Final answer:
The yield to maturity (YTM) of Dylan's bonds is less than the original YTM but greater than the coupon rate, and the yield calculation considers both interest payments and capital gains.
Step-by-step explanation:
The student is asking about the relationship between the yield to maturity (YTM), coupon rate, and bond prices. Dylan purchased bonds when the YTM was 12.5%. Now, the current YTM is less than the original YTM but greater than the coupon rate. This is because the coupon rate remains constant (at 8% in this example) after the bond is issued, but the YTM can fluctuate based on market interest rates and bond prices.
When market interest rates rise, bond prices fall, leading to a higher YTM for new potential buyers because they can purchase the bonds at a discount to their face value. Conversely, when market interest rates fall, bonds sell at a premium, resulting in a YTM that's lower than the coupon rate for new buyers. In Dylan's case, since he purchased at a 12.5% YTM and now the current YTM is less than that but more than the coupon rate, it suggests that market interest rates have fallen since the purchase but not below the bond's coupon rate.
To calculate the bond yield, which includes interest payments and capital gains, one would use this formula: Yield = (Total annual interest + (Face value - Purchase price)) / Purchase price. Applying this to Dylan's situation where he receives the bond's face value and last year's interest, the yield would be ($1080 - $964) / $964 = 12%.