Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

9 10 in a market with competitors you must realize

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Unformatted text preview: ase in value over the period is 26.67 percent [= ($380 / $300) – 1]. If the project is unsuccessful and the company’s value falls, the percentage decrease in value over the period is –30 percent [= ($210 / $300) –1]. We can determine the risk-neutral probability of an increase in the value of the company as: Risk-free rate = (ProbabilityRise)(ReturnRise) + (ProbabilityFall)(ReturnFall) Risk-free rate = (ProbabilityRise)(ReturnRise) + (1 – ProbabilityRise)(ReturnFall) 0.07 = (ProbabilityRise)(.2667) + (1 – ProbabilityRise)(–.30) ProbabilityRise = .6529 or 65.29% And the risk-neutral probability of a decline in the company value is: ProbabilityFall = 1 – ProbabilityRise ProbabilityFall = 1 –.6529 ProbabilityFall = .3471 or 34.71% Using these risk-neutral probabilities, we can determine the expected payoff to the equityholders’ call option at expiration, which will be: Expected payoff at expiration = (.6529)($60,000,000) + (.3471)($0) Expected payoff at expiration = $39,176,470.59 Since this payoff occurs 1 year from now, we must discount it at the risk-free rate in order to find its present value. So: PV(Expected payoff at expiration) = ($39,176,470.59 / 1.07) PV(Expected payoff at expiration) = $36,613,523.91 Therefore, the current value of the company’s equity is $36,613,523.91. The current value of the company is equal to the value of its equity plus the value of its debt. In order to find the value of company’s debt, subtract the value of the company’s equity from the total value of the company: VL = Debt + Equity $300,000,000 = Debt + $36,613,523.91 Debt = $263,386,476.09 460 b. To find the price per share, we can divide the total value of the equity by the number of shares outstanding. So, the price per share is: Price per share = Total equity value / Shares outstanding Price per share = $36,613,523.91 / 500,000 Price per share = $73.23 c. The market value of the firm’s debt is $263,386,476.09. The present value of the same face amount of riskless debt is $299,065,420.56 (= $320,000,000 / 1.07). The firm’s debt is worth less than the present value of riskless debt since there is a risk that it will not be repaid in full. In other words, the market value of the debt takes into account the risk of default. The value of riskless debt is $299,065,420.56. Since there is a chance that the company might not repay its debtholders in full, the debt is worth less than $299,065,420.56. The value of Strudler today is $300 million. It will either increase to $445 million or decrease to $185 million in one year as a result of the new project. If the firm’s value increases to $445 million, the equityholders will exercise their call option, and they will receive a payoff of $125 million at expiration. However, if the firm’s value decreases to $185 million, the equityholders will not exercise their call option, and they will receive no payoff at expiration. Equityholders’ call option price with a strike of $320 (in millions) Today 1 year $125 ? $185 $0 =Max(0, $185 – 320) =Max(0, $445 – 320) d. Value of company (in millions) Today 1 year $445 $300 If the project is successful and the company’s value rises, the increase in the value of the company over the period is 48.33 percent [= ($445 / $300) – 1]. If the project is unsuccessful and the company’s value falls, decrease in the value of the company over the period is –38.33 percent [= ($185 / $300) –1]. We can use the following expression to determine the risk-neutral probability of an increase in the value of the company: Risk-free rate = (ProbabilityRise)(ReturnRise) + (ProbabilityFall)(ReturnFall) Risk-free rate = (ProbabilityRise)(ReturnRise) + (1 - ProbabilityRise)(ReturnFall) 0.07 = (ProbabilityRise)(.4833) + (1 – ProbabilityRise)(–.3833) ProbabilityRise = .5231 or 52.31 percent So the risk-neutral probability of a decrease in the company value is: ProbabilityFall = 1 – ProbabilityRise ProbabilityFall = 1 – .5231 ProbabilityFall = .4769 or 47.69% 461 Using these risk-neutral probabilities, we can determine the expected payoff to the equityholders’ call option at expiration, which is: Expected payoff at expiration = (.5231)($125,000,000) + (.4769)($0) Expected payoff at expiration = $65,384,615.38 Since this payoff occurs 1 year from now, we must discount it at the risk-free rate in order to find its present value. So: PV(Expected payoff at expiration) = ($65,384,615.38 / 1.07) PV(Expected payoff at expiration) = $61,107,117.18 Therefore, the current value of the firm’s equity is $61,107,117.18. The current value of the company is equal to the value of its equity plus the value of its debt. In order to find the value of the company’s debt, we can subtract the value of the company’s equity from the total value of the company, which yields: VL = Debt + Equity $300,000,000 = Debt + $61,107,117.18 Debt = $238,892,882.82 The riskier project increases the value of the company’s equity and decreases the value of the company’s debt. I...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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