How do discount rates relate to present value?

• A. Higher discount rates decrease present value; lower rates increase present value.
• B. Higher discount rates increase present value; lower rates decrease present value.
• C. Discount rates do not affect present value.
• D. Present value is only affected by future cash flow magnitude.

Answer: (A)

The main idea is that discount rates determine how much a future amount is worth today, and they move in opposite directions to present value. Present value discounts a future cash flow back to the present using PV = FV / (1 + r)^t, where r is the discount rate and t is the time until receipt. When the discount rate rises, the denominator (1 + r)^t gets larger, so the present value becomes smaller. Conversely, lowering the rate reduces the discounting effect and increases the present value.

Think of it this way: the discount rate reflects the opportunity cost of waiting and the risk/return you could earn elsewhere. If you could invest elsewhere at a higher return, you’d require more compensation to defer receiving money, so the amount you’re willing to accept today for a future payment drops as the rate climbs. For example, $100 to be received in one year has a present value of about $95.24 at a 5% rate and about $90.91 at a 10% rate. In two years, it’s about $90.70 at 5% and $82.64 at 10%. These examples show the inverse relationship: higher discount rates reduce present value, lower rates increase it.