Bushman Inc issues 400000 of 9 bonds that pay interest semia

Bushman, Inc., issues $400,000 of 9% bonds that pay interest semiannually and mature in 10 years. Compute the bond issue price assuming that the bonds\' market rate is:

a. 6% per year compounded semiannually.
(Use a calculator or Excel for your calculations. Round your answers to the nearest dollar.)

b. 8% per year compounded semiannually.
(Use a calculator or Excel for your calculations. Round your answers to the nearest dollar.)

Solution

Face Value of Bonds = $400,000;

Stated Rate or Coupon Rate = 9% i.e., 4.5% per 6 months.

Term = 10 years or 20 periods of 6 months.

It is known fact that, when the Market Interest < Coupon Rate, the bonds would be issued at premium because the company is going to pay a higher interest than the interest that would be served normally in market.

a. 6% per year compounded semiannually:

1. Present Value of Principal repayment = $400,000 x PV factor of 3% at 20th period

= $400,000 x 0.554

= $221,600

2. Present Value of Interest Payments = Interest payment x Annuity factor of 3% for 20 periods

Interest Payment = $400,000 x 4.5% = $18,000

Present Value of Interest Payments = $18,000 x 14.878

= $267,804

3. Selling Price of bonds = Present value of principal repayment + Present value of interest payments

= $221,600 + $267,804

= $489,404

b. 8% per year compounded semiannually:

1. Present Value of Principal repayment = $400,000 x PV factor of 4% at 20th period

= $400,000 x 0.456

= $182,400

2. Present Value of Interest Payments = Interest payment x Annuity factor of 4% for 20 periods

Interest Payment = $400,000 x 4.5% = $18,000

Present Value of Interest Payments = $18,000 x 13.590

= $244,620

3. Selling Price of bonds = Present value of principal repayment + Present value of interest payments

= $182,400 + $244,620

= $427,020

Hope this is helpful!!