chprobSM_ch17

# chprobSM_ch17 - Chapter 17 Capital Structure Limits to the...

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Chapter 17: Capital Structure: Limits to the Use of Debt 17.1 a. The value of a firm’s equity is the discounted expected cash flow to the firm’s stockholders. If there is a boom, Good Time will generate cash flow of \$250 million. Since Good Time owes its bondholders \$150 million, the firm’s stockholders will receive \$100 million (= \$250 million - \$150 million) if there is a boom. If there is a recession, Good Time will generate a cash flow of \$100 million. Since the bondholder’s have the right to the first \$150 million that the firm generates, Good Time’ stockholders will receive \$0 if there is a recession. The probability of a boom is 60%. The probability of a recession is 40%. The appropriate discount rate is 12%. The value of Good Time’s equity is: {(0.60)(\$100 million) + (0.40)(\$0)} / 1.12 = \$53.57 million The value of Good Time’s equity is \$53.57 million. b. Promised Return = (Face Value of Debt / Market Value of Debt) – 1 Since the debt holders have been promised \$150 million at the end of the year, the face value of Good Time’s debt is \$150 million. The market value of Good Time’s debt is \$108.93 million. The promised return on Good Time’s debt is: Promised Return = (Face Value of Bond / Market Value of Bond) – 1 = (\$150 million / \$108.93 million) – 1 = 0.3770 The promised return on Good Time’s debt is 37.70%. c. The value of a firm is the sum of the market value of the firm’s debt and equity. The value of Good Time’s debt is \$108.93 million. As shown in part a , the value of Good Time’s equity is \$53.57 million. The value of Good Time is: V L = B + S = \$108.93 million + \$53.57 million = \$162.5 million The value of Good Time Company is \$162.5 million. d. The market value of a firm’s debt is the discounted expected cash flow to the firm’s debt holders. Answers to End-of-Chapter Problems B-252

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If there is a boom, Good Time will generate cash flow of \$250 million. Since Good Time owes its debt holders \$150 million, the firm’s bondholders will receive \$150 million if there is a boom. While the firm’s debt holders are owed \$150 million, Good Time will only generate \$100 million of cash flow if there is a recession. The firm’s debt holders cannot receive more than the firm can afford to pay them. Therefore, Good Time’s debt holders will only receive \$100 million if there is a recession. The probability of a boom is 60%. The probability of a recession is 40%. The appropriate discount rate is 12%. If no bankruptcy costs are priced into the debt, the value of Good Time’s debt is: {(0.60)(\$150 million) + (0.40)(\$100)} / 1.12 = \$116.07 million Therefore, in a world with no bankruptcy costs, Good Time’s debt would be worth \$116.07 million. e. The market value of a firm’s debt is the discounted expected cash flow to the firm’s debt holders. We know that the debt holders will receive \$150 million in a boom and that the market value of the debt is \$108.93 million. Let X be the amount that bondholders expect to receive in the event of a recession: \$108.93 million = {(0.60)(\$150 million) + (0.40)(X)} / 1.12 X = \$80 million Therefore, the market value of Good Time’s debt indicates that the firm’s bondholders expect to receive \$80 million in the event of a recession.
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