describe the relationship between the coupon rate and the required rate of return that will result in a bond selling at:
a - a discount
b - face value
c - a premium
If you bought a bond that paid a coupon (interest) rate less than prevailing interest rates for that rating and maturity, would you pay face (maturity)value for the bond? I wouldn't. Use similar reasoning to deduce your own answers.
The relationship between the coupon rate and the required rate of return plays a significant role in determining the price at which a bond will be sold. Let's break down each scenario:
a) Bond selling at a discount:
When the coupon rate is lower than the required rate of return, the bond is likely to be sold at a discount. In this case, the bond's coupon rate generates lower interest payments compared to the expected return demanded by investors. As a result, the bond's price can be expected to be lower than its face value.
b) Bond selling at face value:
When the coupon rate is equal to the required rate of return, the bond is expected to be sold at its face value. In this scenario, the interest payments (coupon rate) align with the investor's required rate of return. This means that the bond's price will be neither at a discount nor at a premium, but at the same value as the face value.
c) Bond selling at a premium:
When the coupon rate is higher than the required rate of return, the bond may be sold at a premium. In this case, the bond's coupon rate generates higher interest payments compared to the expected return required by investors. Consequently, investors are willing to pay more than the face value to acquire the bond, which results in a premium price.
In summary, when the coupon rate is lower than the required rate of return, the bond is sold at a discount. When the coupon rate equals the required rate of return, the bond is sold at face value. And when the coupon rate is higher than the required rate of return, the bond is sold at a premium.