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 12 percent, which is paid semiannually. The yield to maturity on the bonds is 14 percent annual interest. There are 20 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 15 years to maturity, if yield to maturity goes down substantially to 10 percent, what will be the new price of the bonds?

Answer 1

(a)-The price of the bond with 20 years to maturity

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the Bond = $1,000

Semi-annual Coupon Amount = $60 [$1,000 x 12% x ½]

Semi-annual Yield to Maturity = 7% [14% x ½]

Maturity Period = 40 Years [20 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $60[PVIFA 7%, 40 Years] + $1,000[PVIF 7%, 40 Years]

= [$60 x 13.33171] + [$1,000 x 0.06678]

= $799.90 + $66.78

= $866.68

(b)-The price of the bond with 15 years to maturity and yield to maturity of 10%

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the Bond = $1,000

Semi-annual Coupon Amount = $60 [$1,000 x 12% x ½]

Semi-annual Yield to Maturity = 5% [10% x ½]

Maturity Period = 30 Years [15 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $60[PVIFA 5%, 30 Years] + $1,000[PVIF 5%, 30 Years]

= [$60 x 15.37245] + [$1,000 x 0.23138]

= $922.34 + $231.38

= $1,153.72

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.