A company's bonds pay a 6% coupon annually on a $100 nominal value and are redeemable at par in five years. They currently trade at $95 ex interest. Corporation tax is 20%. Using linear interpolation between discount rates of 5% and 7%, what is the after-tax cost of debt (to 1 decimal place)?

Correct answer: B) 6.0%

Explanation

After-tax interest = 6 x (1 - 0.20) = 4.80 a year. The after-tax cost of debt is the IRR of: time 0 -95; years 1-5 +4.80; year 5 +100. At 5%: -95 + 4.80 x 4.329 + 100 x 0.784 = +4.18. At 7%: -95 + 4.80 x 4.100 + 100 x 0.713 = -4.02. Kd = 5% + 4.18 / (4.18 + 4.02) x 2% = 6.02%, i.e. 6.0% to 1 decimal place (the exact IRR is 5.99%). 7.2% is the pre-tax yield to maturity, 6.3% is the pre-tax coupon divided by the price (6/95), and 5.1% ignores the gain on redemption (4.80/95).