1. Hyundai Corporation plans to issue 4-year bonds with a par value of $1,000 that will pay $50 every year. The firm will issue these bonds to the buyers at $840 each. (6 points)
a. Compute the before-tax cost of debt. (Hint: Try solving this like you solve for IRR; i.e. try 5%, try 15% etc.
b.b. If Hyundai is in the 25% tax bracket, what is the after-tax cost of debt?
To determine the before-tax cost of debt, we need to calculate the yield to maturity (YTM) of the bond. YTM is the rate of return an investor would earn if they hold the bond until maturity and reinvest all coupon payments at the same rate.
a. To calculate the before-tax cost of debt, we can use the bond's cash flows and the current market price. The cash flows in this case are the annual coupon payment of $50 for four years and the par value of $1,000 at the end of the four-year period.
We can plug different discount rates into the YTM calculation formula to find the rate at which the present value of the bond's cash flows equals the current market price. Here's how:
N = 4 (number of years)
PMT = $50 (annual coupon payment)
FV = $1,000 (par value)
PV = -$840 (current market price)
Using a financial calculator or a spreadsheet software, we can find the YTM that makes the present value of the bond's cash flows equal to the market price. By iterating with different rates, we can find the YTM that results in a present value closest to the market price of -$840.
b. To calculate the after-tax cost of debt, we need to multiply the before-tax cost of debt by (1 - tax rate). In this case, the tax rate is 25%.
Once we have the before-tax cost of debt from part a, we can calculate the after-tax cost of debt as:
After-tax cost of debt = Before-tax cost of debt * (1 - tax rate)
Let's calculate the before-tax cost of debt first using the YTM calculation, and then we can use that result to find the after-tax cost of debt.