Kiss Greetings planned to raise $500,000 by issuing bonds. The bond certificates were printed bearing a stated interest rate of 6%, which was equal to the yield rate of interest. However, before the bonds could be issued, economic conditions forced the yield rate up to 7%. If the life of the bonds is 10 years and interest is paid annually on December 31, how much will the company receive from the sale of the bonds?

Question

Quizplus · Accepted Answer

When Kiss Greetings planned to issue bonds with a stated interest rate of 6%, it intended to issue them at par value, meaning investors would pay $500,000 for the bonds, and in return, they would receive annual interest payments based on the 6% interest rate. However, economic conditions changed, and the yield rate demanded by the market increased to 7%.
The yield rate represents the return that investors require for a bond investment. When the market yield rate exceeds the stated interest rate on the bonds, the bonds become less attractive to investors unless they can purchase them at a discount to compensate for the lower interest payments they will receive compared to the current market rate.
Therefore, to sell the bonds in a market where investors expect a 7% return, Kiss Greetings will have to offer the bonds at a price lower than the face value of $500,000. This discount makes the effective yield of the bonds match the market rate of 7%. The actual amount received by the company will be the present value of the bond's cash flows (interest payments and principal repayment at maturity) discounted at the market yield rate of 7%.
The cash flows from the bond consist of 10 annual interest payments of 6% of the $500,000 face value ($30,000 each year) and a single payment of the $500,000 face value at the end of the 10-year period. The present value of these cash flows, discounted at the 7% market yield rate, will be less than the face value of the bonds, meaning Kiss Greetings will receive less than $500,000 from the sale of the bonds.

Kiss Greetings Planned to Raise $500,000 by Issuing Bonds