Question

You learned that XYZ, Inc. has a bond with $1,000 face value. The bond carries a 8% coupon, paid semiannually, and matures in 15 years. What is the fair market value of the bond if the yield to maturity is only 7%?

Answer 1

The fair market value of the bond, given a yield to maturity of 7%, is $997.08.

Step-by-step explanation:

When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. Conversely, when interest rates fall, bonds previously issued at higher interest rates will sell for more than face value.

Considering that the yield to maturity is 7%, we can calculate the fair market value of the bond as follows:

1. Calculate the present value of the coupon payments: Since the bond has a coupon rate of 8% and pays semiannually, the coupon payment would be $40 ($1,000 * 0.08 / 2) every six months for a total of 30 periods. We can calculate the present value of these cash flows using the formula: PV = (coupon payment / (1 + yield to maturity/2))^n, where n is the number of periods. Summing up the present value of all the coupon payments gives us $725.70.
2. Calculate the present value of the face value at maturity: The face value of the bond is $1,000, which will be received in 15 years. Using the same formula as above, we can calculate the present value of the face value as $271.38.
3. Add the present values of the coupon payments and the face value to get the fair market value of the bond: $725.70 + $271.38 = $997.08

Therefore, the fair market value of the bond, given a yield to maturity of 7%, is $997.08.