Final answer:
Bond prices are calculated based on the present value of future cash flows, with premium bonds priced above and discount bonds priced below face value. Over time, assuming unchanged YTMs, premium bond prices decrease toward face value, while discount bond prices increase toward face value. After 19 years, both bonds will be worth their face value.
Step-by-step explanation:
To calculate the price of Bond X and Bond Y, we must determine the present value of their future cash flows discounted back at their respective yields to maturity (YTM). Since Bond X is a premium bond with a coupon rate above the YTM, its price will be greater than its face value. Conversely, Bond Y is a discount bond with a coupon rate below the YTM, and its price will be less than its face value.
Bond prices are expected to change over time as they approach maturity. Generally, the price of a premium bond decreases towards its face value, while the price of a discount bond increases towards its face value as the maturity date approaches, assuming that the YTM remains constant. This process is known as amortization of the premium or accretion of the discount.
For a simple calculation example, consider a $3,000 bond with an 8% coupon rate. If the discount rate is also 8% (matching the coupon rate), the bond's present value will reflect the face value of the bond since the coupon rate matches the required return. However, if the discount rate rises to 11%, the present value of the bond will decrease, reflecting the lower price an investor is willing to pay for the same level of coupon payments in a higher interest rate environment.
After 19 years, when the bonds mature, both will converge to their face value of $1,000, as the final principal repayment is made. The present value dynamics, explained with the simple two-year bond example, is applicable to longer-term bonds like Bond X and Y, but involve more complex calculations due to the multiple periods.