Question

Faber-Overdrive Autoparts issued at par value a 15-year 6% semiannual coupon bond, face value $1,000. At the end of 2 years, the market yield increased to 7%. One year later, the market yield was 8%. If you purchased the bond at the end of Year 2 and sold it one year later, how much was your capital gain or loss?

Answer 1

Bond Par Value = $ 1000, Coupon Rate = 6 % payable semi-annually, YTM = 7 % at the end of Year 2 and 8 % at the end of Year 3

Semi-Annual Coupon Payment = 0.06 x 1000 x 0.5 = $ 30 and Original Bond Tenure = 15 years or 30 half-years

Price at the end of Year 2 = P2 = Total Present Value of Remaining Coupons + Redeemed Par Value at Maturity = 30 x (1/0.035) x [1-{1/(1.035)^(26)}] + 1000 / (1.035)^(26) (3.5 % is the applicable semi-annual yield at the end of Year 2 remaining tenure is 26 half-years) = $ 915.548

Price at the end of Year 3 =  Total Present Value of Remaining Coupons + Redeemed Par Value at Maturity = 30 x (1/0.035) x [1-{1/(1.035)^(26)}] + 1000 / (1.035)^(26) (4 % is the applicable semi-annual yield at the end of Year 3 remaining tenure is 24 half-years) = $ 847.53

Capital Gain/Loss = % Profit Earned Due to Price Change Only (Coupon Income Excluded) = [(847.53 - 915.55) / 915.55] x 100 = - 7.429 % ~ - 7.43 %