Question

# A bond that matures in 11 years has a ​\$1,000 par value. The annual coupon interest...

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.)

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