Net Present Value (NPV): formula
OpenStax Principles of Finance: net present value NPV method
Net Present Value (NPV): worked example
| Discount rate | 8.0% |
|---|---|
| Initial investment | $10,000 |
| Cash flow, year 1 | $3,000 |
| Cash flow, year 2 | $3,500 |
| Cash flow, year 3 | $4,000 |
| Cash flow, year 4 | $4,000 |
| Cash flow, year 5 | $4,500 |
| Net present value | $4,957 |
| Profitability index | 1.50× |
| Present value of inflows | $14,957 |
NPV depends on the forecast cash flows and the discount rate, and both are uncertain. A small change in the rate can flip the sign for long-lived projects. It ignores the value of flexibility, such as the option to expand or stop.
Comparing projects of different lengths needs care.
Net Present Value (NPV): changing Discount rate
| 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% (example) | $4,957 | 1.50× | $14,957 |
| 10.0% | $4,151 | 1.42× | $14,151 |
| 12.0% | $3,411 | 1.34× | $13,411 |
Net Present Value (NPV): compare input ranges
| Input | Tested from | To | Net present value: low input | Net present value: high input | Swing |
|---|---|---|---|---|---|
| Initial investment | $9,000 | $11,000 | $5,957 | $3,957 | $2,000 (40%) |
| Discount rate | 6.0% | 10.0% | $5,835 | $4,151 | $1,683 (34%) |
| Cash flow, year 3 | $3,600 | $4,400 | $4,639 | $5,274 | $635 (13%) |
| Cash flow, year 5 | $4,050 | $4,950 | $4,650 | $5,263 | $613 (12%) |
| Cash flow, year 2 | $3,150 | $3,850 | $4,656 | $5,257 | $600 (12%) |
| Cash flow, year 4 | $3,600 | $4,400 | $4,663 | $5,251 | $588 (12%) |
| Cash flow, year 1 | $2,700 | $3,300 | $4,679 | $5,234 | $556 (11%) |
Net Present Value (NPV): individual input comparisons
| Input | Value | Net present value | Profitability index | Present value of inflows |
|---|---|---|---|---|
| Discount rate | 4.0% | $6,794 | 1.68× | $16,794 |
| 6.0% | $5,835 | 1.58× | $15,835 | |
| 8.0% | $4,957 | 1.50× | $14,957 | |
| 10.0% | $4,151 | 1.42× | $14,151 | |
| 12.0% | $3,411 | 1.34× | $13,411 | |
| Initial investment | $8,000 | $6,957 | 1.87× | $14,957 |
| $9,000 | $5,957 | 1.66× | $14,957 | |
| $10,000 | $4,957 | 1.50× | $14,957 | |
| $11,000 | $3,957 | 1.36× | $14,957 | |
| $12,000 | $2,957 | 1.25× | $14,957 | |
| Cash flow, year 1 | $2,400 | $4,401 | 1.44× | $14,401 |
| $2,700 | $4,679 | 1.47× | $14,679 | |
| $3,000 | $4,957 | 1.50× | $14,957 | |
| $3,300 | $5,234 | 1.52× | $15,234 | |
| $3,600 | $5,512 | 1.55× | $15,512 | |
| Cash flow, year 2 | $2,800 | $4,356 | 1.44× | $14,356 |
| $3,150 | $4,656 | 1.47× | $14,656 | |
| $3,500 | $4,957 | 1.50× | $14,957 | |
| $3,850 | $5,257 | 1.53× | $15,257 | |
| $4,200 | $5,557 | 1.56× | $15,557 | |
| Cash flow, year 3 | $3,200 | $4,321 | 1.43× | $14,321 |
| $3,600 | $4,639 | 1.46× | $14,639 | |
| $4,000 | $4,957 | 1.50× | $14,957 | |
| $4,400 | $5,274 | 1.53× | $15,274 | |
| $4,800 | $5,592 | 1.56× | $15,592 | |
| Cash flow, year 4 | $3,200 | $4,369 | 1.44× | $14,369 |
| $3,600 | $4,663 | 1.47× | $14,663 | |
| $4,000 | $4,957 | 1.50× | $14,957 | |
| $4,400 | $5,251 | 1.53× | $15,251 | |
| $4,800 | $5,545 | 1.55× | $15,545 | |
| Cash flow, year 5 | $3,600 | $4,344 | 1.43× | $14,344 |
| $4,050 | $4,650 | 1.47× | $14,650 | |
| $4,500 | $4,957 | 1.50× | $14,957 | |
| $4,950 | $5,263 | 1.53× | $15,263 | |
| $5,400 | $5,569 | 1.56× | $15,569 |
Net Present Value (NPV): combined input changes
| 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 |
Net Present Value (NPV): which assumptions move the result?
Net Present Value (NPV): values and definitions
| Quantity and definition | Value used |
|---|---|
| Discount rate | 8.0% |
| Initial investment | $10,000 |
| Cash flow, year 1 | $3,000 |
| Cash flow, year 2 | $3,500 |
| Cash flow, year 3 | $4,000 |
| Cash flow, year 4 | $4,000 |
| Cash flow, year 5 | $4,500 |
| Net present value | $4,957 |
| Profitability index | 1.50× |
| Present value of inflows | $14,957 |
The discount rate is the return you require, reflecting the risk and the alternatives, such as the cost of capital for a business or a safe rate plus a premium for a personal project. Initial investment is the upfront cost, and the yearly cash flows are the net amounts you expect in each year after costs and taxes. Include any salvage or resale value in the final year.
Compare the valuation at a higher and a lower discount rate.
Common error: 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.
Investing & Returns calculators: Continuous Compounding Calculator, Compound Interest & Future Value Calculator, Investment Return Calculator, CAGR and Required Annual Return Calculator, Present Value Calculator, Dividend Yield Calculator.
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.
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.
NPV, IRR, MIRR and payback summarize different properties of the same cash flows. The present value calculator handles a single future sum, and the compound interest page projects growth forward. For a business decision, run the flows at two discount rates to see how far the answer moves.
Net Present Value (NPV) Calculator: quantities and terminology
What discount rate should I choose?
Use your required return for this risk level. Businesses use their weighted cost of capital, and individuals often use the return they could earn elsewhere on an investment of similar risk.
What is the profitability index?
It is the present value of the inflows divided by the initial investment. A value above 1 means value is created, and higher values rank better when capital is limited.
What does a positive NPV mean?
The project is expected to earn more than your required return, adding value in today's dollars equal to the NPV.