Question

1) A 10-year corporate bond has a coupon rate of 10% with annual payments. If interest rates rise to 8% on similar bonds, then what is the value of the bond in the marketplace?

2) A 10-year corporate bond has a coupon rate of 10% with quarterly payments. If interest rates rise to 8% on similar bonds, then what is the value of the bond in the marketplace?

3) A 100-year corporate bond has a coupon rate of 10% with annual payments. If interest rates drop to 4% on similar bonds, then what is the value of the bond in the marketplace?

Answer 1

1)

Assuming face value to be $1000

Coupon = 0.1 * 1000 = 100

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

Value of bond = 100 * [1 - 1 / (1 + 0.08)¹⁰] / 0.08 + 1000 / (1 + 0.08)¹⁰

Value of bond = 100 * 6.710081 + 463.193488

Value of bond = $1,134.20

2)

Assuming face value to be $1000

Number of periods = 10 * 4 = 40

Coupon = (0.1 * 1000) / 4 = 25

Rate = 8% / 4 = 2%

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

Value of bond = 25 * [1 - 1 / (1 + 0.02)⁴⁰] / 0.02 + 1000 / (1 + 0.02)⁴⁰

Value of bond = 25 * 27.355479 + 452.890415

Value of bond = $1,136.78

3)

Assuming face value to be $1000

Coupon = 0.1 * 1000 = 100

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

Value of bond = 100 * [1 - 1 / (1 + 0.04)¹⁰⁰] / 0.04 + 1000 / (1 + 0.04)¹⁰⁰

Value of bond = 100 * 24.504999 + 19.80004

Value of bond = $2,470.30