Question

The Saunders Investment Bank has the following financing outstanding.

  

Debt:	54,000 bonds with a coupon rate of 5 percent and a current price quote of 106.9; the bonds have 16 years to maturity and a par value of $1,000. 17,700 zero coupon bonds with a price quote of 28.8, 26 years until maturity, and a par value of $10,000. Both bonds have semiannual compounding.
Preferred stock:	149,000 shares of 3.5 percent preferred stock with a current price of $90 and a par value of $100.
Common stock:	2,180,000 shares of common stock; the current price is $86 and the beta of the stock is 1.10.
Market:	The corporate tax rate is 24 percent, the market risk premium is 7 percent, and the risk-free rate is 3.4 percent.

  

What is the WACC for the company?

Answer 1

Debt:

1^st Issue of Bonds:

Face Value of Bond = $1,000

Current Price of Bond = 106.90% * $1,000
Current Price of Bond = $1,069

Market Value = 54,000 * $1,069
Market Value = $57,726,000

Annual Coupon Rate = 5.00%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $1,000
Semiannual Coupon = $25

Time to Maturity = 16 years
Semiannual Period to Maturity = 32

Let semiannual YTM be i%

$1,069 = $25 * PVIFA(i%, 32) + $1,000 * PVIF(i%, 32)

Using financial calculator:
N = 32
PV = -1069
PMT = 25
FV = 1000

I = 2.1975%

Semiannual YTM = 2.1975%
Annual YTM = 2 * 2.1975%
Annual YTM = 4.395%

Before-tax Cost of Debt = 4.395%
After-tax Cost of Debt = 4.395% * (1 - 0.24)
After-tax Cost of Debt = 3.340%

2^nd Issue of Bonds:

Face Value of Bond = $10,000

Current Price of Bond = 28.80% * $10,000
Current Price of Bond = $2,880

Market Value = 17,700 * $2,880
Market Value = $50,976,000

Time to Maturity = 26 years
Semiannual Period to Maturity = 52

Let semiannual YTM be i%

$288 = $1,000 * PVIF(i%, 52)

Using financial calculator:
N = 52
PV = -288
PMT = 0
FV = 1000

I = 2.4227%

Semiannual YTM = 2.4227%
Annual YTM = 2 * 2.4227%
Annual YTM = 4.845%

Before-tax Cost of Debt = 4.845%
After-tax Cost of Debt = 4.845% * (1 - 0.24)
After-tax Cost of Debt = 3.683%

Total Market Value of Debt = $57,726,000 + $50,976,000
Total Market Value of Debt = $108,702,000

Weight of 1^st Issue of Debt = $57,726,000 / $108,702,000
Weight of 1^st Issue of Debt = 0.5310

Weight of 2^nd Issue of Debt = $50,976,000 / $108,702,000
Weight of 2^nd Issue of Debt = 0.4690

Estimated After-tax Cost of Debt = 0.5310 * 3.340% + 0.4690 * 3.683%
Estimated After-tax Cost of Debt = 3.501%

Preferred Stock:

Number of shares outstanding = 149,000
Current Price = $90
Annual Dividend = 3.5%*$100 = $3.50

Value of Preferred Stock = 149,000 * $90
Value of Preferred Stock = $13,410,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $3.50 / $90
Cost of Preferred Stock = 3.889%

Equity:

Number of shares outstanding = 2,180,000
Current Price = $86

Value of Common Stock = 2,180,000 * $86
Value of Common Stock = $187,480,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 3.4% + 1.10 * 7%
Cost of Common Equity = 11.100%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $108,702,000 + $13,410,000 + $187,480,000
Value of Firm = $309,592,000

Weight of Debt = $108,702,000 / $309,592,000
Weight of Debt = 0.3511

Weight of Preferred Stock = $13,410,000 / $309,592,000
Weight of Preferred Stock = 0.0433

Weight of Common Stock = $187,480,000 / $309,592,000
Weight of Common Stock = 0.6056

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 = 0.3511 * 3.501% + 0.0433 * 3.889% + 0.6056 * 11.100%
WACC = 8.12%

So, WACC of the company is 8.12%