Question

Deep Mines has 43,800 shares of common stock outstanding with a beta of 1.54 and a market price of $51 a share. There are 10,000 shares of 7 percent preferred stock outstanding with a stated value of $100 per share and a market value of $83 a share. The 8 percent semiannual bonds have a face value of $1,000 and are selling at 96 percent of par. There are 5,000 bonds outstanding that mature in 13 years. The expected market rate of return is 7.5 percent, risk-free rate is 3.6 percent, and the tax rate is 21 percent. What discount rate should the firm apply to a new project's cash flows if the project has the same risk as the company's typical project? a. 9.3%. b. 8.4%. c. 7.7%. d. 10.7%.

Answer 1

The discount rate, or WACC, for new projects at Deep Mines with the same risk as typical projects is calculated using the CAPM for cost of equity, the dividend yield formula for cost of preferred stock, and the yield on bonds adjusted for taxes for cost of debt. The calculated WACC is 10.7%.

Step-by-step explanation:

The question is asking for the discount rate that should be applied to a new project of Deep Mines, which has the same risk as the company's typical project. The discount rate is essentially the company's weighted average cost of capital (WACC). The WACC calculation involves considering the cost of equity, cost of preferred stock, and cost of debt, weighting them according to their proportion in the company's capital structure, and adjusting for taxes where appropriate.

Step-by-Step Calculation of WACC

To calculate the cost of equity, we use the Capital Asset Pricing Model (CAPM) formula: cost of equity = risk-free rate + (beta * (market rate of return - risk-free rate)). The cost of preferred stock is calculated by dividing the dividend by the market price of preferred shares. The after-tax cost of debt is the yield on the company's bonds adjusted for the tax shield, using the formula: after-tax cost of debt = (coupon rate * (1 - tax rate)). Finally, we calculate WACC by multiplying the cost of each component by its respective weight in the company's capital structure and summing them up.

After performing the calculations considering the provided data, the WACC or discount rate for evaluating new projects at Deep Mines assuming they carry the same risk as the company's typical project is option d, 10.7%.

Answer 2

A. 9.3%

E = 43,800 ($51) = $2,233,800

P = 10,000 ($83) = $830,000

D = 5,000 ($1,000) (0.96) = $4,800,000

V = $2,233,800 + 830,000 + 4,800,000

V = $7,863,800

RE = 0.036 + 1.54 (0.075)

RE = 0.1515

RP = [0.07 ($100) ] / $83

RP = 0.0843

RD = 0.96 ($1,000) = [0.08 ($1,000) / 2] [(1 − {1 / [1 + (r / 2)] 13 (2) / (r / 2)] + $1,000 / [1 + (r/2) ] 13 (2)

RD = 0.0851

WACC =

($2,233,800 / $7,863,800) (0.1515) + ($830,000 / $7,863,800) (0.0843) + ($4,800,000 / $7,863,800) (0.0851) (1 − 0.21)

WACC =

0.0930, or 9.30%

Step-by-step explanation:

MV of Equity = Price of Equity * Number of Shares Outstanding MV of Equity

$51 * 43,800 = 2,233,800 MV of Bond =

Par Value * Bonds Outstanding * % Age of Par MV of Bond =

$1,000 * 5,000 * 0.96 = 4,800,000 MV of Preferred Equity