Question

# A bond that matures in 14 years has a ​\$1000 par value. The annual coupon interest...

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 ​\$?

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