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 10 percent, which is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 25 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. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. With 20 years to maturity, if yield to maturity goes down substantially to 8 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 the bonds = face value / (1+ yield)^{number of payments} + interest [1-(1+ yiled)^{-number of payments}] / yield

=1000 / (1+0.06)^25*2 + (1000 * 5%) [1-(1+ 0.06)^-25*2] / 0.06

=1000 / (1.06)⁵⁰ + 50 [1-(1.06)^-50] / 0.06

=1000 / 18.420154 + 50 [1- 1/18.420154] / 0.06

= 54.29 + 788.09

= $842.38

b. price of the bonds = face value / (1+ yield)^{number of payments} + interest [1-(1+ yiled)^{-number of payments}] / yield

=1000 / (1+0.04)^20*2 + (1000 * 5%) [1-(1+ 0.04)^-20*2] / 0.04

=1000 / (1.04)⁴⁰ + 50 [1-(1.04)^-40] / 0.04

=1000 / (1.04)⁴⁰ + 50 [1- 1 /(1.04)⁴⁰] / 0.04

=1000 / 4.801021 + 50 [1- 1 /4.801021] / 0.04

= 208.29 + 989.64

= $1197.93