Question

Testing Company, Inc. has the following combination of Debt and Equity:

Common Stock:

15.5 million shares outstanding

Par value of $5/share

Book value of $20/share

Current price on the market of $65.25

Current Beta per a reliable source 1.13

Debt:

Maturity value of $500,000,000

Current price on the market of 97.3

Coupon rate if 4%

Semiannual payments

10 years until maturity

Other information:

Treasury bill rates — 2.45%

Market premium on this type of stock — 7.1%

Tax rate — 21%

What is the company’s weighted average cost of capital (WACC)?

Answer 1

Debt:

Face Value of Debt = $500,000,000

Market Value of Debt = 97.30% * Face Value of Debt
Market Value of Debt = 97.30% * $500,000,000
Market Value of Debt = $486,500,000

Annual Coupon Rate = 4.00%
Semiannual Coupon Rate = 2.00%
Semiannual Coupon = 2.00% * $500,000,000
Semiannual Coupon = $10,000,000

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$486,500,000 = $10,000,000 * PVIFA(i%, 20) + $500,000,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -486500000
PMT = 10000000
FV = 500000000

I = 2.168%

Semiannual YTM = 2.168%
Annual YTM = 2 * 2.168%
Annual YTM = 4.336%

Before-tax Cost of Debt = 4.336%
After-tax Cost of Debt = 4.336% * (1 - 0.21)
After-tax Cost of Debt = 3.425%

Equity:

Number of shares outstanding = 15,500,000
Current Price = $65.25

Market Value of Equity = 15,500,000 * $65.25
Market Value of Equity = $1,011,375,000

Cost of Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Equity = 2.45% + 1.13 * 7.10%
Cost of Equity = 10.473%

Market Value of Firm = Market Value of Debt + Market Value of Common Stock
Market Value of Firm = $486,500,000 + $1,011,375,000
Market Value of Firm = $1,497,875,000

Weight of Debt = $486,500,000 / $1,497,875,000
Weight of Debt = 0.3248

Weight of Equity = $1,011,375,000 / $1,497,875,000
Weight of Equity = 0.6752

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Equity * Cost of Equity
WACC = 0.3248 * 3.425% + 0.6752 * 10.473%
WACC = 8.18%