FIN 4424: Exam 2, Math Problems

Assume the marginal corporate tax rate is 30 percent. The firm has no debt in its capital structure. It is valued at $100 million. What would be the value of the firm if it issued $50 million in perpetual debt and repurchased the same amount of equity?

$115 million

If a firm permanently borrows $50 million at an interest rate of 10 percent, what is the present value of the interest tax shield? Assume a 30 percent marginal corporate tax rate.

$15 million

If a firm permanently borrows $100 million at an interest rate of 8 percent, what is the present value of the interest tax shield? (Assume that the marginal corporate tax rate is 30 percent.)

$30 million

The correlation coefficient between a stock and the market portfolio is +0.6. The standard deviation of return of the stock is 30 percent and that of the market portfolio is 20 percent. Calculate the beta of the stock.

.9

If a firm borrows $50 million for one year at an interest rate of 9 percent, what is the present value of the interest tax shield? Assume a 30 percent marginal corporate tax rate.

1.24 million

The covariance between YOHO stock and the S&P 500 is 0.05. The standard deviation of the stock market is 20 percent. What is the beta of YOHO?

1.25

What is the relative tax advantage of debt? Assume that personal and corporate taxes are given by TC = (corporate tax rate) = 35 percent; TpE = personal tax rate on equity income = 30 percent; and Tp = personal tax rate on interest income = 20 percent.

1.76

Suppose you invest equal amounts in a portfolio with an expected return of 16 percent and a standard deviation of returns of 18 percent and a risk-free asset with an interest rate of 4 percent. Calculate the expected return on the resulting portfolio.

10%

Assume the following data for U&P Company: Debt (D) = $100 million; Equity (E) = $300 million; rD = 6%; rE = 12%; and TC = 30%. Calculate the after-tax weighted average cost of capital (WACC):

10.05%

Suppose the beta of Exxon-Mobil is 0.65, the risk-free rate is 4 percent, and the expected market rate of return is 14 percent. Calculate the expected rate of return on Exxon-Mobil.

10.5%

A firm has a total market value of $10 million while its debt has a market value of $4 million. What is the after-tax weighted average cost of capital if the before-tax cost of debt is 10 percent, the cost of equity is 15 percent, and the tax rate is 35 percent?

11.6%

Assume the following data: Risk-free rate = 4.0 percent; average risk premium = 7.7 percent. Calculate the required rate of return for the risky asset.

11.7%

Suppose the beta of Microsoft is 1.13, the risk-free rate is 3 percent, and the market risk premium is 8 percent. Calculate the expected return for Microsoft.

12.04%

A firm has zero debt in its capital structure. Its overall cost of capital is 10 percent. The firm is considering a new capital structure with 60 percent debt. The interest rate on the debt would be 8 percent. Assuming there are no taxes, its cost of equity capital with the new capital structure would be

13%

A firm's return on assets is 12 percent and the cost of the firm's debt is 7 percent. Given a 0.7 debt-equity-ratio, what is the levered cost of equity? Assume that there are no taxes.

15.5%

Stock A has an expected return of 10 percent per year and stock B has an expected return of 20 percent. If 40 percent of a portfolio's funds are invested in stock A and the rest in stock B, what is the expected return on the portfolio of stock A and stock B?

16%

The M&M Company is financed by $10 million in debt (market value) and $40 million in equity (market value). The cost of debt is 10 percent and the cost of equity is 20 percent. Calculate the weighted average cost of capital, assuming no taxes.

18%

Suppose the beta of Amazon is 2.2, the risk-free rate is 5.5 percent, and the market risk premium is 8 percent. Calculate the expected rate of return for Amazon.

23.1%

If the average annual rate of return for common stocks is 11.7 percent, and 4.0 percent for U.S. Treasury bills, what is the average market risk premium?

7.7%

Given are the following data: Cost of debt = rD = 6%; Cost of equity = rE = 12.1%; Marginal tax rate = 35%; and the firm has 50 percent debt and 50 percent equity. Calculate the after-tax weighted average cost of capital (WACC).

8%

The M&M Company is financed by $4 million (market value) in debt and $6 million (market value) in equity. The cost of debt is 5 percent and the cost of equity is 10 percent. Calculate the weighted average cost of capital. (Assume no taxes.)

8%

Assume the following data for a stock: Beta = 0.9; risk-free rate = 4 percent; market rate of return = 14 percent; and expected rate of return on the stock = 13 percent. Then the stock is

correctly priced

Assume the following data for a stock: Beta = 1.5; risk-free rate = 4 percent; market rate of return = 12 percent; and expected rate of return on the stock = 15 percent. Then the stock is

overpriced

Assume the following data for a stock: Beta = 0.5; risk-free rate = 4 percent; market rate of return = 12 percent; and expected rate of return on the stock = 10 percent. Then the stock is

underpriced

If a firm borrows $50 million for one year at an interest rate of 10 percent, what is the present value of the interest tax shield? Assume a 30 percent marginal corporate tax rate.

$1.36 million