Question

A $100,000 bond was issued on 1/1/10. It pays interest (coupon) of 6% per annum, with payments occurring every six months. The bond is due in 2 years. A potential investor wanted to know what the bond should be worth on the day of issue, if the prevailing rate for similar bonds (market rate) was 8%. An inexperienced accountant attempted to calculate what the bond should be worth on 1/1/10. Review the work of the accountant, and answer the questions below pertaining to possible mistakes. The entries in the period of interest column:

1) are correct
2) should be 0, 1, 2, 3, 4
3) should be 1, 2, 3, 4, 4
4) should be 1, 2, 3, 4, 5

Answer 1

To value the bond on the day of issue when the market rate of interest is 8%, the bond's future cash flows should be discounted at this market rate. The correct entry for the periods of interest when valuing the bond should be '1, 2, 3, 4, 5' which considers semi-annual interest payments over the two-year term and the repayment of principal at the end.

Step-by-step explanation:

The question pertains to the valuation of a bond when the coupon rate is different from the market interest rate. Specifically, the bond in question pays a 6% coupon semi-annually, has a face value of $100,000, and matures in 2 years. The market rate for similar bonds is 8%. To value the bond on the day of issue, one must discount the future cash flows of the bond (interest payments and principal repayment) at the market rate of 8%.

In the scenario presented (which is similar but uses different numbers for the sake of example), consider a two-year bond issued at $3,000 with an 8% coupon rate. The bond will pay $240 annually in interest (which is $3,000 × 8%), and in the second year it will pay another $240 in interest plus the $3,000 principal amount. If the discount rate is also 8%, the present value of these cash flows can be calculated to find the bond's worth. If the market interest rates rise to 11%, the present value of the bond's future cash flows would be calculated using the new discount rate of 11%.

In answering the question about the periods of interest in valuing the semi-annual coupon bond, the correct answer would be option 4) 'should be 1, 2, 3, 4, 5' because interest would be paid at the end of each six-month period over the two-year life of the bond, which results in five periods when factoring the final repayment of principal.