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**

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