Capital Structure in Perfect Capital Markets
For problems in this section assume no taxes or distress costs.
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 projectâ€™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 wayâ€”that is, what is the initial market value of the unlevered equity?
c. 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?
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 firmâ€™s equity must you sell to raise the additional $1 million you need?
c. What is the value of your share of the firmâ€™s equity in cases (a) and (b)?
16. Rogot Instruments makes fine violins, violas, and cellos. It has $1 million in debt outstanding, equity valued at $2 million, and pays corporate income tax at a rate of 35%. Its cost of equity is 12% and its cost of debt is 7%.
a. What is Rogotâ€™s pretax WACC?
b.What is Rogotâ€™s (effective after-tax) WACC?