Allegiant issues $5\%, 20$-year bonds with a par value of $[tex]2,000,000[/tex] and semiannual interest payments. In each separate situation, determine whether the bond is issued at par value, at a discount, or at a premium.
| Situation | Bond issued |
|---|---|
| 1. Market rate for the bond is $4 \%$. | |
| 2. Market rate for the bond is $5 \%$. | |
| 3. Market rate for the bond is $6 \%$. | |
Answer (2)
If the market rate (4%) is less than the coupon rate (5%), the bond is issued at a premium.
If the market rate (5%) equals the coupon rate (5%), the bond is issued at par value.
If the market rate (6%) is greater than the coupon rate (5%), the bond is issued at a discount.
Therefore, the bond is issued at a premium, par value, and discount, respectively. P re mi u m , P a r , D i sco u n t
Explanation
Understanding the Problem We need to determine whether the bond is issued at par value, at a discount, or at a premium for each of the given market rates. The key is to compare the bond's coupon rate with the market rate.
Situation 1: Market rate is 4% If the market rate is less than the coupon rate, the bond is issued at a premium because investors are willing to pay more for a bond that offers a higher interest rate than the current market rate.
Situation 2: Market rate is 5% If the market rate is equal to the coupon rate, the bond is issued at par value because the bond's interest rate is exactly what the market expects.
Situation 3: Market rate is 6% If the market rate is greater than the coupon rate, the bond is issued at a discount because investors will pay less for a bond that offers a lower interest rate than the current market rate.
Final Answer Based on the analysis:
When the market rate is 4%, which is less than the coupon rate of 5%, the bond is issued at a premium.
When the market rate is 5%, which is equal to the coupon rate of 5%, the bond is issued at par value.
When the market rate is 6%, which is greater than the coupon rate of 5%, the bond is issued at a discount.
Examples
Bonds are a common investment tool for both individuals and institutions. Understanding whether a bond is issued at a premium, discount, or par value is crucial for making informed investment decisions. For example, if a company issues bonds at a premium, it indicates strong financial health and investor confidence. Conversely, bonds issued at a discount might signal higher risk or less favorable market conditions. Knowing these dynamics helps investors assess the potential returns and risks associated with bond investments, enabling them to diversify their portfolios effectively.
The bond is issued at a premium when the market rate is 4%, at par value when the market rate is 5%, and at a discount when the market rate is 6%.
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