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 / 1.13^{11}

= $ 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 / 1.065^{22}

= $ 45 x 11.53519562 + $ 250.212285

= $ 519.0838029 + $ 250.212285

**= $ 769.30**

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percent. What would be the value of this bond if it paid interest
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The value of this bond if it paid interest annually would be
$_
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