Question

Bond A has the following features: Face value = $1,000, Coupon Rate = 10%, Maturity = 9 years, Yearly coupons The market interest rate is 3.41% If interest rates remain at 3.41%, what is the percentage capital gain or loss on bond A if you sell the bond in year 1? State your answer to 2 decimal places (e.g., 3.56, 0.29) If there is a capital loss make sure to include a negative sign in your answer (e.g., -0.23)

Answer 1

Bond's Purchase Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{4%*$1,000} * {(1 - (1 + 0.0389)^-(8)) / (0.0389)}] + [$1,000 / {1 + 0.0389}^(8)]

= [$40 * {0.2631 / 0.0389}] + [$1,000 / 1.3570]

= [$40 * 6.7634] + $736.90

= $270.54 + $736.90 = $1,007.44

Bond's price in year 1 = [{4%*$1,000} * {(1 - (1 + 0.0389)^-(7)) / (0.0389)}] + [$1,000 / {1 + 0.0389}^(7)]

= [$40 * {0.2344 / 0.0389}] + [$1,000 / 1.3062]

= [$40 * 6.0265] + $765.57

= $241.06 + $765.57 = $1,006.63

% capital gain/loss = [P1/P0] - 1

= [$1,006.63 / $1,007.44] - 1

= 0.9992 - 1 = -0.0008, or -0.08%