Question

A bond that matures in 11 years has a ​$1,000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 13 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?

(Round to the nearest​ cent.)

Answer 1

a. The value is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= ($ 1,000 x 9%) x [ [ (1 - 1 / (1 + 0.13)¹¹ ] / 0.13 ] + $ 1,000 / 1.13¹¹

= $ 90 x 5.686941129 + $ 260.6976532

= $ 511.8247016 + $ 260.6976532

= $ 772.52

b. The value of the bond is computed as follows:

The coupon payment is computed as follows:

= 9% / 2 x $ 1,000

= $ 45

The YTM will be as follows:

= 13% / 2

= 6.5% or 0.065

N will be as follows:

= 11 x 2

= 22

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 45 x [ [ (1 - 1 / (1 + 0.065)²² ] / 0.065 ] + $ 1,000 / 1.065²²

= $ 45 x 11.53519562 + $ 250.212285

= $ 519.0838029 + $ 250.212285

= $ 769.30