NPV / IRR Calculator
Enter a cash flow schedule to get Net Present Value, Internal Rate of Return, MIRR, Payback Period, and Profitability Index — with a cash flow timeline, an NPV profile chart, and step-by-step math. Also compare two mutually exclusive projects side by side and find the crossover rate between them.
Background
Every capital budgeting decision comes down to the same question: does a project create more value than it costs, once you account for the time value of money? Net Present Value (NPV) answers that in dollars — discounting every future cash flow back to today and summing them up. Internal Rate of Return (IRR) answers a related question in percentage terms — it's the discount rate at which NPV would be exactly zero. Both come from the same cash flow schedule; this calculator computes both at once, along with the supporting metrics investors and instructors actually ask for.
How to use this calculator
- Choose Single project to find one project's NPV, IRR, MIRR, and payback period, or Compare two projects to see which of two mutually exclusive options creates more value.
- Enter your discount rate, then build your cash flow schedule — period 0 is usually the initial investment, entered as a negative number. Add or remove periods as needed.
- Click Calculate to see NPV, IRR, a cash flow timeline, an NPV profile chart, and a full step-by-step solution.
How this calculator works
- NPV: every cash flow is discounted back to today at your required rate, then summed: NPV = Σ CFₜ / (1+r)ᵗ. A positive NPV means the project is expected to create value above your required return.
- IRR: the discount rate that makes NPV exactly zero. There's no algebraic formula for this — this calculator scans a wide range of rates and solves numerically, which is also how it correctly catches cases with more than one valid IRR.
- MIRR: a corrected version of IRR that assumes interim cash inflows are reinvested at a realistic rate (rather than at the IRR itself), and always returns exactly one answer even when plain IRR doesn't.
- Payback period: how many periods it takes for cumulative cash flow to turn positive — a simple liquidity check, not a substitute for NPV.
- Crossover rate (compare mode): the discount rate at which two projects have identical NPV — useful for understanding exactly where and why NPV and IRR rankings can disagree.
Formula & Equations Used
Net Present Value: NPV = Σₜ CFₜ / (1+r)ᵗ, for t = 0 to n
Internal Rate of Return: the rate r such that Σₜ CFₜ / (1+r)ᵗ = 0
MIRR: MIRR = [FV(positive flows) / |PV(negative flows)|]^(1/n) − 1
Profitability Index: PI = PV(future cash flows) / |initial investment| = 1 + NPV/|C₀|
Payback period: the period t at which cumulative cash flow first reaches zero
Example Problems & Step-by-Step Solutions
Example 1 — Basic NPV and IRR
Initial investment \)10,000. Inflows of \$3,000/year for 5 years. Discount rate 10%.
- NPV = −10,000 + 3,000/1.1 + 3,000/1.1² + ... + 3,000/1.1⁵ ≈ \$1,372.36 — positive, so accept.
- IRR ≈ 15.24% — the rate at which NPV would be exactly zero.
Example 2 — The multiple-IRR trap
A project costs \$4,000, pays back \$25,000 in year 1, then requires a \$25,000 cleanup cost in year 2 (a common pattern in mining or decommissioning projects).
- This cash flow changes sign twice, so NPV = 0 has two solutions: IRR ≈ 25% and IRR ≈ 400%.
- Neither number alone tells the whole story — NPV at your actual required rate (or MIRR) is the reliable way to evaluate this project.
Example 3 — Crossover rate between two projects
Project A: −\$5,000, then \(3,000/year for 3 years. Project B: −\)5,000, then \$1,000, \$1,000, \$8,000.
- At a 5% discount rate, Project B (back-loaded, higher total) has the higher NPV.
- At a 20% discount rate, Project A (front-loaded) wins instead — high rates punish cash flows that arrive later.
- The crossover rate is about 15.83% — below it, B wins; above it, A wins.
Example 4 — MIRR vs. IRR
Using Example 1's cash flows, with both the finance and reinvestment rate set to 10%.
- IRR ≈ 15.24%, but this assumes interim inflows are reinvested at 15.24% too — often unrealistic.
- MIRR ≈ 12.87%, using the more conservative (and more realistic) 10% reinvestment assumption instead.
Related Calculators
ROI Calculator
A simpler, single-period return measure — useful for quick comparisons, but it doesn't discount multi-period cash flows the way NPV and IRR do.
Break-Even Point Calculator
Answers a related but different question — how many units or how much revenue is needed before a business turns a profit, rather than whether a multi-year investment is worthwhile.
Frequently Asked Questions
What does a negative NPV mean?
It means the project is expected to destroy value at your required rate of return — the cash it generates isn't enough to justify the investment once you account for the time value of money. The project should generally be rejected.
Why can a project have more than one IRR?
IRR is the solution to a polynomial equation, and a cash flow series that changes sign more than once (outflow, then inflow, then outflow again, for example) can satisfy that equation at more than one rate — or at none at all. NPV never has this problem, which is one reason it's considered the more reliable metric.
Should I use NPV or IRR to choose between two projects?
Use NPV. When NPV and IRR rank two mutually exclusive projects differently — usually because they differ in scale or in the timing of their cash flows — NPV is the theoretically correct choice, because it directly measures the dollar value each project adds.
What discount rate should I use?
Typically your cost of capital — the return investors require for a project of similar risk. In coursework, this is usually given directly as "the required rate of return" or "the discount rate."
What's the difference between IRR and MIRR?
IRR implicitly assumes every interim cash inflow gets reinvested at the IRR itself, which can be an unrealistic assumption when the IRR is very high. MIRR instead uses an explicit, more realistic reinvestment rate, and always produces exactly one answer — even for cash flow patterns where plain IRR is ambiguous.
Can this calculator handle uneven cash flows?
Yes — every period's cash flow is entered independently, so there's no assumption that inflows are the same amount each year. Add or remove periods freely to match your actual schedule.
All calculators