Final answer:
The present value (PV) decreases when the discount rate increases because future cash flows are discounted at a higher rate, reflecting increased opportunity cost. For bonds, rising interest rates after issuance lead to selling prices below face value, while falling interest rates lead to selling above face value.
Step-by-step explanation:
When you increase the discount rate, referred to as r, the present value (PV) of future cash flows decreases. This phenomenon occurs because the future cash flows are discounted at a higher rate, reflecting a higher opportunity cost of capital. For instance, if a bond's interest rate increases from 8% to 11%, the actual dollar payments remain fixed, but the present value of these payments is lower when discounted at the new, higher interest rate. Conversely, a decrease in the discount rate results in an increase in the present value of the future cash flows. Such changes affect the value of investments like bonds. A bond will sell for more than its face value if interest rates decrease after it was issued due to locking in a higher rate. However, if interest rates increase and an investor is locked into a lower rate, the bond's selling price will be less than its face value.