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