An investor bought a bond when it was originally issued with a maturity of 30 years. The bond pays semi-annual coupons of $60. The first coupon occurs 181 days after issue, the second 365 days, the third 547 days, and the fourth 730 days. It is now 120 days into the life of the bond and its price is $1,012.85 (including accrued interest). The investor wants to sell the bond two days after its fourth coupon. The risk-free rate is currently 7 percent. At what price could the investor enter into a forward contract to sell the bond two days after its fourth coupon?

Correct Answer: $881.73

Only the first four coupons occur during the life of the forward contract. At this time point the next occurs in 61 days, followed by 245 days, 427 days, and 610 days. The present value of the coupons is: $60/(1.07)^61/365 + $60/(1.07)^245/365 + $60/(1.07)^427/365 + $60/(1.07)^610/365 = $225.68.

The forward contract expires in 612 days (732 - 120). F(0, T) = F(0, 612/365) = ($1,012.85 - $225.68) (1.07)^612/365 = $881.73.