Answer first
What this calculator tells you
Calculate the net present value and profitability index of an investment from its cash flows and discount rate. Test whether a project's future cash flows are worth more than its cost today. Formula: NPV = −initial investment + Σ cash flow(t) ÷ (1 + r)ᵗ; profitability index = PV of inflows ÷ initial investment. At the worked-example inputs, the net present value is $4,957. Holding every other input steady, moving discount rate from 4.0% to 12.0% moves the result from $3,411 to $6,794.
Transparent method
The formula
Test whether a project's future cash flows are worth more than its cost today.
Worked example
Example inputs
How to interpret the result
Net present value shrinks each future payment by the return you could earn elsewhere, then subtracts the cost today. A $10,000 investment that returns $3,000, $3,500, $4,000, $4,000 and $4,500 over five years is worth about $14,957 in today's money at an 8 percent rate. That leaves an NPV of about $4,957, positive, so the project beats the 8 percent alternative. A profitability index of 1.5 says the same in ratio form.
At the worked-example inputs the net present value is $4,957. It rises with cash flow, year 3, cash flow, year 5, cash flow, year 2, cash flow, year 4 and cash flow, year 1 and falls as initial investment and discount rate increase.
Investment returns are uncertain; taxes, fees, volatility and cash-flow timing can materially change results.
Before you rely on it
What to check
Stress the discount rate. A project that looks good at 8 percent may turn negative at 15, and that gap shows how fragile the case is.
The common error
Where people go wrong with net present value (NPV) calculator
Adding up the cash flows without discounting them. A dollar in year five is worth less than a dollar today, so the plain sum overstates the value.
Sensitivity evidence
How discount rate changes the net present value
Holding every other input at the worked-example value, moving discount rate from 4.0% to 12.0% moves the net present value from $3,411 to $6,794: a spread of $3,383, or 68% of the worked-example result.
| Discount rate | Net present value | Profitability index | Present value of inflows |
|---|---|---|---|
| 4.0% | $6,794 | 1.68× | $16,794 |
| 6.0% | $5,835 | 1.58× | $15,835 |
| 8.0%worked example | $4,957 | 1.50× | $14,957 |
| 10.0% | $4,151 | 1.42× | $14,151 |
| 12.0% | $3,411 | 1.34× | $13,411 |
Every input, tested
Which input moves the net present value most
Of the 7 inputs, initial investment moves the net present value most ($2,000 across the range tested) and cash flow, year 1 moves it least ($556).
| Input | Tested from | To | Net present value at each end | Swing |
|---|---|---|---|---|
| Initial investment | $9,000 | $11,000 | $5,957 to $3,957 | $2,000 (40%) |
| Discount rate | 6.0% | 10.0% | $5,835 to $4,151 | $1,683 (34%) |
| Cash flow, year 3 | $3,600 | $4,400 | $4,639 to $5,274 | $635 (13%) |
| Cash flow, year 5 | $4,050 | $4,950 | $4,650 to $5,263 | $613 (12%) |
| Cash flow, year 2 | $3,150 | $3,850 | $4,656 to $5,257 | $600 (12%) |
| Cash flow, year 4 | $3,600 | $4,400 | $4,663 to $5,251 | $588 (12%) |
| Cash flow, year 1 | $2,700 | $3,300 | $4,679 to $5,234 | $556 (11%) |
Two variables at once
Net present value by discount rate and initial investment
Across the grid the net present value runs from $1,411 to $8,794. Moving discount rate from 4.0% to 12.0% shifts it by $3,383 at the middle column, and moving initial investment from $8,000 to $12,000 shifts it by $4,000 at the middle row, so initial investment is the bigger lever here.
| Discount rate \ Initial investment | $8,000 | $10,000 | $12,000 |
|---|---|---|---|
| 4.0% | $8,794 | $6,794 | $4,794 |
| 6.0% | $7,835 | $5,835 | $3,835 |
| 8.0% | $6,957 | $4,957 | $2,957 |
| 10.0% | $6,151 | $4,151 | $2,151 |
| 12.0% | $5,411 | $3,411 | $1,411 |
The highlighted cell is the worked example: $4,957.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Discount rate | 8.0% | Enter the discount rate used in this calculation. |
| Initial investment | $10,000 | Enter the initial investment used in this calculation. |
| Cash flow, year 1 | $3,000 | Enter the cash flow, year 1 used in this calculation. |
| Cash flow, year 2 | $3,500 | Enter the cash flow, year 2 used in this calculation. |
| Cash flow, year 3 | $4,000 | Enter the cash flow, year 3 used in this calculation. |
| Cash flow, year 4 | $4,000 | Enter the cash flow, year 4 used in this calculation. |
| Cash flow, year 5 | $4,500 | Enter the cash flow, year 5 used in this calculation. |
| Net present value | $4,957 | |
| Profitability index | 1.50× | |
| Present value of inflows | $14,957 | |
Inputs, definitions and assumptions
Discount rate
Enter the discount rate used in this calculation. The prefilled worked-example value is 8.0%.
Initial investment
Enter the initial investment used in this calculation. The prefilled worked-example value is $10,000.
Cash flow, year 1
Enter the cash flow, year 1 used in this calculation. The prefilled worked-example value is $3,000.
Cash flow, year 2
Enter the cash flow, year 2 used in this calculation. The prefilled worked-example value is $3,500.
Cash flow, year 3
Enter the cash flow, year 3 used in this calculation. The prefilled worked-example value is $4,000.
Cash flow, year 4
Enter the cash flow, year 4 used in this calculation. The prefilled worked-example value is $4,000.
Cash flow, year 5
Enter the cash flow, year 5 used in this calculation. The prefilled worked-example value is $4,500.
How to use this calculator
- 1Verify the inputs. Gather discount rate, initial investment, cash flow, year 1, cash flow, year 2, cash flow, year 3, cash flow, year 4 and 1 more from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the net present value at $4,957. Store your own version of it as Scenario A.
- 3Test one change. Start with initial investment, the input with the biggest effect here: moving initial investment from $9,000 to $11,000 takes the net present value from $5,957 to $3,957, a swing of 40% of the worked-example figure.
- 4Check the boundary. Read the interpretation boundary above before acting on the result.
People also ask
Frequently asked questions
How do you calculate net present value (NPV)?
NPV = −initial investment + Σ cash flow(t) ÷ (1 + r)ᵗ; profitability index = PV of inflows ÷ initial investment. Enter discount rate in percent, initial investment in dollars, cash flow, year 1 in dollars, cash flow, year 2 in dollars and cash flow, year 3 in dollars (8 means 8%). At the worked-example inputs the net present value is $4,957.
What does the net present value (NPV) result mean?
Test whether a project's future cash flows are worth more than its cost today. At the worked-example inputs the net present value is $4,957. It rises with cash flow, year 3, cash flow, year 5, cash flow, year 2, cash flow, year 4 and cash flow, year 1 and falls as initial investment and discount rate increase.
How much does discount rate change the net present value?
Holding every other input at the worked-example value, moving discount rate from 4.0% to 12.0% moves the net present value from $3,411 to $6,794, a spread of $3,383.
What are the limits of this net present value (NPV) calculator?
Investment returns are uncertain; taxes, fees, volatility and cash-flow timing can materially change results. The tables on this page test discount rate only from 4.0% to 12.0%; a value outside that range is not tabulated here.
Which input moves the net present value most in the net present value (NPV) calculator?
Ranked by how far each moves the net present value across the range tested: initial investment ($2,000, 40%), discount rate ($1,683, 34%), cash flow, year 3 ($635, 13%) and cash flow, year 5 ($613, 12%).
How much does initial investment matter in the net present value (NPV) calculator?
The worked example uses $10,000. With the other inputs left at the worked example, moving initial investment from $9,000 to $11,000 takes the net present value from $5,957 to $3,957, a swing of 40% of the worked-example figure.
How much does cash flow, year 1 matter in the net present value (NPV) calculator?
The worked example uses $3,000. Holding every other input at its worked-example value, moving cash flow, year 1 from $2,700 to $3,300 takes the net present value from $4,679 to $5,234, a swing of 11% of the worked-example figure.
How much does cash flow, year 2 matter in the net present value (NPV) calculator?
The worked example uses $3,500. With the other inputs left at the worked example, moving cash flow, year 2 from $3,150 to $3,850 takes the net present value from $4,656 to $5,257, a swing of 12% of the worked-example figure.
How much does cash flow, year 3 matter in the net present value (NPV) calculator?
The worked example uses $4,000. Holding every other input at its worked-example value, moving cash flow, year 3 from $3,600 to $4,400 takes the net present value from $4,639 to $5,274, a swing of 13% of the worked-example figure.
How much does cash flow, year 4 matter in the net present value (NPV) calculator?
The worked example uses $4,000. With the other inputs left at the worked example, moving cash flow, year 4 from $3,600 to $4,400 takes the net present value from $4,663 to $5,251, a swing of 12% of the worked-example figure.
How much does cash flow, year 5 matter in the net present value (NPV) calculator?
The worked example uses $4,500. Holding every other input at its worked-example value, moving cash flow, year 5 from $4,050 to $4,950 takes the net present value from $4,650 to $5,263, a swing of 12% of the worked-example figure.
Which inputs change the profitability index in the net present value (NPV) calculator?
At the worked-example inputs it is 1.50×. Discount rate takes it from 1.58× to 1.42×, initial investment takes it from 1.66× to 1.36×, cash flow, year 1 takes it from 1.47× to 1.52× and cash flow, year 2 takes it from 1.47× to 1.53×.
Which inputs change the present value of inflows in the net present value (NPV) calculator?
At the worked-example inputs it is $14,957. Discount rate takes it from $15,835 to $14,151, cash flow, year 1 takes it from $14,679 to $15,234, cash flow, year 2 takes it from $14,656 to $15,257 and cash flow, year 3 takes it from $14,639 to $15,274.
Sources and evidence
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