NPV, Present Value & Future Value Calculator

The time value of money behind the NPV calculator

1,000 today is worth more than 1,000 in five years, for three reasons: you could invest it, inflation erodes it, and a future promise carries risk that cash in hand does not. Discounting puts a number on that difference.

Future value — compounding forward

FV = PV × (1 + r)ⁿ

100,000 at 8% for five years grows to 146,932.81.

Present value — discounting back

PV = FV ÷ (1 + r)ⁿ

100,000 receivable in five years is worth 68,058.32 today at an 8% discount rate.

Net present value

NPV = Σ (Cash flow_t ÷ (1 + r)^t) − Initial investment

Discount every future cash flow back to today, add them up, subtract what you paid. A positive NPV means the investment earns more than your required return.

A worked example

Invest 100,000 today, receive 30,000 a year for five years, required return 8%:

• Present value of the cash flows = 119,781.31
• Less the initial investment = 100,000
• NPV = 19,781.31 — accept

The discount rate does most of the work

Change the rate by two points and marginal projects flip from accept to reject. It deserves as much thought as the cash flows, and it usually gets far less.

What the rate should represent: your cost of capital, or the return you could get on an alternative of similar risk. A higher rate for riskier projects is correct — that is how risk gets priced into the decision rather than being handled by optimism.

Try it in the calculator. Take the example above and raise the rate to 15%: NPV turns negative and the same project should be rejected. Nothing about the cash flows changed.

Reading the schedule

Expand the discounted cash flow table and look at the discount factor column. At 8%, a cash flow in year one is worth 0.9259 of its face value; by year five it is 0.6806.

The cumulative NPV column shows when the project turns positive — the discounted payback point. That is more honest than the simple payback period because it accounts for the time value of the money you got back.

What NPV assumes

• That you can forecast the cash flows. NPV is precise about numbers that are usually estimates. Precision is not accuracy.
• That the discount rate is constant across the whole period.
• That intermediate cash flows are reinvested at the discount rate.
• That risk is fully captured in a single rate, which is a simplification.

Run the numbers at a few different rates and see how robust the answer is. A project that is positive at 8% and negative at 10% is a much weaker proposition than one positive at both.

Before you rely on the result

The arithmetic here is exact and has been checked against worked examples. What a calculator cannot do is know your situation — your contract, your licence category, the elections available to you, or the exceptions that might apply. It applies a formula to the figures you give it.

Use it to get a sense of scale, to sanity-check something you have been quoted, or to work a problem through for yourself. Where the number is going into a decision that matters, have the assumptions underneath it checked. That conversation is free and it usually takes twenty minutes.