Question

Makai Metals Corporation has 9.1million shares of common stock outstanding and 230,000   6.2 percent semiannual bonds outstanding, par value $1000 each.  The common stock currently sells for $41 per share and has a beta of 1.20, and the bonds have 20 years to maturity and sell for 104 percent of par.  The market risk premium is 7 percent, T-bills are yielding 3.1 percent, and the tax rate is 35 percent.  

a. What is the firm's market value capital structure?

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?  

Answer 1

Debt:

Number of bonds outstanding = 230,000
Face Value = $1,000

Current Price = 104% * $1,000
Current Price = $1,040

Value of Debt = 230,000 * $1,040
Value of Debt = $239,200,000

Annual Coupon Rate = 6.20%
Semiannual Coupon Rate = 3.10%
Semiannual Coupon = 3.10% * $1,000
Semiannual Coupon = $31

Time to Maturity = 20 years
Semiannual Period to Maturity = 40

Let Semiannual YTM be i%

$1,040 = $31 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -1040
PMT = 31
FV = 1000

I = 2.929%

Semiannual YTM = 2.929%
Annual YTM = 2 * 2.929%
Annual YTM = 5.858%

Before-tax Cost of Debt = 5.858%
After-tax Cost of Debt = 5.858% * (1 - 0.35)
After-tax Cost of Debt = 3.808%

Equity:

Number of shares outstanding = 9,100,000
Current Price = $41

Value of Equity = 9,100,000 * $41
Value of Equity = $373,100,000

Cost of Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Equity = 3.10% + 1.20 * 7.00%
Cost of Equity = 11.50%

Answer a.

Value of Firm = Value of Debt + Value of Equity
Value of Firm = $239,200,000 + $373,100,000
Value of Firm = $612,300,000

Weight of Debt = $239,200,000 / $612,300,000
Weight of Debt = 0.3907

Weight of Equity = $373,100,000 / $612,300,000
Weight of Equity = 0.6093

Answer b.

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Equity * Cost of Equity
WACC = 0.3907 * 3.808% + 0.6093 * 11.50%
WACC = 8.49%

So, the firm should use a discount rate of 8.49% in order to evaluate the project.