The George Company, Inc., has two issues of debt. Issue A has a maturity value of 8 million dollars, a coupon rate of 8%, paid annually, and is selling at par. Issue B was issued as a 15 year bond 5 years ago. Its coupon rate is 9%, paid annually. Investors demand a pre-tax return of 9.3% on this bond. The maturity value of Issue B is 6 million dollars. The George company has a marginal tax rate of 35%. What is the company's after tax cost of debt?

Question

Quizplus · Accepted Answer

For Issue A: 
Coupon rate = 8%
Maturity value = $8,000,000
Since it is selling at par, the yield to maturity is also 8%.

For Issue B: 
Coupon rate = 9%
Maturity value = $6,000,000
Investor's demand pre-tax return = 9.3%
This means that the yield to maturity on this bond is also 9.3%.

The after-tax cost of debt can be calculated using the formula:
After-tax cost of debt = Yield to maturity x (1 - Marginal tax rate)

For Issue A: 
Yield to maturity = 8%
Marginal tax rate = 35%
After-tax cost of debt = 8% x (1 - 0.35) = 5.2%

For Issue B: 
Yield to maturity = 9.3%
Marginal tax rate = 35%
After-tax cost of debt = 9.3% x (1 - 0.35) = 6.045%

Weighted average cost of debt can be calculated as: 
Weighted average cost of debt = (Market value of issue A / Total market value of debt) x After-tax cost of debt for Issue A + (Market value of issue B / Total market value of debt) x After-tax cost of debt for Issue B

Total market value of debt = $8,000,000 + $6,000,000 = $14,000,000

Market value of issue A = $8,000,000
Market value of issue B = Present value of remaining payments on Issue B = $6,000,000 x PVIFA(9.3%,10) = $3,636,501.47 (using financial calculator)

Weighted average cost of debt = ($8,000,000 / $14,000,000) x 5.2% + ($3,636,501.47 / $14,000,000) x 6.045% = 5.56%

Therefore, the after-tax cost of debt is 5.56%, making option B the correct answer.