Question

8) Assume that a bond has a coupon rate of 10 percent, makes annual coupon payments, and has a par value of $1,000. Calculate the bond’s value under the following conditions.

1. The bond matures in 5 years and the YTM is 5%:
2. The bond matures in 5 years and the YTM is 10%:
3. The bond matures in 5 years and the YTM is 15%:

4. The bond matures in 15 years and the YTM is 5%:
5. The bond matures in 15 years and the YTM is 10%:
6. The bond matures in 15 years and the YTM is 15%:

9) Looking at the prices that you calculated in problem 8, what effects do time and YTM have on a bond’s price?

10) Calculate the single and annual coupon payments assuming the following:

1. Semiannual bond, Coupon rate of 8 percent, Par value of $1,000:
2. Annual bond, Coupon rate of 4.5 percent, Par value of $100:
3. Monthly bond, Coupon rate 12 percent, Par value $850:

Answer 1

Coupon = 10% of 1000 = 100

a)

Value = Coupon * [1 - 1 / (1 +r)ⁿ] / r + FV / (1 + r)ⁿ

Value = 100 * [1 - 1 / (1 + 0.05)⁵] / 0.05 + 1000 / (1 + 0.05)⁵

Value = 100 * [1 - 0.783526] / 0.05 + 783.526166

Value = 100 * 4.32948 + 783.526166

Value = $1,216.47

b)

When coupon rate is equal to YTM, bond will always sell at par. There is no need for calculation.

Value = $1000

c)

Value = Coupon * [1 - 1 / (1 +r)ⁿ] / r + FV / (1 + r)ⁿ

Value = 100 * [1 - 1 / (1 + 0.15)⁵] / 0.15 + 1000 / (1 + 0.15)⁵

Value = 100 * [1 - 0.497177] / 0.15 + 497.176735

Value = 100 * 3.352155 + 497.176735

Value = $832.39

d)

Value = Coupon * [1 - 1 / (1 +r)ⁿ] / r + FV / (1 + r)ⁿ

Value = 100 * [1 - 1 / (1 + 0.05)¹⁵] / 0.05 + 1000 / (1 + 0.05)¹⁵

Value = 100 * [1 - 0.481017] / 0.05 + 481.017098

Value = 100 * 10.379658 + 481.017098

Value = $1,518.98