Titan Mining Corporation has 9.3 million shares of common stock outstanding, 370

Question

Titan Mining Corporation has 9.3 million shares of common stock outstanding, 370,000 shares of 6 percent preferred stock outstanding, and 195,000 8.1 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $41 per share and has a beta of 1.15, the preferred stock currently sells for $91 per share, and the bonds have 20 years to maturity and sell for 112 percent of par. The market risk premium is 8.1 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. Round your answers to 4 decimal places, e.g., 32.1616.) Market value weight Debt Preferred stock Equity 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

Explanation / Answer

Debt:

Number of bonds outstanding = 195,000
Face Value = $1,000
Current Price = 112%*$1,000 = $1,120

Value of Debt = 195,000 * $1,120
Value of Debt = $218,400,000

Annual Coupon Rate = 8.1%
Semiannual Coupon Rate = 4.05%
Semiannual Coupon = 4.05%*$1,000 = $40.50

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

Let semiannual YTM be i%

$1,120 = $40.5 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -1120
PMT = 40.5
FV = 1000

I = 3.489%

Semiannual YTM = 3.489%
Annual YTM = 2 * 3.489%
Annual YTM = 6.978%

Before-tax Cost of Debt = 6.978%
After-tax Cost of Debt = 6.978% * (1 - 0.40)
After-tax Cost of Debt = 4.1868%

Preferred Stock:

Number of shares outstanding = 370,000
Current Price = $91
Annual Dividend = 6.0%*$100 = $6

Value of Preferred Stock = 370,000 * $91
Value of Preferred Stock = $33,670,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $6.00 / $91
Cost of Preferred Stock = 6.593%

Equity:

Number of shares outstanding = 9,300,000
Current Price = $41

Value of Common Stock = 9,300,000 * $41
Value of Common Stock = $381,300,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 4% + 1.15 * 8.1%
Cost of Common Equity = 13.315%

Answer a.

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $218,400,000 + $33,670,000 + $381,300,000
Value of Firm = $633,370,000

Weight of Debt = $218,400,000/$633,370,000
Weight of Debt = 0.3448

Weight of Preferred Stock = $33,670,000/$633,370,000
Weight of Preferred Stock = 0.0532

Weight of Common Stock = $381,300,000/$633,370,000
Weight of Common Stock = 0.6020

Answer b.

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Preferred Stock*Cost of Preferred Stock + Weight of Common Stock*Cost of Common Stock
WACC = 0.3448*4.1868% + 0.0532*6.593% + 0.6020*13.315%
WACC = 9.81%

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