) Hydroelectric Project CF0 = ($100,000) CF1 = $20,000 CF2 = $30,000 CF3 = $40,000 CF4 = $90,000
Geothermal Project CF0 = ($100,000) CF1 = $60,000 CF2 = $40,000 CF3 = $20,000 CF4 = $10,000
b) NPVhydro (k = 6%) = $50,441.02 NPVgeo (k = 6%) = $44,181.07 Accept the Geothermal Upgrade project. c) NPVhydro (k = 15%) = $17,834.06 NPVgeo (k = 15%) = $25,253.98 Neither project would be accepted because the NPV for each is negative. d) Approximately 9.58%. This is where the NPV profiles cross. e) Greater than 21.66% f) Greater then 31.92%
73
10-16. The Chalk Line Machine, Gel Padded Glove, Insect Repellant, and Recycled Base Cover projects collectively have initial cash outlays of $90,000 (under the budget limit) and have NPVs that sum to $12,950. No other combination of projects gives a higher total NPV and stays under the budget limit.
10-17. Given Information: Initial investment
$5,669.62
Year 1 Year 2 Year 3 Required rate of return
$2,200 $2,200 $2,200 12%
Year: Annual cash flows PV of cash flows NPV b. Comment on the acceptability of the investment:
0 ($5,670) ($5,670) ($386)
Yearly net cash flows:
a. NPV of the investment: 1 $2,200 $1,964
2 $2,200 $1,754
5% 322
10% (199)
Comment: The project is unacceptable because it has a negative NPV. You would not accept it even if you had cash available. c. NPV Profile: Discount rate NPV
0% 930
NPV
NPV PROFILE 930
$900 $700 $500 $300 $100 ($100) ($300) ($500)
322
(199)
0%
5%
10%
DISCOUNT RATE
Comment: Comment: According to the NPV profile, the discount rate would have to be less than about 8% in order for the project's NPV to be positive. d. Comment: Comment: The IRR is that discount rate which produces an NPV of zero. Therefore, the IRR could be calculated to determine the "hurdle rate" below which the project's NPV would be positive (8% in this case).
10-18. STD(IRR) = [(.05x(0%-6%)2 + .1x(1%-6%)2 + .2x(3%-6%)2 + .3x(6%-6%)2 + .2x(9%-6%)2 + .1x(11%-6%)2 + .05x(12%-6%)2].5 = 3.49%
74
3 $2,200 $1,566
COEFF. OF VARIATION (CV) = 3.49%/6% = .5817 10-19. PORT. STD. WITH A = [(.22x.022)+(.82x.032)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5 = .0262 = 2.62% E(IRR) of portfolio with A = (.2x14%)+(.8x13%) = 13.2% CV of portfolio with A = 2.62%/13.2% = .1985 PORT. STD. WITH B = [(.22x.062)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5 = .0317 = 3.17% E(IRR) of portfolio with B = (.2x16%)+(.8x13%) = 13.6% CV of portfolio with B = .0317/.136 = .2331 PORT. STD. WITH C = [(.22x.052)+(.82x.032)+(2x.2x.8x.5x.05x.03)].5 = .0303 = 3.03% E(IRR) of portfolio with C = (.2x11%)+(.8x13%) = 12.6% CV of portfolio with C = .0303/.126 = .2405 PORT. STD. WITH D = [(.22x.042)+(.82x.032)+(2x.2x.8x.5x.04x.03)].5 = .0288 = 2.88% E(IRR) of portfolio with D = (.2x14%)+(.8x13%) = 12.6% CV of portfolio with B = .0288/.132 = .2182 Project A has the lowest risk and Project C the highest as measured by the CV.
10-20. a)
1. CVA = 2%/10% = .2 2. E(IRR) of new combined portfolio = (700,000/900,000 x 10%) + (200,000/900,000 x 11% = 10.22% 3. STD. Of new combined portfolio = [(.7782x.022)+(.2222x.03)+(2x.222x.778x.9x.02x.03)].5 = .0218 = 2.18% 4. CV of new combined portfolio = .0218/.1022 = .2133
b)
.2133 - .20 = .0133 change in CV
c)
average risk
d)
1. Ave. Risk: NPV = $55,000/1.131 + 55,000/1.132 + 55,000/1.133 + 100,000/1.134 - 200,000 = ($8,805) 2. High Risk: NPV = $55,000/1.161 + 55,000/1.162 + 55,000/1.163 + 100,000/1.164 - 200,000 = ($21,247) 3. Low Risk: NPV = $55,000/1.101 + 55,000/1.102 + 55,000/1.103 + 100,000/1.104 - 200,000 = $5,078
10-21. a) (.125x2%)+(.20x5%)+(.35x9%)+(.20x13%)+(.125x16%) = 9.00% b) .125(.02-.09)2 + .2(.05-.09)2 + .35(.09-.09)2 + .2(.13-.09)2 + .125(.16-.09)2 = .001865 = .1865% square root of .001865 = .0432 = 4.32% standard deviation c) CV of existing portfolio = .02/.08 = .25 d) E(IRR) of new combined portfolio = (.8x8%)+(.2x9%) = 8.20%
75
e) STD. DEV. of the combined portfolio = [(.22x.04322)+(.82x.022)+(2x.2x.8x1x.0432x.02)].5 = .0246 = 2.46% f) CV of combined portfolio = .0246/.0820 = .3005 g) .3005 - .25 = .0505 increase in CV
10-22.
Proj. A
Proj. B
Proj.C
Proj. D
Standard deviation of existing portfolio: Standard deviation of new project: Standard deviation of combined portfolio
4.00% 9.00% 3.71%
4.00% 5.00% 3.63%
4.00% 3.00% 3.61%
4.00% 1.00% 3.60%
expected return E(R) of new project: expected return E(R) of existing portfolio: expected return E(R) of combined portfolio:
18.00% 12.00% 12.60%
15.00% 12.00% 12.30%
11.00% 12.00% 11.90%
8.00% 12.00% 11.60%
a. Coefficient of variation of existing portfolio:
33.33%
b.&c. Coefficient of variation of combined portfolio:
29.45%
29.55%
30.36%
31.05%
d.
A IS THE LOWEST RISK PROJECT
D IS THE HIGHEST RISK PROJECT
10-23. a. CV of existing portfolio = 5%/15% = 33.33% b. WT of existing portfolio of PROJ1 is added = $820,000/($820,000+$194,000) = .809 = 8.09% c. WT of PROJ1 if added to existing portfolio = 1 - .809 = .191 = 19.1% d. STD. DEV. of combined portfolio = [(.8092x.052)+(.1912x.09)+(2x.809x.191x1x.05x.09)].5 = .0577 = 5.77% The combined portfolio standard deviation is higher than that of the existing portfolio (5.77% versus 5.00%). e. CV of the combined portfolio = 5.77%/[(.809x15%)+(.191x18%)] = 5.77%/15.57% = .3706
10-24. 1 1 - (1.08)10 a) NPV = $298,500 x - $2,000,000 .08
= $298,500 x 6.7100814 - $2,000,000 = $2,002,959.30 - $2,000,000 = $2,959.30
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1 1 - (1.10)10 - $2,000,000 b) NPV = $298,500 x .10 = $298,500 x 6.14456711 - $2,000,000 = $1,834,153.28 - $2,000,000 = ($165,846.72) c) The project should not be adopted. d)
1 1 - (1.10)10 - $2,000,000 NPV = $0 = CF x .10 NPV = $0 = CF x 6.14456711 - $2,000,000 $2,000,000 = CF x 6.14456711 CF = $325,490.79
10-25 (Comprehensive Problem) Given Information: Project 1
Project 2
($200,000) $0 $0 $20,000 $30,000 $40,000 $60,000 $90,000 $100,000
($200,000) $90,000 $70,000 $50,000 $30,000 $10,000 $10,000 $10,000 $10,000
Weighted average cost of capital
7.2%
Yearly net cash flows: Initial investment Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8
a. NPVs of the projects:
NPV
Project 1
Project 2
$19,398
$33,705
Project 1
Project 2
b. IRRs of the projects:
77
IRR
8.8%
14.4%
2% 99,769 65,526
4% 65,182 52,380
c. NPV Profiles: Discount rate NPV Project 1 NPV Project 2
6% 35,340 40,396
8% 9,502 29,435
10% (12,943) 19,376
12% (32,504) 10,118
14% (49,605) 1,573
16% (64,600) (6,337)
NPV PROFILES $120,000 $100,000 $80,000 $60,000 NPV
$40,000
Project 1
$20,000
Project 2
$0 ($20,000)
2%
4%
6%
8%
10%
12%
14%
16%
($40,000) ($60,000) ($80,000) DISCOUNT RATE
Comment:
Both projects have the same NPV at a discount rate of approximately 5.5%. At that discount rate the NPV of both projects is about $45,000.
d. Project selection at other WACCs: Select i. WACC > 5.4% Project 2 ii. WACC > 8.81% Project 2 iii. WACC > Neither project 14.39%
Reason Project 2's NPV is higher Project 1's NPV is negative The NPV for both projects is negative
e) Look at the NPV profile. If the discount rate is 5%, this is to the left of the crossover point. Project 1 would have a higher NPV than Project 2. This would create a ranking conflict if the projects were mutually exclusive. Project 2 has a higher IRR (14.3% for Project 2 versus 8.81 percent for Project 1). At a discount rate below 5.4%, NPV and IRR give conflicting ranking signals. At a discount rate of 5.4% or more, the ranking of the two projects is the same. f)
a. Both projects would be accepted at a 7.2% cost of capital.
78
Chapter 11 Solutions
Answers to Review Questions 1.
Why do we focus on cash flows instead of profits when evaluating proposed capital budgeting projects? We focus on cash flows instead of profits when evaluating proposed capital budgeting projects because it is cash flow that changes the value of a firm. You can spend cash but you can not spend profit.
2.
What is a sunk cost? Is it relevant when evaluating a proposed capital budgeting project? Explain. A sunk cost is a cash flow that has already occurred, or that will occur, whether a project is accepted or rejected. It is irrelevant when evaluating a proposed project.
3.
How do we estimate expected incremental cash flows for a proposed capital budgeting project? We estimate expected incremental cash flows for a proposed project by estimating the changes in sales and expenses that are incremental to the project, adding back the incremental depreciation expense since depreciation expense is a non-cash expense.
4.
What role does depreciation play in estimating incremental cash flows? Depreciation expense is a tax deductible expense and therefore affects cash flow through its effect on taxes. Depreciation expense that is incremental to a proposed project therefore affects incremental cash flows.
5.
How and why does working capital affect the incremental cash flow estimation for a proposed large capital budgeting project? Explain. Many large projects require additional working capital. This investment in additional working capital becomes part of the initial investment. This investment is recovered at the end of the project‘s life. There may be some spontaneous increase in current liabilities associated with a project, but the change in net working capital, if any, is likely to be a positive value requiring an increase in the initial investment of that amount.
6.
How do opportunity costs affect the capital budgeting decision-making process? Opportunity costs reflect the foregone benefits of the alternative not chosen when a capital budgeting project is selected. Any decrease in the cash flows of the firm directly tied to the selection of a new project could be part of the opportunity cost value and included in our capital budgeting analysis. 79
7.
How are financing costs generally incorporated into the capital budgeting analysis process? Financing costs are usually captured in the discount or hurdle rate when doing NPV or IRR analysis. The operating cash flows usually do not include financing costs because this would be double counting.
Answers to End-of—Chapter Problems 11-1.
Price of Selected Model Attachments Paint Name Garage and Maint. Facility
$6,000 5,000 300 12,000 $23,300
Cash Flow t0 = ($23,300) 11-2. (a) Resale Price: $60,000 Price of Equipment: Resale Value: Years Used: MACRS Classification: Income Tax: Accumulated Depreciation: Book Value: Taxable Gain (Loss): Tax (Refund): Net Cash Flow:
$200,000 $60,000 3 5 years 40% 20% + 32% + 19.2% = 71.2% or, 0.712 X $200,000 = $142,400 $200,000 - $142,400 = $57,600 $60,000 - $57,600 = $2,400 $2,400 X 0.40 = $960 $60,000 - $960 = $59,040
(b) Resale Price: $80,000 Price of Equipment: Resale Value: Years Used: MACRS Classification: Income Tax: Accumulated Depreciation: Book Value: Taxable Gain (Loss): Tax (Refund): Net Cash Flow:
$200,000 $80,000 3 5 years 40% 20% + 32% + 19.2% = 71.2% or, 0.712 X $200,000 = $142,400 $200,000 - $142,400 = $57,600 $80,000 - $57,600 = $22,400 $22,400 X 0.40 = $8,960 $80,000 - $8,960 = $71,040
80
11-3.
a) $10,000 - $3,000 - $2,000 = $5,000 b ) $5,000 X .35 = $1,750 c ) $5,000 - $1,750 = $3,250 d ) $3,250 + $2,000 depr. add back = $5,250 e ) Interest Expense. It is included in the cost of funds when calculating NPV and when setting the IRR hurdle rate.
11-4.
Mower Annual Revenues (increase) Operating Costs (increase)
Depreciation (20%) EBIT Taxes (35%) Depreciation Net operating CF
$20,000 100,000 30,000
Year 1 $100,000 - 30,000 70,000 - 4,000 66,000 - 23,100 42,900 + 4,000 $46,900
The net operating incremental cash flow for year 1 is $46,900 11-5.
$2,000 * (1 – 0.35) = $1,300
11-6. Initial Cost of new Equipment $375,000 End of year:
1
2
3
4
5
6
Earnings Before Depreciation and Taxes (EBDT) $120,000 $90,000 $70,000 $70,000 $70,000 $70,000 Discount rate Tax rate Year MACRS depreciation percentages for five-year class life equipment
13% 40% 1 20.00%
2
3
4
5
32.00% 19.20% 11.50% 11.50%
6 5.80%
Calculations: Incremental Cash Flows: Year
1
2
3
4
5
6
EBDT $120,000 $90,000 $70,000 $70,000 $70,000 $70,000 New depreciation expense (75,000) (120,000) (72,000) (43,125) (43,125) (21,750)
81
Change in Operating Income Income tax on new income Change in earnings after tax Add back depreciation
45,000 (30,000) (2,000) 26,875 (18,000) 12,000 800 (10,750) 27,000 (18,000) (1,200) 16,125 75,000 120,000 72,000 43,125
26,875 (10,750) 16,125 43,125
48,250 (19,300) 28,950 21,750
Net incremental operating cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $50,700 Present value of cash flows
$90,265 $79,881 $49,068 $36,339 $32,159 $24,352
Total present value of cash flows $312,064 Less initial cost ($375,000) = NPV ($62,936)
The NPV is negative so the project should be rejected.
11-7. Rhodes Manufacturing Corporation (with salvage value) Given: Initial Cost of new Equipment End of year:
$375,000 1
2
Earnings Before Depreciation and Taxes (EBDT)
$120,000
Discount rate Tax rate
13% 40%
Year MACRS depreciation percentages for five-year class life equipment Resale value of equipment
1 20.00%
3
4
5
6
$90,000 $70,000 $70,000 $70,000 $70,000
2 32.00%
3 19.20%
4 11.50%
5 11.50%
6 5.80%
$50,000 at the end of the sixth year
Calculations: Incremental Cash Flows: Year
1
2
3
4
5
6
EBDT New depreciation expense Change in Operating Income Income tax on new income Change in earnings after tax Add back depreciation
$120,000 $90,000 $70,000 $70,000 $70,000 $70,000 (75,000) (120,000) (72,000) (43,125) (43,125) (21,750) 45,000 (30,000) (2,000) 26,875 26,875 48,250 (18,000) 12,000 800 (10,750) (10,750) (19,300) 27,000 (18,000) (1,200) 16,125 16,125 28,950 75,000 120,000 72,000 43,125 43,125 21,750
Net incremental operating cash flows
$102,000 $102,000 $70,800 $59,250 $59,250 $50,700
Resale value of equipment 50,000 Less income tax on sale (20,000) Net cash flow from equipment sale 30,000 Total Net cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $80,700
82
Present value of cash flows
$90,265 $79,881 $49,068 $36,339 $32,159 $38,762
Total present value of cash flows $326,474 Less initial cost ($375,000) = NPV ($48,526)
The NPV is negative so the project should be rejected.
11-8. a ) $85,000 + $20,000 = $105,000 b)
$125,000 X .10 = Oper. Exp. Depr. Exp.
$12,500 -20,000 -10,500 -18,000 7,200 -10,800 10,500 -300
Tax Saving@40% Add back Depr. Net Incremental Oper. Cash flow c)
End of year 5 at the time of the sale
11-9. GHOST SQUADRON HISTORICAL AIRCRAFT, INC. ASSUMPTIONS: MACRS Depreciation
Yr 1 14.3%
Tax rate Cost of capital
35% 12%
Yr 2 24.5%
Yr 3 17.5%
Yr 4 12.5%
Yr 5 8.9%
Yr 6 8.9%
Yr 7 8.9%
ESTIMATED INCREMENTAL CASH FLOWS: Initial Investment at t=0: Crew transport & wreckage collection Transport to restoration facility Plane restoration Total Initial Investment
($100,000) ($35,000) ($600,000) ($735,000)
Year:
1
2
3
4
5
6
7
New Revenues Additional operating expenses Depreciation on plane Change in Operating Income Tax on new income Change in Earnings after tax Add back depreciation
($40,000) ($105,105) ($145,105) $50,787 ($94,318) $105,105
($40,000) ($180,075) ($220,075) $77,026 ($143,049) $180,075
$70,000 ($40,000) ($128,625) ($98,625) $34,519 ($64,106) $128,625
$70,000 ($40,000) ($91,875) ($61,875) $21,656 ($40,219) $91,875
$70,000 ($40,000) ($65,415) ($35,415) $12,395 ($23,020) $65,415
$70,000 ($40,000) ($65,415) ($35,415) $12,395 ($23,020) $65,415
$70,000 ($40,000) ($65,415) ($35,415) $12,395 ($23,020) $65,415
Net Incremental Cash Flows
$10,787
$37,026
83
$64,519 $51,656 $42,395
$42,395 $42,395
Yr 8 4.5%
Additional Cash Flows at the end of year 7: Proceeds from sale of plane $500,000 Book value of plane $33,075 Taxable gain(loss) $466,925 Tax on gain $163,424 Net cash flow from sale of plane $336,576 (Salvage value less tax on gain)
SUMMARY OF NET CASH FLOWS: Time:
0
1
($735,000)
$10,787
2
3
4
5
$37,026 $64,519 $51,656
6
$42,395 $42,395 $378,972
Net present Value: ($400,138) Internal rate of Return:
11-10. a )
-2.7%
NWC = Current Assets - Current Liabilities = ($8,000 + $10,000 + $12,000) - ($6,000 + $2,500) = $21,500
b)
Outflow
c)
Beginning of year 1
11-11. Given: Initial Cost of new Equipment End of year: New revenues Discount rate Tax rate Year MACRS depreciation percentages for three-year class life equipment Resale value of equipment
$90,000 1 $50,000 11% 30% 1 33.30% $10,000
2 $30,000
3 $20,000
4 $20,000
2
3
4
44.50% 14.80% 7.40% at the end of the fourth year
Calculations: Incremental Cash Flows: Year Revenues New depreciation expense Change in Operating Income Income tax on new income Change in earnings after tax Add back depreciation Net incremental operating cash flows
Total Net cash flows Present value of cash flows Total present value of cash flows
84
1 $50,000 (29,970) 20,030 (6,009) 14,021 29,970
2 $30,000 (40,050) (10,050) 3,015 (7,035) 40,050
7
3 $20,000 (13,320) 6,680 (2,004) 4,676 13,320
4 $20,000 (6,660) 13,340 (4,002) 9,338 6,660
$43,991 $33,015 $17,996 Resale value of equipment Less income tax on sale Net cash flow from equipment sale $43,991 $33,015 $17,996 $39,632 $26,796 $13,159 $94,735
$15,998 10,000 (3,000) 7,000 $22,998 $15,149
Less initial cost = NPV
($90,000) $4,735
Comments: Yes, since the project has a positive NPV at the company's cost of capital, Flower Belle should recommend that it be accepted.
11-12. MACRS 3 YEARS
33.30%
44.50% 14.80% 7.40%
PRICE OF NEW EQUIPMENT: 90,000 YEARS USED
4
INCOME TAX RATE:
40.00% COST OF CAPITAL 10.00% SALVAGE VALUE OF NEW EQPT. 10,000
1 2 3 4 MACRS CLASSIFICATION: 3 YEARS DEPRECIATION RATE 33.30% 44.50% 14.80% 7.40% ACCUM. DEP. %)
100%
CASH FLOW FROM SALE OF NEW EQUIPMENT
6,000
CASH FLOW FROM SALE OF OLD EQUIPMENT SALE PRICE 10,000 BOOK VALUE 20,000 TAXABLE GAIN (LOSS) (10,000) TAX (REFUND) (4,000) NET CASH FLOW 14,000 INCREMENTAL CASH FLOW YEAR 1
1
2
3
4
REVENUE STREAM DEPRECIATION EXPENSE
50,000 30,000 20,000 20,000 29,970 40,050 13,320 6,660
CHANGE IN OPERATING INCOME TAX ON NEW INCOME
20,030 (10,050) 6,680 13,340 8,012 (4,020) 2,672 5,336
CHANGE IN EARNINGS ADD BACK DEPRECIATION
12,018 (6,030) 4,008 8,004 29,970 40,050 13,320 6,660
NET INCREMENTAL OP. CASH FLOW 41,988 34,020 17,328 14,664 NET CASH FLOW NEW EQUIPMENT OLD EQUIPMENT
0 (90,000) 14,000
1
2
3
4
OPERATING CF SALVAGE VALUE
41,988 34,020 17,328 14,664
NET CASH FLOW
(76,000) 41,988 34,020 17,328 14,664
DISCOUNT RATE NPV
10.00% $17,419.18
85
11-13. Initial Cost of new equipment End of year: New revenues Discount rate Tax rate
$90,000 1 $50,000 10% 40%
Year MACRS depreciation percentages for three-year classlife equipment
1 33.30%
2 $30,000
2 44.50%
3 4 $20,000 $20,000
3 14.80%
4 7.40%
Book value of old equipment Resale value of old equipment Resale value of new equipment Additional current assets required Expected increase in current liabilities Calculations: Incremental Cash Flows: Gain(loss) on sale of old equipment (Tax)refund on transaction Net cash received for old equipment Cost of New Equipment Net Cash Outflow at T-0 for equipment Additional net working capital required
$20,000 $10,000 $10,000 at the end of the fourth year $10,000 $5,000
($10,000) $4,000 $14,000 ($90,000) ($76,000) ($5,000)
Total Net Cash Outflow at T-0
($81,000)
Year Revenues New depreciation expense Change in Operating Income Income tax on new income Change in earnings after tax Add back depreciation
1 $50,000 (29,970) 20,030 (8,012) 12,018 29,970
2 $30,000 (40,050) (10,050) 4,020 (6,030) 40,050
3 4 $20,000 $20,000 (13,320) (6,660) 6,680 13,340 (2,672) (5,336) 4,008 8,004 13,320 6,660
Net incremental operating cash flows
$41,988
$34,020
$17,328 $14,664
Resale value of equipment 10,000 Less income tax on sale (4,000) Net cash flow from equipment sale 6,000 Recovery of net working capital investment 5,000
11-14. a )
Total Net cash flows Present value of cash flows Total present value of cash flows Less initial cash outflow at T-0
$41,988 $38,171 $96,834 ($81,000)
= NPV
$15,834
Book Value = $20,000 - $12,000 = $8,000
b)
Taxable Gain = $18,000 - $8,000 = $10,000
c)
Tax on Gain = $10,000 X 0.3 = $3,000
d)
Cash Flow = $18,000 - $3,000 = $15,000 This is an inflow.
86
$34,020 $28,116
$17,328 $25,664 $13,019 $17,529
e)
Incremental Cash Flow for to = $40,000 - $15,000 = $25,000 outflow
f)
b ) Taxable Income (Loss) = $6,000 - $8,000 = ($2,000) c ) Tax Credit on Loss = $2,000 X 0.3 = $600 d ) Cash Flow = $6,000 + $600 = $6,600 This is an inflow. e ) Incremental Cash Flow for to = $40,000 - $6,600 = $33,400 outflow
87
11-15. MACRS 3 YEARS 33.30% 44.50% 14.80% 7.40% PRICE OF NEW EQUIPMENT: PRICE OF OLD EQUIPMENT: RESALE VALUE OF OLD EQPT: YEARS USED
$22,000 0 0 4
INCOME TAX RATE:
40.00% COST OF CAPITAL 14.00% SALVAGE VALUE OF NEW EQUIP. $0
MACRS CLASSIFICATION:
3
YEARS
1
2
3
4
DEPRECIATION RATE 33.30% 44.50% 14.80% 7.40% ACCUMULATED DEPR.(%)
100%
CASH FLOW FROM CHANGE IN NWC CHANGE IN CURRENT ASSETS CHANGES IN CURRENT LIABS. CHANGE IN NWC INCREMENTAL CASH FLOW YEAR CHANGE IN SALES: INCREASE IN OPERATING EXPENSES TOTAL INFLOW DEPRECIATION EXPENSE
5000 3000 2000
1 2 3 4 20,000 20,000 10,000 10,000 (4,000) (4,000) (2,000) (2,000) 16,000 16,000 8,000 8,000 7,326 9,790 3,256 1,628
CHANGE IN OPERATING INCOME TAX ON NEW INCOME
8,674 3,470
6,210 2,484
4,744 6,372 1,898 2,549
CHANGE IN EARNINGS
5,204
3,726
2,846 3,823
7,326 9,790 12,530 13,516
3,256 1,628 6,102 5,451
ADD BACK DEPRECIATION NET INCREMENTAL OP. CASH FLOW NET CASH FLOW a.
NEW EQUIPMENT
b.
OPERATING CF
c.
NET CASH FLOW
0 (22,000) (2,000)
NWC
DISCOUNT RATE
1
2
3
12,530 13,516
2,000 6,102 5,451
(24,000) 12,530 13,516
6,102 7,451
14.00% $5,922.36 27.24%
NPV IRR
Yes, Brenners should add this machine to their factory.
88
4
11-16. Given: Initial Cost of new Equipment
$150,000
Installation and calibration costs
$7,500
Decrease in operating expenses
$50,000
Discount rate
10%
Tax rate
35%
Year
1
annually
2
3
4
MACRS depreciation percentages for three-year class
33.30%
44.50%
14.80%
7.40%
life equipment Calculations: Incremental Cash Flows at T-0: Cost of New Equipment
($150,000)
Installation and calibration costs
($7,500)
Total Net Cash Outflow at T-0
($157,500)
Incremental cash flows in years 1 - 5: Year
1
2
3
4
5
Reduction in operating costs
$50,000
$50,000
$50,000
$50,000
$50,000
New depreciation expense
(52,448)
(70,088)
(23,310)
(11,655)
0
Change in Operating Income
(2,448)
(20,088)
26,690
38,345
50,000
Income tax on new income
857
7,031
(9,342)
(13,421)
(17,500)
Change in earnings after tax
(1,591)
(13,057)
17,349
24,924
32,500
Add back depreciation
52,448
70,088
23,310
11,655
0
$50,857
$57,031
$40,659
$36,579
$32,500
Present value of cash flows
$46,233
$47,133
$30,547
$24,984
$20,180
Total present value of cash flows
$169,077
Less initial cash outflow at T-0
($157,500)
Net incremental operating cash flows a. NPV of the investment:
a. NPV = $11,577 b. Yes, since the NPV of the investment is positive at RHPS's cost of capital, Weiss and Majors should go forward with the project.
89
11-17. Chemical Company of Baytown Given: Original cost of old equipment Resale value of old equipment
$40,000 on Dec 31, 2004 $4,000 on Dec 31, 2006
Discount rate Tax rate Year MACRS depreciation percentages for three-year class life equipment
6% 40% 1
2
33.30%
44.50%
3 14.80%
4 7.40%
Calculations: a. Cash flows from sale of old equipment: Year 2005 Depreciation expense on old equipment Total accumulated depreciation Book value of old equipment Resale value of old equipment Gain(loss) on sale of old equipment (Tax)refund on transaction Net cash received for old equipment
Year 2006
$13,320 $17,800 $31,120 $8,880 on Dec 31, 2006 $4,000 on Dec 31, 2006 ($4,880) $1,952 $5,952
b. New net working capital requirements: Additional current assets required: Cash Receivables Inventory Total Expected increase in current liabilities: Accounts payable Accrued expenses Total
$1,000 $5,000 $10,000 $16,000 $6,000 $3,000 $9,000
Incremental cash flow for net working capital
$7,000
c. Net cash outflow at the end of 2006 if new process line is installed: Cost of New Equipment Additional net working capital Less proceeds from sale of old equipment Net cash outflow at the end of 2006
$180,000 $7,000 ($5,952) $181,048
d. Incremental cash flows for 2007 - 2010: End of year: New revenues Reduction in operating expenses New depreciation expense Change in Operating Income Income tax on new income Change in earnings after tax Add back depreciation
2007 $60,000 6,000 (59,940) 6,060 (2,424) 3,636 59,940
90
2008 $60,000 6,000 (80,100) (14,100) 5,640 (8,460) 80,100
2009 $60,000 6,000 (26,640) 39,360 (15,744) 23,616 26,640
2010 $60,000 6,000 (13,320) 52,680 (21,072) 31,608 13,320
Net incremental operating cash flows
$63,576
$71,640
$50,256 $44,928
e. NPV and IRR of the investment: (Given) Resale value of new equipment
$20,000 at the end of the fourth year Resale value of equipment 20,000 Less income tax on sale (8,000) Net cash flow from equipment sale 12,000 Recovery of net working capital investment
Total Net cash flows
7,000
$63,576
$71,640
1
2
Present value of cash flows
$59,977
$63,759
$42,196 $50,637
Total present value of cash flows Less initial cash outflow at T-0
$216,570 ($181,048)
= NPV
$35,522
Year Net Cash Flow
0 ($181,048)
1 $63,576
2 3 4 $71,640 $50,256 $63,928
IRR
14.4%
Year
$50,256 $63,928 3
4
Summary of all cash flows:
f. NPV Profile Year
0
1
2
3
4
Net Cash Flow ($181,048) $63,576 $71,640 $50,256 $63,928 Assumed cost of capital NPV of cash flows
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% $68,352 $62,338 $56,556 $50,994 $45,641 $40,487 $35,522 $30,736 $26,122 $21,672 $17,377
NPV Profile, Chemical Company of Baytown Project $80,000
NPV
$70,000
$68,352 $62,338 $56,556 $50,994 $45,641 $40,487 $35,522 $30,736 $26,122 $21,672 $17,377
$60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 0%
1%
2%
3%
4%
5%
6%
Cost of Capital
91
7%
8%
9%
10%
11-18. PROBLEM 11-18 Real Options Decision Tree NPV Analysis J & T's Double Diamond Brewhouse
Time t0
Time 1
25%
($300,000)
50%
25%
$200,000
$100,000
Time 2
100%
Time 3
$100,000
Time 4
Time 5
|-------- Part b. --------| Joint Path Probability NPV
|- Part c. -| JP x NPV
50%
$400,000
$400,000
$400,000
12.5%
$666,954
$83,369
30%
$200,000
$200,000
$200,000
7.5%
$309,669
$23,225
20%
$90,000
$90,000
$90,000
5.0%
$113,163
$5,658
100%
$100,000
100%
$100,000
$100,000
$100,000
50.0%
$43,308
$21,654
0%
($40,000)
100%
($40,000)
($40,000)
($40,000)
0.0%
($437,323)
$0
100%
$0
100%
$0
$0
$0
25.0%
($335,088)
($83,772)
Total NPV of the Deal:
$50,135
($40,000)
Cost of Capital:
14%
The Time 2 cash flow for the smash hit scenario is $200,000 from operations minus $100,000 for the expansion.
92
Chapter 12 Solutions
Answers to Review Questions 1.
Describe the general pattern of cash flows from a bond with a positive coupon rate. Cash flows from a bond with a positive coupon rate consist of periodic interest payments and the face value payment at maturity. Coupon interest payments occur at regular intervals throughout the life of the bond. The face value payment occurs on the maturity date.
2.
How does the market determine the fair value of a bond? The fair value of a bond is the present value of the bond's coupon interest payments plus the present value of the face value payment at maturity, discounted at the market‘s required rate of return for the bond in question. Equation 9-1 in the text is use to solve for the fair (present) value of a bond.
3.
What is the relationship between a bond's market price and its promised yield to maturity? Explain. A bond's market price depends on its yield to maturity (YTM). When a bond has a YTM greater than its coupon rate, it sells at a discount from its face value. When the YTM is equal to the coupon rate, the market price equals the face value. When the YTM is less than the coupon rate, the bond sells at a premium over face value.
4.
All other things held constant, how would the market price of a bond be affected if coupon interest payments were made semiannually instead of annually? Most bonds issued in the United States pay interest semiannually (twice per year). With semiannual interest payments, we must adjust the bond valuation model (Equation 9-1 in the text) by multiplying n, the number of years to maturity, by two, and dividing k, the annual interest rate, by two.
5.
What is the usual pattern of cash flows for a share of preferred stock? How does the market determine the value of a share of preferred stock, given these promised cash flows? Preferred stock has no maturity date, so it has no maturity value. Its future cash payments are dividend payments that are paid to preferred stockholders at regular time intervals for as long as they (or their heirs) own the stock. Cash payments from preferred stock dividends are scheduled to continue forever. To value preferred stock, we adapt the discounted cash flow model to reflect that preferred stock dividends are a perpetuity. See Equation 9-4 in the text.
6.
Name two patterns of cash flows for a share of common stock. How does the market determine the value of the most common cash flow pattern for common stock?
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Cash flows for a share of common stock consist of dividend payments and the price received for the eventual sale of the share. Common stock valuation is complicated by the fact that common stock dividends are difficult to predict compared to the interest and principal payments on a bond, or dividends on preferred stock. Indeed, corporations may pay common stock dividends irregularly, or not pay dividends at all. As with bonds and preferred stock, the market values common stock by estimating the present value of the expected future cash flows from the common stock. See Equation 9-6 in the text.
7.
Define the P/E valuation method. Under what circumstances should a stock be valued using this method? The P/E ratio indicates how much investors are willing to pay for each dollar of a stock's earnings. A high P/E ratio indicates that investors believe the stock's earnings will increase, or that the risk of the stock is low, or both. Financial analysts often use a P/E model to estimate common stock value for businesses that are not public. First, analysts compare the P/E ratios of similar companies within an industry to determine an appropriate P/E ratio for companies in that industry. Second, analysts calculate an appropriate stock price for firms in the industry by multiplying each firm's earnings per share (EPS) by the industry average P/E ratio. See Equation 9-9 in the text.
8.
Compare and contrast the book value and liquidation value per share for common stock. Is one method more reliable? Explain. The Book Value of a firm's common stock is found by subtracting the value of the firm's liabilities, and preferred stock, if any, as recorded on the balance sheet, from the value of its assets. The result is the book value or net worth of the company's common stock. To find the book value per share of common stock, divide the company's book value by the number of outstanding common stock shares. See Equation 9-10 in the text. The liquidation value and book value valuation methods are similar, except that the liquidation method uses the market values of the assets and liabilities, not book values. The market values of the assets are the amounts the assets would earn on the open market if they were sold (or liquidated). The market values of the liabilities are the amounts of money it would take to pay off the liabilities. Since it is based on market values, the liquidation value method is more reliable than the book value method. However, liquidation value is a worst-case valuation assessment. A company's common stock should be worth at least the amount generated per share at liquidation.
9. Answer the following questions about the discounted free cash flow model illustrated in Figure 12-4: a. What are ―free cash flows?‖
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Free cash flows represent the total cash flows from business operations that are available to be distributed to the suppliers of a firm‘s capital each year either in the form of interest to the debt holders, or dividends to the stockholders. b. Explain the terminal value calculation at the end of the forecast period. Why is it necessary? The firm whose business operation is being valued is not expected to suddenly cease operating at the end of the discrete forecasting period, but to continue operating indefinitely into the future as a going concern. The terminal value calculation estimates the values of the cash flows that occur in the year following the discrete forecasting period and beyond. c. Explain the term ―present value of the firm‘s operations‖ (also known as Enterprise Value). What does this number represent? The present value of the company‘s free cash flows represents the market value of the firm‘s core income producing operations. In the world of finance and investing this is sometimes called the firm‘s Enterprise Value. It is not the total market value of the entire company, however, or the total market value of the company‘s assets, because the current, or non-operating assets of the company have not yet been accounted for. d. Explain the adjustments necessary to translate enterprise value to the total present value of common equity. To obtain the value of the company‘s common stock, add the value of the firm‘s current assets to the enterprise value (this produces the value of the firm‘s total assets). Next, subtract the values of current liabilities, long-term debt, and preferred stock. The result is the present value of common equity.
10. Explain the difference between the discounted free cash flow model as it is applied to the valuation of common equity and as it is applied to the valuation of complete businesses. The Free Cash Flow Model values the complete business as a part of the procedure to value common equity. The value of a complete business is the sum of the values of the operating, or incomeproducing assets, plus the value of the non-operating, or current assets. All that is necessary to use the Free Cash Flow Model to value a complete business, then, is to add the value of the company‘s operations to the value of the company‘s current assets.
11. Why is the replacement value of assets method not generally used to value complete businesses? The replacement value of assets method is not often applied to complete business valuations because it is frequently very difficult to locate similar assets for sale on the open market, and because some of a business‘s assets are difficult to define and quantify.
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Answers to End-of-Chapter Problems 12-1.
a) b) c)
$1,000 X .06 = $60 $60 X [(1-1/1.0810)/.08] + $1,000 X [1/1.0810] = $865.80 Yes.
12-2.
a) b) c)
$1,000 X .12 = $120 $120 X [(1-1/1.0815)/.08] + $1,000 X [1/1.0815] = $1,342.38 $60 X [(1-1/1.0430)/.04] + $1,000 X [1/1.0430] = $1,345.84
12-3.
3 X $2,000 = $6,000
12-4.
Semi-annual interest payment = .10 X $1,000 X 6/12 = $50 Price = $50 X [(1-1/1.0410)/.04] + $1,000 X [1/1.0410] = $1,081.11
12-5.
Since $1,100 > $1,000, YTM < Coupon Rate; YTM < 9% $90 * [1-1/ (1 + k)10/k] + $1,000 * (1/1 + k10) = $1,100 k = 7.54%
12-6.
a) b) c)
12-7.
Since $872 < $1,000, k > 7% $70 X [(1-1/(1+k)10/k] + $1,000 X [1/(1+k)10] = $872 If k=8%, VB = $932.90 If k=9%, VB = $871.65. So, k 9%.
12-8.
$10/0.12 = $83.33 per share
12-9.
kP = $1.75 /$ 20 = 0.0875 or 8.75%
Since, $1,125 > $1,000, YTM < Coupon Rate YTM < 12% $120 X [(1-1/1.1010)/.10] + $1,000 X [1/1.1010] = $1,122.89; YTM 10% YTM = 12%; YTM = Coupon Rate if Market Price = Par
12-10. a ) b)
VP = $8/0.13 = $61.54 per share kP = $8/$50 = 16 %
12-11. a ) b)
$4/(.16-.01) = $26.67 $4/$26.67 = 15%
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12-12. $2/$15 + .04 = 17.33%
12-13. a ) b)
P0 = $8/(.14 - .03) = $72.72 ks = $8/$65 + .03 = 15.31%
12-14. $90 * [1-1/ (1.12)5/0.12] + $1,000 * (1/1.125) = $891.86 12-15. $35 * [1-1/ (1.055)20/0.055] + $1,000 * (1/1.05520) = $761 12-16. $80/ (1 + 0.23)1 = $65.04 $150/ (1 + 0.23)2 = $99.15 $1,500/ (1 + 0.23)3 = $806.08 $65.04 + $99.15 + $806.08 = $970.27
12-17. $3.00/0.12 = $25.00
12-18. $2.20/(0.18 - 0.09) = $2.20/0.09 = $24.44
12-19. D6 = $1.22 (1+ 0.10) = $1.342 $1.342/ (0.12 – 0.10) = $67.10 $0.70 / (1+0.12)1 + $0.83 / (1+0.12)2 + $0.96 / (1+0.12)3 + $1.09 / (1+0.12)4 + $1.22 / (1+0.12)5 + $67.10 / (1+.12)6 0.625 + 0.66167 + 0.6833 + 0.6927 + 0.6923 + $33.99 =$37.34
12-20. D1 = 3.82(1 + 0.07) = 4.09 k = 4.09/82 + 0.07 k = .1199 = 11.99% 12-21. $85 * [1-1/ (1 + k)10/k] + $1,000 * (1/1 + k10) = $1,250 k = 5.23% 12-22. $2,100,000 / (0.18 – 0.09) = $23,333,333.33
12-23. Find the present values of cash flows for each year. Add them together to get the present value of the firm. Year 1 = $1,231,920,000 * [1/ (1 + 0.12)1] = $1,099,928,571 Year 2 = $1,453,665,600 * [1/ (1 + 0.12)2] = $1,158,853,316
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Year 3 = $1,686,252,096 * [1/ (1 + 0.12)3] = $1,200,240,935 Year 4 = $1,922,327,389 * [1/ (1 + 0.12)4] = $1,221,673,808 Year 5 = $2,153,006,676 * [1/ (1 + 0.12)5] = $1,221,673,809 Year 6 CF = Year 5 CF * (1 + .10) = $2,153,006,676 * 1.10 = 2,368,307,344 Year 6 - ∞ = (((2,368,307,344 / (0.12 - 0.10)) * (1/1.12)5 ) = $67,192,060,000 Enterprise value of the firm today = $1,099,928,571 + $1,158,853,316 + $1,200,240,935 + $1,221,673,808 + $1,221,673,809 + $67,192,060,000 = $73,094,430,440
12-24. a ) b)
$675,000 - $120,000 = $555,000 $555,000/100,000 = $5.55 per share
12-25. a ) b) c) d) e)
Net Worth = $38,400 - ($13,400 + $6,000) = $19,000 (in '000 dollars) Book Value = $19,000,000/500,000 = $38 per share EPS = $5,610,000/500,000 = $11.22 Stock Price = EPS X P/E ratio = $11.22 X 6 = $67.32 Since $67.32 (the stock price) > $38.00 (the book value), the firm seems to have goingconcern value. ($50,000,000 - $20,000,000)/500,000 = $60 per share.
f)
12-26. a)
Corporate Bond
Let YTM = k $130 X [(1-1/(1+k)16)/k] + $1,000 X [1/(1+k)16] = 1,147.58 Solving, kd = 11% b)
Preferred Stock
k = $14/$140 kp = 10% c)
Common Stock
Let ks be the required rate of return for a similar common stock ks = D1/Po + g = $39/$300 + .03 = .16 = 16% Remember that these are three different companies. The cost of preferred stock for Supernova could be lower than the cost of debt for Star, as suggested by the above numbers. Lucky should choose the alternative that, in his opinion, gives the best return/risk tradeoff. There is no clear answer here as to which investment is the best.
98
12-27. The Nonconstant, or Supernormal Dividend Growth Model Flash in the Pan Corporation Given: Year 1 Dividend growth rates Dividend expected in 1 year Assumed required rate of return
Year 2 20%
Year 3 30%
Year 4 20%
Year Year 5 6 and on 10% 5%
$3.00 15%
Calculations: a. Present value of Dividends during the supernormal growth period: Expected future dividends during the supernormal growth period
$3.00
$3.60
$4.68
$5.62
$6.18
Present values of dividends during the supernormal growth period
$2.61
$2.72
$3.08
$3.21
$3.07
Total
$14.69
b. Present value of dividends during the normal growth period (year 6 and on) Terminal value at end of year 5 per Equation 12-7 Present value of terminal value c. Total present value per share of Flash in the Pan Corp. stock
$64.86 $32.25
$46.94
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12-28. The Discounted Free Cash Flow Model for Total Common Equity Hardi-Pets Corporation Forecasting Variables: Revenue growth factor Expected gross profit margin S, G, & A expense % of revenue Depr. & Amort. % of revenue Capital expenditure growth factor Net working capital to sales ratio Income tax rate Assumed long-term sustainable growth rate Discount rate
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 10% 15% 20% 25% 30% 25% 20% 15% 10% 5% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 20% 20% 20% 20% 20% 20% 20% 20% 20% 20% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% -10% -10% -10% -10% -10% -10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 40% 5% per year after 2016 20%
FORECAST:
Total revenue
Actual 2006
Years Ending December 31 |--------------------------------------------------------- Forecast ----------------------------------------------------------------------------------| 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
$1,000,000
$1,100,000 $1,265,000 $1,518,000 $1,897,500 $2,466,750 $3,083,438 $3,700,125 $4,255,144 $4,680,658 $4,914,691
Cost of Goods Sold Gross profit
500,000 500,000
550,000 550,000
632,500 632,500
759,000 759,000
948,750 948,750
1,233,375 1,233,375
1,541,719 1,541,719
1,850,063 1,850,062
2,127,572 2,127,572
2,340,329 2,340,329
2,457,346 2,457,345
Selling, general and administrative expenses Earnings before interest, taxes, depr. & amort. (EBITDA)
200,000 300,000
220,000 330,000
253,000 379,500
303,600 455,400
379,500 569,250
493,350 740,025
616,688 925,031
740,025 1,110,037
851,029 1,276,543
936,132 1,404,197
982,938 1,474,407
Depreciation and amortization Earnings before Interest and taxes (EBIT)
100,000 200,000
110,000 220,000
126,500 253,000
151,800 303,600
189,750 379,500
246,675 493,350
308,344 616,687
370,013 740,024
425,514 851,029
468,066 936,131
491,469 982,938
Federal and State Income Taxes Net Operating Profit After-Tax (NOPAT)
80,000 120,000
88,000 132,000
101,200 151,800
121,440 182,160
151,800 227,700
197,340 296,010
246,675 370,012
296,010 444,014
340,412 510,617
374,452 561,679
393,175 589,763
Add back depreciation and amortization Subtract Capital Expenditures Subtract New Net Working Capital Free Cash Flow
100,000 (15,000)
110,000 (16,500) (10,000) $215,500
126,500 (18,150) (16,500) $243,650
151,800 (19,965) (25,300) $288,695
189,750 (21,962) (37,950) $357,538
246,675 (19,766) (56,925) $465,994
308,344 (17,789) (61,669) $598,898
370,013 (16,010) (61,669) $736,348
425,514 (14,409) (55,502) $866,220
$205,000
468,066 491,469 (12,968) (11,671) (42,551) (23,403) $974,226 $1,046,158
Terminal value, 2016 Present Value of Free Cash Flows @ 20%
$7,323,106 179,583
169,201
100
167,069
172,424
187,273
200,570
205,501
201,455
188,812
1,351,683
Total Present Value of Company Operations Plus Current Assets Less Current Liabilities Less Long-Term Debt Less Preferred Stock
$3,023,571 100,000 (80,000) (500,000) 0
Net Market Value of Common Equity
$2,543,571
from Hardi-Pets December 31, 2006 Balance Sheet from Hardi-Pets December 31, 2006 Balance Sheet from Hardi-Pets December 31, 2006 Balance Sheet from Hardi-Pets December 31, 2006 Balance Sheet
12-29. The Discounted Free Cash Flow Model for a Complete Business Great Expectations Company Forecasting Variables:
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Revenue growth factor Expected gross profit margin S, G, & A expense % of revenue Depr. & Amort. % of revenue Capital expenditure growth factor Net working capital to sales ratio Income tax rate Assumed long-term sustainable growth rate Discount rate
20% 50% 50% 10% 40% 19%
40% 52% 30% 10% 30% 17%
50% 53% 29% 10% 25% 16%
60% 54% 28% 10% 20% 15%
50% 55% 27% 10% -10% 14%
40% 56% 26% 10% -15% 13%
30% 57% 25% 10% -20% 12%
20% 58% 24% 10% -25% 11%
10% 59% 23% 10% -30% 10%
40% 5% per year after 2016 20%
FORECAST: Actual 2006 Total revenue
30% 51% 40% 10% 35% 18%
Years Ending December 31 |---------------------------------------------------------------------- Forecast -----------------------------------------------------------------------------| 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
$2,000,000 $2,400,000 $3,120,000 $4,368,000 $6,552,000 $10,483,200 $15,724,800 $22,014,720 $28,619,136 $34,342,963 $37,777,260
Cost of Goods Sold Gross profit
1,200,000 800,000
1,200,000 1,200,000
1,528,800 1,591,200
2,096,640 2,271,360
3,079,440 3,472,560
4,822,272 5,660,928
7,076,160 9,686,477 12,306,228 14,424,045 15,488,676 8,648,640 12,328,243 16,312,908 19,918,918 22,288,584
Selling, general and administrative expenses Earnings before interest, taxes, depr. & amort. (EBITDA)
1,200,000 (400,000)
1,200,000 0
1,248,000 343,200
1,310,400 960,960
1,900,080 1,572,480
2,935,296 2,725,632
4,245,696 4,402,944
5,723,827 6,604,416
7,154,784 8,242,311 8,688,770 9,158,124 11,676,607 13,599,814
Depreciation and amortization Earnings before Interest and taxes (EBIT) Available tax-loss carryforwards Net taxable earnings
200,000 (600,000) 0 0
240,000 (240,000) (600,000) 0
312,000 31,200 (840,000) 0
436,800 524,160 (808,800) 0
655,200 917,280 (284,640) 632,640
1,048,320 1,677,312 0 1,677,312
1,572,480 2,830,464 0 2,830,464
2,201,472 4,402,944 0 4,402,944
2,861,914 6,296,210 0 6,296,210
3,434,296 8,242,311 0 8,242,311
3,777,726 9,822,088 0 9,822,088
Federal and State Income Taxes Net Operating Profit After-Tax (NOPAT)
0 (600,000)
0 (240,000)
0 31,200
0 524,160
253,056 664,224
670,925 1,006,387
1,132,186 1,698,278
1,761,178 2,641,766
2,518,484 3,777,726
3,296,924 4,945,387
3,928,835 5,893,253
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Add back depreciation and amortization Subtract Capital Expenditures Subtract New Net Working Capital Free Cash Flow
200,000 240,000 312,000 436,800 655,200 1,048,320 1,572,480 2,201,472 2,861,914 3,434,296 3,777,726 (1,000,000) (1,400,000) (1,890,000) (2,457,000) (3,071,250) (3,685,500) (3,316,950) (2,819,408) (2,255,526) (1,691,645) (1,184,151) 76,000 129,600 212,160 349,440 589,680 733,824 817,690 792,530 629,621 343,430 ($1,400,000) ($1,324,000 ($1,417,200 ($1,283,880 ($1,402,386 ($1,041,113 $687,632 $2,841,521 $5,176,644 $7,317,659 $8,830,257 ) ) ) ) )
Terminal value, 2016
$61,811,799
Present Value of Free Cash Flows @ 20%
(1,103,333)
(984,167)
(742,986)
(676,305)
(418,400)
Total Present Value of Company Operations Plus Current Assets
$11,129,331 500,000 from Great Expectations' December 31, 2006 Balance Sheet
Total Market Value of Great Expectations' Assets
$11,629,331
102
230,287
793,016
1,203,922
1,418,211 11,409,086
Chapter 13 Solutions
Answers to Review Questions 1.
What is the operating leverage effect and what causes it? What are the potential benefits and negative consequences of high operating leverage? The operating leverage effect is the phenomenon whereby a small change in sales triggers a relatively large change in operating income. It is caused by the presence of fixed operating costs. The potential benefits are that if sales are rising operating income will rise more quickly. The negative consequences are that falling sales will cause operating income to fall more quickly, including negative values.
2.
Does high operating leverage always mean high business risk? Explain. High operating leverage does not always mean high business risk. If the companies sales are quite stable then the variation in operating income would be small even if the degree of operating leverage were large.
3.
What is the financial leverage effect and what causes it? What are the potential benefits and negative consequences of high financial leverage? Financial leverage is the additional volatility of net income caused by the presence of fixed-cost funds. The potential benefits are that if operating income is rising net income will rise more quickly. The negative side is that if operating income is falling net income will fall more quickly, including possibly negative values.
4.
Give two examples of types of companies likely to have high operating leverage. Find examples other than those cited in the chapter. Long distance telephone companies and electricity generating companies are likely to have operating leverage. These two types of companies have very high fixed costs, because they are capital intensive, and have relatively low variable costs.
5.
Give two examples of types of companies that would be best able to handle high debt levels. Companies that handle local telephone service and those that handle natural gas delivery to consumers would be expected to comfortably be able to handle high debt levels. This is because the sales of these two types of companies tend not to react very much to the business cycle. Their sales tend to grow with the population. They are often regulated and protected from competition, although this is not so much true as it was a few years ago.
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6.
What is an LBO? What are the risks for the equity investors and what are the potential rewards? A leveraged buyout is a purchase of a publicly owned corporation by a small group of investors using a large amount of borrowed money. The risks for the equity investors are those that exist whenever a high degree of financial leverage exists. So too are the rewards, where small returns become large returns because of leverage.
7.
If an optimal capital structure exists, what are the reasons why too little debt is as undesirable as is too much debt? Too little debt may be as undesirable as too much debt because if a firm has a very conservative capital structure it may be losing the opportunity to reap the positive benefits of financial leverage. A company with a bright future is probably not maximizing shareholder wealth if it has a very small amount of debt in its capital structure. A more aggressive capital structure may create more value for the owners.
Answers to End-of-Chapter Problems 13-1.
a) Breakeven sales per month = $2,300/($50 – 5.75) = 51.98 units b) New Breakeven sales per month = $2,300 x .7 / ($45 – 5.75) = 41.02 units
13-2.
a) 30 x $125 + 30 x $90 + 30 x 55 = $8,100 b) $10,000 + 90 x $15 = $11,350 c) 10 x $125 + 15 x $90 + 35 x $55 = $4,525 d) $10,000 + 60 x $15 = $10,900
13-3.
DOL = (17,900,000 – 9,220,000) / 9,220,000 ÷ (25,000,000 – 15,000,000) / 15,000,000 = 1.41 or DOL = (15,000,000 – 1,980,000) / (15,000,000 – 1,980,000 – 3,800,000) = 1.41
13-4.
DOL = (11,333,000 – 5,257,000) / 5,257,000 ÷ (17,900,000 – 9,220,000) / 9,220,000 = 1.23 or DOL = 9,220,000 / (9,220,000 – 1,710,000) = 1.23
13-5.
a)
Contribution Margin = $28 - $16 = $12
b)
Unit Sales b.e. = $20,000/($28 - $16) = 1,666.67 units; 1,667 units rounded up DOLLARS b.e = $28 x 1,667 units = $46,676
c)
(i) Operating profit (loss) = 1,500 units X $12/unit - $20,000 = ($2,000) (ii) Operating profit (loss) = 3,000 units X $12/unit - $20,000 = $16,000
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d) $180,000 $160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000
1, 00 0 1, 50 0 2, 00 0 2, 50 0 3, 00 0 3, 50 0 4, 00 0 4, 50 0 5, 00 0 5, 50 0 6, 00 0
50 0
0
$0
FIXED COST
13-6. a)
VAR. COST
TOT. COST
REVENUE
Contribution Margin = $28 - $20 = $8
b)
Unit Sales b.e. = $10,000/($28 - $20) = 1,250 units DOLLARS b.e = $28 x 1,250 units = $35,000
c)
(i) Operating profit (loss) = 1,500 units X $8/unit - $10,000 = $2,000 (ii) Operating profit (loss) = 3,000 units X $8/unit - 10,000 = $14,000
d) $180,000 $160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 0
500
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000
FIXED COST
VAR. COST
105
TOT. COST
REVENUE
e) Howard Beal Co., having higher fixed costs, and a lower variable cost per unit, has a higher profit potential once they break-even. However, they have a greater loss potential, and need to achieve a higher sales level to break even, because of the high fixed costs.
13-7. YEAR
2006
2007
SALES IN UNITS
3000
3300
SALES IN DOLLARS
$84,000
$92,400
VAR.COST, $16/unit
$48,000
$52,800
FIXED COST
$20,000
$20,000
OP. INCOME (EBIT)
$16,000
$19,600
$2,000
$2,000
$14,000
$17,600
INTEREST EXP. EBT TAX @30%
$4,200
$5,280
NET INCOME
$9,800
$12,320
%CHANGE IN SALES
10.00%
%CHANGE IN EBIT
22.50%
%CHANGE IN NI
25.71%
a)
Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5% Percentage change in sales = ($92,400 - $84,000)/$84,000 = 10%
b)
Due to presence of fixed costs a given percentage change in sales gives a higher percentage change in operating income (EBIT) (10% and 22.5% respectively). This is the operating leverage effect.
c)
(i) DOL = % EBIT/% SALES = [($19,600 - $16,000)/$16,000]/[($92,400 $84,000)/$84,000] = 22.5%/10% = 2.25 (ii) DOL = (SALES-VC)/(SALES-VC-FC) = ($84,000 - $48,000)/($84,000 - $48,000$20,000) = $36,000/$16,000 = 2.25
d)
(i) shows the effect of operating leverage -- EBIT varies at a larger percentage than sales. (ii) pinpoints the source of operating leverage -- fixed operating costs.
13-8.
a) Percentage change in NI = ($12,320 - $9,800)/$9,800= 25.71% Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5% b) Due to presence of fixed interest expense a given percentage change in EBIT gives a higher percentage change in net income (22.5% and 25.71% respectively). This is the financial leverage effect.
c)
(i) DFL = % NI/% EBIT = [($12,300 - $9,800)/$9,800]/[($19,600 - $16,000)/$16,000] = 25.71%/22.5% = 1.14 (ii) DFL = EBIT/(EBIT - I) = $16,000/($16,000 - $2,000) = 1.14
d)
(i) shows the effect of financial leverage -- NI varies by a larger percentage than operating income (EBIT).
106
(ii) pinpoints the source of financial leverage -- fixed interest expense.
13-9.
a)
$9,000/($15 - $1.50) = 666.67 sq. yards
b)
Break-even point in sales units
c)
666.67 X $15 = $10,000
d)
$9,000/($18 - $1.50) = 545.5 sq. yards, break-even units 545.5 X $18 = $9,819, break-even dollar sales
e) SALES IN UNITS
14,000 sq.yards
SALES IN DOLLARS, units x $18 each
$252,000
VAR.COST, units x $1.50 each
$21,000
FIXED COST
$9,000
OP. INCOME (EBIT)
$222,000
INTEREST EXP.
$3,000
EBT
$219,000
TAX @40%
$87,600
NET INCOME
$131,400
13-10. a ) Contribution Margin = $800 - $250 = $550 per unit Sale of 600 suits: Op. Income = 600 X $550 - $200,000 = $130,000 Sale of 3,000 suits: Op. Income = 3,000 X $550 - $200,000 = $1,450,000 b ) Sale of 600 suits: DOL Sale of 3,000 suits: DOL
= [600 X ($800 - $250)]/[600 X ($800 - $250) - $200,000] = 2.5 = [3,000 X ($800 - $250)]/[3,000 X ($800 - $250) - 200,000] = 1.1
c)
Unit Sales b.e. = $200,000/$550 = 363.64 units; rounded up to 364 DOLLARS b.e = 364 suits X $800 price per suit = $291,200
d)
Unit Sales b.e. = $200,000/($800 - $350) = 444.44 units; rounded up to 445 DOLLARS b.e = 445 suits X $800 price per suit = $356,000
e)
Let P be the selling price per unit. 3,000 units X (P - $350) - $200,000 fixed costs = $1,450,000 op. income P - $350 = ($1,450,000 + $200,000)/$3,000 = $550 P = $550 + $350 = $900 Tom should increase price per unit by $100 ($900 - $800)
13-11.
COMPANY A
COMPANY B
COMPANY C
12,000
12,000
12,000
$120,000
$120,000
$120,000
$60,000
$48,000
$12,000
$0
$10,000
$40,000
$60,000
$62,000
$68,000
SALES IN UNITS SALES IN DOLLARS, units x $10 each VARIABLE COST, $5, $4, and $1 per unit respectively FIXED COST OPERATING INCOME (EBIT)
107
b)
C, B, A.
13-12. a )
Year 1: $30 X 50,000 = $1,500,000 Year 1: $30 X 60,000 = $1,800,000
b)
($1,800 - $1,500)/$1,500 = 0.2 or 20% METHOD 1
c) YEAR 1 UNITS
METHOD 2
YEAR 2
YEAR 1
YEAR 2
50,000
60,000
50,000
60,000
1,500,000
1,800,000
1,500,000
1,800,000
FC
700,000
700,000
100,000
100,000
VC, units x $6 each for Method 1 and x $16.50 each for Method 2
300,000
360,000
825,000
990,000
$500,000
$740,000
$575,000
$710,000
SALES, units x $29 each
EBIT
d)
METHOD 1: % EBIT = ($740,000 - $500,000)/$500,000 = 0.48 OR 48% METHOD 2: % EBIT = ($710,000 - $575,000)/$575,000 = 0.235 OR 23.5%
e)
METHOD 1: DOL = 0.48/0.20 = 2.4 METHOD 2: DOL = 0.235/0.20 = 1.175
f) METHOD 1: DOL = ($1,500,000 - $300,000)/($1,500,000 - $300,000 - $700,000) = 2.4 METHOD 2: DOL = ($1,500,000 - $825,000)/($1,500,000 - $825,000 - $100,000) = 1.175 g)
METHOD 1
h)
The high fixed operating costs METHOD 1
i) YEAR 1 UNITS SALES, units x $30 each
METHOD 2
YEAR 2
YEAR 1
YEAR 2
50,000
53,000
50,000
53,000
1,500,000
1,590,000
1,500,000
1,590,000
FC
700,000
700,000
100,000
100,000
VC, units x $6 each for Method 1 and x $16.50 each for Method 2
300,000
318,000
825,000
874,500
$500,000
$572,000
$575,000
$615,500
EBIT
% SALES = ($53,000 - $50,000)/$50,000 = .06 or 6% METHOD 1: % EBIT = ($572,000 - $500,000)/$500,000 = 0.144 or 14.4% METHOD 2: % EBIT = ($615,500 - $575,000)/$575,000 = 0.0704 or 7.04% METHOD 1: DOL = 0.144/0.06 = 2.4 METHOD 2: DOL = 0.0704/0.06 = 1.17
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13-13. a ) C, B, A. b)
COMPANY A:DFL = $100,000/($100,000 - $0) = 1.0 COMPANY B: DFL = $100,000/($100,000 - $2,000) = 1.02 COMPANY C: DFL = $100,000/($100,000 - $40,000) = 1.67 Answer to part a) was correct.
c) CAPITAL STRUCTURE
COMPANY A
COMPANY B
COMPANY C
ALL EQUITY
90% EQUITY
10% EQUITY
$100,000
$100,000
$100,000
EBIT INTEREST EXP.
$0
$2,000
$40,000
$100,000
$98,000
$60,000
TAXES @40%
$40,000
$39,200
$24,000
NET INCOME
$60,000
$58,800
$36,000
EBT
13-14. a.
EBIT INTEREST EXPENSE EBT TAXES @40% NET INCOME
MICHAEL DORSEY
DOROTHY MICHAELS
YEAR 1 YEAR 2
YEAR 1 YEAR 2
$50,000 $9,100 $40,900 $16,360 $24,540
$50,000 $900 $49,100 $19,640 $29,460
$60,000 $9,100 $50,900 $20,360 $30,540
b. %CHANGE in NI
24.45%
20.37%
c. %CHANGE in EBIT
20.00%
20.00%
d. DFL
1.22
1.02
e. DFL
1.22
1.02
$60,000 $900 $59,100 $23,640 $35,460
f. MICHAEL DORSEY'S COMPANY g. HIGHER DFL DUE TO GREATER AMOUNT OF INTEREST EXPENSE
h.
MICHAEL DORSEY DOROTHY MICHAELS YEAR 1 YEAR 2
YEAR 1
EBIT INTEREST EXPENSE EBT TAXES @40% NET INCOME
$50,000 $9,100 $40,900 $16,360 $24,540
$50,000 $900 $49,100 $19,640 $29,460
DFL
1.22
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$53,000 $9,100 $43,900 $17,560 $26,340
1.02
YEAR 2 $53,000 $900 $52,100 $20,840 $31,260
13-15. DCL = (200,000 – 75,000) / 75,000 ÷ (400,000 – 230,000) / 230,000 = 2.25 13.16. FUNNY GIRLS COMICS YEAR 1
YEAR 2
SALES
$200,000
$225,000
EBIT
$95,000
NET INCOME
$30,000
DOL
1.35
DFL
1.09
a. %CHANGE in SALES =
12.50%
%CHANGE in EBIT = DOL X %CHANGE in SALES b. EBIT IN YEAR 2 = 1.1688*95,000 = c. %CHANGE in NI = DFL X %CHANGE in EBIT d. NI in YEAR 2 = 1.1839 X 30,000 = e. DCL = DOL X DFL =
16.8750% $111,031.25 18.3938% $35,518.13 1.4715
f. %CHANGE in SALES =
20.00%
%CHANGE in NI = DCL X %CHANGE in SALES NI in YEAR 2 = 1.2943 X 30,000 =
29.43% $38,829.00
13-17. Interest Expense = $2,000,000 X 0.10 = $200,000 DCL = DOL X DFL =1.4 X [$600,000/($600,000 - $200,000)= 1.4 X 1.5= 2.1
13-18. a) DOL = ($5,000,000 - $700,000)/($5,000,000 - $700,000 - $300,000) = 1.075 b)
Interest Expense = $16,666,666.67 X 0.09 = $1,500,000 EBIT = $2,500,000 + $1,500,000 = $4,000,000
DFL = $4,000,000/($4,000,000 - $1,500,000) = 1.600 Also, DFL = DCL/DOL = 1.720/1.075 = 1.600 c)
%NI = $Sales x DCL %NI = 20% x 1.72 = 34.4%
110
13.19. Soccer International, Inc. Given: 2005
2006
Sales Variable Costs Fixed Costs
$560,000 $240,000 $160,000
$616,000 $264,000 $160,000
Interest Expense
$40,000
$40,000
Price of each soccer ball
$16
a. Completed income statements: 2005
2006
$560,000 $240,000 $160,000 $160,000 $40,000 $120,000 $36,000 $84,000
$616,000 $264,000 $160,000 $192,000 $40,000 $152,000 $45,600 $106,400
2005
2006
Number of balls sold Variable cost per ball Contribution margin
35,000 $6.86 $9.14
38,500 $6.86 $9.14
Breakeven point in units
17,500
17,500
2006
2007
$280,000
$280,000
Sales Variable Costs Fixed Costs EBIT Interest Expense EBT Income Taxes (30%) Net Income b. Breakeven point in units:
c. Breakeven point in dollars:
Breakeven point in dollars
d. Unit sales required to produce $200,000 in operating income in 2005: Fixed costs Operating profit requirement Total dollars needed Contribution margin, each ball Number of balls needed to be sold
$160,000 $200,000 $360,000 $9 39,375
e. Effect on operating profit of greater or lesser sales in 2005: Assumed number of balls sold 18,000
24,000
$164,571 $160,000 $4,571
$219,429 $160,000 $59,429
2005
2006
2.0
1.83
Total contribution margin Fixed costs Operating profit f. Degree of Operating Leverage (DOL):
DOL
111
h. Degree of financial leverage (DFL):
DFL
2005
2006
1.33
1.26
2005
2006
2.67
2.32
2005
2006
j. Degree of combined leverage (DCL):
DCL k. Effect of a price increase that produces higher sales:
Sales
$560,000
% increase in net income
$650,000 given 16.1% 42.86%
Net income in dollars
$84,000
13-20. %NI = % x DFL %NI = ($50,000 - $35,000)/$35,000 x 1.71 %NI = $15,000/$35,000 x 1.71 %NI = .429 x 1.71 %NI = .733, or 73.3%
112
$120,000
Chapter 14 Solutions
Answers to Review Questions 1.
How does a mortgage bond compare to a debenture? A mortgage bond is a secured bond while a debenture is an unsecured bond.
2.
How does a sinking fund function in the retirement of an outstanding bond issue? A sinking fund is where a company puts payments that are then used to buy back outstanding bonds.
3.
What are some examples of restrictive covenants that might be specified in a bond‘s indenture? An indenture might include limitations on future borrowings, restrictions on dividend payments, and/or requirements that working capital be maintained at least at some minimum level.
4.
Define the following terms that relate to a convertible bond: conversion ratio, conversion value, and straight bond value. The conversion ratio is the number of shares of common stock that would be obtained if a convertible bond were converted. The conversion value is the total value of the common stock that would be obtained. The straight bond is the value a convertible bond would have without the conversion feature.
5.
If a convertible bond has a conversion ratio of 20, a face value of $1,000, a coupon rate of 8 percent, and the market price for the company‘s stock is $15 per share, what is the convertible bond‘s conversion value? The conversion value would equal the conversion ratio of 20 times the $15 market price of the stock or $300.
6.
What is a callable bond? What is a putable bond? How do each of these features affect their respective market interest rates? A callable bond can be retired early at the discretion of the issuer. A putable can be retired early at the discretion of the investor. A call provision increases the market interest rate and a put provision decreases it.
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Answers to End-of-Chapter Problems 14-1.
VB = $80 X [(1 - 1/1.1210)/.12] + $1,000 X 1/1.1210 = $773.99
14-2.
VB = $40 X [(1 - 1/1.0620)/.06] + $1,000 X 1/1.0620 = $770.60
14-3.
Conversion Value = $60 X 20 = $1,200
14-4.
$32 * 26.5 = $848 $848 * 6 = $5,088.00
14-5.
22.5 [ 1-(1/(1.0375)60)/0.0375] + 1,000/(1.0375)60 22.5 * 23.7379 + 109.828 = $643.93
14-6.
$85 * 30 = $2,550
14-7. 33.75 [1 – (1/1.0430)/0.04] + 1,000/1.0430 = $891.92
14-8.
Funds required to buy 1,000 bonds from the open market = $800 X 1,000 = $800,000. Therefore savings from buying the bonds back instead of depositing $1 million in the sinking fund = $1,000,000 - $800,000 = $200,000.
14-9.
(7.0% - 5.0%) * 30,000 * 1,000 = $600,000
14-10. Yearly savings = (10% - 8%) X 20,000 X $1,000 = $400,000
14-11. Face Value + Call Premium = $1,000 + 0.5 X $1,000 = $1,050 Annual interest paid over last ten years = 0.10 X $1,000 = $100 $950 = $100 X (PVIFAk,10) + $1,050 X (PVIFk,10) Realized return for Brooks = k = 11.15%
0
1
2
3
4
5
6
YEARS 7 8 9
10 11 12 13 14 15 16 17 18 19 20
-950 100 100 100 100 100 100 100 100 100 100 1050 -950 100 100 100 100 100 100 100 100 100 1150 11.15% IRR
114
14-12. a)
b)
Annual interest to be paid over next ten years = 0.08 X $1000 = $80 $950 = $80 X (PVIFAk,10) + $1,000 X (PVIFk,10) Return for Brooks for the newly issued bond = k = 8.77% Overall return if the is bond held to maturity = 10.52% (See table below) Return on the bond in Problem #4 if they had not been called = 10.61% (See table below). Brooks didn't welcome the recall (10.61% > 10.52%). YEARS 0 1 PROB 14-12a -950 -950 8.77% -950
2
3
4
5
6
7
8
9
80 80 80 80 80 80 80 80 80
10 11 12 13 14 15 16 17 18 19 80 1000
80 80 80 80 80 80 80 80 80 1080 IRR 100 100 100 100 100 100 100 100 100 100 80 80 80 80 80 80 80 80 80 1050 -950
-950 10.52%
20
80 1000
100 100 100 100 100 100 100 100 100 200 80 80 80 80 80 80 80 80 80 1080 IRR
PROB 14-12b -950
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
-950 10.61%
1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 1100 IRR
14-13. Conversion Value = $70 X 20 = $1,400 14-14. VB = $90 X [(1 - 1/1.0714)/.07] + $1,000 X 1/1.0714 = $1,174.90 He would consider converting, but since the market value of the convertible bond would be greater than the larger of the conversion value or straight bond value he would sell the bond instead if he wanted to cash out.
14-15. Conversion Value = $30 X 30 = $900 VB = 110 X [(1 - 1/1.135)/.13] + 1,000 X 1/1.135 = $929.66 No, he should not convert. The straight bond value is greater than the conversion value. 14-16. VB = $90 X [(1 - 1/1.1314)/.13] + $1,000 X 1/1.1314 = $747.90 Since the putable bond can be redeemed at a higher price, i.e., $900, Ms. Carter should redeem the bond.
115
$1,000 = $90 X (PVIFAk,6) + $900 X (PVIFk,6) Realized return for Ms. Carter = k = 7.62% 14-17. VB = $90 X [(1 - 1/1.145)/.14] + $1,000 X 1/1.145 = $828.34 Since the bond can be redeemed at a higher price, i.e., $900, Diana should redeem the bond. $1,000 = $90 X (PVIFAk,5) + $900 X (PVIFk,5) Realized return for Diana from original bond = k = 7.27% $900 = $130 X (PVIFAk,5) + $1,000 X (PVIFk,5) Realized return for Diana from new bond = k = 16.06% YEARS
0
1
2
3
4
5
-1000
90
90
90
90
90
6
7
8
9
130
130
130
130
10
900 -900
130 1000
CF
-1000
90
90
90
90
90
130
130
130
0.1051 = 10.51%IRR
Realized overall return for Diana = k = 10.51% 14-18. VB = $80 X [(1 - 1/1.2510)/.25] + 1,000 X 1/1.2510 = $393.01 14-19. 1st Mortgage bonds 2nd Mortgage bonds Senior Debentures Subordinated Debentures Common Stock Total
Claim $5 million 5 million 10 million 4 million 10 million 34 million
Received 5 million 5 million 10 million 0 0 20 million
14-20. a) Call Premium paid New Bond Underwriting Costs Total incremental Cash Outflow
$60,000,000 * .04 = $60,000,000 * .03 =
$2,400,000 $1,800,000 $4,200,000
b) Savings = (8% - 6%) = 2% annually Total Savings in interest payments = 2% * $60,000,000 = $1,200,000 c) Interest on old bonds: $60,000,000 * .08 = $4,800,000
116
130
1130
Interest on new bonds: $60,000,000 * .06 = $3,600,000 $1,200,000 difference each year for 10 years Less taxes on the additional income at 40%: $1,200,000 * (1 - .40) = $720,000 Net Savings = $720,000 per year d) Present value of the net savings for 10 years at 3.6% $720,000 * ((1-(1/(1.036)10))/.036) = $720,000 * 8.274844044 = $5,957,887.71 e) Note: Call premiums are tax deductible and amortized over the life of the bond $60,000,000 * .04 * .40 = $960,000 Amortized over 10 years = $960,000/10 = $96,000 per year f) Present Value of the annual tax savings for 10 years: $96,000 * ((1-(1/(1.036)10))/.036) = $96,000 * 8.274844044 = $794,385.03 g) Unamortized amount = $60,000,000 * .02 * (10/20) = $600,000 current deduction PV of unamortized amount if bond is not called: ($600,000/10) * ((1-(1/(1.036)10))/.036 = $60,000 * 8.274844044 = $496,490.64 Net Tax Savings = $600,000 - $496,490.64 = $103,509.36 h) ($60,000,000 * .03)/10 = $180,000 annual write off Tax Savings = $180,000 * .40 = $72,000 i) PV of tax Savings = $72,000 * ((1-(1/(1.036)10))/.036 = $72,000 * 8.274844044 = $595,788.77 j) PV Total Inflows = $5,957,887.71 + $794,385.03 + $103,509.36 + $595,788.77 = $7,451,570.87 k) NPV of the bond proposal = PV of total cash inflows – Total outflows NPV = $7,451,570.87 - $4,200,000 = $3,251,570.87
117
14-21. Aurora Glass Fibers Lease-Buy Analysis Part a, the buy option: Assumptions: Cost of new computers Expected Life Salvage value Amount to be borrowed Interest rate on loan
$800,000 4 years $100,000 $800,000 10%
MACRS Depreciation: (3-year asset class)
Yr 1 33.3%
Cost of capital Tax rate
Yr 2 44.5%
Yr 3 14.8%
Yr 4 7.4%
6% (after-tax cost of debt) 40%
Estimated Incremental Cash Flows to Equity: Year: Cost of new computers Amount to be borrowed Depreciation on new computers Tax savings on depreciation Interest payments on loan Tax savings on interest Repayment of principal on loan Salvage value of new computers Tax on gain Net Incremental Cash Flows PV of Cash Flows
0 ($800,000) 800,000
1
2
3
4
($266,400) 106,560 (80,000) 32,000
($356,000) 142,400 (80,000) 32,000
($118,400) 47,360 (80,000) 32,000
$58,560 $55,245
$94,400 $84,016
($640) ($537)
($59,200) 23,680 (80,000) 32,000 (800,000) 100,000 (40,000) ($764,320) ($605,413)
Total PV of Cash Flows Associated With the Buy Option =
($466,689)
$0 $0
Part b, the lease option: Assumptions: Annual lease payment Lease term Value at termination of lease
($200,000) paid at the end of each year 4 years $0
Estimated Incremental Cash Flows to Equity: Year: Lease payment Tax savings on lease payment Net Incremental Cash Flows PV of Cash Flows
0
3 ($200,000) $80,000 ($120,000) ($100,754)
4 ($200,000) $80,000 ($120,000) ($95,051)
Total PV of Cash Flows Associated With the Lease Option =
($415,813)
$0 $0
118
1 ($200,000) $80,000 ($120,000) ($113,208)
2 ($200,000) $80,000 ($120,000) ($106,800)
Part c, comparison of alternatives and decision: Total PV of Cash Flows Associated With the Buy Option = Total PV of Cash Flows Associated With the Lease Option =
($466,689) ($415,813)
Net Advantage to Leasing (NAL) =
$50,877
Decision:
119
Lease
Chapter 15 Solutions
Answers to Review Questions 1.
What are some of the government requirements imposed on a public corporation that are not imposed on a private, closely held corporation? Public corporations must submit audited financial statements to the government for release to the public. Private corporations can keep their financial information confidential.
2.
How are the members of the board of directors of a corporation chosen and to whom do these board members owe their primary allegiance? Members of a corporation‘s board of directors are elected by the common stockholders and owe their allegiance to these stockholders
3.
What are the advantages and the disadvantages of a new stock issue? A new stock issue raises funds and decreases the riskiness of the firm. It also tends to send a negative signal to the market since many investors believe a company would only sell new stock if future financial prospects were dim.
4.
What does an investment banker do when underwriting a new security issue for a corporation? When underwriting a new security issue an investment banker buys it and then resells it to investors.
5.
How does a preemptive right protect the interests of existing stockholders? A preemptive right protects the interests of existing stockholders by giving them the opportunity to preempt other investors in the purchase of new shares. If these rights are exercised, existing shareholders would maintain their same percentage of ownership after the new stock issue as before.
6.
Explain why warrants are rarely exercised unless the time to maturity is small? Warrants are rarely exercised until the time to expiration is small because the market price of the warrant is greater than the exercise value. The holder of the warrant would therefore sell it in the secondary market instead of exercising it if he or she wanted to cash in.
7.
Under what circumstances is a warrant‘s value high? Explain.
120
A warrant‘s value would be high when the stock price, time to expiration, and/or expected stock price volatility are high.
Answers to End-of-Chapter Problems 15-1.
Original Ownership = 20,000/1,000,000 = 2% Diluted Ownership = 20,000 /1,500,000 = 1.33%
15-2.
1. Book Value Approach: (200mil. - 150mil.)/5mil. = $10 per share 2. Liquidation Value Approach: (250 - 150)/5 = $20 per share 3. Replacement Value Approach: (400 - 150)/5 = $50 per share 4. Dividend Growth Model: $2/(0.13 - 0.08) = $40 per share
Ms. Phinlay should buy the stock as the share is selling at a price ($20) which is lower than what she is prepared to pay ($40) to get her required rate of return.
15-3.
a) .45(2,500,000) = 1,125,000 [(1,125,000 - 1) * (5 + 1)] / 2,500,000 = 2.669 2 directors b) .55(2,500,000) = 1,375,000 [(1,375,000 – 1) * (5 + 1)] / 2,500,000 = 3.299 3 directors
15-4. a) [(1 * 2,500,000) / (5 + 1)] + 1 = 416,667 b) [(3 * 2,500,000) / (5 + 1)] + 1 = 1,250,001 c) [(5 * 2,500,000) / (5 + 1)] + 1 = 2,083,334
15-5.
a) .35 (2,500,000) = 875,000 [(875,000 – 1) (5 + 1)] / 2,500,000 = 2.1 2 directors b) [(2 * 2,500,000)/ (5 + 1)] + 1 = 833,334
15-6.
Length of term = (9/3) X 3 = 9 years for each board members
15-7.
NUM DIR = [(0.35 X 1,000,000 - 1) X (4 + 1)]/1,000,000 = 1.75 rounded down to 1 The minority group can elect 1 of their people to the board
121
out of the 4 to be elected.
15-8.
NUM VOTING SHARES NEEDED = [(1 X 200,000)/(7 + 1)] + 1 = 25,001. Since Ms. O'Niel holds more shares than required, she can elect herself to the board.
15-9.
a) How many directors can the young stockholders elect under (i) cumulative voting procedure NUM DIR = (600,000 X 0.30-1) X (13 + 1)/600,000 = 4.2 rounded down to 4 (ii) majority rule: NONE b) What percentage of voting shares and/or proxies the dissident group must have to be able to elect 7 out of the 13 board members? NUM VOTING SHARES NEEDED=[(7 X 600,000)/(13 + 1)] + 1=300,001 Percentage of voting shares and/or proxies = 300,001/600,000 50% (slightly greater than 50%)
15-10. Number of rights required to buy a share = 500,000/50,000 = 10
15-11. N = 2,000,000/500,000 = 4 Approx. Market Value of a Right = R = (65 - 55)/(4 + 1) = $2
15-12. Market Price of stocks selling ex-rights = 65 - 2 = $63 Approx. Market Value of a Right = R = (63 - 55)/(4) = $2
15-13. N = 7 Approx. Market Value of a Right = R = (77 - 65)/(7 + 1) = $1.50 Market Price of stocks selling ex-rights = 77 - 1.5 = $75.50
15-14. a) Approx. Market Value of a Right = R = (72 - 60)/(4 + 1) = $2.40 b) Maximum number of new shares that Johnny can buy = 700/4 = 175 c) Amount Johnny would spend = 175 X 60 = $10,500 d) Selling price of all of Johnny's rights = 700 X 2.40= $1,680
15-17. a) Approx. Market Value of a Right = R = (62 - 50)/(4 + 1) = $2.40 b) Ex-rights price = $62 - $2.40 = $59.60 per share Diluted price after issue of new stock = $59.6 X 4/5 = $47.68
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Option I: Sell rights and hold stocks at diluted value: Amount obtained by selling rights Value of stocks held at diluted price Unused Cash
= $2.40 X 60 = $144.00 = 60 X $47.68 = $2,860.80 = $750.00
Net worth from Option I = $3,784.80 Option II: Buy new shares: Number of shares Selena can buy = 60/4 = 15 Amount to be spent to buy 15 shares = $50 X 15 = $750. So, Selena can buy all the 15 new shares with her available cash. Diluted price of stocks = $47.68 Net worth from Option II = $47.68 X (60 + 15) = $3,576.00 So, Selena should go for Option I, that is, Sell rights and hold her stocks at diluted value.
15-18. XV = (100 - 85) X 5 = $75 What happens to the exercise value of the warrant if the stock price changes to a) $110 : XV = (110 - 85) X 5 = $125 b) $80 : XV = $0
15-19. Issue of new common stock by Wilkerson Corporation: Current Market Price per share of Common Stock Number of Common Shares outstanding Amount of additional funds needed Net Income for the year Number of shares owned by Guy Hamilton
$40 600,000 $2,000,000 $1,000,000 10,000
Possible Subscription Prices
$36
a.
Number of shares to be issued Number of Rights required to buy one share
b.
EPS before the rights issue EPS after the rights issue
c.
Max number of new shares Guy can buy Guy's claim to earning before the rights issue Guy's claim to earning after the rights issue
123
$33
$29
$26
55,556 60,606 68,966 76,923 10.8 9.9 8.7 7.8 $1.67 $1.53
$1.67 $1.51
$1.67 $1.49
$1.67 $1.48
926 1,010 1,149 1,282 $16,667 $16,667 $16,667 $16,667 $16,667 $16,667 $16,667 $16,667
Chapter 16 Solutions
Answers to Review Questions 1.
Explain the role of cash and of earnings when a corporation is deciding how much, if any, cash dividends to pay to common stockholders. In the long-run earnings are necessary to maintain dividend payments, but at the time an actual dividend payment is made, adequate cash is necessary.
2.
Are there any legal factors that could restrict a corporation in its attempt to pay cash dividends to common stockholders? Explain. A firm may be legally restricted as to the dividends it can pay by existing bond indentures or loan agreements. It may also be restricted as to the payment of common stock dividends is scheduled preferred stock dividends have not been paid.
3.
What are some of the factors that common stockholders consider when deciding how much, if any, cash dividends they desire from the corporation in which they have invested? Common stockholders would consider the company‘s investment opportunity, their need for income, and their tax bracket when deciding on their desire for dividends.
4.
What is the Modigliani and Miller theory of dividends? Explain. The Modigliani-Miller theory of dividends says that dividend theory is irrelevant. They claim that it is the income produced by assets that is important, not how funds are distributed.
5.
Do you believe an increased common stock cash dividend can send a signal to the common stockholders? If so, what signal might it send? An increase in cash dividends is often seen as a positive signal. A company would be unlikely to increase its dividend if it did not believe its future prospects were good enough to sustain the higher level of dividends. This is because the market usually frowns upon a cut in dividends.
6.
Explain the bird in the hand theory of cash dividends. The bird in the hand dividends theory says that dividends received now are better than a promise of future dividends. Uncertainty is resolved when a dividend is paid.
124
7.
What is the effect of stock (not cash) dividends and stock splits on the market price of common stock? Why do corporations declare stock splits and stock dividends? Stock splits and stock dividends decrease the price per share of the common stock but should not increase the total market value of all common stock outstanding unless other positive things are perceived to occur. Many companies believe that a stock split or stock dividend makes their stock more affordable and therefore more attractive to a wider range of potential investors.
Answers to End-of-Chapter Problems 16-1.
Retention Ratio = $600/$1,000 = 0.6 or 60% ∴ Payout Ratio = 1-.6 = .4 = 40%
16-2.
Dividend Paid = 0.4 X $50 million = $20 million Addition to Retained Earnings = $50 mil. - $20 mil. = $30 million
16-3.
Retained Earnings Maintain Retained Earnings end of 2005 Additional needed for maintenance
$1,000,000 750,000 $250,000
Earnings Avail. to Common Stockholders Needed for maintenance Dividend Payout
$800,000 250,000 $550,000
$550,000 / $800,000 = .6875 = 68.75%
16-4.
Net income Dividend Payout (35%) Addition to retained earnings
$4,000,000 1,400,000 $2,600,000
Retained earnings end of 2005 Addition to retained earnings Retained earnings end of 2006
$1,200,000 2,600,000 $3,800,000
16-5. (Figures in $ millions) Year 1 Year 2 Year 3 Net Income 30 20 25 Dividend Payout ratio 0.3 0.3 0.3 Dividend Paid 9 6 7.5 Addition to RE 21 14 17.5 Total Addition to RE = 21 + 14 + 17.5 = 52.5
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16-6. (Figures in $ millions) Year 1 Year 2 Net Income 30 20 Dividend Paid 10 10 Dividend Payout ratio 0.33 0.5 Addition to RE 20 10 Total Addition to RE = 20 + 10 + 15 = 45
16-7.
Year 3 25 10 0.4 15
Equity Investment = $14mil. X 0.6 = $8.4 million Dividend to be Paid = $10mil. - $8.4 mil. = $1.6 million
16-8.a) Equity Investment = $14mil. X 0.6 = $8.4 million Dividend to be Paid = $16 mil. - $8.4 mil. = $7.6 million b)
16-9.
Equity Investment = $14 mil. X 0.6 = $8.4 million Dividend to be Paid = $0
Equity funds needed $12,000,000 * .80 = $9,600,000 Amount avail. to stockholders $24,000,000 – 9,600,000 = $14,400,000 Dividend per share $14,400,000 / 20,000,000 = $0.72
16-10. 20% Stock Dividend ($000s) Increase in number of shares = 0.2 X $2 million Increase in common stock account = 400 X $1 Increase in capital in excess of par account Total increase = $12,000 + $400 = $12,400
= 400 thousand = $400 = 400 X $30 = $12,000
This increase is greater than the Retained Earnings of $10,000. Hence it is not possible to pay a 20% stock dividend. 10% Stock Dividend($000s) Increase in number of shares = 0.1 X $2 million = 200 thousand Increase in common stock account = 200 X $1 = $200 Increase in capital in excess of par account = 200 X $30 = $6,000 Total increase = $6,000 + $200 = $6,200 This increase can be covered by a matching decrease in the retained earning account keeping the total equity capital unchanged. The new retained earning will be 10,000 - 6,200 = $3,800. Hence it is possible to pay a 10% stock dividend.
126
16-11.
($000s) 2,000
Common Stock ( 2 million shares, $1 par) Capital in excess of par Retained Earnings Total Common Equity
8,000 10,000 20,000
After Payment of Dividend: ($000s) Common Stock ( 2.2 million shares, $1 par) Capital in excess of par = 8,000 + 6000 = Retained Earnings = 10,000 - 6,000 - 200 = Total Common Equity
2,200 14,000 3,800 20,000
New Market Price of the Stock = $31 X 2,000/2,200 = $28.18 per share.
16-12. a) 800,000 * (1 + 0.30) = 1,040,000 new total shares 1,040,000 – 800,000 = 240,000 new shares b) CIEP = Capital in Excess of Par CIEPbefore = $13,600,000 CIEPafter = $13,600,000 + (240,000 new shares * ($40 - $3)) CIEPafter = $22,480,000 c) CS = Common Stock CSbefore = 800,000 * $3 = $2,400,000 CSafter = 1,040,000 * $3 = $3,120,000 RE = Retained Earnings REbefore = $60,000,000 REafter = $60,000,000 – ($3,120,000 - $2,400,000) – ($22,480,000 - 13,600,000) REafter = $50,400,000 16-13. 800,000 * $40 = $32,000,000 x = new stock price 1,040,000 * x = $32,000,000 New stock price = $30.77
16-14. Before the stock split Common Stock ( 3 million shares, $1.00 par) Capital in excess of par Retained Earnings Total Common Equity
3,000 7,000
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10,000 20,000
After the stock split Common Stock ( 9 million shares, $0.33 1/3 par) 3,000 Capital in excess of par 7,000 Retained Earnings 10,000 Total Common Equity 20,000 New Market Price of the stock = 33 X 1/3 = $11.00 per share.
16-15. EPS (Before the stock split) = $800,000/3,000,000 = $0.27 EPS (After the stock split) = $800,000/9,000,000 = $0.09 The P/E ratio will remain the same (123.75) before and after the split unless other factors influence the market‘s perception of this stock‘s value.
16-16. a) Dividend per share last year = $1.33 X 5/1 = $6.65 b) Dividend per share last year = $1.33/1.1 X 5/1 = $6.05
16-17. Dividend per share = EPS X Payout Ratio = ($10/1) X 0.4 = $4 Price of stock (ex-dividend) = $30 - $4 = $26 per share.
16-18. Spring Field Manufacturing Company's Dividend Payments: NUMBER OF SHARES OF COMMON STOCK OUTSTANDING = NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU = NET YEAR 2007 2008 2009 2010 2011
INCOME $1,000,000 $1,100,000 $1,200,000 $1,300,000 $1,400,000
CAPITAL INVESTMENTS
EQUITY DIVIDEND DIVIDEND DIVIDEND FINANCING PAYMENT PER SHARE RECEIVED
$800,000 $480,000 $1,000,000 $600,000 $2,000,000 $1,200,000 $800,000 $480,000 $1,000,000 $600,000
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500,000 500
$520,000 $500,000 $0 $820,000 $800,000
$1.04 $1.00 $0.00 $1.64 $1.60
$520 $500 $0 $820 $800
16-19. Spring Field Payments:
Manufacturing
Company's
Dividend
NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU =
YEAR
NET INCOME
2007 $1,000,000 2008 $1,100,000 2009 $1,200,000 2010 $1,300,000 2011 $1,400,000
CAPITAL INVESTMENTS
$800,000 $1,000,000 $2,000,000 $800,000 $1,000,000
EQUITY FINANCING
$480,000 $600,000 $1,200,000 $480,000 $600,000
AMOUNT FROM NEW SHARES
500 NO. OF SHARES DIVIDEND DIVIDEND DIVIDEND OUTSTANDING PAYMENT PER RECEIVED SHARE 500,000 500,000 600,000 600,000 600,000
$600,000
$520,000 $500,000 $600,000 $820,000 $800,000
$1.04 $1.00 $1.00 $1.37 $1.33
$520 $500 $500 $683 $667
16-20. Comprehensive Problem: a)
Expected Dividend per share = $3,000,000 X 0.5/500,000 = $3 Repurchase Price = $47 + $3 = $50 per share
b)
Number of shares that could be repurchased
c)
Before Repurchase of Stock
= $3,000,000/$50 = 60,000
Common Stock (500,000 shares, $3 par) Capital in excess of par ($7/share) Retained Earnings Total Common Equity
($ 000s) 1,500 3,500 5,000 10,000
After Repurchase of Stock Common Stock (440,000 shares, $3 par) Capital in excess of par = 7 X 440 = Retained Earnings = 5,000 + (1,500 - 1,320) + (3,500 - 3,080) = Total Common Equity
($ 000s) 1,320 3,080 5,600 10,000
d) If net income next year is expected to be $4 million, what would be the EPS next year with and without the repurchase? EPS (without repurchase) = $4,000,000/500,000 = $8 EPS (with repurchase) = $4,000,000/440,000 = $9.09 e) If you own 50 shares of common stock of the company, would you like the company's decision of buying back the stocks instead of paying a dividend? Without Repurchase: Dividend Earning Last Year = $3/Share X 50 shares = $ 150 Value of stock = $47/share X 50 shares = $2,350 Total = $2,500
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With Repurchase: Price of stock = $50/share X 500/440 = $56.82 per share Value of stock = $56.82 X 50 = $2,841.00 The decision to buy back instead of paying a dividend would be preferred if the stock price were to increase to $56.82 per share with the repurchase. The taxes that may be owed on the $150 in dividends under the no repurchase scenario would decrease further the attractiveness of this alternative.
16-21. Before the split # of shares Common Stock Par Value Capital in Excess of Par Retained Earnings Total Common Stock Equity
300,000 $1,200,000 $4 $1,500,000 $10,000,000 $12,700,000
After the split # of shares Common Stock Par Value Capital in Excess of Par Retained Earnings Total Common Stock Equity
1,200,000 $1,200,000 $1 $1,500,000 $10,000,000 $12,700,000
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Chapter 17 Solutions
Answers to Review Questions 1.
What is working capital? Working capital consists of the current assets of the firm.
2.
What is the primary advantage to a corporation of investing some of its funds in working capital? By investing in working capital a firm gets the liquidity it needs helping it to pay its bills. The risk of the firm is therefore reduced.
3.
Can a corporation have too much working capital? Explain. A firm can have too much working capital if it is losing the opportunity to invest in high returning fixed assets and if it goes beyond the amount of working capital needed for reasonable liquidity needs.
4.
Explain how a firm determines the optimal level of current assets. The optimal level of working capital is determined by finding the amount that balances the need for liquidity and for profitability.
5.
What are the risks associated with using a large amount of short-term financing for working capital? Using a large amount of short-term financing generally allows funds to be raised at a lower cost but increases the firm‘s risk.
6.
What is the matching principle of working capital financing? What are the benefits of following this principle? The matching principle is when short-term financing is used for temporary current assets while longterm financing is used for permanent current assets and fixed assets. The main benefit of this approach is that as temporary current assets are sold off the proceeds can be used to pay off the shortterm debt.
7.
What are the advantages and disadvantages of the aggressive working capital financing approach? An aggressive working capital financing approach usually results in a lower cost of funds for a firm but a higher level of risk. 131
8.
What is the most conservative type of working capital financing plan a company could implement? Explain. An all equity capital structure would be the most conservative type of working capital financing plan approach. The more long-term financing used the more conservative the financing plan, and equity is permanent financing.
Answers to End-of-Chapter Problems 17-1.
a) ($150,000 + $120,000 + $80,000) = $350,000 b) $350,000 – ($100,000 + $90,000) = $160,000 c) ($150,000 + $120,000 + $80,000) * 0.25 = $87,500 d) ($150,000 + $120,000 + $80,000) * 0.75 = $262,500
17-2.
Firm 1: $10,000 + $3,000 + $2,500 = $15,500 (working capital) $15,500 - $7,500 - $4,000 = $4,000 (net working capital) Current ratio = $15,500 / ($7,500 + $4,000) = 1.35 Quick ratio = ($15,500 - $3,000) / $11,500 = 1.09 Firm 2: $8,000 + $6,000 + $3,500 = $17,500 (working capital) $17,500 - $3,500 - $11,000 = $3,000 (net working capital) Current ratio = $17,500 / ($3,500 + $11,000) = 1.21 Quick ratio = ($17,500 - $6,000) / $14,500 = 0.79 Firm 1 is more liquid due to its higher liquidity ratios.
17-3.
Company A: NWC = ($1,000 + $400) - $900 = $500 Company B: NWC = ($80 + $880) - $600 = $360 Company A has the higher net working capital and would therefore generally be considered the more liquid company. Although Company A has a slightly smaller current ratio value (1.56 for A and 1.6 for B) Company A has a much higher percentage of cash in its current assets, so would likely be considered by most analysts the more liquid firm.
17-4. a)
CA = $30,000 + $15,000 + $130,000 = $175,000
b)
CL = $100,000 + $60,000 = $160,000
c)
NWC = $175,000 - $160,000 = $15,000
d)
160/(175 X .5) or 183.86% of TCA is financed by CL. This is an aggressive approach since all TCA and most of PCA are being financed with riskier short-term funds. 132
17-5. a)
17-6.
CA = $30,000 + $15,000 + $130,000 = $175,000
b)
CL = $30,000 + $20,000 = $50,000
c)
NWC = $175,000 - $50,000 = $125,000
d)
50/(175 X .5) or 57.14% of TCA is financed by CL. This is a relatively conservative approach. Long-term financing of $625,000 exceeds the total of fixed assets and permanent current assets, $587,500, by $37,500. Only $50,000 of the $87,500 in temporary current assets is being financed with short-term funds.
a)
CA = $50 + $0 + $40 + $70 = $160
b)
CL = $80 + $90 = $170 NWC = $160 - $170 = ($10)
c)
All of LuLu Belle‘s current assets, and some of the fixed assets, are financed with short-term funds (current liabilities). This is an aggressive approach.
d)
Reduce short-term debt, increase long-term debt and equity and invest in marketable securities. This will increase net working capital and the current ratio.
17-7. Cash $100,000 Inventory $200,000 Accounts Receivable $150,000 Net Fixed Assets $550,000 Total Assets $1,000,000
Accounts Payable $35,000 Notes Payable $60,000 Long-term Debt $505,000 Common Equity $ 400,000 Total Liabilities and Equity $1,000,000
Permanent assets, net fixed assets and a small portion of temporary assets are financed with long-term debt and equity. This is using a very conservative approach. Your exact numbers are likely to be different, but the point is that long-term debt and equity financing are emphasized.
17-8.
PCA = $225,000 * 0.60 = $135,000 PCA + FA = $135,000 + $475,000 = $610,000 LTD + CSEQ = $410,000 + $200,000 = $610,000 a) Cash Accounts Receivable Inventory Fixed Assets
$50,000 25,000 150,000 475,000 $700,000
Accounts Payable__$40,000_ Notes Payable ___50,000_ Long-term Debt __410,000_ Common Equity __ 200,000_
133
b) Cash Accounts Receivable Inventory Fixed Assets
17-9.
$50,000 25,000 150,000 475,000 $700,000
Accounts Payable__$30,000_ Notes Payable ___60,000_ Long-term Debt __185,000_ Common Equity __425,000_
a) Accounts payable = $180,000 Notes payable = $320,000 Long-term debt = $0 Common Equity = $200,000 Your exact numbers are likely to be different, but the point is that short-term debt is emphasized.
17-10.
CA = $30,000 + $15,000 + $130,000 = $175,000 Perm. CA = $15,000 + $5,000 + $80,000 = $100,000 Temp. CA = $175,000 - $100,000 = $75,000 CL = Short-Term Debt + $20,000 = $75,000 = Temp.CA (By Matching Principle) Short-Term Debt = $75,000 - $20,000 = $55,000 Long-Term Debt = $675,000 - $450,000 - $55,000 - $20,000 = $150,000
17-11.
NWC = CA - CL $25,000 = ($30,000 + $15,000 + $130,000) - ($20,000 + Short-Term Debt) Short-Term Debt = $175,000 - $25,000 - $20,000 = $130,000 Long-Term Debt = $675,000 - $450,000 - $130,000 - $20,000 = $75,000
17-12. AGG.(A)(HIGH RISK)
MOD.(M)(MOD. RISK)
CON.(C)(LOW RISK)
Temporary CA
75
75
75
Permanent CA
100
100
100
Fixed Assets
500
500
500
Total Assets
675
675
675
Current Liabilities
160
75
50
Long Term Debt
90
150
150
Stockholders' Equity
425
450
475
Net Income
70
70
70
NWC
15
100
125
LOWEST FOR A, HIGHEST FOR C
Current Ratio
1.09
2.33
3.50
LOWEST FOR A, HIGHEST FOR C
Debt to Asset
0.37
0.33
0.30
HIGHEST FOR A, LOWEST FOR C
ROE
16.47%
15.56%
14.74%
HIGHEST FOR A, LOWEST FOR C
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COMMENTS
17-13. Assumption (i) (a) Interest Expense: 0.13 X 5 X $500,000 = $325,000 (b) Interest Expense: .11 X 5 X $500,000 = $275,000 Alternative (b) will save $50,000 Assumption (ii) (a) Interest Expense: 0.13 X 5 X $500,000 = $325,000 (b) Interest Expense: (0.11 X 2 X $500,000) + (.14 X 2 X $500,000) + (.16 X $500,000) = $330,000 Alternative (a) will save $5,000
17-14. Data for graph: Total assets Fixed assets Date (given) (given) 31-Jan 28-Feb 31-Mar 30-Apr 31-May 30-Jun 31-Jul 31-Aug 30-Sep 31-Oct 30-Nov 31-Dec
$45 $46 $34 $48 $40 $30 $28 $39 $45 $39 $52 $50
Permanent Temporary Current Liabilities Current Current if Matching Principle Assets Assets is Followed
$14 $14 $14 $14 $14 $14 $14 $14 $14 $14 $14 $14
$14 $14 $14 $14 $14 $14 $14 $14 $14 $14 $14 $14
$17 $18 $6 $20 $12 $2 $0 $11 $17 $11 $24 $22
$17 $18 $6 $20 $12 $2 $0 $11 $17 $11 $24 $22
Working Capital Trends $60 $50 $40 $30
Temporary Current Assets
Temporary Current Assets
Permenant Current Assets
$20 $10
Fixed Assets
$0 31Jan
28- 31Feb Mar
30Apr
31May
30Jun
31Jul
135
31- 30Aug Sep
31Oct
30- 31Nov Dec
17-15. Working Capital Trends $60 Temporary Current Assets $55 $50 $45
Permanent Current Assets
$40 Fixed Assets $35 $30 Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct MONTH/ YEAR
b) Sep. of year 4: TA= $52.04 TCA= $4.00 PCA= $9.04 FA= $39.00
Aug. of year 5: TA= $54.80 TCA= $5.00 PCA= $10.80 FA= $39.00
c) Sep. of year 4: (i) aggressive approach CL = over $4.00 LT Financing = the remainder of $52.04 (ii) moderate approach CL = $4.00 LT Financing = $48.04 (iii) conservative approach CL = less than $4.00 LT Financing = the remainder of $52.04 Aug. of year 5: (i) aggressive approach CL = over $5.00 LT Financing = the remainder of $54.80 (ii) moderate approach CL = $5.00 LT Financing = $49.80 (iii) conservative approach CL = less than $5.00 LT Financing = the remainder of $54.80
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17-16. Working Capital Trends $120 $110 $100 $90 $80 $70 $60 $50 $40
Temporary Current Assets
Permenant Current Assets Fixed Assets Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
MONTH/ YEAR
17-16.
b) Sep. of year 2: TA = $89.00 TCA = $18.00 PCA = $16.00 FA = $55.00
Oct. of year 4: TA = $101.00 TCA = $22.50 PCA = $23.50 FA = $55.00
Year 5 minimum total assets occur in January in the amount of $79.40. Year 5 maximum total assets occur in December in the amount of $115.70. c) Sep. of year 2: (i) aggressive approach CL = over $18.00 LT Financing = the remainder of $89.00 (ii) moderate approach CL = $18.00 LT Financing = $71.00 (iii) conservative approach CL = less than $18.00 LT Financing = the remainder of $89.00 Oct. of year 4: (i) aggressive approach CL = over $22.50 LT Financing = the remainder of $101.00 (ii) moderate approach CL = $22.50 LT Financing = $78.50 (iii) conservative approach CL = less than $22.50 LT Financing = the remainder of $101.00
137
Chapter 18 Solutions
Answers to Review Questions 1.
What are the primary reasons that companies hold cash? Companies hold cash to make necessary payments, to take advantage of opportunities as they arise, and to cover unforeseen emergencies.
2.
Explain the factors affecting the choice of a minimum cash balance amount. The minimum cash balance amount is determined by how easy it is to raise funds when needed, how predictable the cash flows are, and how risk averse managers are.
3.
What are the negative consequences of a company holding too much cash? A company holding too much cash would be giving up the opportunity to invest more in income producing assets
4.
Explain the factors affecting the choice of a maximum cash balance amount. The maximum cash balance amount is determined by available investment opportunities, the expected return on investments, and the transaction cost of making investments.
5.
What is the difference between pro forma financial statements and a cash budget? Explain why pro forma financial statements are not used to forecast cash needs. Pro forma income statements deal with revenues and expenses that are not always cash flows while cash budgets deal only with projected cash inflows and outflows.
6.
What are the benefits of ―collecting early‖ and how do companies attempt to do this? Money has time value. The sooner cash is collected, the better. Companies use regional collection centers and lock boxes to facilitate this.
7.
What are the benefits of ―paying late‖ (but not too late) and how do companies attempt to do this? Because money has time value, the later cash is paid, but not too late, the better. Companies use remote disbursement banks to facilitate holding onto funds longer.
138
8.
Refer to the Bulldog battery company‘s cash budget in Table 18-7. Explain why the company would probably not issue $1 million worth of new common stock in January to avoid all short-term borrowing during the year. Common stock financing is long-term financing so it would probably not be used to meet this shortterm financing need.
Answers to End-of-Chapter Problems 18-1. Miller-Orr Model: H = 3Z - 2L Target Cash Balance = Z = (H + 2L)/3 = ($9,000 + 2 X $3,000)/ 3 = $5,000 18-2. Miller-Orr Model: a)
Z=3
3 X TC X V +L 4r
OR
Z=3
3 X $40 X $39,000 + $2,200 4 X .03/365
Target Cash Balance = Z = $2,424 + $2,200 = $4,624 b)
Upper Limit of cash balance = H = 3Z -2L = 3 X $4,624 - 2 X $2,200 = $9,472
18-3. Miller-Orr Model: a)
Z=3
3 X TC X V +L 4r
OR
Z=3
3 X $40 X $52,000 + $3,900 4 X .03/365
Target Cash Balance = Z = $2,667 + $3,900 = $6,567 b)
Upper Limit of cash balance = H = 3Z -2L = 3 X $6,567 - 2 X $3,900 = $11,901 3
18-4.
Z = √ [(3 * $25 * $65,580) / (4 * (.05/365))] + $15,000 139
3
Z = √ (4,918,500 / .000547945) + $15,000 3
Z = √ 8,976,265,866 + $15,000 Z = $2,078.25 + $15,000 Z = $17,078.25
18-5.
H = (3 * $17,078.25) – (2 * $15,000) H = $51,234.75 – $30,000 H = $21,234.75
140
18-6. Lifelong Appliances Cash Collections Given: 20% of customers pay off their accounts in month of sale 70% of customers pay off their accounts in first month following sale 10% of customers pay off their accounts in second month following sale 2006 ---> Nov Sales ($000s)
Dec $131
2007 ---> Jan
$129
Aug Sep Oct Nov Dec
2008 ---> Jan Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143
$136 $139
Feb
$126
Mar
Apr May Jun
Jul
Monthly Cash Collections Worksheet: (in $000s) 2006 ---> Nov
Dec
2007 ---> Jan
Cash collections: in month of sale first month after sale second month after sale Total monthly cash collections
Feb
$25 90 13 $129
Mar
Apr May Jun
Jul
Aug Sep Oct Nov Dec
2008 ---> Jan Feb
$27 $28 $29 $38 $45 $48 $45 $37 $35 $33 $29 88 93 97 100 134 158 169 157 129 121 116 13 13 13 14 14 19 23 24 22 18 17 $128 $134 $139 $152 $193 $226 $237 $218 $186 $173 $162
18-7. Lifelong Appliances Cash Collections with Stricter Credit Terms Given: 40% of customers pay off their accounts in month of sale 55% of customers pay off their accounts in first month following sale 5% of customers pay off their accounts in second month following sale 2006 ---> Nov Sales ($000s)
$131
Dec $129
2007 ---> Jan $126
Feb $133
Aug Sep Oct Nov Dec
2008 ---> Jan Feb
$139 $143 $191 $226 $242 $224 $184 $173 $166 $143
$136 $139
Mar
Apr May Jun
Jul
Monthly Cash Collections Worksheet: (in $000s) 2006 ---> Nov Cash collections: in month of sale first month after sale second month after sale Total monthly cash collections
Dec
2007 ---> Jan $50 71 7 $128
Feb $53 69 6 $129
Mar
Apr May Jun
Jul
Aug Sep Oct Nov Dec
$56 $57 $76 $90 $97 $90 $74 $69 $66 $57 73 76 79 105 124 133 123 101 95 91 6 7 7 7 10 11 12 11 9 9 $135 $140 $162 $203 $231 $234 $209 $182 $171 $157
141
2008 ---> Jan Feb
18-8.
a) ($18,366 * .45) + ($16,523 * .40) + ($17,956 * .15) = $8,264.70 + $6,609.20 + $2693.40 = $17,567.30 b) ($22,980 * .45) + ($22,890 * .40) + ($19,500 * .15) = $10,341 + $9,156 + 2,925 = $22,422 c) ($21,650 * .45) + ($23,000 * .40) + ($23,157 * .15) = $9,742.50 + $9,200 + $3,473.55 = $22,416.05
18-9.
a) $2,000 + ($17,956 * .05) + $62.50 = $2,960.30 b) $2,000 + ($22,890 * .05) + $62.50 +$1,125 = $4,332.00 c) $2,000 + ($19,250 * .05) + $62.50 = $3,025.00
18-10. Lifelong Appliances Cash Expenditures Given: 2006 ---> Nov Sales ($000s)
2007 ---> Dec
$131
Jan $129
Dec Materials purchasing Schedule: Order materials
Feb $126
Mar Apr May Jun
Jul
2008 ---> Aug Sep Oct Nov Dec Jan Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139
Jan Feb Mar Manufacture Appliances Sell appliances Repeat each month
Cost of materials = 30% of sales Payment for materials one month after purchase Production costs other than purchases = Selling and marketing Expenses = General and Administrative Expenses = Interest Payments = Tax payments = Dividend payments =
80% 19% $11 $31 $100 $50
of purchases of sales thousand each month thousand, paid in December thousand, paid in 4 installments in April, June, September, and December thousand each, paid in June and December
142
Monthly Cash Expenditures Worksheet: (in $000s) 2006 ---> Nov
2007 ---> Dec
Materials Purchases (reference only; not a cash flow) Payments for materials purchases: Other cash payments: Production costs other than purchases Selling and marketing Expenses General and Administrative Expenses Interest Payments Tax payments Dividend payments Total Cash Outflows
Jan $40
Feb
Mar Apr May Jun
Jul
2008 ---> Aug Sep Oct Nov Dec Jan Feb
$42
$43 $57 $68 $73 $67 $55 $52 $50 $43 $41 $42
$40
$42 $43 $57 $68 $73 $67 $55 $52 $50 $43 $41
$33 $24 $11
$34 $46 $54 $58 $54 $44 $42 $40 $34 $33 $33 $25 $26 $27 $36 $43 $46 $43 $35 $33 $32 $27 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $31 $25 $25 $25 $25 $50 $50 $112 $126 $175 $173 $255 $168 $150 $163 $128 $118 $218
$108
18-11. Lifelong Appliances Cash Expenditures, Revised Given: 2006 ---> Nov Sales ($000s)
2007 ---> Dec
$131
Jan $129
Dec Materials purchasing Schedule: Order materials Cost of materials =
Feb $126
Mar Apr May Jun
Jul
2008 ---> Aug Sep Oct Nov Dec Jan Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139
Jan Feb Mar Manufacture Appliances Sell appliances Repeat each month
30% of sales
Payment schedule for materials: 30% paid in cash in month of purchase 70% paid in cash in month following month of purchase Production costs other than purchases = Selling and marketing Expenses = General and Administrative Expenses = Interest Payments = Tax payments = Dividend payments =
80% 19% $11 $31 $100 $50
of purchases of sales thousand each month thousand, paid in December thousand, paid in 4 installments in April, June, September, and December thousand each, paid in June and December
143
Monthly Cash Expenditures Worksheet: (in $000s) 2006 ---> Nov
2007 ---> Dec
Materials Purchases (reference only; not a cash flow) Payments for materials purchases: in month of purchase in month following month of purchase Other cash payments: Production costs other than purchases Selling and marketing Expenses General and Administrative Expenses Interest Payments Tax payments Dividend payments Total Cash Outflows
Jan $40
Feb
Mar Apr May Jun
Jul
2008 ---> Aug Sep Oct Nov Dec Jan Feb
$42
$43 $57 $68 $73 $67 $55 $52 $50 $43 $41 $42
$13 $28
$13 $17 $20 $22 $20 $17 $16 $15 $13 $12 $13 $29 $30 $40 $47 $51 $47 $39 $36 $35 $30 $29
$33 $24 $11
$34 $46 $54 $58 $54 $44 $42 $40 $34 $33 $33 $25 $26 $27 $36 $43 $46 $43 $35 $33 $32 $27 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $31 $25 $25 $25 $25 $50 $50 $113 $130 $178 $175 $254 $165 $149 $162 $126 $117 $219
$109
18-12. Fit-and-Forget Fittings Cash Budget Given: Sales:
2006 ---> Nov
Sales ($000s)
$2,266
Dec $2,230
2007 ---> Jan
Feb $2,116
$2,300
Mar $2,402
Apr
30% of customers pay off their accounts in month of sale 65% of customers pay off their accounts in first month following sale 5% of customers pay off their accounts in second month following sale Purchases & Expenses: Jan Manufacture Products
Feb Sell Products
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
2008 ---> Feb
$2,420 $3,390 $3,909 $4,164 $3,933 $3,163 $2,912 $2,886 $2,424 $2,353 $2,442
Collections:
Dec Materials purchasing Order Schedule: materials
May
Mar Repeat each month
Cost of materials 20% of sales = Payment schedule for materials: 20% paid in cash in month of purchase 80% paid in cash in month following month of purchase
144
Production costs other than purchases = Selling and marketing Expenses = General and Administrative Expenses = Interest Payments = Tax payments = Dividend payments = Cash Inflows:
14% 16% $180 $500 $1,600 $855
(in $000s) 2006 ---> 2007 ---> Nov Dec Jan Feb Mar
Cash collections: in month of sale first month after sale second month after sale Total monthly cash collections Cash Outflows:
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
2008 ---> Jan Feb
$635 $690 $721 $726 $1,017 $1,173 $1,249 $1,180 $949 $874 $866 $727 1,450 1,375 1,495 1,561 1,573 2,204 2,541 2,707 2,556 2,056 1,893 1,876 113 112 106 115 120 121 170 195 208 197 158 146 $2,198 $2,177 $2,321 $2,402 $2,710 $3,497 $3,960 $4,082 $3,714 $3,126 $2,917 $2,749 (in $000s) 2006 ---> 2007 ---> Nov Dec Jan Feb Mar
Materials Purchases (reference only; not a cash flow) Payments for materials purchases: in month of purchase in month following month of purchase Other cash payments: Production costs other than purchases Selling and marketing Expenses General and Administrative Expenses Interest Payments Tax payments Dividend payments Total Cash Outflows
$460
Net Cash Gain(Loss) Cash Flow Summary:
of purchases of sales thousand each month thousand, paid in December thousand, paid in 4 installments in April, June, September, and December thousand each, paid in June and December
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
$480
$484
$678
$782
$833
$787
$633
$582
$577
$485
$471
$488
$96 $368
$97 $384
$136 $387
$156 $542
$167 $625
$157 $666
$127 $629
$116 $506
$115 $466
$97 $462
$94 $388
$98 $376
$67 $339 $180
$68 $368 $180
$95 $384 $180
$109 $387 $180
$117 $542 $180
$110 $625 $180
$89 $666 $180
$82 $629 $180
$81 $506 $180
$68 $466 $180
$66 $462 $180
$68 $388 $180 $500 $400 $400 $400 $400 $855 $855 $1,050 $1,097 $1,182 $1,775 $1,631 $2,994 $1,691 $1,513 $1,748 $1,273 $1,190 $2,865 $1,148 $1,080 $1,139
$627 $1,079
$503 $2,269 $2,569 $1,965 $1,854 $1,727
($117)
Apr
Jun
Dec
(in $000s) Jan
1. Cash Balance at start of month 2. Net Cash Gain(Loss) during month 3. Cash balance at end of month before financing (line 1 plus line 2) 4. Minimum Cash Balance Desired 5. Surplus cash(deficit) (Line 3 minus line 4)
Feb
Mar
May
Jul
Aug
Sep
Oct
Nov
$1,133 $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093 1,148 1,080 1,139 627 1,079 503 2,269 2,569 1,965 1,854 1,727 (117) 2,281 3,361 4,500 5,127 6,206 6,709 8,978 11,547 13,512 15,366 17,093 16,976 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 $1,171 $2,251 $3,390 $4,017 $5,096 $5,599 $7,868 $10,437 $12,402 $14,256 $15,983 $15,866
145
2008 ---> Jan Feb
External Financing Summary:
(in $000s)
6. External financing balance at start of month 7. New financing required (negative amount from line 5) 8. Financing repayments (positive amount from line 5) 9. External financing balance at end of month
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
$0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10. Cash balance at end of month after financing $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093 $16,976
146
Chapter 19 Solutions
Answers to Review Questions 1.
Accounts receivable are sometimes not collected. Why do companies extend trade credit when they could insist on cash for all sales? Extending trade credit almost always leads to more sales. If the incremental cashflows, including the investment in accounts receivable give a positive NPV, the decision to extend trade credit would increase the value of the firm.
2.
Inventory is sometimes thought of as a necessary evil. Explain. Inventory ties up funds and these funds are not earning an explicit return. Some inventory is often necessary, however, as companies try to hold the lowest acceptable amount.
3.
What are the primary variables being balanced in the EOQ inventory model? Explain The primary variables being balanced in the EOQ model are carrying costs and ordering costs. The more frequent orders are placed the lower the firm‘s carrying costs and the higher its ordering costs.
4.
What are the benefits of the JIT inventory control system? The just-in-time (JIT) inventory control system lowers inventory carrying costs and tends to increase quality.
5.
What are the primary requirements for a successful JIT inventory control system? For a JIT system to be successful the supplier must be willing and able to deliver materials immediately and the quality of delivered materials must be high.
6.
Can a company have a default rate on its accounts receivable that is too low? Explain. A company could have a default rate on AR that would be considered too low if by liberalizing credit terms a significant increase in sales revenue and cash inflows were to result. If the increase in the default rate is more than offset by the increase in sales revenue, after all incremental cash flows are considered a positive NPV could result.
7.
How does accounts receivable factoring work? What are the benefits to the two parties involved? What are the risks?
147
Factoring is when one firm sells accounts receivable (AR) to another. The purchasing firm is called a factor. The factor makes a profit by purchasing the AR at a discount. Its risk is that some of the AR may default. The selling firm gets the cash it needs.
Answers to End-of-Chapter Problems 19-1. Accounts Receivable, ACP: Accounts Receivable = ACP X Sales/365 = 22 X $8,030,000/365 = $484,000
19-2. Accounts Receivable, ACP: Accounts Receivable = ACP X Sales/365 = 26 X $7,600,000/365 = $541,369.86 The company appears to have relaxed its credit policy since accounts receivable increased as did the average collection period.
19-3. Accounts Receivable, ACP, Credit Policy: (a) ACP = 0.4 X 15 + 0.57 X 60 + 0.03 X 100 = 43.2 days (b) AR = 43.2 X $730,000/365 = $86,400
19-4. Accounts Receivable, ACP, Credit Policy: ACP = 0.4 X 10 + 0.58 X 30 + 0.02 X 100 = 23.4 days AR = 23.4 X $657,000/365 = $42,120
19-5.
(0.25 * 10) + (0.60 * 20) + (0.15 * 30) = 2.5 + 12 + 4.5 = 19 days
19-6.
(0.32 * 10) + (0.67 * 30) + (0.01 * 45) = 3.2 + 20.1 + 0.45 = 23.75 days No, the new policy should not be implemented because the ACP would increase.
148
19-7 Effect of Change of Credit Policy: Given: All sales on credit Old credit terms New credit terms
2/15, n40 2/15, n60
Sales expected under old credit policy: Sales change expected with new credit policy:
$350,000 20% increase
Under old credit policy:
40% of customers take discount, pay in 15 days 58% of customers pay at the end of 40 days 2% of customers pay in 100 days
Under new credit policy:
40% of customers take discount, pay in 15 days 57% of customers pay at the end of 60 days 3% of customers pay in 100 days
Bad debt expenses under old credit policy: Bad debt expenses under new credit policy: Short-term interest rate Long term interest rate Income tax rate Cost of capital Cost of goods sold Other operating expenses
2% 3%
of sales of sales
7% 10% 40% 11% 80% of sales $10,000 under old credit policy
Question a: Average collection period under old policy Average collection period under new policy Accounts Receivable under old policy Accounts Receivable under new policy
31.2 days (weighted average of customers paying) 43.2 days (weighted average of customers paying) $29,918 AR = ACP * Credit sales per day $49,710 AR = ACP * Credit sales per day
Question b: East-West Trading Company Financial Statements INCOME STATEMENT With old With new credit credit terms: terms: 2/15, n40 2/15, n60 (given) (pro forma) Sales (all on credit) Cost of Goods Sold Gross Profit Bad debt expenses Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes Net Income
$350,000 280,000 70,000 7,000 10,000 53,000 5,450 47,550 19,020 $28,530
$420,000 $336,000 84,000 12,600 $12,000 59,400 5,940 53,460 21,384 $32,076
20% increase increase in proportion with sales from assumptions increase in proportion with sales (ST Debt * ST Cost of Debt) + (LT Debt * LT Cost of Debt)
149
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities Accounts Receivable Inventory Total Current Assets Property, Plant & Equipment, Net Total Assets Liabilities & Equity Current Liabilities: Accounts Payable Notes Payable Total Current Liabilities Long-Term Debt Total Liabilities Common Stock Capital in Excess of Par Retained Earnings Total Stockholders' Equity Total Liabilities & Equity
$15,000 29,918 50,000 94,918 120,000 $214,918
$18,000 49,710 60,000 127,710 120,000 $247,710
increase in proportion with sales from Tab a increase in proportion with sales
$14,918 35,000 49,918 30,000 79,918 25,000 60,000 50,000 135,000 $214,918
$17,902 $42,000 59,902 30,000 89,902 25,000 60,000 50,000 135,000 $224,902
increase in proportion with sales increase in proportion with sales
AFN to balance:
same
same same same same
$22,808 obtain from ST sources
Question c: Incremental cash flows associated with the credit policy change Initial investment at T-0
($22,808) AFN from Tab B
Future incremental cash flows, T-1 onward: Inflows: Increase in Sales Outflows: Increase in Cost of Goods Sold Increase in Bad Debt Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows
$70,000 $56,000 $5,600 $2,000 $490 $2,364 $66,454
Net future incremental cash flows
$3,546 each year from T-1 onward
Question d, Investment Decision: NPV of the Credit Policy Change: Initial Investment ($22,808) NPV =
Future Cash Flows $3,546
per year
$9,428 at a cost of capital of
150
11%
19-8. Given: All sales on credit Old credit terms New credit terms
2/15, n40 2/15, n60
Sales expected under old credit policy: Sales change expected with new credit policy:
$350,000 20% increase
Under old credit policy:
40% of customers take discount, pay in 15 days 58% of customers pay at the end of 40 days 2% of customers pay in 100 days
Under new credit policy:
30% of customers take discount, pay in 15 days 60% of customers pay at the end of 60 days 10% of customers pay in 100 days
Bad debt expenses under old credit policy: Bad debt expenses under new credit policy: Short-term interest rate Long term interest rate Income tax rate Cost of capital Cost of goods sold Other operating expenses
2% 4%
of sales of sales
7% 10% 40% 11% 80% of sales $10,000 under old credit policy
Question a: Average collection period under old policy Average collection period under new policy Accounts Receivable under old policy Accounts Receivable under new policy
31.2 days (weighted average of customers paying) 50.5 days (weighted average of customers paying) $29,918 AR = ACP X Credit sales per day $58,110 AR = ACP X Credit sales per day
Question b: East-West Company Financial Statements INCOME STATEMENT With old With new credit credit terms: terms: 2/15, n40 2/15, n60 (given) (pro forma) Sales (all on credit) Cost of Goods Sold Gross Profit Bad debt expenses Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes
$350,000 280,000 70,000 7,000 10,000 53,000 5,450
$420,000 $336,000 84,000 16,800 $12,000 55,200 5,940
47,550 19,020
49,260 19,704
151
20% increase increase in proportion with sales from assumptions increase in proportion with sales (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt)
Net Income
$28,530
$29,556
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities Accounts Receivable Inventory Total Current Assets Property, Plant & Equipment, Net Total Assets Liabilities & Equity Current Liabilities: Accounts Payable Notes Payable Total Current Liabilities Long-Term Debt Total Liabilities Common Stock Capital in Excess of Par Retained Earnings Total Stockholders' Equity Total Liabilities & Equity
$15,000 29,918 50,000 94,918 120,000 $214,918
$18,000 increase in proportion with sales 58,110 60,000 increase in proportion with sales 136,110 120,000 same $256,110
$14,918 35,000 49,918 30,000 79,918 25,000 60,000 50,000 135,000 $214,918
$17,902 $42,000 59,902 30,000 89,902 25,000 60,000 50,000 135,000 $224,902
AFN to balance:
increase in proportion with sales increase in proportion with sales same same same same
$31,208 obtain from ST sources
Question c: Incremental cash flows associated with the credit policy change Initial investment at T-0
($31,208) AFN
Future incremental cash flows, T-1 onward: Inflows: Increase in Sales Outflows: Increase in Cost of Goods Sold Increase in Bad Debt Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows
$70,000 $56,000 $9,800 $2,000 $490 $684 $68,974
Net future incremental cash flows
$1,026 each year from T-1 onward
Question d, Investment Decision: NPV of the Credit Policy Change: Initial Investment Future Cash Flows ($31,208) NPV =
$1,026 per year
($21,881) at a cost of capital of 11%
152
19-9. Effect of Change of Credit Policy: Given: All sales on credit Old credit terms New credit terms
3/10, n40 3/15, n30
Sales expected under old credit policy: Sales change expected with new credit policy:
$2,000,000 -10%
decrease
Under old credit policy:
30% of customers take discount, pay in 60% of customers pay at the end of 10% of customers pay in
10 days 40 days 100 days
Under new credit policy:
42% of customers take discount, pay in 57% of customers pay at the end of 1% of customers pay in
15 days 30 days 100 days
Bad debt expenses under old credit policy: Bad debt expenses under new credit policy: Short-term interest rate Long term interest rate Income tax rate Cost of capital Cost of goods sold Other operating expenses
3% 1%
of sales of sales
8% 11% 40% 13% 80% of sales $60,000 under old credit policy
Question a: Average collection period under old policy Average collection period under new policy Accounts Receivable under old policy Accounts Receivable under new policy
37 days (weighted average of customers paying) 24.4 days (weighted average of customers paying) $202,740 AR = ACP X Credit sales per day $120,329 AR = ACP X Credit sales per day
Question b: A-Z Trading Company Financial Statements INCOME STATEMENT With old With new credit credit terms: terms: 3/10, n40 3/15, n30 (given) (pro forma) Sales (all on credit) Cost of Goods Sold Gross Profit Bad debt expenses Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes Net Income
$2,000,000 $1,800,000 10% decrease 1,600,000 $1,440,000 decrease in proportion with sales 400,000 360,000 60,000 18,000 from assumptions 60,000 $54,000 decrease in proportion with sales 280,000 288,000 34,810 33,210 (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt) 245,190 254,790 98,076 101,916 $147,114 $152,874
153
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities $86,000 $77,400 Accounts Receivable 202,740 120,329 Inventory 285,000 256,500 Total Current Assets 573,740 454,229 Property, Plant & Equipment, Net 652,000 652,000 Total Assets $1,225,740 $1,106,229 Liabilities & Equity Current Liabilities: Accounts Payable $85,000 $76,500 Notes Payable 200,000 $180,000 Total Current Liabilities 285,000 256,500 Long-Term Debt 171,000 171,000 Total Liabilities 456,000 427,500 Common Stock 143,000 143,000 Capital in Excess of Par 342,000 342,000 Retained Earnings 285,000 285,000 Total Stockholders' Equity 770,000 770,000 Total Liabilities & Equity $1,225,740 $1,197,500 AFN to balance:
decrease in proportion with sales decrease in proportion with sales same
decrease in proportion with sales decrease in proportion with sales same same same same
($91,271) excess financing
Question c: Incremental cash flows associated with the credit policy change Initial investment at T-0
$91,271
Future incremental cash flows, T-1 onward: Inflows: Increase in Sales Outflows: Increase in Cost of Goods Sold Increase in Bad Debt Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows
($200,000) ($160,000) ($42,000) ($6,000) ($1,600) $3,840 ($205,760)
Net future incremental cash flows
$5,760 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change: Initial Investment Future Cash Flows
$91,271
NPV =
$5,760 per year
$135,579 at a cost of capital of 13%
154
19-10. Economic Order Quantity EOQ = [2 X 500 X $250/$300] = 28.87 units 29 units Number of orders per year = 500/29 = 17.24 orders 17 orders Ordering Cost = 17 X $250 = $4,250
19-11. Economic Order Quantity: EOQ = [2 X 500 X $250/$330] = 27.52 units 28 units Number of orders per year = 500/28 = 17.86orders 18 orders Ordering cost = 18 X $250 = $4,500 19-12. a) √ (2 * 1,200 * $250) / $100 = √ 6,000 = 77.46 units per order b) 1200 / 78 = 15.38 orders per year
19-13. Sales (2007) = 200 * (1 + 0.25) = 250 units Carrying Costs = $150 * (1 + 0.10) = $165 Ordering Costs = $50 * (1 + 0.10) = $55 √ (2 * 250 * $55) / $165 = √ 166.66
= 12.91 units
19-14. Credit Scoring Total Score = 3 + 4 + 3 + 4 + 3 + 2 = 19 > 12. Yes, Danny should approve the credit.
19-15. Criteria Length of payment:
Points
Score
time since last delinquent Greater 2.5 years 2-2.5 years 1.5-2 years 1-1.5 years Less than 1 year
Length of Time in Business Greater 5 years 4-5 years 3-4 years 2-3 years Less than 2 years
155
4 3 2 1 0
___4____ _______ _______ _______ _______
4 3 2 1 0
___4____ _______ _______ _______ _______
Net Income
Greater $100,000 $75,000-$100,000 $50,000-$75,000 $25,000-$50,000 Less than $25,000
4 3 2 1 0
_______ _______ ___2____ _______ _______
Total Score: 10 $1,200,000 * 0.30 = $360,000 Yes, they will be approved. TWI will be approved for $360,000. 19-16. Sunrise Corporation Inventory Policy Given: Present inventory level Proposed inventory level
60 100
Sales expected under old inventory policy: Sales expected with new inventory policy: Ordering cost Carrying cost Unit sales price Unit purchase price
350 450
units per year units per year
$200 per order $600 per unit per year $10,000 $8,000
Short-term interest rate 7% Long term interest rate 10% Income tax rate 40% Cost of capital 11% Cost of goods sold 80% of sales Other operating expenses $100,000 under current inventory policy
Question a: Under old inventory policy Under new inventory policy 60 units 100 units E.O.Q Number of orders per year Ordering cost Carrying cost Total inventory cost
15 23 $4,583 $36,000 $40,583
156
17 26 $5,196 $60,000 $65,196
Question b: Sunrise Company Financial Statements INCOME STATEMENT Under old inventory policy 60 units (given)
Sales (all on credit) Cost of Goods Sold Gross Profit Inventory costs Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes Net Income
Under new inventory policy 100 units (pro forma)
$3,500,000 $4,500,000 unit sales x price, from assumptions 2,800,000 3,600,000 unit sales x purchase price, from assumptions 700,000 900,000 40,583 65,196 from Tab a 100,000 128,571 increase in proportion with sales 559,417 706,232 13,150 15,050 (ST Debt * ST Cost of Debt) + (LT Debt * LT Cost of Debt) 546,267 691,182 218,507 276,473 $327,760 $414,709
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities Accounts Receivable Inventory Total Current Assets Property, Plant & Equipment, Net Total Assets Liabilities & Equity Current Liabilities: Accounts Payable Notes Payable Total Current Liabilities Long-Term Debt Total Liabilities Common Stock Capital in Excess of Par Retained Earnings Total Stockholders' Equity Total Liabilities & Equity
$55,000 105,000 480,000 640,000 100,000
70,714 increase in proportion with sales 135,000 increase in proportion with sales 800,000 assumed inventory level x unit purchase price, from assumptions 1,005,714 100,000 same
$740,000 $1,105,714
$100,000 95,000 195,000 65,000 260,000 60,000 220,000 200,000 480,000 $740,000
AFN to balance:
128,571 122,143 250,714 65,000 315,714 60,000 220,000 200,000 480,000 $795,714
increase in proportion with sales increase in proportion with sales same same same same
$310,000
Question c: Incremental cash flows associated with the credit policy change Initial investment at T-0
($310,000) AFN
Future incremental cash flows, T-1 onward: Inflows:
157
Increase in Sales Outflows: Increase in Cost of Goods Sold Increase in Inventory Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows
$1,000,000 $800,000 $24,614 $28,571 $1,900 $57,966 $913,051
Net future incremental cash flows
$86,949 each year from T-1 onward
Question d, Investment Decision: NPV of the Credit Policy Change: Initial Investment
Future Cash Flows
($310,000) NPV =
$86,949
per year
$480,445 at a cost of capital of
11%
19-17. Given: Present inventory level Proposed inventory level
60 90
Sales expected under old inventory policy: Sales expected with new inventory policy: Ordering cost Carrying cost Unit sales price Unit purchase price Short-term interest rate Long term interest rate Income tax rate Cost of capital Cost of goods sold Other operating expenses
350 390
units per year units per year
$200 per order $600 per unit per year $10,000 $8,000 7% 10% 40% 11% 80% of sales $100,000 under current inventory policy
Question a: Under old inventory policy Under new inventory policy 60 units 90 units E.O.Q Number of orders per year Ordering cost Carrying cost Total inventory cost
15 23 $4,583 $36,000 $40,583
158
16 24 $4,837 $54,000 $58,837
Question b: Sunrise Company Financial Statements INCOME STATEMENT Under old inventory policy 60 units (given) Sales (all on credit) Cost of Goods Sold Gross Profit Inventory costs Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes Net Income
Under new inventory policy 90 units (pro forma)
$3,500,000 2,800,000 700,000 40,583 100,000 559,417 13,150
$3,900,000 3,120,000 780,000 58,837 111,429 609,734 13,910
546,267 218,507 $327,760
595,824 238,330 $357,494
unit sales x price, from assumptions unit sales x purchase price, from assumptions
increase in proportion with sales (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt)
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities Accounts Receivable Inventory
$55,000 61,286 increase in proportion with sales 105,000 117,000 increase in proportion with sales 480,000 720,000 assumed inventory level x unit purchase price, from assumptions Total Current Assets 640,000 898,286 Property, Plant & Equipment, Net 100,000 100,000 same Total Assets $740,000 $998,286 Liabilities & Equity Current Liabilities: Accounts Payable $100,000 111,429 increase in proportion with sales Notes Payable 95,000 105,857 increase in proportion with sales Total Current Liabilities 195,000 217,286 Long-Term Debt 65,000 65,000 same Total Liabilities 260,000 282,286 Common Stock 60,000 60,000 same Capital in Excess of Par 220,000 220,000 same Retained Earnings 200,000 200,000 same Total Stockholders' Equity 480,000 480,000 Total Liabilities & Equity $740,000 $762,286 AFN to balance:
$236,000
Question c: Incremental cash flows associated with the credit policy change Initial investment at T-0
($236,000) AFN
Future incremental cash flows, T-1 onward: Inflows: Increase in Sales Outflows: Increase in Cost of Goods Sold
$400,000 $320,000
159
Increase in Inventory Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows
$18,255 $11,429 $760 $19,823 $370,266
Net future incremental cash flows
$29,734 each year from T-1 onward
Question d, Investment Decision: NPV of the Credit Policy Change: Initial Investment Future Cash Flows ($236,000) NPV =
$29,734 per year
$34,309 at a cost of capital of 11%
19-18. Given: Inventory Level in Units Present inventory level Proposed inventory level (1) Proposed inventory level (2) Proposed inventory level (3)
70 80 90 100
Expected Sales 340 375 390 400
Ordering cost Carrying cost
units per year units per year units per year units per year
$160 per order $400 per unit per year
Unit sales price Unit purchase price
$16,000 $12,800
Short-term interest rate Long term interest rate Income tax rate Cost of capital Cost of goods sold Other operating expenses
7% 11% 40% 13% 80% of sales $130,000 under current inventory policy
Question a: Under old inventory policy 70 units E.O.Q Number of orders per year Ordering cost Carrying cost Total inventory cost
Under new inventory policy (1) 80 units
Under new inventory policy (2) 90 units
Under new inventory policy (3) 100 units
16 21
17 22
18 22
18 22
$3,298 $28,000 $31,298
$3,464 $32,000 $35,464
$3,533 $36,000 $39,533
$3,578 $40,000 $43,578
160
Question b: Windermere Corporation INCOME STATEMENT Under old inventory policy 70 units (given) Sales (all on credit) Cost of Goods Sold Gross Profit Inventory costs Other operating expenses Operating Income Interest Expense Before-Tax Income Income Taxes Net Income
Under new inventory policy (1) 80 units (pro forma)
Under new inventory policy (2) 90 units (pro forma)
Under new inventory policy (3) 100 units (pro forma)
$5,440,000 4,352,000 1,088,000 31,298 130,000
$6,000,000 4,800,000 1,200,000 35,464 143,382
$6,240,000 4,992,000 1,248,000 39,533 149,118
$6,400,000 5,120,000 1,280,000 43,578 152,941
926,702 13,800 912,902 365,161 $547,741
1,021,154 14,485 1,006,669 402,668 $604,001
1,059,350 14,778 1,044,572 417,829 $626,743
1,083,481 14,974 1,068,508 427,403 $641,105
BALANCE SHEET, as of Dec 31 Assets Current Assets: Cash & Securities $65,000 71,691 74,559 Accounts Receivable 114,000 125,735 130,765 Inventory 896,000 1,024,000 1,152,000 Total Current Assets 1,075,000 1,221,426 1,357,324 Property, Plant & Equipment, Net 113,000 113,000 113,000 Total Assets $1,188,000 $1,334,426 $1,470,324 Liabilities & Equity Current Liabilities: Accounts Payable $110,000 121,324 126,176 Notes Payable 95,000 104,779 108,971 Total Current Liabilities 205,000 226,103 235,147 Long-Term Debt 65,000 65,000 65,000 Total Liabilities 270,000 291,103 300,147 Common Stock 80,000 80,000 80,000 Capital in Excess of Par 320,000 320,000 320,000 Retained Earnings 518,000 518,000 518,000 Total Stockholders' Equity 918,000 918,000 918,000 Total Liabilities & Equity $1,188,000 $1,209,103 $1,218,147 AFN to balance:
$125,324
$252,176
76,471 134,118 1,280,000 1,490,588 113,000 $1,603,588
129,412 111,765 241,176 65,000 306,176 80,000 320,000 518,000 918,000 $1,224,176 $379,412
Question c: Incremental cash flows associated with the credit policy changes Under new inventory policy Under new inventory policy Under new inventory policy (3) (1) (2) 80 units 90 units 100 units Initial investment at T-0
($125,324)
($252,176) ($379,412) Excess financing (AFN)
161
Future incremental cash flows, T-1 onward: Inflows: Increase in Sales Outflows: Increase in Cost of Goods Sold Increase in Inventory Expense Increase in Other Operating Exps Increase in Interest Expense Increase in Taxes Total Outflows Net future incremental cash flows
$560,000
$800,000 $960,000
$448,000
$640,000 $768,000
$4,166 $13,382
$8,234 $19,118
$685 $37,507 $503,740
$12,279 $22,941
$978 $1,174 $52,668 $62,242 $720,998 $866,636
$56,260
$79,002
$93,364 each year from T-1 onward
Question d, Investment Decision: NPV of the Credit Policy Change: Initial Investment Future Cash Flows per Year
Under new inventory policy (1) Under new inventory policy (2) Under new inventory policy (3)
($125,324) ($252,176) ($379,412)
$56,260 $79,002 $93,364
NPV
at a cost of capital of 13%
$307,449 $355,532 $338,770
Comments: All three proposed inventory policy changes have positive NPVs, and would therefore be acceptable at the firm's cost of capital of 13%. Policy #2, inventory level of 90 units, has the highest NPV, so it should be the alternative selected.
162
Chapter 20 Solutions
Answers to Review Questions 1.
Companies with rapidly growing levels of sales do not need to worry about raising funds from outside the firm. Do you agree or disagree with this statement? Explain. Disagree. Rapidly growing firms need more assets to accommodate the increasing sales. Such firms are more likely, not less, to seek outside financing. Internal funds are often insufficient.
2.
Banks like to make short-term, self-liquidating loans to businesses. Why? Banks like to be able to see where the funds are likely to come from such that the borrower is able to use to make the required loan payments. Short term, self-liquidating loans do this since the borrowed funds are used to purchase assets that generate the needed funds.
3.
What are compensating balances and why do banks require them from some customers? Under what circumstances would banks be most likely to impose compensating balances? Compensating balances are funds that a bank requires a customer to maintain in a non-interest bearing account until the loan is retired. Banks sometimes impose compensating balance requirements so as to increase the bank‘s return on a loan. Compensating balances are most likely to be used when the stated interest rate on a loan is below the bank‘s required rate of return.
4.
What happens when a bank charges discount interest on a loan? When a bank charges discount interest on a loan the required interest payment is subtracted from the loan proceeds at the time the loan is made. This makes the effective interest rate greater than the stated rate.
5.
What is trustworthy collateral from the lenders‘ perspective? Explain whether accounts receivable and inventory are trustworthy collateral. Assets that are readily marketable, of stable value, and not likely to ―disappear‖ make for trustworthy collateral. Accounts receivable and inventory could meet this test depending upon their particular characteristics.
6.
Trade credit is free credit. Do you agree or disagree with this statement? Explain. Trade credit is not free. It has a cost. Who bears that cost depends on the terms of the transaction between the grantor and the recipient of the trade credit.
163
7.
What are the pros and cons of commercial paper relative to bank loans for a company seeking shortterm financing? Commercial paper is usually a cheaper source of short-term financing for a firm, compared to bank loans. Also, a larger amount of funds can often be raised by issuing commercial paper. Bank loans are usually a more flexible source of short-term financing and establishing an on-going business relationship with a bank may prove beneficial when money is tight.
Answers to End-of-Chapter Problems 20-1.
a) at the end of the year $1,600/$20,000 = 8% b) at the beginning of the year (discount loan) $1,600/($20,000 - $1,600) = 8.696%
20-2.
Effective annual interest
= $2,400/($40,000 - $2,400 - $40,000 X 0.10) = $2,400/$33,600 = 7.143%
20-3.
a) Effective annual interest = 1,800/20,000 = 9% b) Interest = $20,000 X 0.08 = $1,600 Effective annual interest = 1,600/(20,000-1,600) = 1,600/18,400 = 8.70% c) Interest = $20,000 X 0.075 = $1500 Compensating balance = $20,000 X 0.10 = $2,000 Effective annual interest = $1,500/($20,000 - $2,000) = 1,500/18,000 = 8.33% (i) Which alternative is best for Ralph from minimum effective interest rate point of view? Alternative c (ii)
Let B be the amount Ralph should borrow So, X - 0.1 X B = $20,000 Solving, B = $22,222.22 So, Ralph should borrow $22,222.22 and Interest payment = 22,222.22 X .075 = $1,666.67
20-4.
Interest = 14,000 X (0.16/4) = $560 Compensating Balance = 14,000 X 0.10 = $1400 Effective annual interest = {1 + [560/(14,000 - 1,400 - 560)]}4 - 1 = 19.94%
20-5.
Duration of loan = 2 weeks = 1/26 year Interest = 10,000 X (0.07/26) = $26.92 Compensating Balance = 10,000 X 0.10 = $1,000 Effective annual interest = [1 + 26.92/(10,000 - 1,000 - 26.92)]26 - 1 = 8.10%
164
20-6.
a) Discount = 0.06 X $1,000,000 X 60/360 = $10,000 b) Price = $1,000,000 - $10,000 = $990,000 c) Effective annual interest rate = [$1,000,000/$990,000]365/60 - 1 = 6.305%
20-7.
Discount = 0.04 X $2,000,000 X 60/360 = $13,333.33 Price = $2,000,000 - $13,333.33 = $1,986,666.67 Effective annual interest rate = [$2,000,000/$1,986,666.67]365/60 - 1 = 4.15%
20-8.
[1 + 2/98]365/(45 - 15) - 1 = 27.86%
20-9.
a) 3/10, n 60
[1 + 3/97]365/(60 - 10) - 1 = 24.90%
b) 2/15, n 30
[1 + 2/98]365/(30 - 15) - 1 = 63.49%
Re-calculate the costs assuming payments were made on the 40th day in each of the above cases. Compare your results. a) 3/10, n 60
[1 + 3/97]365/(40 - 10) - 1 = 44.86% (Higher)
b) 2/15, n 30
[1 + 2/98]365/(40 - 15) - 1 = 34.31% (Lower)
20-10. k = [1 + (3 / (100 – 3)) (365 / (45 –15))] – 1 k = .4486 = 44.86%
20.11. a) (.038 * $2,000,000 * 90) / 360 = $19,000 b) $2,000,000 - $19,000 = $1,981,000 c) ($2,000,000 / $1,981,000)(365/90) – 1 = .03947 = 3.95%
20-12. $20,000 * 0.065 = $1,300 (interest) $1,300 / ($20,000 - $1,300) = .0695 = 6.95%
20-13. $30,000 * 0.10 = $3,000 $30,000 * 0.13 = $3,900 $3,000 / ($30,000 - $3,900) = .1149 = 11.5%
20-14. a) b) c) d)
1.00512 – 1 = 0.0617 = 6.17% 1.00612 – 1 = 0.0744 = 7.44% 1.0075 12 – 1 = 0.0938 = 9.38% 1.008 12 – 1 = 0.1003 = 10.03%
165
20-15. a) [1 + 1/99]365/(45 - 10) - 1 =11.05% (Lower) b) Interest = $100,000 X 0.10 = $10,000 Effective annual interest = $10,000/($100,000 - $10,000) = 11.11% a is the better source since 11.11% is higher than 11.05%. 20-16. a) [1 + 1/99]365/(60 - 15) - 1 = 8.49% b) Interest = $100,000 X 0.10 = $12,000 Compensating Balance = $100,000 X 0.12 = $12,000 Effective annual interest = $10,000/($100,000 - $10,000 - $12,000) = 12.82% a is still the better source. 20-17. $1,500,000 / (1 - 0.09 – 0.12) = $1,898,734.18
166
Chapter 21 Solutions
Answers to Review Questions 1.
What does it mean when the U.S. dollar weakens in the foreign exchange market? When the U.S. dollar weakens in the foreign exchange market one U.S. dollar buys fewer units of another country‘s currency. It costs more U.S. dollars to buy a given quantity of another country‘s currency.
2.
What kinds of U.S. companies would benefit most from a stronger dollar in the foreign exchange market? Explain. U.S. companies that import goods from other countries would benefit from a stronger dollar. More units of a foreign currency could be purchased for a given number of dollars. Other things equal, this would lower the cost of foreign goods for the U.S. importer.
3.
Under what circumstance would the U.S. dollar and the Canadian dollar be said to have achieved purchasing power parity? The U.S. dollar and the Canadian dollar would be considered to have achieved purchasing power parity when the exchange rate reflects the relative prices of a market basket of traded goods and services at the current exchange rate. There would be no incentive to convert U.S. dollars to Canadian dollars nor to convert Canadian dollars to U.S. dollars and purchase goods or services in the other country.
4.
What are some of the primary advantages when a corporation has operations in countries other than its home country? What are some of the risks? Foreign operations may reduce a company‘s labor or material costs, and may increase its sales. Risks include possible seizure of company assets by a foreign government, possible cultural blunders that lead to lost sales, and exchange rate risks.
5.
What is GATT, and what is its goal? GATT is the General Agreement on Tariffs and Trade. It is a treaty that seeks to reduce trade barriers among participant nations.
167
Answers to End-of-Chapter Problems 21-1.
a) British pound 1,000,000/1.8508 b) Indian rupee 1/.02122 c) Japanese yen 1/.008800 d) Australian dollar 1/.7514 e) Mexican peso 1/.0900 f) Israeli shekel 1/.2315
= = = = = =
£540,307 Rs47.125 million ¥113.636 million A$1.331 million Peso 11.111 million Shekel 4.320 million
21-2.
a) Chilean pesos 1/.001855 b) HK dollars 1/.1287 c) Singaporean dollars 1/.6321 d) euros 1,000,000/1.2810 e) Indian rupees 1/.02122 f) Mexican pesos 1/.0900 g)Thai bahts 1/.0314
= = = = = = =
Pesos 539.084 million HK$7.770 million S$1.582 million 780,640.12 Rs47.125 million Peso 11.111 million Baht 31.847 million
21-3.
a) 2 million Australian dollars b) 1.6 million Singaporean dollars c) 5 million euros d) 2.6 million Mexican pesos e) 2 million Japanese yen f) 25 million Thai bahts
2 X 0.7514 1.6 X 0.6321 5 X 1.2810 2.6 X 0.0900 2 X 0.00880 25 X 0.02186
= = = = = =
$1,502,800 $1,011,360 $6,405,000 $234,000 $16,000 $546,500
21-4.
a) 1.2810 b) (1) $100,000 * 113.6363636 = 11,363,636 (2) $100,000 * 0.540306894 = 54,031 (3) $100,000 * 1.113957892 = 111,396 (4) $100,000 * 11.1111111 = 1,111,111
21-5.
a) 113.6363636 * 0.0900 = 10.2273 ¥ / peso b) 11.1111111 * 1.8508 = 20.5644 pesos / ₤ c) .780640125 * 0.8977 = 0.7008 € / Canadian Dollar d) 113.6363636 * 0.8977 = 102.0114 ¥ / Canadian Dollar
21-6.
0.6471 X 1/0.2003 = 3.23
21-7.
1 euro = 58 rupees = 9.67 HK dollars 1 HK dollar = 58/9.67 = 6.00 rupees
21-8.
1 British pound = 16.9 Mexican pesos = 2.8 Singapore dollars 10 million Mexican pesos = 10 X 2.8/16.9 = 1.657 million Singapore dollars 168
21-9.
If one British pound is equivalent to 1.5 euros, and one euro can purchase 60 baht, how many baht can one purchase with 1 million British pounds? 1 British pound = 1.5 euros = 60 X 1.5 = 90 baht 1 million British pounds = 90 million baht
21-10. British pound = 1.5 euros; .8 X 1.5 euros = 1.2 dinars; 1.2 dinars X 160 yen = 192 yen; 1 million British pounds = 192 million yen
21-11. a) 16.5 * 1/.9188 = $17.96 per share $17.96 * 100 = $1,796 b) 16.5 * 1/.70 = $23.57 per share $23.57 * 100 = $2,357 c) 16.5 * 1/1.212 = $13.61 per share $13.61 * 100 = $1,361
21-12. 55,150 * 1.020408163 = $56,275.51
21-13. 230,000 ¥ / $2,000 = 115 ¥ / $
21-14. Initial Investment = Current Value = Return on Investment =
$100,000 $100,000 X 119/100 = $119,000 ($119,000 - $100,000)/$100,000 = 19%
21-15. Initial Investment = Current Value = Return on Investment =
1,000 shares X $37/shareXRs42/$ = Rs1,554,000 1,000 shares X $37/shareXRs44/$ = Rs1,628,000 (Rs1,628,000 - Rs1,554,000)/Rs1,554,000 = 4.76%
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