Describe the relationship between the coupon rate and the required rate that will result in a bond selling at a discount?
To understand the relationship between the coupon rate and the required rate that will result in a bond selling at a discount, we need to first define these terms.
The coupon rate refers to the fixed interest rate that a bond issuer promises to pay to bondholders annually or semi-annually as a percentage of the bond's face value. It is typically stated as a percentage.
The required rate, also known as the yield or discount rate, is the rate of return that investors demand for taking on the risk of investing in a particular bond. It represents the minimum rate of return an investor expects to earn on their investment to compensate for the risk and opportunity cost.
When a bond is issued, its price can either be at par (equal to its face value), at a premium (higher than face value), or at a discount (lower than face value). The relationship between the coupon rate and the required rate determines whether the bond will sell at a discount or a premium.
If the coupon rate is higher than the required rate, it means the bond offers a higher interest rate relative to what investors demand. In this case, investors are willing to pay more for the bond, driving the price up, and causing the bond to sell at a premium.
Conversely, if the coupon rate is lower than the required rate, it means the bond offers a lower interest rate relative to what investors demand. In this situation, investors are less interested, as they can earn a higher return elsewhere. The bond's price drops, resulting in the bond selling at a discount.
Therefore, the relationship that will result in a bond selling at a discount is when the coupon rate is lower than the required rate.