Question

A bond that matures in 14 years has a $1000 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 $?

Answer #1

a)

Coupon = 0.09 * 1000 = 90

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

Value of bond = 90 * [1 - 1 / (1 + 0.13)^{14}] / 0.13 +
1,000 / (1 + 0.13)^{14}

Value of bond = 90 * 6.30249 + 180.67655

Value of bond = $747.9

**The value of this bond if it paid interest annually
would be $747.9**

You can also find this using a financial calculator:

FV 1000

PMT 90

I/Y 13

N 28

CPT PV

b)

Coupon = (0.09 * 1000) / 2 = 45

Number of periods = 14 * 2 = 28

Rate = 13% / 2 = 6.5%

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

Value of bond = 45 * [1 - 1 / (1 + 0.065)^{28}] / 0.065
+ 1,000 / (1 + 0.065)^{28}

Value of bond = 45 * 12.74648 + 171.47902

Value of bond = $745.1

**The value of this bond if it paid interest semi-annually
would be $745.1**

You can also find this using a financial calculator:

FV 1000

PMT 45

I/Y 6.5

N 28

CPT PV

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