Suppose Bond X has an original price of $1,000 and a coupon rate of 8% and therefore is worth $1,080 after a year. The market has now changed so that other bonds are selling with a coupon rate of 12%. How would you calculate the right price to pay for Bond X?

Question

a. Calculate the dollar figure that would generate $1,120 at the current interest rate and pay no more than that for the bond.
b. The right price for a bond is always the face value plus the interest rate for one year.
c. With a 12% coupon rate, the bond’s face value is now $880, so pay no more than that for the bond.
d. Calculate the dollar figure that would generate $1,080 at an interest rate of 12% and pay no more than that for the bond.

Answer 1

d. Calculate the dollar figure that would generate $1,080 at an interest rate of 12% and pay no more than that for the bond.

The expected payments from the bond one year from now are $1,080, because in the bond’s last year the issuer of the bond will make the final interest payment and then also repay the original $1,000. Given that interest rates are now 12%, you know that you could invest $964 in an alternative investment and receive $1,080 a year from now; that is, $964(1 + 0.12) = $1,080. Therefore, you will not pay more than $964 for the original $1,000 bond.