Question

Bonus Value. You have a bond that pays $ 100 of annual interest, with a value of $ 1,000 and matures in 15 years. Your required rate of return is 12%.

a. Calculate the value of the bonus

b. How does the value change if your required rate of return:

1. Increase to 15%

2. Decrease to 8%

Answer 1

a)

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

Value = 100 * [1 - 1 / (1 + 0.12)¹⁵] / 0.12 + 1000 / (1 + 0.12)¹⁵

Value = 100 * 6.810864 + 182.696261

Value = $863.78

b:

1)

Increase to 15%:

Value = 100 * [1 - 1 / (1 + 0.15)¹⁵] / 0.15 + 1000 / (1 + 0.15)¹⁵

Value = 100 * 5.84737 + 122.894485

Value = $707.631495

Value will change by = $707.631495 - $863.78

Value will change by = -$156.15

2)

Decrease to 8%:

Value = 100 * [1 - 1 / (1 + 0.08)¹⁵] / 0.08 + 1000 / (1 + 0.08)¹⁵

Value = 100 * 8.559479 + 315.241705

Value = $1,171.189574

Value will change by = $1,171.189574 - $863.78

Value will change by = $307.41

b:

1)

Increase to 15%:

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

Value = 100 * 3.352155 + 497.176735

Value = $832.3922

Value will change by = $832.3922 - $863.78

Value will change by = -$31.39

2)

Decrease to 8%:

Value = 100 * [1 - 1 / (1 + 0.08)⁵] / 0.08 + 1000 / (1 + 0.08)⁵

Value = 100 * 3.992871 + 680.583197

Value = $1,079.8542

Value will change by = $1,079.8542 - $863.78

Value will change by = $216.07