Answer to the Corporate Finance
Chapter 14
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
b. c.
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 .
14-2.
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.
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
b. c.
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 .
14-2.
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.