A company's 8% convertible bonds ($100 nominal) are trading at $102 ex interest. In four years' time each bond can be converted into 25 ordinary shares or redeemed at par. The current share price is $3.50 and is expected to grow at 5% a year. Corporation tax is 25%. Using linear interpolation between discount rates of 5% and 8%, what is the after-tax cost of the convertible debt (to 1 decimal place)?

Correct answer: C) 6.9%

Explanation

Conversion value in 4 years = 25 x 3.50 x 1.05^4 = $106.36, which exceeds the redemption value of $100, so investors are expected to convert. After-tax interest = 8 x 0.75 = 6. Cash flows: time 0 -102; years 1-4 +6; year 4 +106.36. NPV at 5% = -102 + 6 x 3.546 + 106.36 x 0.823 = +6.81; NPV at 8% = -102 + 6 x 3.312 + 106.36 x 0.735 = -3.95. Kd = 5% + 6.81 / (6.81 + 3.95) x 3% = 6.90%, i.e. 6.9% (exact IRR 6.85%). Assuming redemption at par gives 5.5%, ignoring tax relief on interest gives 8.7%, and 5.9% is simply after-tax interest divided by price (6/102).