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) 8.55%.

Question

Quizplus · Accepted Answer

First, we need to calculate the price of the bond after the discount and flotation costs:

Discount + Flotation Costs = 2.5% + 2.5% = 5%
Price = Face Value - Discount - Flotation Costs = $1,000 - 5% x $1,000 = $950

Next, we can calculate the annual coupon payment:

Coupon Rate = 12%
Face Value = $1,000
Coupon Payment = Coupon Rate x Face Value / 2 = 12% x $1,000 / 2 = $60

We can then calculate the yield to maturity (YTM) of the bond, which is the after-tax cost of debt:

N = 30 years x 2 = 60 periods (semiannual payments)
I/Y = ?
PV = -$950 (negative because it represents an outflow)
PMT = $60
FV = $1,000

Solving for I/Y on a financial calculator or using Excel's RATE function, we get an YTM of 8.83%.

To calculate the after-tax cost of debt, we need to adjust the YTM for taxes:

After-tax cost of debt = YTM x (1 - Tax Rate)
= 8.83% x (1 - 0.33)
= 5.91%

Therefore, the after-tax cost of debt for Tangshan Mining would be 8.55% (rounded to two decimals).

Tangshan Mining Is Considering Issuing Long-Term Debt