Question

A bond that matures in 20 years has a $1,000 par value. The annual coupon interest rate is 11 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 15 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually?

The value of this bond if it paid interest annually would be $_

The value of this bond if it paid interest semiannually would be $_

Answer 1

1)

Coupon = 11% of 1000 = 110

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

Value of bond = 110 * [1 - 1 / (1 + 0.15)^20] / 0.15 + 1000 / (1 + 0.15)^20

Value of bond = 110 * [1 - 0.0611] / 0.15 + 61.100279

Value of bond = 110 * 6.259333 + 61.100279

Value of bond = $749.63

2)

Coupon = (11% of 1000) / 2 = 55

Number of periods = 20 * 2 = 40

Rate = 15% / 2 = 7.5%

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

Value of bond = 55 * [1 - 1 / (1 + 0.075)^40] / 0.075 + 1000 / (1 + 0.075)^40

Value of bond = 55 * [1 - 0.055419] / 0.075 + 55.41935

Value of bond = 55 * 12.594409 + 55.41935

Value of bond = $748.11