Answer:
To calculate the yield to maturity (YTM) of a bond, we need to use the bond's current market price, coupon rate, and time to maturity.
1. Bond selling for $870.00:
For a bond selling at a discount, meaning its market price is lower than its par value, the YTM will be higher than the coupon rate. In this case:
- Par value (F) = $1,000
- Coupon rate (C) = 8% of $1,000 = $80 (annual coupon payment)
- Time to maturity (n) = 10 years
- Current market price (P) = $870.00
Using these values, we can calculate the YTM using financial formulas or financial calculators. The YTM for this bond selling for $870.00 would be approximately 9.71%.
2. Bond selling for $1,100:
For a bond selling at a premium, meaning its market price is higher than its par value, the YTM will be lower than the coupon rate. In this case:
- Par value (F) = $1,000
- Coupon rate (C) = 8% of $1,000 = $80 (annual coupon payment)
- Time to maturity (n) = 10 years
- Current market price (P) = $1,100.00
Using these values, we can again calculate the YTM. The YTM for this bond selling for $1,100.00 would be approximately 6.48%.
The relationship between the YTM and the coupon rate depends on whether the bond is selling at a discount or a premium:
- Discount: When a bond sells at a discount, the YTM is higher than the coupon rate. This indicates that investors are demanding a higher yield to compensate for the bond's lower market price.
- Premium: When a bond sells at a premium, the YTM is lower than the coupon rate. This suggests that investors are willing to accept a lower yield due to the bond's higher market price.
In summary, the bond's selling price provides insights into the relationship between the required yield (rd) or YTM and the coupon rate. When the bond sells at a discount, the YTM is higher than the coupon rate, indicating higher required yield. Conversely, when the bond sells at a premium, the YTM is lower than the coupon rate, indicating a lower required yield.