Issue Price The following terms relate to independent bond issues: 500 bonds; $1

Question

Issue Price

The following terms relate to independent bond issues:

500 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments

500 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments

800 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments

2,000 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

Use the appropriate present value table:

Assuming the market rate of interest is 10%, calculate the selling price for each bond issue. If required, round all calculations to the nearest dollar.

Explanation / Answer

500 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments:

Annual coupon amount = 1000*8% = 80

Market rate of interest = 10%

Selling price of each bond = 80*Present value annuity factor(10%,5) + 1000*Present value interest factor(10%,5)

= 80*3.7907 + 1000*0.6209 = 303.256 + 620.90 = 924.156

500 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments

Semi annual coupon amount = 1000*8%*1/2 = 40

Semmi annual yield = 10%/2 = 5%

Maturity in 6 months periods = 5*2 = 10

Selling price of each bond = 40*Present value annuity factor(5%,10) + 1000*Present value interest factor(5%,10)

= 40*7.7217 1000*0.6139 = 308.868 + 613.90 = 922.77

800 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments

Semi annual coupon amount = 1000*8%*1/2 = 40

Semmi annual yield = 10%/2 = 5%

Maturity in 6 months periods = 10*2 = 20

Selling price of each bond = 40*Present value annuity factor(5%,20) + 1000*Present value interest factor(5%,20)

= 40*12.4622 + 1000*0.3768 = 498.48 + 376.80 = 875.28

2,000 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

Semi annual coupon amount = 500*12%*1/2 = 30

Semmi annual yield = 10%/2 = 5%

Maturity in 6 months periods = 15*2 = 30

Selling price of each bond = 30*Present value annuity factor(5%,30) + 500*Present value interest factor(5%,30)

= 30*15.3724 + 500*0.2313 = 461.17 + 115.65 = 576.82

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