Final answer:
To calculate the capital gain or loss of the bond, we need to compare the current price to the price after 6 months. The remaining coupons can be calculated using the present value of an annuity formula. The capital gain or loss is then found by subtracting the current price from the price after 6 months.
Step-by-step explanation:
The capital gain or loss that the bond will generate can be calculated by comparing the current bond price to the price immediately after receiving the coupon in 6 months. Since the yield to maturity remains constant, we can assume that the price after 6 months will be equal to the present value of the remaining coupons plus the present value of the face value of the bond.
To calculate the present value of the remaining coupons, we can use the formula for the present value of an annuity. In this case, the remaining coupons will be received for 9.5 years, instead of the original 10 years, since 6 months have already passed. The annual coupon payment is $80 (8% of the face value), and the discount rate is the yield to maturity divided by 2 since the coupons are received semiannually.
Using these values, we can calculate the present value of the remaining coupons to be $820.39. Adding this to the face value of the bond ($1,000) gives us a total price of $1,820.39 after 6 months. Therefore, the capital gain or loss can be calculated as the difference between the current bond price ($1,050) and the price after 6 months ($1,820.39), which is $770.39.