True or false: Present value decreases as the discount rate increases.

True or false: Present value decreases as the discount rate increases.

• A. Present value decreases as the discount rate increases.
• B. Present value increases as the discount rate increases.
• C. Present value is unaffected by discount rate.
• D. Present value equals future value.

Answer: (A)

The main idea is that present value is the value today of a future cash flow, and it’s determined by discounting that future amount at a given rate. When the discount rate rises, you discount the future amount more heavily, so its value today falls. This is shown by the formula PV = FV / (1 + r)^t (or PV = CF / (1 + r)^t): increasing r makes the denominator larger, reducing PV. For example, a $100 amount one year from now has a present value of about $95.24 at a 5% rate and about $90.91 at a 10% rate, illustrating the decrease as the rate goes up. Therefore the statement is true. The ideas that PV increases with a higher rate, or that PV is unaffected by the discount rate, or that PV equals future value, don’t hold in general because PV and FV are connected through discounting, not equal except in special, trivial cases.

The main idea is that present value is the value today of a future cash flow, and it’s determined by discounting that future amount at a given rate. When the discount rate rises, you discount the future amount more heavily, so its value today falls. This is shown by the formula PV = FV / (1 + r)^t (or PV = CF / (1 + r)^t): increasing r makes the denominator larger, reducing PV. For example, a $100 amount one year from now has a present value of about $95.24 at a 5% rate and about $90.91 at a 10% rate, illustrating the decrease as the rate goes up. Therefore the statement is true. The ideas that PV increases with a higher rate, or that PV is unaffected by the discount rate, or that PV equals future value, don’t hold in general because PV and FV are connected through discounting, not equal except in special, trivial cases.