Final answer:
The value of a bond is determined by discounting its future cash flows at the current market interest rate. If the market rate is equal to the bond's coupon rate, the bond retains its face value. When the market rate exceeds the coupon rate, the bond's present value decreases and is worth less than its face value.
Step-by-step explanation:
The student's question involves calculating the present value of bond payments with different discount rates. To determine how much a simple two-year bond with an initial value of $3,000 and an interest rate of 8% is worth in the present, we must discount the expected future cash flows of the bond. When applying a discount rate equal to the coupon rate (8% in this case), the present value of the bond does not change; it's worth its nominal value, which means the bond is worth $3,000.
If the discount rate changes to 11%, the present value (PV) of the bond payments received in the future can be calculated using the formula PV = C / (1 + r)^1 + F / (1 + r)^2, where C is the annual coupon payment, r is the discount rate, and F is the face value of the bond. For year one, we calculate PV as $240 / 1.11, and for year two as ($240 + $3,000) / 1.11^2.When valuing a bond with a market interest rate higher than the coupon rate, the bond's present value falls below its face value, making it worth less than its original price. Using the previous example, if we are looking to purchase a bond just one year before its maturity and the current market interest rate is 9% while the coupon rate is 6%, the bond would be discounted and therefore purchased for less than $10,000.
\