Question

The Saunders Investment Bank has the following financing outstanding.

Debt: 90,000 bonds with a coupon rate of 6 percent and a current price quote of 106.4.; the bonds have 20 years to maturity. 280,000 zero coupon bonds with a price quote of 15.8 and 30 years until maturity. Both bonds have par value of $1000. Both bonds have semiannual compounding.

Preferred Stock: 150,000 shares of 4 percent preferred stock with a current price of $84, and a par value of $100. Common stock: 2,600,000 shares of common stock; the current price is $68, and the beta of the stock is 1.15.

Market: The corporate tax rate is 40 percent, the market risk premium is 7 percent, and the risk-free rate is 3.2 percent. What is the WACC for the company?

Answer 1

1st Issue of Bonds:

Face Value = $1,000
BookValue = 90,000* $1,000 = $90,000,000

Current Price = 106.4% * $1,000
Current Price = $1,064

Market Value = $1,064 * 90,000
Market Value = $95,760,000

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3% * $1,000
Semiannual Coupon = $30

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

Let semiannual YTM be i%

$1,064 = $30 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -1,064
PMT = 30
FV = 1,000

I = 2.73%

Semiannual YTM = 2.73%
Annual YTM = 2 * 2.73%
Annual YTM = 5.46%

Before-tax Cost of Debt = 5.46%
After-tax Cost of Debt = 5.46% * (1 – 0.40)
After-tax Cost of Debt = 3.28%

2nd Issue of Bonds:

Face Value = $1,000

Book Value = 280,000 * $1,000 = $280,000,000

Current Price = 15.80% * $1,000
Current Price = $158

Market Value = $158 * 280,000
Market Value = $44,240,000

Time to Maturity = 30 years
Semiannual Period to Maturity = 60

Let semiannual YTM be i%

$158 = $1,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -158
PMT = 0
FV = 1,000

I = 3.12%

Semiannual YTM = 3.12%
Annual YTM = 2 * 3.12%
Annual YTM = 6.24%

Before-tax Cost of Debt = 6.24%
After-tax Cost of Debt = 6.24% * (1 - 0.40)
After-tax Cost of Debt = 3.74%

Total Book Value of Debt = $90,000,000 + $280,000,000
Total Book Value of Debt = $370,000,000

Total Market Value of Debt = $95,760,000 + $44,240,000
Total Market Value of Debt = $140,000,000

Weight of 1st Issue of Debt = $95,760,000/$140,000,000
Weight of 1st Issue of Debt = 0.6840

Weight of 2nd Issue of Debt = $44,240,000/$140,000,000
Weight of 2nd Issue of Debt = 0.3160

Estimated After-tax Cost of Debt = 0.6840 * 3.28% + 0.3160 * 3.74%
Estimated After-tax Cost of Debt = 3.43%

Preferred Stock:

Number of shares outstanding = 150,000
Current Price = $84
Annual Dividend = 4%*$100 = $4

Value of Preferred Stock = 150,000 * $84
Value of Preferred Stock = $12,600,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $4 / $84
Cost of Preferred Stock = 4.76%

Equity:

Number of shares outstanding = 2,600,000
Current Price = $68

Value of Common Stock = 2,600,000 * $68
Value of Common Stock = $176,800,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 3.2% + 1.15 * 7%
Cost of Common Equity = 11.25%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $140,000,000 + $12,600,000 + $176,800,000
Value of Firm = $329,400,000

Weight of Debt = $140,000,000/$329,400,000
Weight of Debt = 0.4250

Weight of Preferred Stock = $12,600,000/$329,400,000
Weight of Preferred Stock = 0.0383

Weight of Common Stock = $176,800,000/$329,400,000
Weight of Common Stock = 0.5367

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 = 0.4250*3.43% + 0.0383*4.76% + 0.5367*11.25%
WACC = 7.68%