CF · NPV
NPV Calculator
Discount uneven cash flows the way the BA II Plus CF worksheet does — CF0 plus up to 24 amount-and-frequency groups — and read net present value, net future value, payback and the profitability index together, with the profile plotted so you can see where the value crosses zero.
- Up to 24 cash-flow groups
- Frequency counts, like Fj
- NPV profile chart
- Every discount factor shown
The idea
What net present value is actually comparing
Net present value answers one question: is this set of cash flows worth more than the alternative? The alternative is hidden inside the discount rate. If you can earn 9% on similar risk elsewhere, then 9% is what the project has to beat, and every future pound it produces is worth less than a pound today by exactly that much per year.
So each flow is pulled back to today, divided by (1 + i) once for every period it has to travel. Add the discounted flows to the outlay — which needs no discounting, because it happens now — and the total is the surplus, in today’s money, over and above what the discount rate would have given you.
NPV = CF0 + CF1 ÷ (1 + i)¹ + CF2 ÷ (1 + i)² + … + CFn ÷ (1 + i)ⁿ
A positive result is a surplus and a negative one is a shortfall. Zero means the flows earn the discount rate exactly, which is the definition of the internal rate of return.
Step by step
How to calculate NPV by hand
Four steps, and the only one that takes any effort is the third. The worked example below runs a £50,000 project that returns £14,000 a year for five years, discounted at 9%.
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Write the flows against their periods
t = 0 : −50,000 | t = 1…5 : +14,000
The outlay sits at t = 0. Five equal receipts follow, so on the hardware this is one group with a frequency of 5 rather than five separate entries.
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Build the discount factor for each period
1 ÷ (1 + i) ^ t
1 ÷ 1.09¹ = 0.917431 · 1 ÷ 1.09² = 0.841680 · 1 ÷ 1.09³ = 0.772183 · 1 ÷ 1.09⁴ = 0.708425 · 1 ÷ 1.09⁵ = 0.649931
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Multiply each flow by its factor and add
14,000 × (0.917431 + 0.841680 + 0.772183 + 0.708425 + 0.649931) = 14,000 × 3.889651
54,455.12
Equal flows share one annuity factor, so the five multiplications collapse into one. The TVM calculator gets the same number from PMT and N directly.
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Add the outlay
−50,000 + 54,455.12
NPV = 4,455.12
Positive, so the project beats 9%. Its IRR is 12.3762% — the rate at which that £4,455 surplus would fall to nothing.
The rate
Matching the rate to the period
This is where most wrong answers come from. The discount rate you type is the rate for one period of your timeline, not the rate per year. If the flows are monthly, the rate must be monthly too.
| Flows arrive | Periods per year | Rate to enter, from 9% a year |
|---|---|---|
| Annually | 1 | 9% |
| Quarterly | 4 | 2.25% |
| Monthly | 12 | 0.75% |
| Weekly | 52 | 0.173077% |
Those are nominal conversions — the annual rate simply divided by the number of periods, which is how a quoted APR is meant to be split. If instead you are given a rate that already compounds annually and you need the true monthly equivalent, that is a different sum: 1.091/12 − 1 = 0.720732%. The interest conversion calculator handles both directions.
Reading the output
What each figure on the results card means
- Net present value
- The surplus in today’s money. Compare it to zero, not to the size of the project.
- NFV — net future value
- The same surplus stated at the last period instead of the first. Useful when a question asks what you end up with rather than what it is worth now.
- Profitability index
- Present value of the inflows divided by the present value of the outflows. Above 1.00 passes. It ranks projects by efficiency, which matters when the budget is fixed.
- Payback and discounted payback
- How many periods until the cumulative cash flow turns positive — first ignoring the time value of money, then respecting it. Interpolated inside the crossover period, so 3.42 means part-way through the fourth.
- Rate where NPV hits zero
- The IRR, shown here because it is the single most useful cross-check on an NPV: if your discount rate is below it, NPV must be positive.
Getting it right
Five mistakes that account for most wrong answers
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Entering the outlay as a positive number
Then NPV is just the sum of everything and always positive. CF0 must be negative for an investment.
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Mixing an annual rate with monthly flows
Discounting twelve monthly receipts at 9% per period rather than 0.75% understates them badly. The rate and the period must agree.
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Putting a repeated amount in the frequency column
The second box counts periods, not money. Five years of £14,000 is amount 14000 with a frequency of 5 — not amount 5 with a frequency of 14,000.
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Forgetting a period with no cash flow
A gap year still occupies a period. Enter it as a group with amount 0 and the right frequency, or every flow after it is discounted from the wrong period.
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Leaving the previous problem in the worksheet
On the hardware, CF 2ND CE|C clears it. On this page the Reset button does the same, and every group row goes back to blank.
Where to go next
When NPV is not the tool you want
Net present value needs a discount rate before it can say anything. If you would rather ask what return the flows themselves imply, the IRR calculator solves the same timeline for the rate that makes NPV zero, and reports MIRR alongside it for the reinvestment problem.
Level cash flows do not need the CF worksheet at all — five equal receipts are an annuity, and the TVM calculator handles them in one pass. A loan is the same shape seen from the other side, which the amortization calculator splits into principal and interest period by period.
Bonds are cash-flow problems with a fixed shape and a market convention attached, so they get their own worksheet in the bond calculator. And if you want the keystrokes rather than the web form, the full BA II Plus emulator runs the CF worksheet exactly as the device does, with the study guides covering the exam-room shortcuts.
FAQ
NPV questions, answered
The sign convention, the rate, and the two places net present value is commonly misread.
What does net present value actually measure?
It measures how much value a set of cash flows creates over and above what the same money would earn at the discount rate. Every future amount is pulled back to today by dividing by (1 + i)t, and the initial outlay is added at face value because it happens now. A net present value of £8,400 means the project is worth £8,400 more than the alternative that returns exactly the discount rate.
Which discount rate should I use?
The rate you could earn on the next-best use of the same money at the same risk. In coursework that is usually given — a required return, a cost of capital, or a hurdle rate. In practice a company uses its weighted average cost of capital. The one rule that matters is that the rate and the cash flows must share a period: annual flows take an annual rate, monthly flows a monthly one.
Why is CF0 entered as a negative number?
Because the sign convention tracks direction, not size. Money leaving you is negative and money coming to you is positive, so an investment starts with a negative CF0 and earns positive flows afterwards. If you enter the outlay as positive, every later inflow adds to it and net present value becomes a meaningless total rather than a comparison.
What is the difference between NPV and NFV?
They are the same number viewed from opposite ends of the timeline. Net present value states the surplus in today’s money; net future value states it as of the final period, which is the same figure compounded forward by (1 + i)n. Both are positive or both are negative — they never disagree about whether a project is worth doing.
How do I enter a cash flow that repeats?
Use the frequency column. Enter the amount once and set the count to the number of consecutive periods that share it, exactly as Fj works on the hardware. Ten years of £9,000 is one group rather than ten rows, which also keeps you inside the 24-group limit on a long project.
What does a negative NPV tell me?
That the flows earn less than the discount rate, so the money is better placed in the alternative that rate represents. It does not mean the project loses money in cash terms — a project can return more than it cost and still have a negative net present value if it takes too long to do it.
Why does the profitability index sometimes disagree with NPV?
It does not disagree about the sign, only about ranking. The profitability index divides the present value of the inflows by the outlay, so it favours projects that produce more per pound invested. When capital is limited, that ranking is the useful one; when it is not, take the highest net present value, because a large surplus beats an efficient small one.
Can NPV and IRR rank two projects differently?
Yes, and net present value is the one to trust. The two measures disagree when projects differ in size or in the timing of their flows, because internal rate of return implicitly assumes every interim cash flow is reinvested at itself. The IRR calculator reports MIRR alongside IRR for exactly this reason.
Keep going
Related calculators
Same engine, same sign convention — pick the worksheet that matches your problem.