A business owner is offered $10,000 today or $11,200 two years from now. Which is worth more? If she can earn 8 percent per year investing the $10,000, it would grow to $10,000 × (1.08)² = $11,664 in two years — more than the $11,200 offered. She should take the $10,000 now. If the available return is only 5 percent, the $10,000 grows to only $11,025 — less than $11,200. She should take the future payment. Present value analysis makes these comparisons rigorous — it converts all cash flows, whenever they occur, into a common metric: their equivalent value today.
The formula
Present Value (PV) = FV / (1 + r)^t
Where:
- FV = future value (the cash flow to be received)
- r = discount rate (the opportunity cost of capital, expressed as a decimal)
- t = time periods until the cash flow is received
For a stream of cash flows, the Net Present Value (NPV) sums the present values of all future flows:
NPV = Σ [CF_t / (1 + r)^t] for t = 1 to n
Subtracting the upfront investment: NPV = –Investment + Σ [CF_t / (1 + r)^t]
If NPV > 0, the investment creates value above its opportunity cost. If NPV < 0, it destroys value.
Reading the result
Present value reflects two related principles:
Time value of money: a dollar today is worth more than a dollar in the future because the present dollar can be invested to grow. This is not about inflation — even in a zero-inflation world, present dollars are more valuable because they can earn a return.
Discounting: future cash flows are discounted at the opportunity cost of capital — the return that could be earned on the best alternative investment of similar risk. Higher discount rates produce lower present values; longer time horizons produce lower present values.
Worked example
An investor is evaluating a rental property. The property costs $300,000 and is expected to generate net rental income of $20,000 per year for 10 years, then be sold for $350,000. Using a discount rate of 7 percent:
- PV of annual income: $20,000 × [(1 – 1/1.07¹⁰) / 0.07] = $20,000 × 7.024 = $140,480
- PV of sale proceeds: $350,000 / 1.07¹⁰ = $350,000 / 1.967 = $177,938
- Total PV of cash flows: $140,480 + $177,938 = $318,418
- NPV: $318,418 – $300,000 = +$18,418
At a 7 percent required return, this property creates $18,418 of value above the opportunity cost of capital — a worthwhile investment. The Federal Reserve's real interest rate data provides benchmark discount rates for risk-free investments; risk-adjusted rates require adding a premium above the risk-free rate.
Where it's used
Present value is the universal tool for capital allocation decisions. The IRS uses present value analysis in transfer pricing regulations. The Congressional Budget Office uses NPV in scoring multi-year budget proposals. Bond prices are the present value of future coupon payments and principal. Stock prices approximate the present value of expected future earnings or dividends. Real estate prices are the present value of future rental income. Every valuation ultimately reduces to this single framework.
