Question

(Related to Checkpoint 9.4) (Bond valuation) A bond that matures in 12 years has a $1000 par value. The annual coupon interest rate is 8 percent and the market's required yield to maturity on a comparable-risk bond is 14 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? a. The value of this bond if it paid interest annually would be $ nothing. (Round to the nearest cent.) b. The value of this bond if it paid interest semiannually would be $ nothing. (Round to the nearest cent.)

Answer #1

1)

Annually:

Coupon = 8% of 1000 = 80

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

Value of bond = 80 * [1 - 1 / (1 + 0.14)^12] / 0.14 + 1000 / (1 + 0.14)^12

Value of bond = 80 * [1 - 0.207559] / 0.14 + 207.559102

Value of bond = 80 * 5.660292 + 207.559102

**Value of bond = $660.38**

2)

Semi annually:

Rate = 14% / 2 = 7%

Number of periods = 12 * 2 = 24

Coupon = (8% of 1000) / 2 = 40

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

Price = 40 * [1 - 1 / (1 + 0.07)^24] / 0.07 + 1000 / (1 + 0.07)^24

Price = 40 * [1 - 0.197147] / 0.07 + 197.14662

Price = 40 * 11.469334 + 197.14662

**Price = $655.92**

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