Question

Marwick Corporation issues 8%, 5-year bonds with a par value of $1,100,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 6%.
What is the bond's issue (selling) price, assuming the following Present Value factors:
1n = i = Present value of an annuity Present value of 1
(Series of payments) (Single sum)
5 8% 3.9927 0.6806
10 4% 8.1109 0.6756
5 6% 4.2124 0.7473
10 3% 8.5302 0.7441

Answer 1

Answer: $1,193,838.80

Explanation:

The price of a bond is the sum of the present value of the coupon payments and the face value at maturity.

= Present value of coupon payments + Present value of face value at maturity

First adjust the variables for semi-annual:

Number of periods = 5 * 2 = 10 semi annual periods

Coupon payment = 8% * 1,100,000 * 1/2 years = $44,000

Yield = 6% / 2 = 3%

Present value of coupon payments:

The coupon payments are constant so are an annuity:

= Annuity * Present value of an annuity factor, 10 periods, 3%

= 44,000 * 8.5302

= $375,328.80

Present value of face value

= 1,100,000 * Present value of 1, 3%, 10 periods

= 1,100,000 * 0.7441

= $818,510

Selling price:

= 375,328.80 + 818,510

= $1,193,838.80