Capital Structure in a Perfect Market
14-1. Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required for the project is $100,000, and the project’s cost of capital is 20%. The risk-free interest rate is 10%. a. What is the NPV of this project? b. 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. How much money can be raised in this way—that is, what is the initial market value of the unlevered equity? c. a. Suppose the initial $100,000 is instead raised by borrowing at the risk-free interest rate. What are the cash flows of the levered equity, and what is its initial value according to MM? E ⎡C (1)⎤ = ⎣ ⎦ 1 (130, 000 + 180, 000) = 155, 000, 2 155, 000 NPV = − 100, 000 = 129,167 − 100, 000 = $29,167 1.20 155, 000 = 129,167 1.20
Equity value = PV ( C (1)) =
Debt payments = 100, 000, equity receives 20,000 or 70,000. Initial value, by MM, is 129,167 − 100, 000 = $29,167 .
You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for $30 million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $2 million. Investors are willing to provide you with $2 million in initial capital in exchange for 50% of the unlevered equity in the firm. a. What is the total market value of the firm without leverage? b. Suppose you borrow $1 million. According to MM, what fraction of the firm’s equity will you need to sell to raise the additional $1 million you need? c. What is the value of your share of the firm’s equity in cases (a) and (b)?
a. b. c.
Total value of equity = 2 × $2m = $4m MM says total value of firm is still $4 million. $1 million of debt implies total value of equity is $3 million. Therefore, 33% of equity must be sold to raise $1 million. In (a), 50% × $4m = $2m. In (b), 2/3 × $3m = $2m. Thus, in a perfect market the choice of capital structure does not affect the value to the entrepreneur.
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Berk/DeMarzo • Corporate Finance, Second Edition 14-3.
Acort Industries owns assets that will have an 80% probability of having a market value of $50 million in one year. There is a 20% chance that the assets will be worth only $20 million. The current risk-free rate is 5%, and Acort’s assets have a cost of capital of 10%. a. If Acort is unlevered, what is the current market value of its equity? b. Suppose instead that Acort has debt with a face value of $20 million due in one year. According to MM, what is the value of Acort’s equity in this case? c. What is the expected return of Acort’s equity without leverage? What is the expected return of Acort’s equity with leverage?
d. What is the lowest possible realized return of Acort’s equity with and without leverage?
E[Value in one year] = 0.8 ( 50 ) + 0.2 ( 20 ) = 44 . E = D=
44 = $40m. 1.10
20 = 19.048 . Therefore, E = 40 − 19.048 = $20.952m. 1.05 44 44 − 20 − 1 = 10% , with leverage, r = − 1 = 14.55%. 40 20.952 20 0 − 1 = −50% , with leverage, r = − 1 = −100%. 40 20.952
Without leverage, r= Without leverage, r=
Wolfrum Technology (WT) has no debt. Its assets will be worth $450 million in one year if the economy is strong, but only $200 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is $250 million. a. What is the expected return of WT stock without leverage? b. Suppose the risk-free interest rate is 5%. If WT borrows $100 million today at this rate and uses the proceeds to pay an immediate cash dividend, what will be the market value of its equity just after the dividend is paid, according to MM? c. What is the expected return of MM...