How do you calculate present value from future value in benefit-cost analysis?

• A. Present value = Future value / (1 + r)
• B. Present value = Future value × (1 + r)
• C. Present value = Future value / (1 + r)^n
• D. Present value = Future value × (1 + r)^n

Answer: (A)

Time value of money is the foundation here: a future amount is worth less today because of the opportunity to earn interest. Present value is the amount today that would grow to the future amount at a given discount rate r over n periods. The standard discounting formula is PV = FV / (1 + r)^n. This shows why the general approach uses the exponent n. If there’s only one period until the future amount, the formula simplifies to PV = FV / (1 + r). In benefit-cost analysis you usually project over several periods, so the full (1 + r)^n form is typically used. The options that multiply by (1 + r) or by (1 + r)^n move values forward in time instead of discounting, so they’re not correct for finding present value. The provided choice matches the single-period case, which is why it can be correct in that specific context.