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 10 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.

 

With 15 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)  prices of bonds with a maturity of 20 years

The price of the bond is the present value of the coupon payment plus the par value.

Par value of the bond = $1,000.

Six-month coupon amount = $60 [$1,000 x 12% x ½].

Six-month maturity yield = 7% [14% x ½].

Maturity Date = 40 years [20 years x ½]

The price of the bond = the present value of the coupon payment + the present value of the par 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 a bond maturing in 15 years with a yield to maturity of 10 percent.

The price of the bond is the present value of the coupon payment plus the par value.

Par value of the bonds = $1,000.

Six-month coupon amount = $60 [$1,000 x 12% x ½].

Six-month maturity yield = 5% [10% x ½]

Expiry date = 30 years [15 years x 2]

The price of the bond = the present value of the coupon payment + the present value of the par 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