1
CHAPTER TWO PROBLEMS
1.
Your Your corpo orpora rati tion on has has the the foll follow owin ing g cash cash flo flow ws: Operating income $250,000 Interest received 10,000 Interest paid 45,000 Dividends received 20,000 Dividends paid 50,000 If the applicable tax table is as follows: Taxable Income Rate ----------------$ 0 - 25,000 16% 25 - 50,000 19 50 - 75,000 30 75 -100,000 40 over 100,000 46 What is the corporation's tax liability? $80,530
2.
3.
Last Last year year Ratt Rattner ner Robot Robotic ics s had had $5 mill millio ion n in in oper operat ating ing inco income me (EBI (EBIT). T). The compa company ny had net depreciation expense of $1 million and an interest expense of $1 million; its corporate tax rate was 40 percent. The company has $14 million million in current assets and $4 million in non-interest-bearing current liabilities; it has $15 million in net plant and equipment. It estimates that it has an after-tax cost of capital of 10 percent. Assume that Rattner’s only non-cash item is depreciation. a.
What What was the the com compa pany ny’s ’s net net inc income ome for for the the yea year? r? $2.4 million
b.
Wha What wa was th the co company’s ne net ca cash flflow? $3.4 million
c.
What What was was the the com compa pany ny’s ’s net net ope opera rati ting ng pro profi fitt aft after er taxe taxes s (NO (NOPA PAT) T)? ? $3.0 million
d.
Wha What was was the co company any’s opera peratting cash flflow? ow? $4.0 million
e.
If ope opera rati ting ng cap capit ital al in in the the prev previo ious us yea yearr was was $24 $24 mil millilion on,, wha whatt was was the the company’s free cash flow (FCF) for the year? $2.0 million
f.
Wha What was was the co company any’s econom nomic va value add added ed? ? $500,000
As an an inst instit ituti utiona onall inve invest stor or payi paying ng a mar margi ginal nal tax tax rat rate e of 46%, 46%, your your afte after-t r-tax ax div divide idend nd
2
yield on preferred stock with a 16% before-tax dividend yield would be: 14.9% 4.
A 7% 7% coup coupon on bond bond issu issued ed by by the the sta state te of of New New Yor York k sel sells ls for $1,000 $1,000 and and thus thus prov provide ides s a 7% yield to maturity. For an investor in the 40% tax bracket, what coupon rate on a Carter Chemical Company bond that also sells at its $1,000 par value would cause the two bonds to provide the investor with the same after-tax rate of return? 11.67%
5.
A corpo corporat ration ion with a mar margin ginal al tax tax rate rate of of 46% 46% wou would ld rece receiv ive e what what AFTER AFTER-TA -TAX X YIE YIELD LD on a 12% coupon rate preferred stock stock bought at par? Answer: 11.172%
6.
You have have just just receiv received ed finan financi cial al infor informat mation ion for for the the past past two two years years for for Powe Powellll Panth Panther er Corporation: Income Statements Ending December 31 (millions of dollars) 2000 Sales $1,200.0 Operating Costs (excluding depreciation) 1,020.0 Depreciation 30.0 Earnings before interest and taxes $ 150.0 Less Interest expense 21.7 Earnings before taxes $ 128.3 Less taxes (40%) 51.3 Net income available to common equity $ 77.0 Common dividends $ 0.605
1999 $1,000.0 850.0 25.0 $ 125.0 20.2 $ 104.8 41.9 $ 62.9 $ 0.464
Balance Sheets Ending December 31 (millions of dollars) 2000 Cash and marketable securities $ 12 12.0 Accounts receivable 180.0 Inventories 180.0 Net plant and equipment 300.0 Total Assets $ 672.0
1999 $ 10 10.0 150.0 200.0 250.0 $ 610.0
Accounts payable Notes payable Accruals Long-term bonds Common stock (50 million shares) Retained earnings Total liabilities and equity a.
$ 108.0 67.0 72.0 $ 150.0 50.0 225.0 $ 672.0
What What is the the net net oper operat atin ing g pro profi fitt (N (NOPAT OPAT)) for for 2000 2000? ?
$
90.0 51.5 60.0 $ 150.0 50.0 208.5 $ 610.0
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$90,000,000 b.
What What are are the the amo amoun unts ts of net net ope opera rati ting ng wor worki king ng cap capit ital al for for 1999 1999 and and 200 2000? 0? $210,000,000 and $192,000,000
c.
What What are are the the amo amoun unts ts of tota totall ope opera rati ting ng capi capita tall for for 1999 1999 and and 2000 2000? ? $460,000,000 and $492,000,000
d.
Wha What is is free ca cash flow for 2000? $58,000,000
e.
How How muc much h did did the the firm firm rein reinve vest st in in itse itself lf ove overr the the acco accoun unti ting ng per perio iod? d? $16,500,000
f.
At the the pre prese sent nt tim time e (12/ (12/31 31/2 /200 000) 0),, how how larg large e a chec check k coul could d the the firm firm wri write te wit witho hout ut it bouncing? $12,000,000
7.
A firm firm's 's oper operat ating ing inco income me (EB (EBIT IT)) was was $400 $400 mill million ion,, their their depre depreci ciati ation on expen expense se was was $40 $40 million, and their increase in net investment in operating capital was $70 million. Assuming that the firm is in the 40% tax bracket, bracke t, what was their free cash flow? $170 million
8.
In its recent income statem tement ent, Smith Soft Softw ware Inc. repor ported $23 mi million of net net income, and in its year-end balance sheet, Smith reported $401 million of retained earnings. The previous year, its balance sheet showed $389 million of retained earnings. What were the total dividends paid to shareholders during the most recent year? $11.0 million 9.
Cox Cox Corp Corpora oratio tion n recen recently tly repor reported ted an EBI EBITD TDA A of of $58 $58 mil millilion on and and $7 $7 mil millilion on of of net net income. The company has $12 million interest expense and the corporate tax rate is 40.0% percent. What was the company's depreciation and amortization expense? $34.33 million
10.
Raving Ravings s Incor Incorpora porated ted recent recently ly repor reported ted net net incom income e of $5.4 $5.4 milli million. on. Its Its operating operating income income (EBIT) was $15 million, and its tax rate was 40 percent. What was the company’s interest expense? $6 million
11.
In its recent recent income income statem statement, ent, Smith Smith Softw Software are Inc Inc.. report reported ed payi paying ng $10 millio million n in dividends to common shareholders, and in its year-end balance sheet, Smith reported $419 million of retained earnings. The previous year, its balance sheet showed $404
4
million of retained earnings. What was the firm’s net income during the most recent year? $25.0 million 12.
Casey Casey Moto Motors rs rece recently ntly reported reported net inco income me of of $19 milli million. on. The firm's firm's tax rate was 40.0% and interest expense was $6 million. The company's after-tax cost of capital is 14.0% and the firm's total investor supplied operating capital employed equals $95 million. What is the company's EVA? $9.30 million
13.
Brooks Brooks Sisters Sisters'' operat operating ing inco income me (EBIT (EBIT)) is is $194 $194 milli million. on. The company company's 's tax tax rate rate is 40.0%, and its operating cash flow is $148.4 million. The company's interest expense is $39 million. What is the company's net cash flow? (Assume that depreciation is the only non-cash item in the firm's financial statements.) $125.0 million
14.
Valuable Valuable Inco Incorpor rporated ated’s ’s stoc stock k curre currentl ntly y sells sells for $45 $45 per share. share. The The firm firm has 20 20 milli million on share of common outstanding. The firm’s total debt equals $600 million and its common equity equals $400 million. What is the firm’s market value added? $500 million CHAPTER THREE PROBLEMS
1.
ABC, ABC, Inc Inc., ., sell sells s all all its its mer merch chand andis ise e on credi credit. t. It has has a profit profit marg margin in of 4%, 4%, an ave averag rage e collection period of 60 days, receivables of $150,000, total assets of $3 million and a debt ratio of 0.64. 0.64. What is the firm's firm's return on on equity? 3.33 percent
2.
The Smyt Smythe he Cor Corpo porat ratio ion's n's comm common on sto stock ck is is curr curren ently tly sell sellin ing g at $100 $100 per per shar share e whic which h represents a P/E ratio of 10. If the firm has 100 shares of common stock outstanding, a return on equity of 0.20, and a debt ratio of 0.67, what is its return on total assets? assets? 6.7 percent
3.
If Wink Winkler ler,, Inc. Inc.,, has has sale sales s of $2 $2 mill millio ion n per per year year (all (all cred credit it)) and and an ave averag rage e coll collec ectio tion n period of 35 days, what is its average amount of accounts receivable outstanding (assume a 360 day year)? $194,444
4.
5.
If a firm firm has total total inter interest est char charges ges of $10, $10,000 000 per per yea year, r, sal sales es of of $1 mil millilion on,, a tax tax rat rate e of 40%, and a net profit margin of 6%, what is the firm's times interest earned ratio? 11 times A fir firm m tha thatt has has an an equi equity ty mult multip iplilier er of of 4.0 4.0 wil willl hav have e a debt debt rat ratio io of: of: 0.75.
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6.
Give Given n the the follow following ing info informa rmati tion on,, calc calcul ulate ate the the mark market et pri price ce per per sha share re of of WAM, WAM, Inc Inc.: .: Earnings after interest and taxes Earnings per share Stockholders' equity Market/Book ratio
= = = =
$200,000 $2.00 $2,000,000 $2,000,00 0 0.20
$4.00 7.
A fire fire has has dest destroy royed ed a lar large ge per perce centa ntage ge of the the fina financ ncial ial recor records ds of of Hanso Hanson n Assoc Associat iates es.. You are charged with piecing together information in order to release a financial report. You have found the return on equity to be 18%. If sales were were $4 million, the debt ratio 0.40, and total liabilities $2 million, what was the return on assets? 10.8%
8.
Assu Assume me Conse Conserv rvati ative ve Corp Corpora orati tion on is 100% 100% equ equity ity financ financed. ed. Calc Calcula ulate te the retur return n on on equity given the following information: 1. 2. 3. 4. 5.
Earnings before taxes taxes = $2,000 Sales = $5,000 Dividend payout ratio = 60% Total asset turnover = 2.0 Applicable tax rate = 50% 40 percent
9.
You are cons conside ideri ring ng a new produ product ct for for your your firm firm to sell sell.. It shoul should d caus cause e a 15% 15% incr increas ease e in your profit margin but it will will also require a 50% increase in total assets. You expect to finance this asset growth entirely by debt. If the following ratios were computed before the change, what will be the new ROE if the new product is sold but sales remain constant? Profit margin = 0.10 Total asset turnover = 2.0 Equity multiplier =2 46 percent
10.
Johnstow Johnstown n Chemic Chemicals als,, Inc., Inc., has a curre current nt rati ratio o of 3.0, a quick quick ratio ratio of of 2.4, 2.4, and and an inventory turnover of 6. Johnstown's total assets are $1 million and its debt ratio is 0.20. (The firm has no long-term debt.) What is Johnstown's sales figure? $720,000
11.
Calcul Calculate ate the the mark market et pric price e of a share share of ABC, ABC, Inc. Inc.,, give given n the followi following ng inform informati ation: on: Stockholders' equity = $1,250; price/earnings ratio = 5; shares outstanding = 25; market/book ratio = 1.5. $75.00
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12.
Jamest Jamestown own,, Inc. Inc.,, has earnings earnings after after inte interest rest deducti deductions ons but before before taxe taxes s of $300. The company's before-tax times interest earned ratio is 7.00. Calculate the company's interest charges. $50.00
13.
The G. Hobb Hobbs s Comp Company any has has det determ ermin ined ed that that its its ret return urn on equi equity ty is is 15%. 15%. Mana Managem gemen entt is interested in the various components that went into this calculation. However, one of the accountants has misplaced the profit margin ratio. As a finance wizard, you know how to calculate the profit margin, given the following information: total debt/total assets = 0.35, and total asset turnover = 2.8. What is the profit margin? 3.48 percent
14.
Lowe Lowe & Compan Company y has a deb debtt ratio ratio of 0.5 0.5,, a capit capital al inte intensi nsity ty rati ratio o of 4, and and a profi profitt margin of 10%. The Board of Directors is unhappy with the current return on equity (ROE), and they think it could be doubled. This could be accomplished (1) by increasing the profit margin to 12% and (2) by increasing debt utilization. Total asset turnover will not change. What new debt ratio, along with the 12% profit margin, is required to double the ROE? 70 percent
15.
The Local Local Compa Company ny is a rela relativ tively ely small, small, privat privately ely owned owned firm firm.. In 1981 Local Local had had an after-tax income of $15,000, and 10,000 shares were were outstanding. The owners were trying to determine the equilibrium market value for Local's stock, prior to taking the company public. A similar firm that is publicly traded had a price/earnings ratio of 5.0. Using only the information given, estimate the market value of one share of Local's stock. $7.50
16.
Epsilon Epsilon Co.'s Co.'s records records have have recent recently ly been been destr destroye oyed d by fire. fire. Give Given n the the follow following ing bits bits of information saved from the inferno, determine Epsilon's net income for 1999. Return on equity 22% Assets/net worth 2.167 Profit margin 5.6% Total assets $650 million $
17.
66.00 million
Delta Delta Cor Corp. p. has has sales sales of of $300,0 $300,000, 00, a prof profit it mar margin gin of of 6.5 per percen cent, t, a tax tax rate rate of 15 15 percent, and annual interest charges of $7,500. What is Delta's times interest earned? 4.06
18.
Coas Coastal tal Pack Packagi aging ng ‘s ROE ROE las lastt year year was was only only 3 perc percent ent,, but its its man manage agemen mentt has developed a new operating operating plan designed to improve improve things. The new plan calls calls for a total debt ratio of 60 percent, which will result in interest charges of $300 per year. Management projects an EBIT of $1,000 on sales of $10,000, and it expects to have a total asset turnover ratio of 2.0. Under these conditions, the average tax rate will will be 30 percent. If the changes are made, what what return on equity will Coastal earn?
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24.5 percent 19.
Yohe Yohe Inc. Inc. has an ROA ROA of of 13.4% 13.4% and a 10% profit profit margi margin. n. The The compa company ny has has sale sales s equal to $5 million. million. What are the company's total assets? $3.73 million
20.
Yohe Inc. Inc. has has a current current ratio ratio of of 2, and a quick quick ratio ratio of 1.4. 1.4. Furt Furtherm hermore ore,, the the firm firm has has $1.5 million in current liabilities. Based upon this information, how much inventory is Yohe holding? $900,000
21.
U KNO, KNO, Inc. Inc. use uses s only only debt debt and comm common on equit equity y funds funds to finan finance ce its its asse assets ts.. This This past past year the firm's return on total assets was 13%. The firm financed 42% percent of its assets using debt. What was the firm's return on common equity? 22.41%
22.
Clev Clevela eland nd Corpor Corporati ation on has 17,49 17,490,0 0,000 00 shares shares of comm common on stoc stock k outst outstan andin ding, g, its its net income is $194 million, and its P/E ratio is 15.1. What is the company’s stock price? $167.49
23.
AAA's AAA's invent inventory ory turno turnove verr rati ratio o is 11.09 11.09 bas based ed on sal sales es of of $15,20 $15,200,0 0,000. 00. The The firm's current ratio equals 3.22 with current liabilities equal to $970,000. What is the firm's quick ratio? 1.81
CHAPTER FOUR PROBLEMS
1.
Inte Intere rest st rate rates s on oneone-ye year ar Trea Treasu sury ry sec secur urit itie ies s are are curr current ently ly 5.6 5.6 perc percent ent,, whil while e two-y two-year ear Treasury securities are yielding 6 percent. If the pure expectations theory is correct, what does the market believe will be the yield on one-year securities one year from
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now? 6.4 percent 2.
Inte Intere rest st rate rates s on four four-y -year ear Tre Treas asury ury secu securi riti ties es are are curr current ently ly 7 per percen cent, t, whil while e intere interest st rates on six-year Treasury securities are currently 7.5 percent. If the pure expectations theory is correct, what does the market believe that two-year securities will be yielding four years from now? 8.5 percent
3.
The real real risk risk-f -free ree rate rate of of int intere erest st is is 3 perce percent. nt. Infl Inflati ation on is is exp expec ected ted to be be 2 perce percent nt thi this s year and 4 percent during the next two two years. Assume that the maturity risk premium is zero. What is the yield yield on 3-year Treasury securities? 6.33 percent
4.
A Tre Treas asury ury bond bond that that matu matures res in 10 years years has a yie yield ld of of 6 perc percent ent.. A 1010-ye year ar corp corpora orate te bond has a yield of 8 percent. Assume that the liquidity premium on the corporate bond is 0.5 percent. percent. What is the default risk premium premium on the corporate corporate bond? 1.5 percent
5.
One-y One-year ear Trea Treasu sury ry secu securit rities ies yield yield 5 per perce cent. nt. The mark market et antic anticipa ipates tes that that 1 year year from from now, one-year Treasury securities will will yield 6 percent. If the pure expectations theory is correct, what should be the yield today for 2-year Treasury securities? 5.5 percent
6.
The real real ris riskk-fr free ee rate rate is 3 perc percent ent,, and and infla inflati tion on is is exp expect ected ed to to be 3 perce percent nt for for the the nex nextt 2 years. years. A 2-year Treasury security yields 6.2 percent. What is the maturity risk risk premium for the 2-year security? 0.2 percent
7.
The real real risk risk-f -free ree rate rate is is 3 perc percent ent.. Infl Inflati ation on is is exp expec ected ted to be 3 perc percent ent this this year, year, 4 percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.0005 X (t-1), where t = number of years to maturity, maturity, What is the nominal interest rate on a 7-year Treasury note? 6.8 percent
8.
Assu Assume me that that the the real real ris riskk-fre free e rate rate is is 2 per perce cent nt and and tha thatt the the matur maturit ity y risk risk premi premium um is zero. If the nominal rate of interest on 1-year bonds is 5 percent and that on comparable risk 2-year bonds is 7 percent, what is the 1-year interest rate that is expected for year two? 7 percent
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9.
You see see that that the the cur curre rent nt 30-d 30-day ay T-bi T-billll rate rate is 4.5%. 4.5%. You You are are told told by by a frien friend d who who works for an investment firm that the best estimates of the current interest rate premiums for relatively safe corporate firms is as follows: inflation premium = 2.1%; default risk premium = 1.4%. Based on this data, what is the real risk-free rate of return? 2.4%
10.
The real real risk-f risk-free ree rate rate of of intere interest st is is 3 perce percent. nt. Infl Inflatio ation n is expecte expected d to be be 5 perce percent nt this this coming year, jump to 6 percent next year, and increase to 7 percent the following year (Year 3). According to the expectations theory, what should be the interest rate on 3year, risk-free securities today? 9 percent
11.
Drongo Drongo Corpo Corporati ration’s on’s 4-year 4-year bonds bonds curr currentl ently y yiel yield d 8.4 percent. percent. The real real riskrisk-free free rate rate of interest, k*, is 2.7 percent and is assumed to be constant. The maturity risk premium (MRP) is estimated to be 0.1%(t - 1), where t is equal to the time to maturity. The default risk and liquidity premiums for this company’s bonds total 0.9 percent and are believed to be the same for all bonds issued by this company. If the average inflation rate is expected to be 5 percent for years 5, 6, and 7, what is the yield on a 7-year bond for Drongo Corporation? Corporation? 8.91 percent
12.
One-yea One-yearr Treas Treasury ury securit securities ies yield yield 6 percent percent,, 2-yea 2-yearr Treasu Treasury ry secu securit rities ies yield yield 6.5 percent, and 3-year Treasury securities yield 7 percent. Assume that the expectations theory holds. What does the market expect will be the yield on 1-year Treasury securities two years from now? 8 percent
13.
Assume Assume that that a 3-ye 3-year ar Treasu Treasury ry note note has no no matur maturity ity risk risk prem premium ium,, and and that that the the real real risk-free rate of interest is 3 percent. If the T-note carries a yield to maturity of 10 percent, and if the expected average inflation rate over the next 2 years is 8 percent, what is the implied expected inflation rate during Year 3? 5 percent
CHAPTER FIVE PROBLEMS
1.
An inv inves estor tor holds holds a dive divers rsifi ified ed port portfol folio io cons consis isti ting ng of of a $5,00 $5,000 0 inve invest stmen mentt in in each each of of 20 different common stocks. The portfolio beta is equal to 1.12. The investor has decided to sell a lead mining stock (beta = 1.0) at $5,000 net and use the proceeds to buy a like amount amount of a steel company stock stock (beta = 2.0). What is the new beta for the portfolio?
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1.17 2.
Cons Conside iderr the the foll follow owing ing infor informa mati tion on and and cal calcu culat late e the the requ requir ired ed rat rate e of retur return n for for the the Winkler Investment Fund. The total investment fund is $2 million. Stock ----A B C D
Investment ---------$ 200,000 300,000 500,000 1,000,000
Beta ---1.50 -0.50 1.25 0.75
The market required rate of return is 15% and the risk-free rate is 7 percent. 13.1 percent 3.
The Sandy Sandy Comp Company any has has dev develo eloped ped the the fol follow lowing ing data data rega regard rding ing a pro projec jectt to to add add new new distribution facilities: STATE PROBABILITY PROJECT RETURN MARKET RETURN 1 .3 0.01 0.10 2 .7 0.15 0.14 A.
W hat is the expected return on the project?
10.8%
B.
W hat is the standard deviation of the project returns?
0.0642
C.
W hat is the coefficient of variation of project returns?
0.594
D.
Wha What is is the covariance nce of of pro projject retur turns with ma market returns rns?
0.0012 0012
E.
What is the corr correl elati ation on coef coeffic ficien ientt betw between een the proje project ct retur returns ns and and the the mark market et returns? 1.00
4.
Calc Calcula ulate te the the requ requir ired ed rat rate e of return return for Manag Manageme ement nt,, Inc. Inc.,, ass assumi uming ng that that inve investo stors rs expect a 5% rate of inflation in the future. The real rate is equal to 3% and the market risk premium is 5%. Management has a beta of 2.0 and has historically historically returned an average of 15%. 18 percent
5.
Firs Firstt Inv Inves estm tment ent Trus Trustt is is a mutua mutuall fund fund inv inves esti ting ng in in the the com commo mon n sto stock ck of six six firm firms. s. The The firms, market value of shares held, and the beta of each stock are as follows: MARKET VALUE OF FIRM SHARES HELD BETA Ace Electronics $ 90 million 0.6 Bob's Industries 110 million 1.2 CBM International 60 million 0.7 Dave's Cen 130 million 1.8 Ed's Eatery 70 million 0.9 Space Deli 40 million 2.5 Total 500 million
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6.
A.
Calculate the beta be ta of the mutual fund.
1.25
B.
Suppose Rm = 16 percent and R f = 6 percent; what is the expected portfolio return? 18.5 percent
The follow following ing data data pert pertain ains s to to the the next next four four quest questio ions ns.. Stock Stocks s A and B hav have e ret return urns s and probability distributions as given below. PROBABILITY 0.25 0.30 0.25 0.20
STOCK A 6% 10% 4% 8%
STOCK B 8% 2% 6% 8%
A.
Calculate the expected expec ted returns for fo r Stocks A and B. 7.1% and 5.7%
B.
What What are are the the stan standa dard rd dev devia iati tion ons s of exp expec ecte ted d retu return rns s for for Stoc Stocks ks A and and B? 2.32% and 2.55%
C.
The The co covariance nce be betwee tween n St Stocks A and and B is is: -0.000367
D.
The The cor corre rela lati tion on coef coeffi fici cien entt bet betwe ween en Stoc Stocks ks A and and B is: is: -0.62
E.
Supp Suppos ose e you you wan wantt to hold hold a port portfo folilio o com compo pose sed d of 50% 50% of Sto Stock ck A and and 50% 50% of Stock B. What will be the the expected return (mean) and risk (standard deviation) of your portfolio? 6.4% and 1.07%
7.
You You are are man manag agin ing g a por portf tfol olio io of of 10 stoc stocks ks whic which h are are held held in in equ equal al amou amount nts. s. The The current beta of the portfolio is 1.64, and the beta o f Stock A is 2.0. If Stock A is sold, what does the beta of the replacement replacement stock have to be to have a new portfolio beta of 1.55? 1.10
8.
Give Given n the the foll follow owin ing g inf infor orma mati tion on conc concer erni ning ng ASSE ASSETS TS X and and Y: Possible Outcomes 1 2 3 4 5
Returns of Probability 0.10 0.20 0.40 0.20 0.10
Assets X 0.00 0.08 0.12 0.30 0.60
Y -0.04 0.10 0.12 0.14 0.16
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A.
What are the expected returns for ASSETS ASSET S X and Y given the above probabilities? 18.40 percent and10.80 percent
B.
What What is the the expe expect cted ed ret retur urn n of a por portf tfol olio io com compr pris ised ed of of 40 per perce cent nt of of an investor's wealth invested in ASSET X and 60 percent invested in ASSET Y? 13.84 percent
C.
What What are are the the stan standa dard rd dev devia iati tion ons s of the the ret retur urns ns of of the the two two secu securi riti ties es? ? 16.4 percent and 5.2 percent
D.
What What is is the the COVA COVARI RIAN ANCE CE betw betwee een n the the two two sec secur urit itie ies? s? 0.005488
E.
What What is is the the COR CORRE RELA LATI TION ON betw betwee een n the these se two two sec secur urit itie ies? s? 0.636
F.
What What is the the stan standa dard rd dev devia iati tion on of of a port portfo folilio o comp compri rise sed d of 40 40 perc percen entt of an an investor's wealth invested in ASSET X and 60 percent invested in ASSET Y? 8.93 percent
CHAPTER SIX PROBLEMS
1.
If you you buy buy a facto factory ry for $250,0 $250,000 00 and and the the ter terms ms are 20% 20% down down,, the the bala balance nce to be paid paid off over 30 years at a 12% rate of interest on the unpaid balance, what are the 30 equal annual payments? payments? $24,829
2.
An inv inves estor tor is cons conside iderin ring g the the purch purchas ase e of 20 acr acres es of land land.. His His anal analys ysis is is that that ifif the the land is used for cattle grazing, it will produce a cash flow of $1,000 per year indefinitely. If the investor requires a return of 10% on investments of this type, what is the most he would be willing to pay for the land?
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$10,000 3.
You start start savin saving g for for your your coll college ege educ educati ation. on. You You begi begin n col colle lege ge at at age age 18 18 and and you you wil willl need $4,000 per year at the end of each of the next 4 years. You will will make a deposit 1 year from today in an account which pays 6% compounded annually and an identical identical deposit each year until you start college. If a deposit of $1,987 will allow you to reach your goal, how old are you now? 12 years old
4.
On January 1, 1995, a graduate student developed a financial plan which which would provide enough money at the end of his graduate work (January (January 1, 2000) to open a business of his own. His plan was was to deposit $8,000 per year, starting immediately, immediately, into an account paying 10% compounded annually. His activities proceeded according to plan except that at the end of his third year he withdrew $5,000 to take a Caribbean cruise, cruise, at the end of the fourth year he withdrew $5,000 to buy a used Camaro, Camaro, and at the end of the fifth year he had to withdraw withdraw $5,000 to pay to have his dissertation dissertation typed. His account, at the end of the fifth year, will be less than the amount he had originally planned on by how much? $16,550
5.
You have have been been give given n the the follow following ing cash cash flow flows. s. What is the pres present ent value value (t = 0) if the discount rate is 12%? 0 1 2 3 4 5 6 --|----------|----------|----------|----------|----------|----------|---$0 $1 $2000 $2000 $2000 $0 -$2000 $3,276
6.
ABC ABC Cor Corpo porat ratio ion n has has been been enjoy enjoying ing a pheno phenomen menal al rate rate of grow growth th sin since ce its its incep inceptio tion n one year ago. Currently assets total $100,000. If growth continues at the current rate of 12% compounded quarterly, what will be total assets in 2 1/2 years? $134,390
7.
Char Charte terr Air Air is is con consi sider derin ing g the the purc purchas hase e of an air aircr craf aftt to suppl supplem ement ent its its cur curren rentt flee fleet. t. In estimating the impact of adding this craft to their fleet, they have developed the following cash flow analysis: End of year 1 2 3 4 5 6 7
-$1,000 $100,000 $100,000 $100,000 $100,000 $100,000 -$300,000
If the discount rate is 10%, what is the present value of these estimated flows?
14
$189,752 8.
Find Find the the pres present ent val value ue for for the the foll follow owing ing inc income ome strea stream m if the the int intere erest st rat rate e is 12 perc percent ent.. YEARS 1-4 5-10 11-15 A. B. C. D. E.
CASHFLOW $ 5,000 $ 7,500 $ 10,000
$56,776 $52,500 $44,740 $40,627 $65,257
F. G. H.
$45,379 $46,390 $57,911
$31,148.50 9.
You are thin thinki king ng abou aboutt buyi buying ng a car, car, and and a loca locall bank bank is will willing ing to lend lend you you $20, $20,000 000 to to buy the car. Under the terms of the loan, it will will be fully amortized over five years (60 monthly payments) and the nominal interest will will be 12 percent. What would be the monthly payment on the loan? $444.89
10.
You have have been been sav saving ing money money for the last last two two years years.. You You made made depo deposi sits ts of of $100 $100 on January 1, 1981, and July 1, 1981, in a savings account paying 10% compounded semi-annually. On January 1, 1982, the bank increased the interest rate paid on savings accounts to 12%, annual compounding. You made a third $100 deposit on April 1, 1982. How much will be in your account on January 1, 1 , 1983? $349.95
11.
12.
You plan plan on work workin ing g for 10 10 years years and and then then leav leaving ing for for the the Ala Alask skan an “bac “back k count country ry”. ”. You You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5 years. In addition, your family has given you a $5,000 graduation gift. If you put the the gift and your future savings in an account paying 8 percent compounded compounded annually, what will your “stake” be when you leave for the wilderness 10 years hence? $31,148 If $100 $100 is is plac placed ed in an an accoun accountt that that earns earns a nomi nominal nal 4%, 4%, com compou pounde nded d quarte quarterly rly,, for 5 years, what will it be worth in 5 years? $122.02
13.
Hess Hess Dis Distr tribu ibuto tors rs is is finan financi cing ng a new new truc truck k with with a loan loan of of $10,00 $10,000 0 to be repa repaid id in 5 annual installments installments of $2,505. W hat annual interest interest rate is the company paying? paying? 8%
14.
You hav have e decide decided d to depos deposit it your your scho scholar larsh ship ip mone money y ($1,00 ($1,000) 0) in a savi savings ngs acc accoun ountt paying 8% interest, compounded quarterly. Eighteen months later, you decide to go to the mountains rather than school and you close out your account. How much money
15
will you receive? $1,126 15.
The pre presen sentt value value (t = 0) of of the fol follow lowing ing cas cash h flow flow stre stream am is is $6,97 $6,979. 9.04 04 when when discounted at 13% annually. What is the value of the MISSING (t = 2) cash flow? 0 1 2 3 4 ---|------------|----------|-----------|-----------|----$0 $ 900 $? $2,100 $1,800 $ 4,627
17.
You want want to to set set up a trus trustt fund. fund. If you you make make a paymen paymentt at the the end end of each each year year for for twenty years and earn 10% per year, how large must your annual payments be so that the trust is worth $100,000 at the end of the twentieth year? $1,745.96
18.
Twel Twelve ve year years s ago ago you you bought bought a $25 sto stock ck whic which h is now wort worth h $78.4 $78.47. 7. Assu Assumi ming ng that that the stock paid no dividends, the rate of return on your investment was: 10%
19.
Start Startin ing g on Janua January ry 1, 1991, 1991, and and then then on each each Janua January ry 1 unti untill 2000 2000 (10 pay payme ments nts), ), you will make payments of $1,000 into an investment which yields yields 10 percent. How much will your investment be worth on December 31 in the year 2010? $45,468.26
20.
Your Your 69-y 69-year ear old old aunt aunt has has sav saving ings s of $35, $35,000 000.. She has has made made arran arrangem gement ents s to enter enter a home for the aged on reaching reaching the age of 80. Your aunt aunt wants to decrease decrease at a constant amount each year for ten years, with with a zero balance remaining. How much can she withdraw each year year if she earns 6 percent annually on her savings? Her first withdrawal would be one year from today. :. $4,755
21.
A rich rich aunt aunt prom promis ises es you you $35,00 $35,000 0 exact exactly ly 5 year years s after after you you gradua graduate te from from coll college ege.. What is the value of the promised $35,000 $35,000 if you could negotiate payment payment upon graduation? Assume Assume an interest rate rate of 12 percent. percent. $19,860.05
22.
In pla planni nning ng to buy buy a hom home e you you are putti putting ng $2,5 $2,500 00 of your your end end of year year bonu bonus s in an an account that earns 10 percent. If your first payment begins in exactly one year, year, how much of a down payment will you be able to afford at the end of 4 years? $11,602.50
23.
Fred Fred Johns Johnson on is is reti retirin ring g one one year year from from today today.. How much much shoul should d Fred Fred current currently ly have in a retirement account earning 10 percent interest to guarantee withdrawals of $25,000 per year for 10 years?
16
$153,615 24.
If you you were were promi promise sed d 10 annual annual pay payme ments nts of of $4,000 $4,000 star starti ting ng wit with h the firs firstt paymen paymentt today, compute the present value of these flows if your opportunity cost is 7 percent. $30,060.80
25.
Find Find the present present value value for the foll followi owing ng income income stre stream am ifif the interes interestt rate rate is is 12 percent. percent. YEARS 1-4 5-10 11-15
CASHFLOW $ 500 $ 800 $1,200
$5,001.82 26.
You place place $5, $5,000 000 in in your your cred credit it unio union n at an an annua annuall inte interes restt rate rate of of 12 perc percent ent compounded monthly. mo nthly. How much will will you have in 2 years if all interest remains in the accounts? $6,348.50
27.
You have just just had had your your thir thirtie tieth th birthda birthday. y. You have two two chil children dren.. One will will go to college college 8 years from now and require four beginning-of-year beginning-of-year payments for college expenses of $12,000, $13,000, $14,000, and $15,000. The second child child will go to college college 14 years from now and require four beginning-of-year beginning-of-year payments of $16,000, $17,000, $18,000, and $19,000. In addition, addition, you plan plan to retire in in 25 years. You want want to be able to withdraw withdraw $60,000 per year (at the end of each year) from an account throughout your retirement. You expect to live 25 years beyond retirement. The first withdrawal will will occur on your fifty-sixth birthday. What equal, annual, end-of-year amount must you save for each of the next 25 years to meet these goals, if all savings savings earn a 13 percent annual rate of return? $ 6,546
28.
Find Find the the prese present nt value value of of the cas cash h flow flows s show shown n using using a disc discoun ountt rate rate of 9 perc percent ent.. YEAR 1-5 6 7 8-16 17-20
CASHFLOW $150/yr. 200 250 150/yr. 300/yr. $ 1,576.20
29.
Acco Accordi rding ng to a loca locall depart departmen mentt store, store, the the stor store e charge charges s custo custome mers rs 1% per per mont month h on the outstanding outstanding balances of their charge accounts. accounts. What is the effective annual rate on such customer credit? Assume the store recalculates your account balance at the end of each month.
17
12.68% 30.
Your Your bank bank has has offer offered ed you you a $15, $15,000 000 loan loan.. The The term terms s of the the loan loan req requi uire re you you to to pay pay back the loan in five equal annual installments of $4,161.00. The first payment will be made a year from today. today. What is the effective rate of interest interest on this loan? :
31.
12%
You have have purcha purchased sed a new new sai sailb lboat oat and and have have the the optio option n of paying paying the the enti entire re $8,00 $8,000 0 now or making equal, annual payments for the next 4 years, the first payment due one year from now. If your time value of money is 7 percent, what would be the largest amount for the equal, annual payments that you would be willing to undertake? $2,362.00
32.
A firm firm purc purchas hases es 100 100 acres acres of land land for $200,0 $200,000 00 and agre agrees es to rem remit it twe twent nty y equal equal annual installments installments of $41,067 each. What is the true annual interest interest rate on this loan? 20 percent
33.
Thirty Thirty years years ago, ago, Jes Jessi sie e Johnso Johnson n bought bought ten ten acres acres of of land land for for $500 $500 per acr acre e in what what is is now downtown Houston. If this land grew in value at a 10 percent per annum rate, what is it worth today? $ 87,245
34.
If you you put you yourr money money in a bank bank offe offerin ring g 12 perc percent ent comp compoun ounded ded quart quarter erly ly,, how muc much h will $1,044 grow to in five years? : $1,885.58
35. 36.
What is is the the future future val value ue of $1,2 $1,250 50 compo compound unded ed at an 8 perc percent ent rat rate e for for ten ten years years? ? $2,698.63 James James Streets Streets'' son son Haro Harold ld is is five five years years old today. today. Harold Harold is already already making making plans plans to go to college on his eighteenth birthday and his father wants to start putting away money now for that purpose. Street estimates that Harold will need $14,000, $15,000, $15,000 , $16,000, and $17,000 for his freshman, sophomore, junior, and senior years. He plans on making these amounts available to Harold at the beginning of each of these years. Street would like to make twelve deposits (the first of which would be made on Harold's sixth birthday, 1 year year from now) in an account earning 12 percent. He wants the account to eventually be worth enough to pay for Harold's college expenses. expenses. Any balances remaining in the account will continue to earn 12 percent. How much will will Street have to deposit in this planning account each year to provide for Harold's education? $2165
37.
In your your analys analysis is of of DBM DBM Corpo Corporati ration on you you find find that that the the curre current nt earni earnings ngs per share share are are $5.00 per share and most analysts are projecting the earnings per share to grow at a 12 percent rate annually. annually. What can you expect the earnings per share share of this firm to be in 7 years?
18
$11.06 38.
Your Your grand grandmot mother her is is thri thrilllled ed that that you you are going going to to colleg college e and plans plans to to reward reward you you at graduation with a Porsche Turbo automobile. She would like to set aside an equal amount at the completion completion of each of your college years years from her meager pension. pension. If her account earns 12 percent and a new Porsche will cost $50,000, how much will she deposit each year? Assume her first deposit is in exactly exactly one year. $10,462.44
39.
Sellzar Sellzar Corpora Corporation tion current currently ly has has sales sales of $100 $100 millio million n and its market marketing ing depart department ment is projecting sales to be $800 million in 4 years. years. What rate of growth in sales are the the marketing people projecting? 68%
40.
Suppos Suppose e that that a local local savi savings ngs and and loan loan asso associ ciati ation on adver adverti tise ses s a 6 percent percent annu annual al rate rate of interest interest on regular accounts, accounts, compounded monthly. monthly. What is the effective annual percentage rate of interest paid by the savings and loan? 6.16%
41.
Greg Greg Perry Perry,, UTEP' UTEP's s renow renowned ned comp compute uterr jock, jock, is gradu graduati ating ng in one one year year and plans plans to to start his own own computer firm, namely Perry's Perry's Periphals, Inc. Being a science fiction buff, Greg is planning to start his firm using $50,000 he earned as a trombone player in the Bits and Discs Jazz Band during college and retire in 20 years in order to take the first Intergalactic Space Shuttle trip at an estimated estimated cost of $10.5 million. million. When Greg returns to earth 10 years thereafter, thereafter, he plans to live off an annuity of $300,000 per year, starting starting on the day of his return. return. This annuity annuity was funded when he left on his space journey and and is earning interest interest at 12 percent per year. year. But one of the side effects of the space shuttle program has been that every traveler dies exactly 20 years from the day of return. Calculate the growth rate of Perry's Periphals that will make Greg's long-range plans possible. 31.1 percent
42.
Jason Jason and and Brya Bryan n McNut McNuttt are are pres presentl ently y 3 and 5 years years old. old. Their Their paren parents ts are are planning planning to send them to college college at age 18 at a cost of $10,000 per year for each. How much must must the parents contribute contribute annually to a college fund to ensure the boys' college education if the interest rate is 12 percent compounded annually? annua lly? The payments start in one year and end when the younger brother starts college. $2,057
43.
If you you have have $5,4 $5,436 36 in in an acc accoun ountt that that has has been been paying paying an an annua annuall rate rate of of 10%, 10%, compounded continuously, continuously, since you deposited some funds 10 years ago, how much was the original deposit? $2,000
44.
For a 10 year year deposi deposit, t, what what annual annual rate rate payable payable semi-a semi-annua nnually lly will will produ produce ce the the same same effective rate as 4% compounded continuously?
19
4.04 percent 45.
How How much much sho should uld you you be wil williling ng to pay pay for for an acco account unt tod today ay that that wil willl have have a value value of of $1,000 in 10 years under continuous compounding compounding if the nominal rate is 10%? $368
46.
Your Your firm firm has has rec recent ently ly borr borrow owed ed $100,0 $100,000 00 from from a loca locall bank bank at an an intere interest st rate rate of of 10 percent. The loan is to be repaid in 5 equal, end-of-year payments. The following is a partial amortization schedule for the loan. Principal Interest Reduction
Year Payment 0 1 $ 26,380 $ 10,000 $ 16,380 2 $ 26,380 $ 8,362 $ A 3 $ 26,380 $ B $ 19,820 4 $ 26,380 $ 4,578 $ 21,801 5 $ 26,380 $ 2,398 $ 23,981 A.
Balance $ 100,000 $ 83,620 $ 65,602 $ 45,783 $ 23,981 $ 0
The missing value for the Principal Reduction in the second year (labeled A) is: $ 18,018
B.
The miss missin ing g valu value e for for the the Inte Interes restt Pay Payme ment nt in in the the thir third d yea yearr (lab (labele eled d B) is: is: $ 6,560
47.
You are valuing valuing an inve investm stment ent that will will pay pay you you $24,00 $24,000 0 per year year for the firs firstt 6 years, years, $28,000 per year for the next 10 years, and $54,000 per year the following following 14 years (all (all payments are at the end of each year). If the appropriate annual discount rate is 6.00%, what is the value of the investment to you today? $460,878 CHAPTER SEVEN PROBLEMS
1.. 1..
Calc Calcula ulate te the the pri price ce of of a 10 year year bond bond pay paying ing a 6 perc percen entt annua annuall coupo coupon n (half (half of the the 6 percent semiannually) on a face value of $1,000 if investors can earn 8 percent on similar risk investments. $863.70
2.
A maj major or auto auto man manufa ufact cture urerr has has exp experi erienc enced ed a mark market et re-e re-eva valua luati tion on lat lately ely due to a number of lawsuits. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8% (paid semiannually). The required rate has now risen to 16%. At what price can these the se securities be purchased purch ased on the market? $549.71
3.
The The cur curre rent nt mark market et pric price e of a Jon Jones es'' Com Compa pany ny bon bond d is $1,2 $1,297 97.5 .58. 8. A 10% 10% coup coupon on interest interest rate is paid semi-annuall semi-annually, y, and the par value is equal to $1,000. $1,000. What is the YTM (on an annual basis) if the bonds mature 10 years from today?
20
6 percent 4.
Comm Commonw onweal ealth th Compa Company ny has 100 bonds bonds outst outstand anding ing (mat (matur urit ity y value value = $1,000 $1,000). ). The The required rate of return on these bonds is currently 10%, and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond. What is the annual annual coupon interest interest rate? rate? 4% percent
5.
You You hav have e jus justt bee been n offe offere red d a bon bond d for for $84 $847. 7.88 88.. The The cou coupo pon n rate rate is 8%, 8%, pay payab able le annually, and interest rates on new issues of the same degree of risk are 10%. You want to know how many more interest payments you will receive, but the party selling the bond cannot remember. Can you help him out? 15
6.
Ford Ford and GM have have sim simililar ar bond bond issu issues es outst outstan andin ding. g. The The Ford Ford bond bond has inte interes restt payments payments of $80 paid annually and matures matures in the year 2002 (20 years from today). The GM bond has interest payments of $80 paid semiannually and also matures in the year 2002. If the required rate of return (kd) is 12%, what is the difference in current selling price of the two bonds? $2.18
7.
Acme Acme Produ Product cts s has has a bond bond outst outstand anding ing with with 8 year years s rem remai ainin ning g to to matu maturi rity ty and a coupon rate of 5% paid semiannually. If the current market market price is $729.05, what is the yield to maturity? 10 percent
8.
Rece Recentl ntly, y, TLE, TLE, Inc. Inc.,, filed filed bankru bankruptc ptcy y pape papers. rs. The firm firm was was reorga reorganiz nized ed as as DL, DL, Inc. Inc.,, and and the court permitted permitted a new indenture on an outstanding outstanding bond issue to be put into effect. The issue has 10 years years to maturity and a coupon rate of 10%, paid annually. The new agreement allows the firm to pay no interest for 5 years and then at maturity to repay principal and any unpaid interest (no interest on the unpaid interest). If the required return is 20%, what should such bonds sell for in the market today? $362.44
9.
In ord order er to to asses assess s accu accurat rately ely the capita capitall stru struct cture ure of a fir firm, m, itit is neces necessa sary ry to to conv convert ert the balance sheet to a market value basis. The current balance sheet is as follows: Long-term debt (bonds) Preferred stock Common stock ($10 par) Retained earnings Total debt and equity
$10,000,000 2,000,000 10,000,000 4,000,000 ----------$26,000,000
The bonds mature in 10 years. years. Interest is payable semiannually and the yield to maturity
21
is 12%. The coupon rate is 4 percent. What is the current market value of the firm's debt? $5.412 million 10.
Calc Calcula ulate te the the yield yield to to matur maturit ity y (on (on an annual annual basi basis) s) of of an 8 percen percentt coupon coupon,, 10-ye 10-year ar bond that pays interest semiannually if its price is now $770.60. 12 percent
11.
You are the the owner owner of 100 100 bond bonds s issu issued ed by Midte Midterm rm Corp Corpora orati tion. on. These These bonds bonds have have 8 years remaining remaining to maturity, maturity, an annual coupon coupon payment of $80, and a par value of $1,000. Unfortunately, Midterm is on the brink of bankruptcy, and the creditors, including including yourself, have agreed to a postponement of the next 4 interest payments. payments. The remaining interest payments payments will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6% and will be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is is now 28%. What is the present value value of each bond? $266.89
12.
The XYZ XYZ Comp Company any rec recen ently tly issu issued ed a 20-y 20-year ear,, 7 perce percent nt semi semiann annual ual coup coupon on bond bond at par. After three months, the market interest interest rates on similar bonds increased to 8 percent. At what what price should the bonds sell? $918.88
13.
IBX IBX has has a bond bond issu issue e outst outstand anding ing tha thatt is cal calla labl ble e in three three year years s at a 5 perc percent ent cal calll premium. premium. The bond pays a 10 percent annual coupon and has a remaining remaining maturity maturity of 23 years. If the current market price is $1000, than what is the yield to call? 11.48 percent CHAPTER EIGHT PROBLEMS
1.
The DAP DAP Com Compan pany y has has deci decided ded to make make a maj major or inves investme tment nt.. The The inv invest estmen mentt wil willl require a substantial early cash out-flow, and inflows will be relatively late. As a result, it is expected that the impact on the firm's earnings for the first 2 years will be a negative growth of 5% annually. Further, it is anticipated that the firm will then experience 2 years of zero growth after which it will begin a positive annual sustainable growth of 6%. If the firm's cost of capital is 10% and its current dividend (D 0) is $2 per share, what should be the current price per share? $38.47
2.
The Radle Radley y Comp Company any has deci decided ded to undert undertak ake e a larg large e new new proje project ct.. Conse Conseque quentl ntly, y, there is a need for additional additional funds. The financial financial manager decides to issue issue preferred stock which which has a stated dividend dividend of $5 per share and a par value of $30. If the required return on this stock is currently 20%, what should be the stock's current market value? $25
22
3.
SNG' SNG's s stoc stock k is is sel selliling ng for for $15 per shar share. e. The firm' firm's s inc incom ome, e, ass asset ets, s, and stoc stock k pri price ce have been growing at an annual 15% rate and are expected to continue continue to grow at this rate for 3 more years. No dividends have been declared as yet, but the firm intends to declare a $2.00 dividend dividend at the end of the last year of its supernormal supernormal growth. growth. After that, dividends are expected to grow at the firm's normal growth rate of 6%. The firm's required rate of return is 18%. You should: Sell the stock; it is overvalued by $3.03.
4.
BBP, BBP, Inc Inc., ., has exper experie ience nced d a rece recent nt resurg resurgenc ence e in busine business ss as it has has gaine gained d new new national identity. Management is forecasting rapid growth over the next 4 years years (annual rate of 15%). After that, it is expected that the firm will will revert to its historical growth rate of 2% annually. annually. The last dividend dividend paid was $1.50 per share, share, and the required return is 10%. What is the current price per share, assuming equilibrium? $29.51
5.
The Club Club Auto Auto Par Parts ts Compa Company ny has just just rece recentl ntly y been been organ organiz ized. ed. It is expec expected ted to experience no growth for the next 2 years as it identifies its market and acquires its inventory. However, Club will will grow at an annual rate of 5% in the third and fourth years and, beginning with the fifth year, should attain a 10% growth rate which it will sustain thereafter. The last dividend paid was $0.50 per share. Club has a cost of capital of 12%. What should be the present price per share of Club common stock? $20.84
6.
7.
A sha share re of of DRV, DRV, Inc. Inc.,, sto stock ck paid paid a divi dividen dend d of $1.50 $1.50 las lastt year year,, and and the the div divide idend nd is is expected to grow at a constant constant rate of 4% in the future. The appropriate appropriate rate of return on this stock is believed to be 12%. What should the stock sell for today? $19.50 The Pet Pet Com Compan pany y has has rec recent ently ly disc discov overe ered d a typ type e of rock rock whic which, h, when when cru crushe shed, d, is is extremely absorbent. It is expected that the firm will will experience (beginning now) an unusually high growth rate (20%) during the period (3 years) when it has exclusive rights to the property where where this rock can be found. However, beginning with the fourth year the firm's competition will have access to the material, and from that time on the firm will assume a normal growth growth rate of 8% annually. During the rapid growth period, the firm's dividend payout ratio will be relatively low (20%), to conserve funds for reinvestment. However, the decrease in growth will be accompanied by an increase in dividend payout to 50%. Last year's earnings were were $2.00 per share (E0) and the firm's cost of equity is 10%. What should be the current price of the common stock? stock? $71.68
8.
IT&M IT&M,, Inc. Inc.,, a large large congl conglome omerat rate, e, has has decide decided d to to acq acqui uire re anot anothe herr firm firm.. Analy Analyst sts s are are forecasting that there will be a period (2 years) of extraordinary growth (20%) followed by another 2 years of unusual growth (10%), and that finally the previous growth pattern of 6% annually will resume. If the last dividend was $1 per share and the required return is 8%, what should the market price be today? $73.74
23
9.
A sha share re of of DRV, DRV, Inc. Inc.,, sto stock ck paid paid a divi dividen dend d of $1.50 $1.50 las lastt year year,, and and the the div divide idend nd is is expected to grow at a constant constant rate of 4% in the future. The appropriate appropriate rate of return on this stock is believed to be 12%. Suppose DRV stock were selling for $25 today. What would be the implied implied value of ks , assuming the other data remain the same? 10.24 percent
10.
The Canni Canning ng Com Compan pany y has has been been hit hit hard hard due due to to inc increa reased sed compe competit tition ion.. The The company's analysts predict that earnings (and dividends) will decline at a rate of 5% annually into into the foreseeable foreseeable future. Assume that that ks = 11% and D0 = $2.00. What will will be the price of the company's stock in three years? $10.19
11.
IBM is current currently ly sellin selling g at at $65 $65 per share. share. Next Next year' year's s divi dividend dend is expected expected to be $2.60. $2.60. If investors on this particular day expect a return of 12% on their investment, what do they think IBM's growth rate will be? 8 percent
12.
The MM Comp Company any has fall fallen en on hard hard tim times es.. Its Its mana managem gement ent expec expects ts to to pay pay no dividends for the next 2 years. However, the dividend for Year 3 (D3) will be $1.00 per share, and it is expected to grow at a rate of 3% in Year 4, 6% in Year 5, and 10% in Year 6 and thereafter. If the required return for MM Co. is 20%, what is the current equilibrium price of the stock? $6.34
13.
Your brotherbrother-inin-law law,, a stock stockbrok broker er at Inve Invest, st, Inc., Inc., is is tryi trying ng to sell sell you you a stock stock with with a current market price of $20. The stock had a last dividend (D0) of $2.00 and a constant growth rate of 8%. Your required return on this stock is 20%. From a strict valuation standpoint, you should: Not buy the stock; it is overvalued by $2.00.
14.
Negat Negativ ive e Limi Limited ted is exp expect ected ed to grow grow for for four four years years at a rate rate of 50 per perce cent. nt. After After four four years, the product fad is expected to decline, and Negative will grow at a negative growth rate of 5 percent. percent. Negative Negative currently pays pays a dividend of $1.00 per share and stockholders stockholders have a required required rate of return of 18 percent. What should be the market value for a share of Negative Limited stock? $18.34
15.
Assu Assume me the the firm firm has has been been grow growing ing at at a 15% 15% annua annuall rate rate and is is expec expected ted to to conti continue nue to to do so for 3 more years. At that time, growth is expected to slow to a constant 4% rate. The firm maintains a 30% payout ratio, and this year's retained earnings were $1.4 million. The firm's beta is 1.25, the risk-free rate is 8%, and the market risk premium is 4%. If the market is in equilibrium, what is the market value value of the firm's common equity (1 million shares outstanding)?
24
$9.16 million 16.
Dexter, Dexter, Inc., Inc., has has just just paid a divide dividend nd of $2.00. $2.00. Its stock stock is is now now selli selling ng for $48 per per share share.. The firm is half as volatile as the market. The expected return on the market is 14% and the yield on U.S. Treasury bonds is 11%. If the market is in equilibrium, what rate of growth is expected? 8 percent
17.
Given Given the the follo followin wing g informa informatio tion, n, calc calcula ulate te the the expect expected ed capita capitall gains gains yield yield for for Bimlo Bimlo Bottle Caps; beta = 0.6; k m = 15%; Rf = 8%; D1 = $2.00; P0 = $25.00. Assume the stock is a constant growth stock and is in equilibrium. 4.2 percent
18.
XYZ XYZ stoc stock k is is cur curren rently tly paying paying a div divide idend nd of $2.00 $2.00 per per share share (D0 = $2) and is in equilibrium. The company has a growth rate of 5% and beta equal to 1.5. The required rate of return on the market is 15%, and the risk-free rate is 7%. XYZ is considering a change in policy that will will increase its beta coefficient to 1.75. If market conditions remain unchanged, what new growth rate will cause the common stock price of XYZ to remain unchanged? 6.76 percent
19.
Union Union Paper' Paper's s stoc stock k is is curre currently ntly in equilib equilibriu rium m sell selling ing at $30 per share. share. The firm firm has has been experiencing a 6% annual growth rate. Earnings per share share (E0) were $4.00 and the dividend payout ratio is 40%. The risk-free rate is 8% and the market risk premium is 5%. If systematic risk risk increases by 50%, all other factors remaining constant, the stock price will increase/decrease by: -$7.31
20.
Charte Charterr Oil Company Company is current currently ly sell selling ing at at its its equil equilibr ibrium ium price price of $100 per per share share.. The beta coefficient currently is 2. The risk-free rate is 10%. The following events will will soon occur: (1) top management will lower Charter's beta to 1.2 by investing in several low risk projects; (2) the Federal Reserve Board will reduce the money supply causing the inflation premium to be reduced by 3 percentage points; and (3) decreased world stability due to global politics will cause the market risk premium to increase 2 percentage points to 5%. The company has a constant growth rate of 5%. What will be the new equilibrium price for a share of Charter Oil common stock after the above events have taken place? (Assume the expected dividend will not change.) $137.50
21.
Wheeler Wheeler,, Inc., Inc., is is prese presentl ntly y in a stage stage of abno abnorm rmal ally ly high high grow growth th becaus because e of the exce excess ss demand for widgets. The company expects earnings and dividends to grow at a rate of 20% for the next 4 years, after which time there will be no growth in earnings and dividends. dividends. The company's company's last last dividend dividend was $1.50. Wheeler has a beta of of 1.6, the return on the market is currently 12.75%, and the risk-free rate is 4%. What should shoul d be the current price per share of common stock? $15.17
25
22. You are are given given the the followin following g data: 1. 2. 3. 4. 5.
The risk-free rate is 0.05. The The req requi uire red d re return on on the the market is is 0. 0.08. 08. The The expe expect cted ed grow growth th rate rate for for the the fifirm is 0.04 0.04.. The The la last div diviiden dend pai paid d wa was $0 $0.80 .80 pe per sh share. re. Beta is 1.3.
Now assume the following changes occur: 1. 2. 3. 4.
The The inf infla lati tion on pre premi mium um dec decreas reases es by by the the amo amoun untt of 0.0 0.01. 1. An inc incre reas ased ed deg degre ree e of ris risk k ave avers rsio ion n caus causes es the the req requi uire red d retu return rn on on the the market market to go to 0.10 after adjusting for the changed inflation premium. premium. The The ex expecte ected d gro grow wth rate increas rease es to to 0. 0.06. 06. Beta rises to 1.5.
What will be the change in price per share assuming the stock was in equilibrium before the changes? -$4.87 23.
You are are cons conside ideri ring ng buying buying com commo mon n stock stock in in Grow Grow On, Inc Inc.. You You have have calcu calcula lated ted that that the firm's free cash flow was $7.60 million last year. You project that free cash flow will grow at a rate of 5.0% per year indefinitely. The firm currently has outstanding debt and preferred stock with a total market value of $22.23 million. The firm has 2.94 million shares of common stock outstanding. If the firm's cost of capital is 19.0%, what is the most you should pay per share for the stock now? $11.83
24.
Due to the the highly highly special specialized ized nature nature of the the electr electronic onic indust industry, ry, Borrett Borrett Indust Industrie ries s inves investt a lot of money in R&D on prospective products. Consequently, it retains all of its earning and reinvests them into the firm. At this time, Borrett does not any plans to pay dividends in the near future. A major pension fund is interested interested in purchasing Borrett's Borrett's stock, which is traded on the NYSE. The treasurer for the pension fund has done research research on the company and has estimated estimated Borrett's free cash flow for the next four years as follows: $3 million, $6 million, million, $10 million and $15 million. million. After the fourth year, free cash flow is projected to grow at a constant 7 percent. Borrett's WACC is 12 percent, it has $60 million of total debt and preferred stock and 10 million shares of common stock. A.
What is the present value of Borrett's free cash flows during the t he next four years? $24,112,308
B.
Wha What is is the compan pany's te terminal va value? ue? $321,000,000
C.
Wha What is is the the tot total value of the fifirm to today day? $228,113,612
26
D.
Wha What is is Bor Borrett's t's price per share? re? $16.81
25.
Assu Assume me that that today today is is Dece Decembe mberr 31, 2000 2000 and and that the the foll follow owing ing infor informat mation ion appl applie ies s to Vermeil Airlines: A. B. C. D. E. F. G. H. I.
After-tax operating oper ating income [EBIT(1-t)] for 2001 is expected to be $500 million. The compa company ny's 's dep deprec reciat iation ion expen expense se for for 2001 2001 is expec expected ted to be $100 $100 mil millilion on.. The compa company ny's 's capi capital tal expen expendit diture ures s for for 2001 2001 are are exp expec ected ted to be be $200 $200 mil millilion on No chang change e is is exp expect ected ed in in the the compa company ny's 's net net opera operati ting ng work working ing capi capital tal.. The The comp compan any' y's s free free cas cash h flow flow is is expe expect cted ed to to grow grow at a con const stan antt rate rate of of 6 percent per year. The The co compan pany's co cost of of eq equit uity is is 14 14 pe percent. nt. The co company's WA WACC is is 10 10 pe percent. The The mar marke kett val value ue of the the com compa pany ny's 's debt debt is $3 bill billio ion. n. The The com compa pany ny has has 200 200 mil million lion share hares s of of sto stoc ck out outst stan andi ding ng..
Using the free cash flow approach, what should the company's stock price be today? $35.00 per share
CHAPTER NINE PROBLEMS
1.
The chie chieff finan financia ciall offic officer er of of Port Portla land nd Oil Oil has has giv given en you you the the ass assig ignme nment nt of of dete determ rmin ining ing the firm's marginal cost cost of capital. The present capital structure which is is considered optimal, is: Book Value Market Value Debt $ 50 million $ 40 million Preferred Stock 10 million 5 million Common Equity 30 million 55 million Total $ 90 million $ 100 million The anticipated financing opportunities are these: Debt can be issued with a 15 percent before-tax cost. Preferred stock will be $100 par, carry a dividend of 13 percent, and can be sold to net the firm $96 per share. share. Common equity equity has a beta of 1.20, the return on the market is 17 percent, and the risk-free rate is 12 percent. If the firm's tax rate is 40 percent, what is its marginal cost of capital? 14.2 percent
2.
Sili Silicon con Corp. Corp. rece recentl ntly y iss issue ued d 10-y 10-year ear,, 12 perce percent nt coup coupon on bond bonds s at par par val value. ue. Sili Silico con' n's s
27
beta is 0.6; the optimal capital structure contains 45 percent debt/55 percent equity; and the marginal tax rate is is 40 percent. If the expected return on the market market is 16 percent and the treasury bill rate is 9 percent, estimate Silicon's weighted average cost of capital. 10.5 percent 3.
Jeffe Jefferso rson n requi requires res $15 mill million ion to fund fund its its curr curren entt year year’s ’s capi capita tall proj projec ects ts.. Jeffe Jefferso rson n will will finance part of its needs with $9 million in internally generated funds. The firms’ common stock market price is $120 per share. The firm’s last dividends dividends was $5 per share and is expected to grow at a rate of 11 percent annually for the foreseeable foreseeable future. Another portion portion of the required funds will come come from the issue of 9,375 shares of 12 percent $100 par preferred stock that will be privately placed. The firm will will net $96 per share from the sale sale of these shares. The remainder remainder of the funding needs will be met with debt. debt. Five thousand thousand 10-year $1,000 par bonds with with a coupon rate of 15 percent will be issues issues to net the firm $1,020 each. Interest will be paid annually on the bonds. The firm’s tax rate is 30 percent. 13.61 percent
4.
Aver Average age Cor Corpor porati ation' on's s stoc stock k curr curren ently tly sell sells s for for $45.0 $45.00 0 per per share share,, it is expec expected ted to pay a dividend of $3.10 next year, its growth rate is a constant 7.0%, and the company will incur a flotation cost of 12.0% of the market value if it sells new common stock. The firm's tax is 40%. What is the firm's cost of retained earnings? 13.89%
5.
You are deter determi mini ning ng XYZ XYZ,, Inc Inc.' .'s s opti optimal mal capit capital al budget budget for for the the next next year year.. You You hav have e identified the following possible INDIVISIBLE capital projects: PROJECT COST A $ 100,000 B 800,000 C 500,000 D 300,000 E 400,000 F 700,000 G 600,000
IRR 16 % 14 % 18 % 15 % 12 % 17 % 20 %
XYZ's marginal cost of capital is: NEW CAPITAL REQUIRED $ 0 - 500,000 $ 500,001 - 999,999 $ 1,000,000 - 1,499,999 $ 1,500,000 - 1,999,999 $ 2,000,000 - 2,499,999 $ 2,500,000 - 3,000,000 ABOVE $ 3,000,000
MARGINAL COST 13.0 % 14.2 % 15.0 % 15.5 % 17.0 % 17.5 % 18.0 %
28
What is XYZ's optimal capital budget for the upcoming year? $1.9 million 6.
Margi Marginal nal Inco Incorpo rporat rated ed has has dete determ rmine ined d that that its its before before-ta -tax x cost cost of of debt debt is 10.0% 10.0%.. Its Its cos costt of preferred stock is 11.0%. Its cost of internal equity is 15.0%, and its cost of external equity is 16.9%. Currently, the firm's capital structure consists of 32% debt, 14% preferred stock, and 54% common equity. The firm's marginal tax rate is 39%. What is the firm's weighted average cost of capital if it will have to issue new common stock to fund the equity portion of its capital budget? 12.62 percent
29
CHAPTER TEN PROBLEMS
1.
An ins insur uranc ance e firm firm agree agrees s to to pay pay you you $3,3 $3,301 01 at at the the end end of of 20 years years if you you pay pay premi premium ums s of $100 per year at the end of each year of the 20 years. Find the internal internal rate of return. Answer: 5 percent
2.
The capi capital tal budge budgetin ting g direc director tor is eva evalu luati ating ng a proj projec ectt that that cos costs ts $200 $200,00 ,000, 0, is is expe expecte cted d to last for 10 years and to produce after-tax income of $29,503 per year. Depreciation applicable to this project would would be $20,000 per year. If the cost of capital of the firm is 14%, what is the project's IRR (tax rate = 40%)? 21.1 percent
3.
Given Given the follo followin wing g net cash cash flows flows,, determin determine e the IRR IRR of the the project: project: Time ---0 1 2 3
Net cash flow ------------$ 1,520 -1,000 -1,500 500 24%
4.
Acme Acme Pro Produc ducts ts,, Inc Inc., ., requi requires res a new new mach machin ine e to produ produce ce a part part for for a heat heat gener generato ator. r. Two companies companies have submitted bids, and you have been assigned the task of choosing one of the machines. Cash flow analysis indicates the following: Year ---0 1 2 3 4 A.
Machine A ---------$1,000 0 0 0 1,938
Machine B ---------$1,000 417 417 417 417
What is the internal rate of return for fo r each machine? IRR A = 0.18; IRRB = 0.24
B.
If the the cos costt of capita capitall for for Acm Acme e Prod Produc ucts ts is 5%, 5%, whic which h of the the foll follow owing ing is true? true? The NPV A > NPVB , therefore accept Machine A.
5.
Projects Projects C and and W are mutua mutually lly exclu exclusiv sive, e, and they they have the the followin following g net cash cash flows: flows:
30
Year ---0 1 2 3 4 5
Project C ---------$50,000 30,000 40,000 50,000 0 0
Project W ---------$100,000 40,000 40,000 40,000 40,000 40,000
You are to use the equivalent annual annuity method for comparing these projects since they have unequal lives. The cost of capital is 10%. Which project should be chosen? Project C since it has a higher equivalent annual annuity. 6.
The Smit Smith h Comp Company any is cons conside iderin ring g two two mutu mutuall ally y excl exclus usiv ive e inve invest stme ments nts that that woul would d increase its capacity to make strawberry tarts. The firm uses a 12 percent cost of capital to evaluate potential investments. The projects have the following costs and cash flow streams: YEAR 0 1 2 3 4 5 6 7 8
ALTERNATIVE A ALTERNATIVE B $ -30,000 $ -30,000 10,500 6,500 10,500 6,500 10,500 6,500 10,500 6,500 -6,500 -6,500 -6,500 -6,500
What are the respective EQUIVALENT ANNUAL ANNUITIES for alternatives A and B? ALTERNATIVE A ALTERNATIVE B : $ 621.35 $ 461.35 7.
What is the the payb payback ack perio period, d, the the NPV NPV at a disc discoun ountt rate rate of 10 10 perc percent ent,, and and the the IRR IRR for a project with the following cash flows? YEAR 0 1 2 3
CASH OUTFLOW $ 1000 ---PAYBACK 1 5/6 yrs
8.
9.
CASH INFLOW -$ 500 600 106
NPV 30
IRR 12 %
A proje project ct has has an an init initia iall cost cost of of $9,42 $9,427. 7. If If itit ret retur urns ns a net cash cash flow flow of $1,0 $1,000 00 at at the the end end of each year for the next 30 years, the internal internal rate of return must be: 10 % What is the IRR IRR of a proj project ect with with the the follow following ing cash cash flow flows? s?
31
TIME 0 1 2 3 4 5
CASH OUTFLOW $ 43,295 ------
CASH INFLOWS -$ 10,000 10,000 10,000 10,000 10,000
5% 10.
Your company company is conside considering ring two two mutual mutually ly excl exclusi usive ve proj projects ects,, X and Y, Y, whose whose cost costs s and cash flows are shown below: Year X Y 0 -$1,000 -$1,000 1 100 1,000 2 300 100 3 400 50 4 700 50 The projects are equally risky, risky, and their cost of capital is 12 percent. What is the modified IRR of each project? X Y 13.59% 13.10%
11.
Conglome Conglomerate rates, s, Inc., Inc., is consider considering ing the purchas purchase e of Small Small & Company Company.. The acquisi acquisitio tion n would require an initial investment of $190,000, but Conglomerates' net cash flows would increase by $30,000 per year and remain at the new level forever. Should Conglomerates buy Small? Assume a cost cost of capital of 15%. Yes, because the NPV = $10,000.
12.
If the required required rate of return return is 12 perce percent, nt, what what is the net present present valu value e of the the proje project ct described below: COST OF NEW EQUIPMENT $ 60,000 LIFE OF EQUIPMENT 6 YEARS SALVAGE VALUE $ 6,000 ANNUAL NET CASH FLOW $ 12,000 $ -7,624
13. What is the IRR IRR of a project project with the following following cash flows? flows? YEAR 0 1 2 3 4 5
$ $ $ $ $ $
CASHFLOW 0 0 -2500 1000 1000 1000
9-10 % 14. What is the the net present present value value of this this investment? investment?
32
INITIAL COST $ 15,000 PROJECT LIFE 5 years SALVAGE VALUE $ ANNUAL NET CASH FLOWS $ 5,000 DISCOUNT RATE 10 %
0
$ 3,954.00 15.
If a capit capital al budge budgetin ting g proje project ct has has an init initial ial out outlay lay of of $1,500 $1,500 and and an NPV of $5, $5,000 000,, what what is its profitability index? 4.33
16.
Cummin Cummings gs Product Products s Compa Company ny is conside considering ring two mutuall mutually y excl exclusi usive ve invest investment ments. s. The project's expected net cash flows are as follows: Expected Net Cash Flows Project A Project B ($300) ($405) (387) 134 (193) 134 (100) 134 600 134 600 134 850 134 (180) 0
Year 0 1 2 3 4 5 6 7 A.
If the cost of capital c apital for each project is 12 percent, what is the NPV for each project? Which project project should be accepted? accepted? $200.41 and $145.93 $145.93 Project A
B.
If the the cos costt of capita capitall for for eac each h proj project ect is 18 per perce cent, nt, what is the the NPV NPV for for each each project? Which project project should be accepted? accepted? $2.66 and $63.68
Project B
C. What is the internal internal rate of return return for each project? project? 18.1% and 24.0% D. What is the the crossover crossover rate? rate? 14.53%
33
CHAPTER ELEVEN PROBLEMS
1.
M&M M&M Inc. Inc.,, is is cons conside iderin ring g the the purc purchas hase e of a new new mach machine ine whic which h wil willl red reduc uce e manufacturing costs by $5,000 annually. M&M will use the straight-line method to depreciate the machine, and it expects to sell the machine at the end of its 5 year life for $10,000. The firm expects to be able to reduce working working capital by $15,000 when the machine is installed. The firm's marginal tax rate is 40% and it uses a 12% cost of capital to evaluate projects of this nature. If the machine costs $60,000, what is the NPV of the project's cash flows? -$22,604
2.
Blake Blake Corpo Corporat ration ion's 's new proj project ect call calls s for for an an inv inves estme tment nt of of $10,0 $10,000. 00. It has an est estim imate ated d life of 10 years. years. The IRR has been calculated to be 15%. If cash flows are evenly distributed and the tax rate is 40%, what is the annual BEFORE-TAX cash flow each year? (Assume depreciation is is a negligible amount.) $3,321
3.
G Mar Mart, t, Inc. Inc.,, is is con consi sider derin ing g the the acqu acquis isiti ition on of equip equipmen mentt to expan expand d its its sale sales. s. The The init initia iall cost of the equipment is $100,000. However, the production manager has estimated the expansion program will increase cash operating costs by $20,000. Assume straight line depreciation depreciation to a zero salvage value, a tax rate of 40%, and a cost of capital of 10%. How much will the additional cash revenue during the 10 year year life of the asset have to be to cause the IRR of the project to be equal to k? $40,457
4.
Blain Blain Corpo Corporat ratio ion n is cons conside ideri ring ng the the pur purch chase ase of a mach machine ine which hich has has an an expec expected ted 8 year life and costs costs $20,000. The annual expected expected NET CASH FLOW from the machine machine is $5,000 for the first 7 years and $9,000 in year 8, excluding excluding salvage values. The asset will be depreciated on a straight line basis to a $4,000 salvage value. It is eligible for a 7% investment tax credit. If the discount rate is 10%, what what is the machine's NPV? $11,807
5.
Preci Precisi sion on Meta Metals ls,, Inc. Inc. is is cons consid ideri ering ng the the repla replace cemen mentt for its its exi exist stin ing g lathe, lathe, whic which h cost cost $200,000 at the time of purchase five years ago, and which now has a remaining life of five years with no salvage value. It can be sold currently for $100,000. A new, more operationally operationally efficient lathe costs $300,000 and has a useful life of five years with a salvage value of $50,000. It is expected to reduce operating costs by $66,000 annually. An investment tax credit cred it of 10 percent perc ent of the purchase price can be used if the lathe is acquired. The firm's required rate of return for replacement decisions is 12 percent. Assume straight-line depreciation dep reciation and a tax rate of 40 percent. The net present value of this capital budgeting decision is: $ 44,380
34
6.
CDB CDB & Asso Associ ciate ates s is is consi consider dering ing the the pur purcha chase se of of a new new piz pizza za oven. oven. The orig origina inall cos costt of the old oven was $30,000. The machine is now now 5 years old and has a current current market value of $5,000. The oven is being depreciated over a 10-year life life toward a zero estimated salvage value on a straight-line basis. Management is contemplating the purchase of a new oven whose cost is $25,000 and whose estimated salvage value is zero. Expected cash savings from the new oven are $2,000 a year (before tax). Depreciation is on a straight-line basis over a 5 year life, and the cost of capital is 10%. Assume a 50% tax rate. rat e. What is the net present value of the new machine? -$7,418
7.
Sandal Sandals, s, Inc Inc., ., is is cons conside ideri ring ng the the pur purch chase ase of a new new leat leather her-cu -cutt tting ing machi machine ne to to repla replace ce an existing existing machine that has a book value of $3,000 and can be sold for $1,500. The estimated salvage value of the old machine in 4 years is zero. The new machine will will reduce costs (before tax) by $7,000 per year; that is, $7,000 cash savings over over the old machine. machine. The new machine machine has a 4 year life, cost $14,000, and can be sold for an expected $2,000 at the end of the fourth year. Assuming straight straight line depreciation for both machines, machines, a 40% tax rate, and a cost of capital of 16%, find the NPV. $3,475
8.
Give Given n the the foll follow owing ing infor informat mation ion,, what what is the the effec effecti tive ve cos costt of the the new new mac machi hine; ne; that that is, is, what is the cash flow at t = 0? Purchase price of new machine Installation charge Market value of old machine Book value of old machine machine Inventory decrease if new machine is installed Accounts payable increase if new machine is installed Tax rate 48% Cost of capital 15%
$8,000 2,000 2,000 1,000 1,000 500
$6,980 9.
Quik, Quik, Inc. Inc.,, is is a fast-f fast-food ood estab establilishm shment ent that that needs needs to to purc purcha hase se new new fry fryola olator tors. s. If the machines are purchased, they will replace old machines purchased 10 years ago for $100,000, being depreciated on a straight line basis to a zero salvage value (20 years depreciable life). The old machines machines can be sold sold for $120,000. The new machines will cost $200,000 installed and will be depreciated on a straight-line basis to a zero salvage value in 10 years. It is expected that there will be increased revenues of $18,000 per year and increased increased cash expenses expenses of $2,500 per year. If the firm's firm's cost of capital (k) is 10%, the tax rate on ordinary income is 40%, and the tax rate on capital gains is 30%, what is the NPV of the machine? -$6,988
10.
PC, PC, Inc. Inc.,, has has a stamp stampin ing g machin machine e which which is 5 year years s old old and whi which ch is expe expect cted ed to last last
35
another 10 years. It has a book value value of $100,000 and is being depreciated by the straight-line method to zero. Tri-State Industries has demonstrated a new machine with an expected useful life of 10 years (scrap value $50,000) that should save PC $15,000 a year in labor labor and maintenance costs. If PC's cost of capital is 10%, should the replacement be made? PC's tax rate is 40%, the new machine will cost $200,000, and an investment tax credit of 10% applies. The market value of the old machine is $10,000 and a $10,000 increase in working capital capital will be needed to support the new machine. No; NPV = -$53,278 11.
GIGO, GIGO, Inc. Inc.,, is conside considering ring replaci replacing ng its its curre current nt compu computer ter with with a new generati generation on model. model. The ABM salesperson has demonstrated a model which would cost GIGO $750,000, should last 10 years, and reduce costs $166,043 per year. ABM estimates that this new computer computer can be sold for $10,000 at the end of its useful life. The computer computer GIGO currently uses has a book value of $450,000 (remaining life of 10 years, a salvage value of $10,000, and a current current market market value of $10,000. If an investment investment tax credit of of 10% is applicable to the new computer, and the new machine will permit a $10,000 decrease in working capital when the computer is installed, what is the NPV (k = 15%, t = 40%, depreciation is straight line)? $78,753
12.
You hav have e been ask asked ed by the the firm' firm's s presi presiden dentt to eval evaluat uate e the propo proposed sed acqu acquis isiti ition on of a new machine. The machine's price is $50,000, and it will cost $10,000 to transport and install. It will will be depreciated by the straight-line method over its 5-year useful life to a $10,000 salvage value. The machine will will increase revenues by $10,000 per year, and it will will decrease operating costs by $20,000 per year. Also, the machine will allow the firm to reduce inventories by $5,000. The new machine (including delivery and installation costs) qualifies for a 10% investment tax credit. If the firm's cost of capital is 12%, and its marginal tax rate is 40%, what is the new machine's NPV? $33,143
13.
Union Union Brick Brick,, Inc., Inc., has an elect electric ric kiln kiln whic which h is 5 years years old and and is expecte expected d to last last another 10 years. It has a book value of $100,000, and it is being depreciated by the straight-line method to a zero salvage salvage value. As Director of Capital Budgeting, you are evaluating evaluating a new gas kiln that should save save UBI $25,000 a year in fuel costs. costs. The new kiln would cost $200,000, and it is eligible for a 10% investment tax credit. It would be depreciated over 10 years by the straight-line straight-line method to a $20,000 salvage value. The market value of the old kiln is $10,000. UBI's marginal tax rate is 40%, and the firm's cost of capital is 10%. What is the NPV NPV of the replacement project? -$14,458
14.
A compan company y is plan plannin ning g to inve invest st $50, $50,000 000 (befo (before re tax) tax) in a per person sonnel nel tra train ining ing prog program ram..
36
The $50,000 outlay will be charged off as an expense by the firm this year (time 0). the returns from the program, in the form of greater productivity and a reduction in employee turnover, are estimated as follows (on an after-tax basis): YEARS 1-10 YEARS 11-20
$ 5,000 per year $ 15,000 per year
The company has estimated its cost of capital to be 15 percent. Assume that the entire $50,000 is paid at time 0 (the beginning of the project). The marginal tax rate for the firm is 40 percent. What is the investment's NPV? $ 13,690 15.
The WRANGLER WRANGLER Corporat Corporation ion is consider considering ing the the acqu acquisi isitio tion n of a new new splici splicing ng mach machine ine to improve the efficiency of its clothing operations. The new machine will will cost $60,000 plus installation costs of $5,000. The machine's efficiency will will create additional output; thus, revenues will increase by $5,000 annually. The amount of wasted wasted material will decline, so operating costs will decline by $2,000 annually. The machine will require a $2,000 increase in inventory and spare parts. The machine's estimated salvage value (at the end of its 5 year life) is $500. (Use this value for depreciation purposes.) The firm's marginal tax rate is 40 percent and its required rate of return is 10 percent. Assume that the firm uses straight-line depreciation depr eciation for analysis of this type. A.
What is the NET COST of the machine? (That is, what is the initial cash outflow?) $ -67,000
B.
What What are are the the net net oper operat atin ing g cas cash h flo flow ws for for Year Year 1 thr throu ough gh 5? $ 9,360
C.
What is the total total val value ue of of the the addi additio tional nal cons conside iderat ratio ions ns at at the the end end of of the the five five years? $ 2,500
D.
What What is the the Net Net Pres Presen entt Val Value ue of the the dec decis isio ion? n? $ -29,966
37
16.
The Nels Nelson on Equip Equipmen mentt Compa Company ny pur purch chase ased d a mach machine ine 5 years years ago at at a cost cost of $200,000. The machine machine had an expected life of 10 years at the time of the purchase purchase and an expected salvage salvage value of $50,000 at the end of the 10 years. It is being being depreciated depreciated by the straight-line straight-line method toward a salvage value of $50,000, or by $15,000 per year. A new machine can be purchased for $400,000 $400,00 0 and require an additional a dditional $15,000 in installation costs. The new machine will require $20,000 in additional spare parts. During its 5-year 5-year life, it will will reduce cash operating expenses by $150,000 per year. Sales are not not expected to change. change. At the end of its useful useful life, the machine machine is estimated to be worth $50,000. ACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life. The old machine can be sold sold today for $175,000. The firm's tax rate is 40 percent and the appropriate discount rate is 12 percent. (The recovery allowance percentages for 3-year property are 33%, 45%, 15%, and 7%.) A.
What is the NET COST of the machine? (That is, what is the initial cash outflow?) $ -280,000
B.
What What are are the the net net ope opera rati ting ng cash ash flo flow ws for for Year Year 1 and and 2? Year 1 $ 138,780
C.
What is the total total val value ue of of the the addi additio tional nal cons conside iderat ratio ions ns at at the the end end of of the the five five years? $
D.
Year 2 $ 158,700
0
What What is is the the Net Net Pres Presen entt Val Value ue of the the rep repla lace ceme ment nt deci decisi sion on? ? $ 156,370
38
17.
MacDou MacDougal' gal's s is is a fast-food fast-food establi establishm shment ent that needs to purchase purchase new fryolat fryolators. ors. If the new fryolators are purchased, they will replace old machines purchased 10 years ago for $150,000. The old machines machines are being depreciated on a straight-line basis to a zero salvage value. The original estimated life life of the old machines was fifteen years. (The old machines have five years years of estimated life remaining.) The old fryolators can currently be sold to another firm in the industry for $40,000. The new machines will cost $250,000 plus an additional $20,000 for installation. The new fryolators have an estimated useful life of five years and have an estimated salvage value value (SCRAP) at the the end of five years of $10,000. The new fryolators fryolators have extra capacity and will, thus, increase revenues by $60,000 annually. The machines will also also reduce operating expenses (electricity) by $10,000 annually. The firm will require $5,000 in additional working capital to support the increased output. MacDougal's depreciates their capital improvements at the maximum rate allowed by the IRS. For property of this type (3-year), the MACRS MACRS rates are 33%, 45%, 15% and 7%. The firm's marginal tax rate is 40 percent and their required rate on projects of this nature is 12 percent. A.
What is the NET COST of the machine? (That is, what is the initial cash outflow?) $ -231,000
B.
What What are are the the net net ope opera rati ting ng cash ash flo flow ws for for Year Year 1 and and 2? Year 1 $ 73,640
C.
Year 2 $ 86,600
What is the total total val value ue of of the the addi additio tional nal cons conside iderat ratio ions ns at at the the end end of of the the five five years? $ 11,000
D.
What What is the the Net Net Pres Presen entt Val Value ue of the the mac machi hine ne? ? $
-876
39
18.
Natural Natural Beverage Beverages s is is cont contempl emplatin ating g the the repla replacem cement ent of of one one of its bottlin bottling g machi machines nes with a newer newer and more efficient one. The old machine machine has a book value of $400,000 and a remaining useful useful life of five years. The salvage value value of the old machine (for depreciation and cash flow purposes) is $50,000. The firm can sell it now to another firm in the industry for $200,000. The new machine has a purchase price of $1.2 million, an estimated useful life of five years, and an estimated salvage value in five years of $20,000. Additional costs of installation will be $25,000. It is expected to economize on operating costs and to reduce the number of defective bottles. In total, an annual saving of $250,000 will will be realized if the new machine machine is installed. installed. The new machine will require an additional $15,000 in inventory (spare parts). The company is in the 40 percent marginal marginal tax bracket and has a 12 percent required rate of return. The machine qualifies as a 3-year property under MACRS (33%, 45%, 15%, 7%). A.
What is the initial investment required requ ired for this replacement repl acement decision? -$960,000
B.
What What are are the the net net oper operat atin ing g cas cash h flo flow ws for for year years s one one and and tw two? $283,700
C.
$342,500
What What is the the val value ue of of the the addi additi tion onal al cons consid ider erat atio ions ns in year ear 5? 5? -$23,000
D.
What What is the the NET NET PRES PRESEN ENT T Val Value ue of of thi this s rep repla lace ceme ment nt deci decisi sion on? ? -$138,998
40
19.
Huang Huang Indus Industri tries es is conside considering ring a propo proposed sed project project for its capital capital budget. budget. The company company estimates that the project's NPV NPV is $12 million. million. This estimate assumes that the economy and market conditions will be average over the next few years. The company's CFO, however, forecasts that there is only a 50 percent chance that the economy will be average. Recognizing this uncertainty, she has performed the following scenario analysis: Economic Scenar Sce nario io Recession Below Average Average Above Average Boom
Probability of Outcom Out come e 0.05 0.20 0.50 0.20 0.05
NPV ($70 million) ($25 million) $12 million $20 million $30 million
What is the project's expected NPV, its standard deviation, and its coefficient of variation? E(NPV) = $3.0 million σNPV = $23. $23.6 6 mi million lion CV = 7.874
41
CHAPTER TWELVE PROBLEMS
1.
Quick Quick Laun Launch ch Roc Rocke kett Comp Company any,, a satel satellilite te laun launch ching ing fir firm, m, exp expec ects ts its its sal sales es to to incr increas ease e by 50 percent in the coming year as a result of NASA's recent problems with the space shuttle. The firm's current EPS is $3.25. Its degree of operating leverage is 1.6, while its degree of financial leverage is 2.1. What is the firm's projected EPS for the coming year using the DTL approach? $ 8.71
2.
A fir firm m expe expect cts s to to have have a 15 15 per perce cent nt incr increas ease e in in sale sales s ove overr the the comi coming ng year year.. If it has operating leverage leverage equal to 1.25 and financial leverage leverage equal to 3.5, then what will be the percentage change in EPS? 66 percent
3.
The Congr Congres ess s Compa Company ny has ident identifi ified ed two two met method hod of produc producing ing play playing ing card cards. s. One method involves involves a machine machine having a fixed cost of $10,000 and variable costs of $1.00 per deck of cards. The other method would use a less expensive machine (fixed costs = $5,000), but it would require greater variable costs ($1.50 per deck of cards). If the selling price per deck of cards will be the same under each method, at what level of output will the two methods produce the same net operating income? 10,000 decks
4.
Assu Assume me that that a fir firm m cur curren rently tly has EBIT EBIT of of $2,0 $2,000, 00,000 000,, DTL DTL of 7.5 7.5,, and and DFL DFL of 1.8 1.875. 75. If sales decline by 20 percent next year, then what will be the firm's expected EBIT in one year? $400,000
5.
Assu Assume me that that a fir firm m has has a DFL DFL of 1.25 1.25.. If sale sales s inc increa rease se by 20 per percen cent, t, the the fir firm m wil willl experience experience a 60 percent increase in EPS, and it will will have an EBIT of $100,000. $100,000. What will be the EBIT for this firm if sales do not increase? Answer: $67,568
6.
Calcul lcula ate th the cu current ent pr price pe per sh share (P0) for Olson Corporation, given the following information. The data all pertain to the year just ended. Sales = 10,000 units Sales price per unit = $10.00 Variable cost per unit = $ 5.00 Fixed cost = $10,000 Debt outstanding = $15,000 Interest rate on debt = 5 percent Tax Rate = 30 percent Common stock shares outstanding = 10,000 shares Beta = 1.5 kRF = 5 percent kM = 9 percent Payout ratio = 40 percent Growth rate in earnings and dividends = 7 percent $ 29.43
42
7.
A com compan pany y cur curren rently tly has has asset assets s of of $5 mill millio ion. n. The firm firm is 100 100 perc percent ent equit equity y finan financed ced.. The company currently has net income of $1 million, and it pays out 40 percent of its net income as dividends. Both net income and dividends are expected to grow at a constant rate rate of 5 percent per year. There are 200,000 shares shares of stock outstanding, outstanding, and it is estimated that the current cost of capital is 13.40 percent. The company is considering a recapitalization where it will issue $1 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the plan, its before tax cost of debt will be 11 percent, and the cost of equity will will rise to 14.5 percent. The company has a 4- percent federal-plus-state tax rate. A.
What is the current share price pr ice (before recapitalization)? recap italization)? $25.00
B.
Assu Assumi ming ng that that the the firm firm maint maintai ains ns the the sam same e payo payout ut rat ratio io,, what what will will be be its its stoc stock k price following the recapitalization? $25.81
8.
The ACE ACE Wine Wine Comp Company any of El Paso Paso prod produce uces s a popula popular, r, lowlow-co cost st wine. wine. The The fir firm m has fixed costs of $100,000 annually and variable costs costs per bottle of $3.00. The division has $150,000 in debt outstanding at an annual interest rate of 12 percent. A.
If the price per bottle b ottle is $7.00, what is the division's breakeven revenue?. $ 175,000
B.
If the the fir firm m expec expects ts to to sell sell 100, 100,000 000 bott bottle les, s, at at what what pri price ce mus mustt it sell sell eac each h bottl bottle e in order to break even? $ 4.00
C.
If the the fir firm m sel sells ls 50,000 50,000 bottl bottles es at at a pri price ce of of $7.00 $7.00,, what what is is the the fir firm' m's s degre degree e of operating leverage? 2.00
D.
If the the fir firm m sel sells ls 50,000 50,000 bottl bottles es at at a pri price ce of of $7.00 $7.00,, what what is is the the fir firm' m's s degre degree e of financial leverage? 1.22
E.
What is the degree degree of tot total al leve leverag rage e at this this lev level el of out output put and and sale sales s pri price ce? ? 2.44
9.
The firm firms s HL HL and and LL are are iden identi tica call excep exceptt for for thei theirr leve leverag rage e rati ratios os and and int intere erest st rat rates es on on
43
debt. Each has $20 million in assets, earned $4 million before interest and taxes in 2000, and has a 40 percent federal-plus-state tax rate. Firm HL, HL, however, has a leverage ratio (D/A) of 50 percent and pays 12 percent interest on its debt, whereas LL has a 30 percent leverage ratio and pays only 10 percent interest on its debt. A.
What is the return on equity e quity for each firm? ROE for LL: ROE for HL:
B.
14.6 percent 16.8 percent
If LL rai raise ses s its its debt debt rat ratio io to to 60 60 perc percent ent and the inte interes restt rate rate on all all of its its debt debt increases to 15 percent, what would its new ROE be? ROE for LL at 60 percent D/A:
10.
16.5 percent
The XYZ XYZ Comp Company any man manufa ufact cture ures s and and sell sells s only only one one produ product ct,, a widg widget et.. The The firm firm sel sells ls every unit that it produces for a sales price of $5.00 a unit. The firm's variable cost per unit is $2.00, and the fixed operating cost is $30,000. XYZ has current current interest costs of $15,000 annually annua lly and a marginal tax rate of 40 percent. If the firm produces and sells 20,000 units: A.
What is the firm's breakeven quantity and revenue? 10,000 units and $50,000
B.
What What is the the fifirm's rm's degr degree ee of oper operat atin ing g lev lever erag age? e? 2.0
C.
What What is the the fifirm's rm's degr degree ee of fin finan anci cial al lever everag age? e? 2.0
D.
What What is the the fifirm's rm's degr degree ee of tot total leve levera rage ge? ? 4.00
11.
A group group of reti retired red col colle lege ge profe professo ssors rs has has decide decided d to form form a smal smalll manufa manufact cturi uring ng
44
corporation. The company will produce a full line of traditional office funiture. Two financing plans have been proposed by investors. Plan A is an all-equity alternative. Under this agreement, one million shares will be sold to net the firm $20 per share. Plan B involves the use of financial leverage. A debt issue with with a 20-year maturity will be privately placed. The debt issue will will carry an interest rate of 10 percent, and the principal borrowed will amount to $6 million. Assume a corporate tax rate of 34 percent. A. Find the EBIT indifference indiff erence level associate with the two financing fi nancing alternatives. alter natives. $2,000,000 B. What is the EPS at this this indifference indifference level of EBIT? $1.32 C. The average annual EBIT has been estimated at $3,000,000; $3,000,000 ; what is the expected EPS of each plan at this this level of EBIT? EBIT? Which plan should be selected? selected? Plan A:
$1.98
Plan B:
$3.43
45
12.
Four Four recent recent liberal liberal arts arts gradua graduates tes have have interes interested ted a group group of venture venture capita capitalis lists ts in in backing a new enterprise. The proposed operation would consist of a series of retail outlets to distribute and service a full line of vacuum cleaners and accessories. These stores would be located in Houston, Dallas Dallas and San Antonio. Two financing plans have been proposed by the graduates. Plan A is an all-common all-common equity structure. Two million dollars would would be raised by selling 80,000 shares of common stock. Plan B would involve the use of long-term debt financing. One million dollars would be raised marketing bonds with an effective interest rate of 12 percent. Under this alternative, another million dollars would be raised by selling 40,000 shares of common stock. With both plans, then $2 million million is needed to launch the new firm’s firm’s operations. operations. The debt funds raised under Plan B are thought to be part of the firm’s permanent permanent capital structure. Assume a 34 percent marginal tax rate for the analysis. A. Find the EBIT indifference indiff erence level between the two proposals. $240,000 B. What is the EPS at at this indifference level level of EBIT? EBIT? $1.98 C.
The The aver averag age e annu annual al EBI EBIT T has has bee been n esti estima mate ted d at $50 $500, 0,00 000; 0; wha whatt is the the expected EPS of each plan plan at this level level of EBIT? Which plan should be selected? Plan A:
13.
$4.125
Plan B:
$6.27
The Wingler Wingler Corpo Corporati ration on suppl supplies ies headphones headphones to airl airlines ines for use with with movi movie e and and stere stereo o programs. The headphones use the latest in electronic components and sell for $28.80 per set. This year's year's sales are expected to be 450,000 units. Variable production costs for the expected sales under present production methods are estimated at $10,200,000, and fixed production production costs at present present are $1,560,000. Wingler has $4,800,000 of debt outstanding at an interest interest rate of 8 percent. There are 240,000 shares of common stock outstanding, and there is no preferred stock. The dividend payout ratio is 70 percent, Wingler is in the 40 percent federal-plus-state tax bracket. The company is considering investing $7,200,000 in new equipment. Sales would not increase, but variable costs per unit would decline by 20 percent. Also, fixed operating costs costs would increase increase from $1,560,000 $1,560,000 to $1,800,000. Wingler could raise raise the required capital by borrowing $7,200,000 at 10 percent or by selling 240,000 additional shares at $30 per share. A.
What would be Wingler's W ingler's EPS under (1) the old production process; (2) under the new process if itit uses debt, and (3) the new process if it uses equity?
Old:
$2.04
B.
At what what unit unit sales sales leve levell woul would d Wingle Winglerr have have the the sam same e EPS EPS if the the new new prod product uction ion process is implemented? What is the EPS at this level?
New debt:
$4.74
339,750 units and $1.80
New equity:
$3.27
46
CHAPTER THIRTEEN PROBLEMS
1.
Crav Craven en Corp Corp.. has has reta retain ined ed earn earning ings s of of $1.75 $1.75 mill millio ion n and and 100, 100,000 000 shares shares of sto stock ck outstanding with a market value of $25 per share. If Craven declares a 15 percent stock dividend, what will Craven's retained earnings be after the dividend? $ 1.375 million
2
A comp compan any y has has a net net inco income me of of $100 $100 mil millilion on and and a pol polic icy y of pay payin ing g out out 60 per perce cent nt of of its its earnings in dividends. How much total financing can be accomplished before the company has to sell common stock? Assume a debt/equity ratio of 66.6 percent. $ 66.66 million
3.
Alton Alton Corp. Corp. has has ear earni nings ngs of $1. $1.5 5 mil millilion on and a poli policy cy of paying paying out out 60 60 perc percent ent of earnings. Alton has $1.8 million in acceptable investments but is unable to issue new equity. Assuming a D/E of 0.4, how much will Alton be able to spend on capital budgeting if it wishes to stick with the 60 percent payout? $ 0.84 million
4.
Before Before a 2-fo 2-for-1 r-1 stoc stock k spl split it,, Dean Dean Comp Company any sold sold for $60 a sha share, re, earnin earning g $15 $15 and and paying $8 dividend per share. After the split, the dividend per share becomes $5.20. By what percentage has the payout ratio risen? 30%
5.
Butle Butlerr Cor Corpor porati ation on has has decla declared red a 10 perce percent nt sto stock ck divi dividen dend. d. Butl Butler er has has 2 mil millilion on shares outstanding with a current market price of $7. Its capital stock account is $1 million, and the firm's retained earnings are $8 million. What balances will the retained earnings and capital stock accounts show after the distribution of the stock dividend? CAPITAL STOCK $ 1,100,000
6.
RETAINED EARNINGS $ 6,600,000
The Sherma Sherman n Stee Steell Com Compan pany y has has an an orde orderr back backlog log of $5 $5 mil millilion on.. It It desi desires res to exp expand and production capacity by 20 percent, which will involve a $15 million investment in plant and equipment. Management desires to maintain 40 percent debt in its capital structure. The dividend policy has been to distribute 25 percent of their after-tax earnings, which this year were $6 million. If management wishes to maintain its dividend policy, how much external equity must the firm seek at the beginning of the year? $ 4,500,000
7.
On Mar March ch 15, the dire direct ctor ors s of Glu Glutt Oil Oil Com Compan pany y met met and and decl declare ared d the the regu regular lar divi dividen dend d of 48 cents a share to holders of record on March 31, payment to made on May 15. Of the 100 shares of Glut Oil you now own, 25 shares at a time were purchased on each of the following following dates: January 1, February 15, March 15, and April 1. What total dividends will you receive? (Assume ex-dividend four days prior to record date.) $ 36.00
47
8.
Wilber Wilbertt Comp Company any expec expects ts nex nextt year year's 's afte after-t r-tax ax inc income ome to be be $10 $10 mill millio ion. n. The The fir firm' m's s current debt-equity ratio is 100 percent. If Wilbert has $12 million of profitable investment opportunities and wishes to maintain its current debt ratio with no external equity financing, how much should it pay out in dividends next year? $ 4,000,000
9.
Jacob Jacobs s Corp Corpora oratio tion n earne earned d $2 mill millio ion n after after-t -tax ax.. The The fir firm m has has 1.6 1.6 mil millilion on shar shares es outstanding. If Jacobs' dividend policy calls for a 40 percent payout ratio, what are the dividends per share? $ 0.50
10.
Cham Champou poux x Hair Hair Factor Factory, y, Inc Inc.. has earn earning ings s before before inte interes restt and taxe taxes s of $100,0 $100,000. 00. Annual interest inter est amounts to $40,000, $4 0,000, and an d the annual annu al depreciation depreciati on is $40,000. $40,000 . Taxes are computed computed at the 40 percent rate. Existing bond obligations require the payment of $20,000 into a sinking sinking fund. Champoux wishes wishes to pay $1 per share dividend on the existing 20,000 shares outstanding. The firm's bond indenture prohibits the payment of dividends unless the cash flow (before tax and sinking fund payments) is greater than the total dividend, interest, and sinking fund obligations. What is the maximum dividend per share that Champeoux can pay? $ 0.80
48
11.
One share share of of Van Van Horn Horn Distri Distribut butors, ors, Inc. Inc. has has a market market price price of $120. $120. The firm firm list lists s the the following on its annual report (dollars in thousands): Common Stock, $2.50 par; authorized, 6,000,000 shares; issued issued and outstanding, outstanding, 4,000,000 shares Additional Paid-In Capital Retained Earnings A.
$ 10,000 3,000 50,000
The firm is considering a 5-for-1 stock split. Which of the following fo llowing would be expected? Approximate Par Value Shares Issued Market Price $ 0.50 20,000,000 $ 24.00
B.
What What woul would d the the bala balanc nces es in in the the equi equity ty acc accou ount nts s be ifif the the firm firm issu issued ed a one one percent stock dividend? Common Stock $ 10,100
12.
Additional Paid-In $ 7,700
Retained Earnings $ 45,200
Aberwal Aberwald d Heatin Heating, g, Inc Inc.. has has a sixsix-mon month th backl backlog og of orders orders for for its its patented patented solar solar heati heating ng system. Management plans to expand production capacity by 50 percent, with an $12 million investment in plant machinery, to meet this demand. The firm wants wants to maintain a 30 percent debt-to-asset ratio in its capital structure; it also wants to maintain its past dividend policy of distributing 30 percent of last year's after-tax earnings. In 1990, after-tax earnings were $2 million. A.
If the firm has 1,000,000 1,0 00,000 shares outstanding, outstanding , what will be the firm's dividends per share (DPS) if it continues the current policy? $ 0.60
B.
What would would the the divi dividen dend d per per shar share e be if the the fir firm m emp employ loys s the the resi residua duall theo theory ry of dividends? Assume 1 million million shares shares outstanding. $ 0.00
C.
If Aberw Aberwald ald is to meet meet bot both h capi capital tal fundin funding g and and divi dividen dend d requ require ireme ments nts,, how how much external funding will be required? $ 7,000,000
49
13.
Jacobs Jacobs Corpora Corporation tion earned earned $2 $2 milli million on in in after after-ta -tax x net net inco income me last last quarter quarter.. The firm has 1.6 million shares outstanding. If Jacobs' dividend policy calls for a 40 percent payout ratio, what are the dividends per share? $0.50 per share
14.
Maxi-T Maxi-Trac rack's k's profit profit marg margin in and and sales sales are expecte expected d to be 10 10 percen percentt and and $50 millio million, n, respectively, for the upcoming quarter. The firm's traditional payout ratio is 40 percent of net income. Due to market conditions, the firm does not wish wish to raise any new equity at this time. Maxi-Track's optimal capital structure contains 40 percent debt/60 percent equity. A.
What is the firm's expected net n et income? $5,000,000
B.
What What is is the the fir firm' m's s expe expect cted ed leve levell of of ret retai aine ned d ear earni ning ngs? s? $3,000,000
C.
What is is the the larg larges estt capit capital al budg budget et that that Max Maxii-Tr Trac ack k sel selec ectt wit withou houtt chang changing ing the the firm's payout policy or capital structure weights? $5,000,000
