UGBA 103 – Introduction to Finance Review Revie w Section Sheisha Kulkarni & Vijayant Bhatnagar UC Berkeley – Haas School of Business
Spring 2016
Capital Structure
Payout Policy
Capital Budgeting and Valuation
Options
Capital Structure
Payout Policy
Capital Budgeting and Valuation
Options
Capital Structure
Capital Structure
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 1. What is the NPV of this project?
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 1. What is the NPV of this project? E [CF 1 ] − initial cash flow NPV = 1 + r c 0.5 × 145, 000 + 0.5 × 195, 000 = 1.30 170, 000 − 120, 000 = 10, 769 = 1.3
−
120, 000
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 2. Suppose that to raise the funds for the initial investment, the project is sold to investors as an all-equity firm. The equity holders will receive the cash flows of the project in one year. What is the initial market value of the unlevered equity?
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 2. Suppose that to raise the funds for the initial investment, the project is sold to investors as an all-equity firm. The equity holders will receive the cash flows of the project in one year. What is the initial market value of the unlevered equity? E [CF 1 ] 1 + r c 0.5 × 145, 000 + 0.5 × 195, 000 = 1.30 170, 000 = = 130, 769 1.3
Equity value =
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 3. Suppose that initial $120,000 is instead raised by borrowing at the risk-free rate. What are the cash flows of the levered equity, and what is its initial value according to MM?
Capital Structure
Question 1 Consider a project with free cash flows in one year of $145,000 or $195,000, with each outcome being equally likely. The initial investment required for the project is $120,000 and the project’s cost of capital is 30%. The risk-free interest rate is 12%. 3. Suppose that initial $120,000 is instead raised by borrowing at the risk-free rate. What are the cash flows of the levered equity, and what is its initial value according to MM?
equity value is total firm value minus debt value value of debt next period is debt value ×r f equity cash flow is the difference between total cash flow and cash to debt.
Debt Equity Total
Value at year 0 120,000 10,769 130,769
CF Strong 134,400 60,600 195,000
CF Weak 134,400 10,600 145,000
Capital Structure
Question 2
Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of equity."
Capital Structure
Question 2
Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of equity." The argument is wrong because any leverage raises the equity cost of capital. Risk-free leverage raises it the most because it does not share any of the risk.
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in risk-free debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 1. What is AOL’s enterprise value?
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in risk-free debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 1. What is AOL’s enterprise value? Enterprise value=Total equity+Debt-Cash Enterprise value=3.3+0.2-1.6=1.9 billion.
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in risk-free debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 1. What is AOL’s enterprise value? Enterprise value=Total equity+Debt-Cash Enterprise value=3.3+0.2-1.6=1.9 billion. 2. What is the beta of AOL’s business assets?
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in risk-free debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 1. What is AOL’s enterprise value? Enterprise value=Total equity+Debt-Cash Enterprise value=3.3+0.2-1.6=1.9 billion. 2. What is the beta of AOL’s business assets? E D β U = β E + β D E + D E + D 3.3 × 0.92 = 1 .6 = 1.9
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 3. What is AOL’s pre-tax WACC?
Capital Structure
Question 3 In mid-2012, AOL Inc. had $200 million in debt, total equity capitalization of $3.3 billion, and an equity beta of 0.92. Included in AOL’s assets was $1.6 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 2.9% and the market risk premium is 4.1%. 3. What is AOL’s pre-tax WACC? r WACC = r f + β U × MRP
= 0 .029 + 1.6 × 0.041 = 0.095 AOL’s pre-tax WACC is 9.5%.
Payout Policy
Payout Policy
Payout Policy
Question 4 EJH Company has a market capitalization of $3.1 billion and 36 million shares outstanding. It plans to distribute $125 million through an open market repurchase. Assuming perfect capital markets: 1. What will the price per share of EJH be right before the repurchase?
Payout Policy
Question 4 EJH Company has a market capitalization of $3.1 billion and 36 million shares outstanding. It plans to distribute $125 million through an open market repurchase. Assuming perfect capital markets: 1. What will the price per share of EJH be right before the repurchase? Price per share=Equity value/shares outstanding=3,100/36=$86.11 2. How many shares will be repurchased?
Payout Policy
Question 4 EJH Company has a market capitalization of $3.1 billion and 36 million shares outstanding. It plans to distribute $125 million through an open market repurchase. Assuming perfect capital markets: 1. What will the price per share of EJH be right before the repurchase? Price per share=Equity value/shares outstanding=3,100/36=$86.11 2. How many shares will be repurchased? Number of shares=amount distributed/price per share=125/86.11=1.45 million shares 3. What will the price per share of EJH be right after the repurchase?
Payout Policy
Question 4 EJH Company has a market capitalization of $3.1 billion and 36 million shares outstanding. It plans to distribute $125 million through an open market repurchase. Assuming perfect capital markets: 1. What will the price per share of EJH be right before the repurchase? Price per share=Equity value/shares outstanding=3,100/36=$86.11 2. How many shares will be repurchased? Number of shares=amount distributed/price per share=125/86.11=1.45 million shares 3. What will the price per share of EJH be right after the repurchase? Price per share=equity value/shares 100−125 outstanding= 336 −1 45 =$86.11 ,
.
Payout Policy
Question 5 The HNH Corporation will pay a constant dividend of $3.50 per share, per year, in perpetuity. Assume all investors pay a 22% tax on dividends and that there is no capital gains tax. Suppose the other investments with equivalent risk to HNH stock offer an after-tax return of 9%. 1. What is the share price of HNH stock?
Payout Policy
Question 5 The HNH Corporation will pay a constant dividend of $3.50 per share, per year, in perpetuity. Assume all investors pay a 22% tax on dividends and that there is no capital gains tax. Suppose the other investments with equivalent risk to HNH stock offer an after-tax return of 9%. 1. What is the share price of HNH stock? CF = Div × (1 − τ d ) = 3.50 × (1 − 0.22) = 2 .73
2.73 P = = 30 .33 0.09 2. Assume that management makes a surprise announcement that HNH will no longer pay dividends but will use the cash to repurchase stock instead. What is the price of a share of HNH stock now? 3.50 CF = 3 .50, P = = 38 .89 0.09
Capital Budgeting and Valuation
Capital Budgeting and Valuation
Capital Budgeting and Valuation
Question 6 Suppose Goodyear Tire and Rubber Company is considering divesting one of its manufacturing plants. The plant is expected to generate free cash flows of $2 million per year, growing at a rate of 3% per year. Goodyear has an equity cost of capital of 9%, a debt cost of capital of 7.5%, a marginal corporate tax rate of 40%, and a debt-equity ratio of 3.1. If the plant has average risk and Goodyear plans to maintain a constant debt-equity ratio, what after-tax amount must it receive for the plant for the divestiture to be profitable?
Capital Budgeting and Valuation
Question 6 Suppose Goodyear Tire and Rubber Company is considering divesting one of its manufacturing plants. The plant is expected to generate free cash flows of $2 million per year, growing at a rate of 3% per year. Goodyear has an equity cost of capital of 9%, a debt cost of capital of 7.5%, a marginal corporate tax rate of 40%, and a debt-equity ratio of 3.1. If the plant has average risk and Goodyear plans to maintain a constant debt-equity ratio, what after-tax amount must it receive for the plant for the divestiture to be profitable? E D r WACC = r E + r D (1 − τ C ) E + D E + D 1 3.1 × 0.09 + × 0.075 × (1 − 0.4) = 0.056 = 1 + 3.1 1 + 3.1 CF 2 V L = = = 76 .9 million r WACC − g 0.056 − 0.03
So the divestiture is profitable only if Goodyear receives more than $76.9 million after tax.
Capital Budgeting and Valuation
Question 7 Suppose Alcatel-Lucent has an equity cost of capital of 12%, market capitalization of $12.06 billion, and an enterprise value of $18 billion with a debt cost of capital of 8% and its marginal tax rate is 40%. 1. What is Alcatel-Lucent’s WACC?
Capital Budgeting and Valuation
Question 7 Suppose Alcatel-Lucent has an equity cost of capital of 12%, market capitalization of $12.06 billion, and an enterprise value of $18 billion with a debt cost of capital of 8% and its marginal tax rate is 40%. 1. What is Alcatel-Lucent’s WACC? E D r WACC = r E + r D (1 − τ C ) E + D E + D 12.06 18 − 12.06 × × 0.08 × (1 − 0.4) = 0.0962 0 12 = . + 18 18 2. If Alcatel-Lucent maintains a constant debt-equity ratio, what is the value of a project with average risk and the following expected free Year 0 1 2 3 cash flows? FCF ($ million) -100 60 110 80
Capital Budgeting and Valuation
Question 7 Suppose Alcatel-Lucent has an equity cost of capital of 12%, market capitalization of $12.06 billion, and an enterprise value of $18 billion with a debt cost of capital of 8% and its marginal tax rate is 40%. 1. What is Alcatel-Lucent’s WACC? E D r WACC = r E + r D (1 − τ C ) E + D E + D 12.06 18 − 12.06 × × 0.08 × (1 − 0.4) = 0.0962 0 12 = . + 18 18 2. If Alcatel-Lucent maintains a constant debt-equity ratio, what is the value of a project with average risk and the following expected free Year 0 1 2 3 cash flows? FCF ($ million) -100 60 110 80 60 110 80 V = + + = 207.01 million 2 3 1.0962 1.0962 1.0962 L
Capital Budgeting and Valuation
Question 8 Acort Industries has 20 million shares outstanding and a current share price of $30 per share. It also has a long-term debt outstanding. This debt is risk free, is four years away from maturity, has an annual coupon rate of 5%, and has a $125 million face value. The first of the remaining coupon payments will be due in exactly one year. The riskless interest rates for all maturities are constant at 3%. Acort has EBIT of $115 million, which is expected to remain constant each year. New capital expenditures are expected to equal depreciation and equal $22 million per year, while no changes to net working capital are expected in the future. The corporate tax rate is 38%, and Acort is expected to keep its debt-equity ratio constant in the future (by either issuing additional new debt or buying back some debt as time goes on). 1. Based on this information, estimate Acort’s WACC.
Capital Budgeting and Valuation
Question 8 1. Based on this information, estimate Acort’s WACC. Calculate equity value: E = 20 × 30 = 600 million
Calculate debt value:
1 1 y
1 FV − D = CPN × + N (1 + y ) (1 + y )N 6.25 1 125 × 1− = + 4 0.03 1.034 (1.03) = 134.29 million
So the enterprise value is E+D=600+134.29=734.29 million.
Capital Budgeting and Valuation
Question 8 To calculate FCF, use FCF = EBIT × (1 − τ C ) + Dep − Capex − ∆NWC
= 115 × (1 − 0.38) = 71 .3 million Since the firm is not expected to grow, the WACC can be computed using the following formula: FCF V = r WACC L
FCF 71.3 = = 0 .0971 ⇒ r WACC = L 734.29 V
2. What is Ascort’s equity cost of capital?
Capital Budgeting and Valuation
Question 8 To calculate FCF, use FCF = EBIT × (1 − τ C ) + Dep − Capex − ∆NWC
= 115 × (1 − 0.38) = 71 .3 million Since the firm is not expected to grow, the WACC can be computed using the following formula: FCF V = r WACC L
FCF 71.3 = = 0 .0971 ⇒ r WACC = L 734.29 V
2. What is Ascort’s equity cost of capital? E D r E + r D (1 − τ C ) E + D E + D 600 134.29 r E + 0.0971 = 0.03(1 − 0.38) ⇒ r E = 0 .1147 734.29 734.29 r WACC =
Ascort’s equity cost of capital is 11.47%.
Options
Options
Options
Question 9 The current price of Estelle Corporation stock is $40.00. Next year, this stock price will either go up by 10% or go down by 10%. The stock pays no dividends. The one-year risk-free interest rate is 4.0% and will remain constant. Using the Binomial Model, calculate the price of a one-year call option on Estelle stock with a strike price of $40.00.
Options
Question 9 The current price of Estelle Corporation stock is $40.00. Next year, this stock price will either go up by 10% or go down by 10%. The stock pays no dividends. The one-year risk-free interest rate is 4.0% and will remain constant. Using the Binomial Model, calculate the price of a one-year call option on Estelle stock with a strike price of $40.00.
Options
Question 9 The current price of Estelle Corporation stock is $40.00. In each of the next two years, this stock price will either go up by 10% or go down by 10%. The stock pays no dividends. The one-year risk-free interest rate is 4.0% and will remain constant. Using the Binomial Model, calculate the price of a one-year call option on Estelle stock with a strike price of $40.00. U − D 44 − 36 m = = = 2 C U − C D 4−0 1 D − mC D C = S − m 1 + r f 1 36 − 2 × 0 40 − = = 2 .69 2 1 + 0.04
Options
Question 10 Suppose a stock is currently trading for $65, and in one period will either go up by 25% or fall by 15%. If the one-period risk-free rate is 4.0%, what is the price of a European put option that expires in one period and has an exercise price of $65? Suppose the option actually sold in the market for $8. Describe a trading strategy that yields arbitrage profits.
Options
Question 10 Suppose a stock is currently trading for $65, and in one period will either go up by 25% or fall by 15%. If the one-period risk-free rate is 4.0%, what is the price of a European put option that expires in one period and has an exercise price of $65? Suppose the option actually sold in the market for $8. Describe a trading strategy that yields arbitrage profits.
Options
Question 10 Suppose a stock is currently trading for $65, and in one period will either go up by 25% or fall by 15%. If the one-period risk-free rate is 4.0%, what is the price of a European put option that expires in one period and has an exercise price of $65? Suppose the option actually sold in the market for $8. Describe a trading strategy that yields arbitrage profits. U − D 81.25 − 55.25 m = = = −2.67 C U − C D 0 − 9.75 1 55.25 + 2.67 × 9.75 P = = 4 .92 65 − −2.67 1 + 0.04
Options
Question 10 Suppose a stock is currently trading for $65, and in one period will either go up by 25% or fall by 15%. If the one-period risk-free rate is 4.0%, what is the price of a European put option that expires in one period and has an exercise price of $65? Suppose the option actually sold in the market for $8. Describe a trading strategy that yields arbitrage profits. U − D 81.25 − 55.25 m = = = −2.67 C U − C D 0 − 9.75 1 55.25 + 2.67 × 9.75 P = = 4 .92 65 − −2.67 1 + 0.04
D − mC D S − mP = 1 + r f 1 D − mC D P = S − m m (1 + r f ) P = −0 37S + 29 27
Options
Question 10
Suppose a stock is currently trading for $65, and in one period will either go up by 25% or fall by 15%. If the one-period risk-free rate is 4.0%, what is the price of a European put option that expires in one period and has an exercise price of $65? Suppose the option actually sold in the market for $8. Describe a trading strategy that yields arbitrage profits. If the put is actually selling for $8, then it is overpriced. The arbitrage trading opportunity will involve selling the put, 0.37 of a stock and invest 29.27.
Options
Question 11 Suppose the current price of Narver Network systems stock $55 per share. In each of the next two years, the stock price will either increase by 25% or decrease by 15%. The 6% one-year risk-free rate of interest will remain constant. Suppose the put option with a strike price of $60 actually sold today for $3.87. You do not know what the option will trade for next period. Describe a trading strategy that will yield arbitrage profits.
Options
Question 11 Suppose the current price of Narver Network systems stock $55 per share. In each of the next two years, the stock price will either increase by 25% or decrease by 15%. The 6% one-year risk-free rate of interest will remain constant. Suppose the put option with a strike price of $60 actually sold today for $3.87. You do not know what the option will trade for next period. Describe a trading strategy that will yield arbitrage profits.
Options
Question 11 Suppose the current price of Narver Network systems stock $55 per share. In each of the next two years, the stock price will either increase by 25% or decrease by 15%. The 6% one-year risk-free rate of interest will remain constant. Suppose the put option with a strike price of $60 actually sold today for $3.87. You do not know what the option will trade for next period. Describe a trading strategy that will yield arbitrage profits. Box 1: 85.94 − 58.44 m = = −17.63 0 − 1.56 1 58.44 + 17.63 × 1.56 P = 68.75 + = 0 .7 −17.63 1 + 0.06
Options
Question 11 Suppose the current price of Narver Network systems stock $55 per share. In each of the next two years, the stock price will either increase by 25% or decrease by 15%. The 6% one-year risk-free rate of interest will remain constant. Suppose the put option with a strike price of $60 actually sold today for $3.87. You do not know what the option will trade for next period. Describe a trading strategy that will yield arbitrage profits. Box 2: 58.44 − 39.74 m = = −1 1.56 − 20.26 1 39.74 + 1 × 20.26 P = 46.75 + = 9 .85 −1 1 + 0.06
Options
Question 11 Suppose the current price of Narver Network systems stock $55 per share. In each of the next two years, the stock price will either increase by 25% or decrease by 15%. The 6% one-year risk-free rate of interest will remain constant. Suppose the put option with a strike price of $60 actually sold today for $3.87. You do not know what the option will trade for next period. Describe a trading strategy that will yield arbitrage profits. Box 3: 68.75 − 46.75 m = = −2.4 0.7 − 9.85 1 46.75 + 2.4 × 9.85 P = 55 − = 4 .76 −2.4 1 + 0.06
