Question

Issue Price

The following terms relate to independent bond issues:

1. 660 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments
2. 660 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments
3. 860 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments
4. 2,020 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

Use the appropriate present value table:

PV of $1 and PV of Annuity of $1

Required:

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

Situation	Selling Price of the Bond Issue
a.	$
b.	$
c.	$
d.	$

Answer 1

The selling price of bond is calculated as sum of present value of all the cash flows from bond till maturity. The cash flows from bond will be interest payment and maturity amount.

The interest payment is calculated using coupon rate of the bond, however, the cash flows are discounted to present value using discounting factors at market interest rate.

Discounting factor = 1/(1+i)^n

where i = market rate of interest and n = number of periods

If the interest is paid semi-annuallye, then the coupon rate is half the annual interesty rate and in that case, the interest rate use for discounting is also half the market interest rate. (In this example, 10%/2= 5% for case b,c and d)

Coupon payments for each bond issue:

a. Coupon payment = 1,000*8% = $80

b and c. Coupon payment = 1,000*8%*6/12 = $40

d. Coupon payment = $500*12%*6/12 = $30

d. The selling price of the bond will be calculated as below Cash flow Period DF @ 5% Present value 0.95238 0.90703 0.86384 0.82270 0.78353 0.74622 0.71068 0.67684 0.64461 0.61391 0.58468 0.55684 0.53032 0.50507 0.48102 0.45811 0.43630 0.41552 0.39573 0.37689 0.35894 0.34185 0.32557 0.31007 0.29530 0.28124 0.26785 0.25509 0.24295 0.23138 Selling price of the bond 30 30 30 30 30 30 30 30 30 30 28.57 27.21 25.92 24.68 23.51 22.39 21.32 20.31 19.34 18.42 17.54 16.71 15.91 15.15 14.43 13.74 13.09 12.47 11.87 11.31 10.77 10.26 9.77 9.30 8.86 8.44 8.04 7.65 7.29 122.63 577 2 4 6 7 30 30 30 30 30 30 30 30 30 30 30 30 30 20 23 24 25 26 27 28 29 30 30 30 30 530

For extra knowledge:

When the coupon rate of the bond is less than the market interest rate, then the bond is issued at the discount to compensate the investor from loss due to lower coupon rate. Same is the case in a, b and c above. When the coupon rate of the bond is more than the market interesr rate, the bond is issued at premium. Same is the case in situation d above.