Final answer:
The dollar price of a treasury bond with a face value of $25,000 and a quoted price of 103.3750 is $25,843.75. Present value calculations of bonds take into account future cash flows discounted at the current interest rate, with the price of the bond decreasing if the discount rate increases.
Step-by-step explanation:
To calculate the dollar price of a treasury bond with a face value of $25,000 and a quoted price of 103.3750, you multiply the face value by the quoted price, expressed as a percentage. Therefore, the calculation is $25,000 * 103.3750% = $25,843.75.
Present Value of a Bond
When considering the present value of a bond, we must discount the future cash flows—the interest payments, as well as the principal repayment at maturity—back to their present value using the current discount rate. As the discount rate changes, the present value of these future cash flows also changes. If interest rates rise, leading to a higher discount rate, the bond's price typically decreases. This is because the bond's fixed interest payments become less attractive compared to new bonds issued at the higher current rates, and the present value of the future cash flows decreases.
Example
For instance, imagine a $3,000 bond issued at an interest rate of 8%. This bond would pay $240 per year in interest. If the market discount rate is also 8%, the present value of these future cash flows would roughly equal the face value of the bond. However, if the market interest rates increase to 11%, the present value calculation at the new discount rate will result in a lower price than the face value of the bond.