Finding the wacc [lo3] titan mining corporation has 7.5 million shares of common stock outstanding, 250,000 shares of 4.2 percent preferred stock outstanding, and 140,000 bonds with a semiannual coupon of 5.1 percent outstanding, par value $1,000 each. the common stock currently sells for $51 per share and has a beta of 1.15, the preferred stock currently sells for $103 per share, and the bonds have 15 years to maturity and sell for 107 percent of par. the market risk premium is 7.5 percent, t-bills are yielding 2.4 percent, and the company’s tax rate is 22 percent. what is the firm’s market value capital structure? 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?

Check the following calculations

Explanation:

Debt:

Number of bonds outstanding = 140,000

Face Value = $1,000

Current Price = 107%*$1,000 = $1,070

Value of Debt = 140,000 * $1,070

Value of Debt = $149,800,000

Annual Coupon Rate = 5.10%

Semiannual Coupon Rate = 2.55%

Semiannual Coupon = 2.55%*$1,000 = $25.50

Time to Maturity = 15 years

Semiannual Period to Maturity = 30

Let semiannual YTM be i%

$1,070 = $25.50 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:

N = 30

PV = -1070

PMT = 25.5

FV = 1000

I = 2.228%

Semiannual YTM = 2.228%

Annual YTM = 2 * 2.228%

Annual YTM = 4.456%

Before-tax Cost of Debt = 4.456%

After-tax Cost of Debt = 4.456% * (1 - 0.22)

After-tax Cost of Debt = 3.476%

Preferred Stock:

Number of shares outstanding = 250,000

Current Price = $103

Annual Dividend = 4.20%*$100 = $4.20

Value of Preferred Stock = 250,000 * $103

Value of Preferred Stock = $25,750,000

Cost of Preferred Stock = Annual Dividend / Current Price

Cost of Preferred Stock = $4.20 / $103

Cost of Preferred Stock = 4.078%

Equity:

Number of shares outstanding = 7,500,000

Current Price = $51

Value of Common Stock = 7,500,000 * $51

Value of Common Stock = $382,500,000

Cost of Equity = Risk-free Rate + Beta * Market Risk Premium

Cost of Equity = 2.40% + 1.15 * 7.50%

Cost of Equity = 11.025%

Answer a.

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock

Value of Firm = $149,800,000 + $25,750,000 + $382,500,000

Value of Firm = $558,050,000

Answer b.

Weight of Debt = $149,800,000/$558,050,000

Weight of Debt = 0.2684

Weight of Preferred Stock = $25,750,000/$558,050,000

Weight of Preferred Stock = 0.0462

Weight of Equity = $382,500,000/$558,050,000

Weight of Equity = 0.6854

WACC = Weight of Debt*After-tax Cost of Debt + Weight of Preferred Stock*Cost of Preferred Stock + Weight of Equity*Cost of Equity

WACC = 0.2684 * 3.476% + 0.0462 * 4.078% + 0.6854 * 11.025%

WACC = 8.68%