Explain the concept of present value with a simple example.

• A. PV is today's value of future cash flows discounted at a rate; example: PV of $100 received in 1 year at 5% is $95.24.
• B. PV equals future value of cash flows at 2%.
• C. PV is the sum of all future cash flows.
• D. PV is the time when cash is received.

Answer: (A)

Present value shows what a future amount is worth today by discounting it at a given rate, reflecting the time value of money—the idea that money now can earn interest over time.

For example, if you expect to receive $100 in one year and the discount rate is 5%, the present value is 100 divided by 1.05, which equals about 95.24. So, $100 a year from now is worth roughly $95.24 today. If you had $95.24 today and invested it at 5%, you’d have about $100 in a year. The general formula is PV = FV / (1 + r)^t, where FV is the future amount, r is the rate, and t is the time in years.

This captures why the present value is lower than the future amount and how the discount rate affects its size. Treating PV as the future value would be incorrect, since PV is about today’s worth. Thinking PV is the sum of all future cash flows ignores the timing of each cash flow, and equating PV with the time when cash is received confuses value with timing.