Final answer:
A bond will sell at a discount if its face rate of interest is below the market rate at the time of issuance as investors seek higher returns available from other investments. This concept is clarified by the present value calculation that adjusts the price of the bond to reflect current interest rates and the bond's desirability. Option c. the face rate of interest is more than the market rate of interest at the time of issue is the correct answer.
Step-by-step explanation:
Bonds will sell at a discount when the face rate of interest is less than the market rate of interest at the time of issue. This scenario occurs because the bond's fixed interest payments are less attractive relative to the higher returns available from other investments in the current market, leading investors to pay less than the bond's face value. The present value calculation is a method that helps to understand the influence of interest rates on the bond's price. If a bond is issued at a coupon rate that is higher than the prevailing market interest rates, it becomes more attractive as it offers a better return, leading it to be sold at a premium.
Conversely, if a bond is issued when market interest rates rise above the bond's coupon rate, the bond becomes less desirable and will be sold at a discount, as investors can find more attractive yields elsewhere. For example, if a company issues a bond with a 5% coupon when the current market interest rates are also at 5%, and then the market rates rise to 6.5%, the bond would be sold at a discount since investors can get a better rate with new issues. Additionally, the risk associated with the bond can influence its price. A riskless bond would ideally sell for its face value, but if market interest rates increase, making other investments more attractive, such a bond would also need to be sold at a discount to entice buyers.