Makai Metals Corporation has 9.8 million shares of common stock outstanding and

Question

Makai Metals Corporation has 9.8 million shares of common stock outstanding and 420,000 5 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $46 per share and has a beta of 1.4, and the bonds have 15 years to maturity and sell for 117 percent of par. The market risk premium is 8.6 percent, T-bills are yielding 4 percent, and the company’s tax rate is 40 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., 32.1616.)

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? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Discount rate            11.34 11.34 Incorrect  %

Explanation / Answer

Debt:

Number of bonds outstanding = 420,000
Face Value = $1,000
Current Price = 117%*$1,000 = $1,170

Value of Debt = 420,000 * $1,170
Value of Debt = $491,400,000

Annual Coupon Rate = 5%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50%*$1,000 = $25

Time to Maturity = 15 years
Semiannual Period to Maturity = 30

Let semiannual YTM be i%

$1,170 = $25 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -1170
PMT = 25
FV = 1000

I = 1.765%

Semiannual YTM = 1.765%
Annual YTM = 2 * 1.765%
Annual YTM = 3.53%

Before-tax Cost of Debt = 3.53%
After-tax Cost of Debt = 3.53% * (1 - 0.40)
After-tax Cost of Debt = 2.118%

Equity:

Number of shares outstanding = 9,800,000
Current Price = $46

Value of Common Stock = 9,800,000 * $46
Value of Common Stock = $450,800,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 4% + 1.4 * 8.6%
Cost of Common Equity = 16.04%

Value of Firm = Value of Debt + Value of Equity
Value of Firm = $491,400,000 + $450,800,000
Value of Firm = $942,200,000

Weight of Debt = $491,400,000/$942,200,000
Weight of Debt = 0.5215

Weight of Equity = $450,800,000/$942,200,000
Weight of Equity = 0.4785

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Equity*Cost of Equity
WACC = 0.5215*2.118% + 0.4785*16.04%
WACC = 8.78%

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