Present Value Present value (PV) is the current worth of a sum of money or stream of cash flows to be received in the future, discounted at an appropriate rate. It reflects the time value of money: a dollar today is worth more than a dollar tomorrow because it can be invested to earn a return. Why it matters
* Helps compare investments that pay off at different times.
* Guides business decisions and capital budgeting by showing the current equivalent of future receipts.
* Used to set hurdle rates and evaluate whether a future payoff justifies an investment today.
Core formula For a single future amount:
PV = FV / (1 + r)^n Explore More Resources
Where:
- PV = present value
- FV = future value (amount to be received)
- r = discount rate (period rate of return, as a decimal)
- n = number of periods For multiple future cash flows, calculate each payment’s PV and sum them:
PV_total = Σ [CF_t / (1 + r)^t] Explore More Resources
Choosing the discount rate The discount rate represents the foregone return if you take money in the future instead of today. Common approaches:
- Use a risk-free rate (e.g., U.S. Treasury yield) for low-risk comparisons.
- Add risk premia for uncertain cash flows or use a company’s required rate of return (hurdle rate).
- Use a real interest rate (adjusted for inflation) when comparing real purchasing power. Higher discount rates reduce present value; lower rates increase it. Explore More Resources
Examples
* Single future payment: $1,000 in 5 years at 5% → PV = 1000 / (1.05^5) ≈ $784.
* Choice between $2,000 today or $2,200 in one year with an expected return of 3%:
PV of $2,200 = 2200 / 1.03 ≈ $2,135.92. Since $2,000 < $2,135.92, waiting for $2,200 is better.
* Stream of cash flows: discount each expected payment back to today and sum the results.
Benefits
* Provides a common basis to compare monetary amounts at different times.
* Helps determine whether an investment meets required returns.
* Useful in valuation, loan analysis, and project evaluation.
Limitations
* Highly sensitive to the chosen discount rate; incorrect estimates yield misleading PVs.
* Long-term forecasts amplify uncertainty (returns, inflation, risk).
* Can be manipulated by selecting favorable rates or assumptions.
Practical steps to calculate PV
1. Identify the future amount(s) and timing (FV and n).
2. Choose an appropriate discount rate r (risk-free plus risk premium, or required return).
3. Apply PV = FV / (1 + r)^n for each cash flow and sum if multiple.
4. Compare the PV to the cost or alternative options to make a decision.
Bottom line Present value translates future money into today’s terms, allowing clear comparisons across time. It is a fundamental tool in finance, but its usefulness depends on selecting realistic discount rates and acknowledging uncertainty, especially over long horizons.