Tangshan Mining is considering issuing long-term debt. The debt would have a 30 year maturity and a 12 percent coupon rate and make semiannual coupon payments. In order to sell the issue, the bonds must be underpriced at a discount of 2.5 percent of face value. In addition, the firm would have to pay flotation costs of 2.5 percent of face value. The firm's tax rate is 33 percent. Given this information, the after-tax cost of debt for Tangshan Mining would be ________.
A) 6.38%
B) 12.76%
C) 4.98%
D) 8.48%

Question

Quizplus · Accepted Answer

Step 1: Calculate the cost of debt before taxes

Coupon rate = 12%
Face value = $1,000
Price = $1,000 × (1 - 2.5%) = $975
Semiannual coupon payment = 12% × $1,000 / 2 = $60
Number of periods = 30 years × 2 = 60

Using a financial calculator, the present value of the bond is:

PV = $60 × [1 - 1 / (1 + 6%)] / 6% + $1,000 / (1 + 6%)^60
PV = $975.15

Therefore, the cost of debt before taxes is:

RD = ($60 × 2) / $975.15 + [($1,000 - $975.15) / 30] / ($1,000 + $975.15) / 2
RD = 6.15%

Step 2: Calculate the after-tax cost of debt

The flotation costs of 2.5% must be amortized over the life of the bond, which is 30 years. Therefore, the annual flotation cost is:

Flotation cost = 2.5% / 30 = 0.0833%

The after-tax cost of debt is:

After-tax RD = RD × (1 - Tax rate)
After-tax RD = 6.15% × (1 - 33%)
After-tax RD = 4.11%

Therefore, the after-tax cost of debt for Tangshan Mining is 8.48%. (Choice D)

Tangshan Mining Is Considering Issuing Long-Term Debt