Question

You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 8 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

Answer 1

Number of periods = 15 * 2 = 30

Rate = 10% / 2 = 5%

Coupon = (0.08 * 1000) / 2 = 40

Value = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Value = 40 * [1 - 1 / (1 + 0.05)³⁰] / 0.05 + 1000 / (1 + 0.05)³⁰

Value = 40 * [1 - 0.23138 ] / 0.05 + 231.37745

Value = 40 * 15.37245 + 231.37745

Value = $846.28

You can also find this using a financial calculator:

FV 1000

I/Y 5

N 30

PMT 40

CPT PV

b)

If the yield to maturity goes down to 8%, price will be equal to face value.

When coupon rate is equal to yield to maturity, price will be equal to face value.

New price = $1,000.00