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Unformatted text preview: lue in that state of the economy. Since this is the only project for the company, the company value will be the same as the project value, so: Lowvolatility project value = .50($2,500) + .50($2,700) Lowvolatility project value = $2,600 Highvolatility project value = .50($2,100) + .50($2,800) Highvolatility project value = $2,450 The lowvolatility project maximizes the expected value of the firm. b. The value of the equity is the residual value of the company after the bondholders are paid off. If the lowvolatility project is undertaken, the firm’s equity will be worth $0 if the economy is bad and $200 if the economy is good. Since each of these two scenarios is equally probable, the expected value of the firm’s equity is: Expected value of equity with lowvolatility project = .50($0) + .50($200) Expected value of equity with lowvolatility project = $100 And the value of the company if the highvolatility project is undertaken will be: Expected value of equity with highvolatility project = .50($0) + .50($300) Expected value of equity with highvolatility project = $150 c. Riskneutral investors prefer the strategy with the highest expected value. Thus, the company’s stockholders prefer the highvolatility project since it maximizes the expected value of the company’s equity. In order to make stockholders indifferent between the lowvolatility project and the highvolatility project, the bondholders will need to raise their required debt payment so that the expected value of equity if the highvolatility project is undertaken is equal to the expected value of equity if the lowvolatility project is undertaken. As shown in part a, the expected value of equity if the lowvolatility project is undertaken is $2,600. If the highvolatility project is undertaken, the value of the firm will be $2,100 if the economy is bad and $2,800 if the economy is good. If the economy is bad, the entire $2,100 will go to the bondholders and stockholders will receive nothing. If the economy is good, stockholders will receive the difference between $2,800, the total value of the firm, and the required debt payment. Let X be the debt payment that bondholders will require if the highvolatility project is undertaken. In order for stockholders to be indifferent between the two projects, the expected value of equity if the highvolatility project is undertaken must be equal to $2,100, so: Expected value of equity = $100 = .50($0) + .50($2,800 – X) X = $2,600 d. 373 8. a. The expected payoff to bondholders is the face value of debt or the value of the company, whichever is less. Since the value of the company in a recession is $85 million and the required debt payment in one year is $120 million, bondholders will receive the lesser amount, or $85 million. The promised return on debt is: Promised return = (Face value of debt / Market value of debt) – 1 Promised return = ($120,000,000 / $94,000,000) – 1 Promised return = .2766 or 27.66% b. c. In part a, we determined bondholders will receive $85 million in a recession. In a boom, the bondholders will receive the entire $120 million promised payment since the market value of the company is greater than the payment. So, the expected value of debt is: Expected payment to bondholders = .60($120,000,000) + .40($85,000,000) Expected payment to bondholders = $106,000,000 So, the expected return on debt is: Expected return = (Expected value of debt / Market value of debt) – 1 Expected return = ($106,000,000 / $94,000,000) – 1 Expected return = .1277 or 12.77% Challenge 9. a. In their no tax model, MM assume that tC, tB, and C(B) are all zero. Under these assumptions, VL = VU, signifying that the capital structure of a firm has no effect on its value. There is no optimal debtequity ratio. In their model with corporate taxes, MM assume that tC > 0 and both tB and C(B) are equal to zero. Under these assumptions, VL = VU + tCB, implying that raising the amount of debt in a firm’s capital structure will increase the overall value of the firm. This model implies that the debtequity ratio of every firm should be infinite. If the costs of financial distress are zero, the value of a levered firm equals: VL = VU + {1 – [(1 – tC) / (1 – tB)}] × B Therefore, the change in the value of this allequity firm that issues debt and uses the proceeds to repurchase equity is: Change in value = {1 – [(1 – tC) / (1 – tB)}] × B Change in value = {1 – [(1 – .34) / (1 – .20)]} × $1,000,000 Change in value = $175,000 b. c. 374 d. If the costs of financial distress are zero, the value of a levered firm equals: VL = VU + {1 – [(1 – tC) / (1 – tB)]} × B Therefore, the change in the value of an allequity firm that issues $1 of perpetual debt instead of $1 of perpetual equity is: Change in value = {1 – [(1 – tC) / (1 – tB)]} × $1 If the firm is not able to benefit from interest deductions, the firm’s taxable income will remain the same regardless of the amount of debt in its capital structure, and no tax s...
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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 TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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