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