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 13 percent, which is paid semiannually. The yield to maturity on the bonds is 8 percent annual interest. There are 10 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.

a. Compute the price of the bonds based on semiannual analysis.

b. With 5 years to maturity, if yield to maturity goes down substantially to 6 percent, what will be the new price of the bonds? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

a. Price of bond = face value / (1+required rate)^{number of payments} + Interest [1 - (1+required rate)^{-number of payments}] / required rate

=$1000 / (1+0.08/2)^10*2 + ($1000*0.13/2) [1 - (1+0.08/2)^-10*2] / (0.08/2)

=$1000 / (1+0.04)²⁰ + 65 [1 - (1+0.04)^-20] / 0.04

=$1000 / (1.04)²⁰ + 65 [1 - 1/(1.04)²⁰] / 0.04

=$1000 / 2.191123 + 65 [1 - 1/2.191123] / 0.04

= 456.39 + 883.37

= $1339.76

b. With 5 years to maturity, if yield to maturity goes down substantially to 6 percent,

new price of the bonds = $1000 / (1+0.06/2)^5*2 + ($1000*0.13/2) [1 - (1+0.06/2)^-5*2] / (0.06/2)

= $1000 / (1+0.03)¹⁰ + 65 [1 - (1+0.03)^-10] / 0.03

= $1000 / (1.03)¹⁰ + 65 [1 - (1.03)^-10] / 0.03

= $1000 / (1.03)¹⁰ + 65 [1 - 1/(1.03)¹⁰] / 0.03

= $1000 /1.343916 + 65 [1 - 1/1.343916] / 0.03

= 744.09 + 554.46

= 1298.55