NPV Calculator

What the figure measures

Net present value discounts each future cash flow back to what it is worth today at a chosen rate, adds those present values together, and subtracts what was paid at the outset. A positive figure means the discounted inflows come to more than the outlay at that rate; a negative one means they come to less. The rate is doing the work: it stands for what the same money would have to earn elsewhere at comparable risk, so the result is a comparison against that alternative rather than a measure of the project on its own.

Why more money back can still read negative

At the sample figures used on this page the cash flows total 125,000 against 100,000 paid out (a quarter more money returned), and the result is still below zero. Nothing is wrong with the arithmetic: the extra 25,000 arrives spread across five years, and at an 8% rate five years of waiting costs slightly more than the extra is worth. Setting the rate to zero shows the raw position, which is exactly +25,000, and every step above zero eats into it until the two sides meet. That meeting point is the break-even discount rate the panel reports, and at the sample figures it is 7.93%, just under the 8% entered, which is the whole of why the headline is negative rather than positive.

Reading the break-even rate

The break-even rate is the discount rate at which the present value of the inflows exactly equals the outlay, so it is the point where the headline crosses zero. Comparing it against the rate entered is quicker than reading the headline's sign, and it says how much room there is: a break-even rate far above the rate entered means the result survives a substantially higher hurdle, while one just below it, as here, means the sign turns on a fraction of a percentage point. The figure is scale-free, so holding the ratio of cash flow to outlay leaves it unchanged whatever the size of either. Two things are worth knowing about how it is reported. It is computed from the figures entered rather than clamped to the panel, so on a very short payback it can sit well above the rate the slider accepts; and it is shown to two decimals, so typing the displayed figure back in does not quite land on zero: at the sample figures the true rate is 7.9308% and entering 7.93% leaves 2.18 on the table. Where the undiscounted inflows match the outlay exactly the rate is zero, which says the project breaks even only if money carries no time cost; where they fall short of it, no rate makes the two meet and the row says so.

Which input moves the result most

Measured on a common basis (the proportional move each input needs to make on its own to flip the sign), the two money figures are the potent ones and the rate is not. At the sample figures used on this page the outlay flips the result with a 0.18% move and the cash flow with 0.18%, while the rate needs 0.86%, nearly five times as far. That ordering is not an artefact of a result sitting near zero: measured against the cash flow, the rate needs 396 times the move at a 0.1% rate and still 1.15 times it at 30%. It does reverse eventually, against the cash flow at about 34%, which the slider will not reach but the engine will accept, so the rate is the least sensitive input across the range on offer rather than universally.

Which of the two money figures leads is a closer question, and the profitability index settles it exactly. The outlay has to move by the net figure divided by the outlay; the cash flow has to move by the net figure divided by the present value of the inflows. The ratio between those two moves is therefore the present value divided by the outlay, which is the profitability index the panel already reports. Above 1 the outlay is the more potent of the two, below 1 the cash flow is, and at 1 they are identical, which is why they sit within four ten-thousandths of each other at the sample figures, where the index is 0.9982. The number of years does not belong on this scale at all, because it moves in whole steps rather than proportionally: at the five-year, 8% settings shown here, one year longer is worth 15.7542% of the outlay and one year shorter 17.0146% of it. What carries across is the scale invariance rather than the values: those two hold at any size of outlay, but not at any length, rate or ratio, and they fall as the term lengthens: the same lever is worth 10.7221% on a ten-year project and 4.9664% on a twenty-year one. Read in that unit the comparison settles itself, since a 1% move in the outlay is worth 1% of the outlay by definition, so at these settings the outlay overtakes the extra year only once it moves by more than 15.7542%, and everything below that leaves the year the larger lever.

Choosing the rate

The rate is the input least determined by the project itself, and, as the section above sets out, not the one the result is most sensitive to. What makes it decisive in practice is that it is an assumption rather than a measurement, and so the input most likely to be wrong by enough to matter. For a company it is commonly the weighted average cost of capital, sometimes with a premium added for project-specific risk; for an individual it is the return the same money could earn elsewhere at comparable risk. Both move with market conditions and with the risk being priced, so the rates used differ widely between organisations and over time. Because the calculation is a comparison against that rate, a figure quoted without the rate behind it cannot be interpreted.

The profitability index, and where ranking by it breaks

The profitability index is the present value of the inflows divided by the outlay, so it exceeds 1 exactly when the net present value is positive. It measures value per unit of capital rather than value in total, which is why it is used where a budget constrains how many projects can be funded. Ranking by it is optimal only under a specific condition: a single-period budget and projects that can be part-funded. Where projects have to be taken whole, a combination of lower-index projects can fill the budget more completely and produce more total value: a 60-cost project with an index of 1.40 taken first leaves 40 of a 100 budget unused and adds 24, while two 50-cost projects indexed at 1.30 and 1.28 use the budget fully and add 29. The index is a ranking aid rather than a selection rule.

Against the internal rate of return

The two answer different questions. Net present value returns an amount in currency; the internal rate of return returns a rate, which is the same quantity this page reports as the break-even discount rate. They rank projects the same way most of the time and part company where projects differ in size or in the timing of their flows, because a rate carries no information about how much capital it is earned on. Where the two disagree, the amount is the figure that adds up across a portfolio; a rate does not.

What's happening under the hood

Each year's cash flow is divided by one plus the rate, raised to the power of that year, so a flow arriving in year five is divided by that factor five times over. Those present values are summed across the whole horizon and the outlay is subtracted. The model uses one constant cash flow, one constant rate and end-of-year timing throughout, which is what makes it a single-line calculation rather than a schedule.

What this calculator does not model

Cash flows are taken as equal and annual, so an uneven profile, a partial year, or a flow arriving mid-year cannot be represented. The rate is held constant for the whole horizon. Tax, inflation beyond whatever is already embedded in the rate, terminal or salvage value, working capital movements, and any outlay after the first are all outside the model. It also assumes the whole outlay falls at the start, which is what allows it to be subtracted rather than discounted.