Question

Young Co. issues $800,000 of 10% bonds dated January 1, Year 1. Interest is payable semiannually on June 30 and December 31. The bonds mature in 5 years. The current market rate for similar bonds is 8%. The entire issue is sold on the date of issue. The following values are given:

Answer 1

The student's question involves calculating the present value of a bond at two different discount rates, reflecting changes in market interest rates. The present value decreases when the discount rate exceeds the bond's coupon rate.

Step-by-step explanation:

The subject matter of the question pertains to the calculation of the present value of a bond. When calculating present value, one must consider the predicted stream of future payments from the bond and discount them back to their value in today's dollars using a particular discount rate. Two scenarios are presented: one where the discount rate is the same as the bond interest rate (8%), and another where the market interest rates have risen, increasing the discount rate to 11%. It's important to remember that a bond's present value will decrease if the discount rate rises above the bond's coupon rate.

To calculate the present value using an 8% discount rate, the formula for the present value of an annuity would be used for the interest payments, and the present value of a lump sum formula would be applied for the principal repayment. If interest rates rise to 11%, the same calculations would be made with a higher discount rate, resulting in a lower present value.

Answer 2

$864,884

Step-by-step explanation:

The proceeds received from the issuance of bonds equal the sum of the present value of the cash flows associated with the bonds (both the face amount and interest payments) discounted at the interest rate prevailing in the market at the time. The present value of the $800,000 face amount discounted at the market interest rate of 8% is equal to $540,448 ($800,000 × .67556). The present value of the semiannual interest payments of $40,000 [$800,000 × 10% × (6 months ÷ 12 months)] discounted at the market interest rate of 8% is equal to $324,436 ($40,000 × 8.11090). Thus, the proceeds on the sale of the bonds equal $864,884 ($540,448 + $324,436).