Titan Mining Corporation has 8.1 million shares of common stock outstanding, 300,000 shares of 4.1 percent preferred stock outstanding, and 185,000 bonds with a semiannual coupon rate of 5.5 percent outstanding, par value $2,000 each. The common stock currently sells for $57 per share and has a beta of 1.15, the preferred stock has a par value of $100 and currently sells for $99 per share, and the bonds have 18 years to maturity and sell for 107 percent of par. The market risk premium is 6.6 percent, T-bills are yielding 3.3 percent, and the company’s tax rate is 24 percent. a. What is the firm’s market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.) b. If the company is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows?

As the new project will have the same risk as that of the firm's typical project, it shall be discounted using the WACC of the firm which is 9.5339%

Explanation:

The capital structure of a company is typically made of at least one or at most all of the following components namely debt, common stock and preferred stock. To calculate the market value of capital structure, we calculate the market value of each component and sum it.

Market value of debt = 185000 * 2000 * 107% = 395900000 or 395.9 million

Market value of preferred stock = 300000 * 99 = 29700000 or 29.7 million

Market value of common stock = 8100000 * 57 = 461700000 or 461.7 million

Total value of capital structure = 395.9 + 29.7 + 461.7 = 887300000 or 887.3 million

b.

The cash flows of a firm having the capital structure mix containing more than one component should be discounted using the WACC or weighted average cost of capital. The WACC is calculated using the following formula,

WACC = wD * rD * (1-tax rate) + wP * rP + wE * rE

Where,

wD, wP, wE represents the weight of debt, preferred stock and common stock in capital structure respectively
rD, rP, rE represents the cost of each component

First we need to determine the cost of equity.

rE = 0.033 + 1.15 * 0.066

rE = 0.1089 or 10.89%

Cost of debt = 5.5* 2 = 11% or 0.11

WACC = 395.9 / 887.3 * 0.11 * (1 - 0.24) + 29.7 / 887.3 * 0.041 +

461.7 / 887.3 * 0.1089

WACC = 0.0953387 or 9.53387% rounded off to 9.5339%

As the new project will have the same risk as that of the firm's typical project, it shall be discounted using the WACC of the firm which is 9.5339%