A company issued $50,000 of 8%, 10-year bonds on January 1. The bonds pay semi annual interest. The present value factor of a single amount of 20 periods at 8% is 0.2145. The present value of 10 periods at 4% is 0.6756. The present value of 20 periods at 4% is 0.4564. Determine the present value of the par value of the bonds.

Question

Anabella Ross

Business

20 March, 06:48

A company issued $50,000 of 8%, 10-year bonds on January 1. The bonds pay semi annual interest. The present value factor of a single amount of 20 periods at 8% is 0.2145. The present value of 10 periods at 4% is 0.6756. The present value of 20 periods at 4% is 0.4564. Determine the present value of the par value of the bonds.

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Teagan Huffman · Answer 1

The present value of the par value of the bond is: $22,820.

Explanation:

As the characteristics of the bond, at the end of the bond period, which is 10 year, the bond's issuer will have to repay the face value of the bond to bond's holders. Thus, the future value of the bond = par value of the bond = 50,000.

As the bond pays coupon twice a year during 10 year with the coupon rate of 8% per year. There are 20 compounding periods, and the discount rate is 8%/2 = 4%. Thus, the present value factor of 20 periods at 4% is 0.4564 (1 / 1.04^20) should be used for calculating the present value of the par value of the bond.

=> Present value of the par value of the bond = future value of the bond x present value factor = 50,000 x 0.4564 = $22,820.