Question

10. Deep Mines has 14 million shares of common stock outstanding with a beta of 1.15 and a market price of $42 a share. There are 900,000 shares of 9 percent preferred stock outstanding, valued at $80 a share. The 10 percent semiannual bonds have a face value of $1,000 and are selling at 91 percent of par. There are 220,000 bonds outstanding that mature in 17 years. The market risk premium is 11% percent, T-bills are yielding 7% percent, and the firm's tax rate is 32 percent. What discount rate should the firm apply to a new project's cash flows if the project has the same risk as the firm's typical project? A. 14.59 percent B. 14.72 percent C. 13.15 percent D. 15.54 percent

Answer 1

Answer:

Debt:

Number of bonds outstanding = 220,000
Face Value = $1,000
Current Price = 91%*$1,000 = $910

Value of Debt = 220,000 * $910
Value of Debt = $200,200,000

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5%
Semiannual Coupon = 5%*$1,000 = $50

Time to Maturity = 17 years
Semiannual Period to Maturity = 34

Let semiannual YTM be i%

$910 = $50 * PVIFA(i%, 34) + $1,000 * PVIF(i%, 34)

Using financial calculator:
N = 34
PV = -910
PMT = 50
FV = 1000

I = 5.598%

Semiannual YTM = 5.598%
Annual YTM = 2 * 5.598%
Annual YTM = 11.196%

Before-tax Cost of Debt = 11.196%
After-tax Cost of Debt = 11.196% * (1 - 0.32)
After-tax Cost of Debt = 7.613%

Preferred Stock:

Number of shares outstanding = 900,000
Current Price = $80
Annual Dividend = 9%*$100 = $9

Value of Preferred Stock = 900,000 * $80
Value of Preferred Stock = $72,000,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $9 / $80
Cost of Preferred Stock = 11.250%

Equity:

Number of shares outstanding = 14,000,000
Current Price = $42

Value of Common Stock = 14,000,000 * $42
Value of Common Stock = $588,000,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 7.50% + 1.15 * 11.50%
Cost of Common Equity = 20.725%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $200,200,000 + $72,000,000 + $588,000,000
Value of Firm = $860,200,000

Weight of Debt = $200,200,000 / $860,200,000
Weight of Debt = 0.2327

Weight of Preferred Stock = $72,000,000 / $860,200,000
Weight of Preferred Stock = 0.0837

Weight of Common Stock = $588,000,000 / $860,200,000
Weight of Common Stock = 0.6836

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 = (0.2327 * 7.613%) + (0.0837 * 11.250%) + (0.6836 * 20.725%)
WACC = 16.88%

The firm should apply discount rate of 16.88% on new project.