Net Present Value (NPV) Calculator — Step-by-Step
Calculate NPV from a series of cash flows and a discount rate to see whether a project or investment is worth it, with each year shown.
Reviewed by Sahil, Senior Finance & Tax Editor
Formula
NPV = -C0 + C1/(1+r) + C2/(1+r)^2 + ... + Cn/(1+r)^n
Where C0 = initial investment, C1 through Cn = future cash flows, r = discount rate, and n = number of periods. Each future cash flow is discounted to its present value, then the initial investment is subtracted to find the net present value.
Worked Examples
Example 1: Manufacturing Equipment Decision
Problem:A company considers investing $100,000 in equipment expected to generate cash flows of $30,000, $35,000, $40,000, $45,000, and $50,000 over 5 years. The discount rate is 10%. Should they proceed?
Solution:PV of Year 1: $30,000 / 1.10 = $27,273\nPV of Year 2: $35,000 / 1.21 = $28,926\nPV of Year 3: $40,000 / 1.331 = $30,053\nPV of Year 4: $45,000 / 1.4641 = $30,735\nPV of Year 5: $50,000 / 1.6105 = $31,046\nTotal PV: $148,033\nNPV: $148,033 - $100,000 = $48,033\nPI: $148,033 / $100,000 = 1.48
Result:NPV: $48,033 (positive) | PI: 1.48 | Accept the project
Example 2: Comparing Two Projects
Problem:Project A: $50,000 investment, cash flows of $20K, $20K, $20K. Project B: $100,000 investment, cash flows of $40K, $40K, $40K. Discount rate 8%.
Solution:Project A:\nPV: $20K/1.08 + $20K/1.1664 + $20K/1.2597 = $51,542\nNPV: $51,542 - $50,000 = $1,542 | PI: 1.031\n\nProject B:\nPV: $40K/1.08 + $40K/1.1664 + $40K/1.2597 = $103,084\nNPV: $103,084 - $100,000 = $3,084 | PI: 1.031\n\nBoth have same PI but Project B creates more total value.
Result:Project A NPV: $1,542 | Project B NPV: $3,084 | Choose B for maximum value creation
Frequently Asked Questions
How do I choose the right discount rate for NPV calculation?
The discount rate should reflect the opportunity cost of capital, which is the return you could earn on alternative investments of similar risk. For corporate projects, the weighted average cost of capital (WACC) is commonly used, which blends the cost of debt and equity financing. WACC typically ranges from 8% to 15% for most companies. For personal investments, use your expected return from comparable alternative investments. If evaluating a real estate deal, compare to the return you could get from REITs or similar investments. Risk adjustments are important: riskier projects should use higher discount rates. Government projects might use the risk-free rate (Treasury yields) plus a small premium. The chosen rate significantly impacts NPV results, so many analysts calculate NPV at multiple rates to understand sensitivity.
What does a positive NPV mean versus a negative NPV?
A positive NPV means the present value of expected future cash flows exceeds the initial investment cost, indicating the project is expected to create wealth above and beyond the required rate of return. The dollar amount of the NPV represents the total value created in today dollars. For example, an NPV of $50,000 means the investment is expected to create $50,000 in value beyond what you could earn at the discount rate. A negative NPV means the investment fails to meet the required rate of return and destroys value. An NPV of exactly zero means the investment earns exactly the discount rate, which represents the minimum acceptable return. When comparing mutually exclusive projects, always choose the one with the highest positive NPV, as it creates the most total value.
What is the Profitability Index and how does it relate to NPV?
The Profitability Index (PI), also called the benefit-cost ratio, is calculated by dividing the present value of future cash flows by the initial investment. A PI greater than 1.0 corresponds to a positive NPV and indicates the investment creates value. A PI of 1.25 means every dollar invested generates $1.25 in present value, creating $0.25 in value per dollar. The Profitability Index is particularly useful when capital is limited and you must choose among multiple positive-NPV projects. While NPV tells you the total value created, PI tells you the value created per dollar invested. A smaller project with a PI of 1.5 creates more value per dollar than a larger project with a PI of 1.1, even if the larger project has a higher absolute NPV. Using PI helps maximize total value creation within budget constraints.
How does NPV account for the time value of money?
NPV accounts for the time value of money by discounting each future cash flow by a factor that increases with time. The discount factor for any period is 1/(1+r)^n, where r is the discount rate and n is the number of periods. At a 10% discount rate, $1 received in year 1 is worth $0.909 today, $1 in year 2 is worth $0.826, $1 in year 5 is worth $0.621, and $1 in year 10 is worth only $0.386. This reflects the reality that money available today can be invested to earn returns. Cash flows further in the future are worth progressively less in present value terms. This is why projects with front-loaded cash flows tend to have higher NPVs than those with back-loaded cash flows, even when total undiscounted cash flows are identical.
References
Reviewed by Sahil, Senior Finance & Tax Editor · Editorial policy