Tangshan Mining is considering issuing long-term debt. The debt would have a 30 year maturity and a 12 percent coupon rate and make semiannually 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, what is the after tax cost of debt for Tangshan Mining?
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To calculate the after-tax cost of debt for Tangshan Mining, we need to consider the discount and flotation costs, as well as the tax rate.
Step 1: Calculate the selling price of the bonds
The selling price of the bonds is calculated as the face value minus the discount and flotation costs:
Selling price = Face value - (Discount + Flotation costs)
Given that the discount is 2.5% and flotation costs are also 2.5% of the face value, the selling price can be calculated as follows:
Selling price = Face value - (0.025 * Face value + 0.025 * Face value)
Selling price = Face value - (0.05 * Face value)
Step 2: Calculate the after-tax cost of debt
To calculate the after-tax cost of debt, we need to consider the coupon payments and the tax savings on interest expense.
The annual coupon payment can be calculated as follows:
Coupon payment = Coupon rate * Face value
Coupon payment = 0.12 * Face value
The tax savings on interest expense can be calculated as follows:
Tax savings = Tax rate * Coupon payment
Tax savings = 0.33 * Coupon payment
Since the coupon payments are made semi-annually, the tax savings need to be halved:
Tax savings = Tax savings / 2
Finally, the after-tax cost of debt can be calculated as follows:
After-tax cost of debt = (Coupon payment - Tax savings) / Selling price
Substituting the values from the information provided:
After-tax cost of debt = (0.12 * Face value - (0.33 * (0.12 * Face value) / 2) / (Face value - (0.05 * Face value))
You can simplify this equation further by factoring out the common term of Face value and performing the calculations.