How to use the NPV calculator
The NPV & PI tool values a single project:
- Enter the initial investment: the cash you pay out today.
- Set the discount rate, the return you require. For a company this is usually the cost of capital; for a personal investment, what the money could earn elsewhere at similar risk.
- Enter the net cash flow for each year, after tax and after any ongoing costs. A year with a net cost, such as a major overhaul, can be negative.
- Add a terminal or salvage value if you expect to sell the equipment or the business at the end.
- Choose the timing. End of year is the standard textbook assumption; mid-year treats cash as arriving evenly through each year.
The Compare projects tool takes two lists of cash flows, each starting with the negative year-0 outlay, and ranks them by NPV, IRR and profitability index.
The formulas
PV of future cash flows = NPV + I
Profitability index = PV of future cash flows ÷ II is the initial investment, CFt the cash flow in year t, r the discount rate, S the salvage value and N the last year. With the mid-year convention, each CFt is discounted over t − 0.5 years; the salvage value is still received at the end of year N.
The IRR shown for reference is the rate at which the NPV is zero, using the same timing.
A worked example
A company considers a $250,000 machine expected to produce net cash of $60,000, $70,000, $80,000, $75,000 and $65,000 over five years, and to sell for $20,000 at the end. Its cost of capital is 9%.
Discounted at 9%, the future cash flows are worth $284,114.21 today, of which $12,998.63 comes from the salvage value. Subtracting the investment leaves an NPV of $34,114.21.
The profitability index is 1.136: each dollar invested returns about $1.14 of present value. The IRR is 13.85%, comfortably above the 9% cost of capital.
In undiscounted terms the machine returns $120,000.00 more than it costs, but $85,885.79 of that disappears once each dollar is valued at the date it arrives. Without the salvage value, the NPV would fall to $21,115.58.
How the discount rate changes the answer
| Discount rate | NPV | Profitability index |
|---|---|---|
| 6% | $58,997.04 | 1.236 |
| 9% (example) | $34,114.21 | 1.136 |
| 12% | $12,212.56 | 1.049 |
| 15% | -$7,153.22 | 0.971 |
The NPV turns negative once the rate passes the IRR of 13.85%. That is why the discount rate deserves as much care as the cash flow forecast: a few points of difference can turn an attractive project into one that destroys value.
NPV, IRR and profitability index: when they disagree
For a single project with a normal pattern of cash flows, the three measures always agree: a positive NPV means an IRR above the discount rate and a PI above 1. They can disagree when you must choose between projects.
Timing. In the comparison example both projects cost $100,000. Project A’s cash comes late, Project B’s early. At 8%, A has the higher NPV ($26,123.13 against $21,014.37), but B has the higher IRR (19.97% against 16.62%). The NPV profiles cross at the crossover rate of 11.79%. Below it, the late cash of Project A is worth more; above it, the early cash of Project B wins. At 15%, Project B also has the higher NPV.
The crossover rate is the IRR of the difference between the two sets of cash flows (A minus B). It tells you how far your discount rate would have to move before the decision changed.
Scale. A $10,000 project that returns $15,000 in a year has an IRR of 50.00%. A $100,000 project that returns $130,000 has an IRR of only 30.00%, yet at 10% its NPV is $18,181.82 against $3,636.36. If you can only do one, the larger project adds more value, even though its percentage return is lower. The profitability index favors the small one too (1.364 against 1.182), which is the right ranking only when capital is the binding limit.
For mutually exclusive projects, rank by NPV at the discount rate that reflects their risk. Use the PI when a fixed budget must be spread across several independent projects: picking the highest PIs first gets the most value from the limited capital.
What this calculator does not include
- Changing discount rates. One rate is applied to every year. If risk or interest rates are expected to change, the NPV can be over- or understated.
- Inflation consistency. Use nominal cash flows with a nominal rate, or real cash flows with a real rate; mixing them distorts the result.
- Working capital and taxes must already be in the cash flows you enter.
- Flexibility. NPV assumes the plan is fixed. The option to expand, delay or abandon a project has value that a simple NPV does not capture.
- Unequal lives. When projects last different lengths of time, comparing NPVs directly can favor the longer one; analysts then use the equivalent annual annuity or repeat the shorter project.