ROI / NPV / IRR Calculator

Time Value of Money

The foundation of NPV and IRR is the time value of money—the idea that a dollar today is worth more than a dollar tomorrow. Why? Because money today can be invested to earn a return, and future cash flows carry opportunity cost, inflation risk, and uncertainty. By discounting future cash flows to present value, we can compare money across different time periods on an apples-to-apples basis.

The discount rate (often denoted as r) summarizes your required rate of return, risk level, and the opportunity cost of capital. A higher discount rate means you value future cash less (perhaps because you have better alternatives or the project is riskier); a lower rate means you're more patient or have fewer good alternatives. Choosing the right discount rate is one of the most important—and most subjective—decisions in investment analysis.

ROI (Return on Investment)

ROI is the simplest and most intuitive investment metric. It measures total return as a percentage of the initial investment:

For example, if you invest $1,000 and receive $1,300 back, your ROI is 30%. ROI is easy to communicate and widely understood, but it has a key limitation: it ignores the timing of cash flows. A 30% ROI earned in 1 year is very different from 30% earned over 10 years, yet basic ROI treats them the same. For quick screenings and simple comparisons, ROI is useful; for more sophisticated analysis, NPV and IRR are preferred.

NPV (Net Present Value)

NPV is the sum of the present values of all cash flows—both outflows (investments) and inflows (returns)—discounted at your chosen rate. Mathematically, for cash flows CF₀, CF₁, …, CF_T at periods 0 through T, and discount rate r:

If NPV is positive, the project is expected to add value above your required rate of return (conceptually, it's "worth more than it costs"). If NPV is negative, the project doesn't meet your hurdle rate. If NPV is zero, the project exactly meets your required return—you're indifferent. NPV is a gold-standard metric in corporate finance because it directly measures value creation in dollar terms, accounts for timing, and follows the additive property (you can add NPVs of independent projects).

IRR (Internal Rate of Return)

IRR is the discount rate that makes the NPV of a project equal to zero. In other words, it's the annualized rate of return the project "earns" under the model's assumptions. If IRR is above your required return (or hurdle rate), the project is attractive; if IRR is below, it's not.

IRR is intuitive and widely used, but it has some quirks:

• Multiple IRRs: Some cash-flow patterns (e.g., negative flows followed by positive, then negative again) can produce more than one IRR or no real IRR at all.
• Reinvestment assumption: IRR implicitly assumes all intermediate cash flows are reinvested at the IRR itself, which may not be realistic.
• Scale blindness: A small project with a high IRR might look better than a large project with a lower (but still acceptable) IRR, even if the large project adds more total value (higher NPV).

For this reason, many finance professionals use IRR as a screening tool or supplement to NPV, not a replacement. When NPV and IRR conflict (which can happen), NPV should generally take precedence.

Payback Period

The payback period is the time it takes for cumulative cash inflows to recover the initial investment. It's often used as a rough screening metric: "How long until we get our money back?" A shorter payback period is generally better (faster recovery, less exposure to uncertainty).

There are two versions:

• Simple payback: Counts cash flows at face value, ignoring time value of money.
• Discounted payback: Counts discounted (present) cash flows, which is more rigorous but still limited.

Payback ignores cash flows after the cutoff point, so a project might have great long-term value but poor early payback and get rejected. Use payback as a supplement to NPV/IRR, not as the sole criterion.

Other Metrics: MIRR, PI, CAGR, WACC

• MIRR (Modified IRR): Assumes positive cash flows are reinvested at a specified reinvestment rate (often the cost of capital) rather than at the IRR. This often gives a more realistic picture of return.
• Profitability Index (PI): The ratio of the present value of future cash inflows to the initial investment. PI > 1 means the project adds value per dollar invested; useful for ranking projects when capital is limited.
• CAGR (Compound Annual Growth Rate): Measures the annualized growth rate from an initial value to a final value over a period. Often used for investment portfolios and growth-focused analysis.
• WACC (Weighted Average Cost of Capital): A blended rate reflecting the cost of equity, debt, and preferred stock, weighted by their proportions in the capital structure. Often used as the discount rate for NPV when evaluating corporate projects.

Mode 1 — Basic ROI

1. Select "ROI & Payback" from the Analysis Type dropdown.
2. Enter your cash flows: Typically, period 0 is your initial investment (as a negative number, e.g., -10000), and subsequent periods are your returns (positive numbers).
3. Click Calculate.
4. Review the ROI percentage and payback period in the results panel. This mode is ideal when you have a simple "invest now, get paid back later" scenario and want a quick percentage return.

Use this mode when: You want a straightforward percentage return and payback timeline without worrying about discounting.

Mode 2 — NPV & IRR Analysis

1. Select "NPV & IRR" from the Analysis Type dropdown.
2. Enter your cash flows: Start with your initial investment at period 0 (negative), then add expected cash inflows and outflows for each subsequent period (years, months, etc.).
3. Enter a discount rate that reflects your required return, risk level, or opportunity cost (e.g., 8%, 10%, 12%). This is the rate used to calculate NPV.
4. Click Calculate.
5. Review the results:
   • NPV: If positive, the project is expected to add value at your chosen discount rate.
   • IRR: Compare this to your required return. If IRR exceeds your hurdle rate, the project clears the bar.
   • Total inflows, outflows, and net cash flow for context.
6. Explore the charts: The "Cash Flow Timeline" shows period-by-period flows and cumulative totals. The "NPV vs Discount Rate" curve shows how sensitive NPV is to changes in your discount rate (useful for risk assessment).

Use this mode when: You want a rigorous, time-value-aware analysis—ideal for corporate capital budgeting, real-estate modeling, and homework problems involving NPV and IRR.

Mode 3 — MIRR & Profitability Index

1. Select "MIRR & Profitability Index" from the Analysis Type dropdown.
2. Enter your cash flows as before.
3. Enter a finance rate (the rate at which you borrow or fund negative flows) and a reinvestment rate (the rate at which you reinvest positive flows). These let MIRR account for more realistic assumptions than IRR.
4. Click Calculate.
5. Review MIRR (often lower and more realistic than IRR) and the Profitability Index (a ratio showing value per dollar invested).

Use this mode when: You want a modified return that accounts for different borrowing and reinvestment rates, or when you need to rank projects by capital efficiency.

Mode 4 — CAGR

1. Select "CAGR" from the Analysis Type dropdown.
2. Enter cash flows representing your starting and ending values (or a series of periodic values).
3. Click Calculate.
4. Review the CAGR percentage, which shows the annualized growth rate over the period.

Use this mode when: You're focused on growth rates (e.g., investment portfolio performance, revenue growth).

Mode 5 — WACC (Weighted Average Cost of Capital)

1. Select "WACC" from the Analysis Type dropdown.
2. Enter your capital structure: amounts of equity, debt, and preferred stock, plus their respective costs (cost of equity, cost of debt, cost of preferred).
3. Enter your tax rate to account for the tax shield on debt.
4. Click Calculate.
5. Review your WACC percentage. This blended rate is often used as the discount rate for NPV analysis in corporate finance.

Use this mode when: You need to determine an appropriate discount rate for a company or project, reflecting its mix of financing sources.

Mode 6 — Depreciation Schedules

1. Select "Depreciation" from the Analysis Type dropdown.
2. Enter the cost basis (purchase price), salvage value (residual value at end of life), and useful life (in years).
3. Choose a depreciation method: Straight Line (SL), Double Declining Balance (DDB), or Sum of Years' Digits (SYD).
4. Enter a tax rate to calculate the annual tax shield (the tax savings from depreciation expense).
5. Click Calculate.
6. Review the depreciation schedule table showing year-by-year depreciation, book value, and tax shield. This is useful for understanding how asset write-downs affect after-tax cash flows.

Use this mode when: You're modeling equipment purchases, vehicle investments, or any capital asset with tax-deductible depreciation.

General Tips for All Modes

• Use consistent time units: If your periods are years, make sure your discount rate is annual. If monthly, convert appropriately.
• Enter initial investments as negative cash flows at period 0 (if that's how your model works).
• Experiment with different discount rates to see how sensitive your NPV is (use the NPV curve chart as a visual aid).
• Check warnings and notes: The calculator will flag issues like no IRR convergence, negative discount rates, or unusual cash-flow patterns.
• Copy or export results for reports, presentations, or further analysis.

ROI (Simple)

Formula:

Variables:

• C₀ = Initial investment (at time 0)
• V_T = Final value at time T (sum of all returns)
• ROI = (V_T − C₀) / C₀

This gives total return as a percentage, but does not account for the time it took to earn that return.

NPV (Net Present Value)

Formula:

Where:

• CF_t = Cash flow at period t (negative for outflows, positive for inflows)
• r = Discount rate (as a decimal, e.g., 0.10 for 10%)
• t = Time period (0, 1, 2, …, T)

Interpretation: A positive NPV means the project is expected to add value above the discount rate. A negative NPV means it falls short. Zero NPV means the project exactly meets your required return.

IRR (Internal Rate of Return)

Definition: IRR is the rate r* that makes NPV = 0:

There's no closed-form solution for r* in general; the calculator uses numerical methods (like Newton-Raphson or bisection) to solve iteratively. Important caveats:

• Some cash-flow patterns have no IRR (or no real/positive IRR).
• Some patterns have multiple IRRs (e.g., sign changes more than once).
• When IRR and NPV conflict, NPV is generally the more reliable decision metric.

Worked Example 1 — Simple ROI

Worked Example 2 — NPV and IRR

Key Takeaway

The formulas are straightforward in principle, but NPV and IRR calculations with multiple cash flows require careful discounting and (for IRR) iterative solving. This calculator automates that work, letting you focus on interpretation, scenario testing, and decision-making rather than manual arithmetic.

1. Corporate Capital Budgeting (Equipment Purchase)

Scenario: A manufacturing company is deciding whether to buy a new machine that costs $100,000. The machine will save $30,000 per year in labor costs for 5 years, and then be sold for $10,000 salvage value. The company's cost of capital is 10%.

Using the calculator: Enter period 0 = -100,000, periods 1–4 = +30,000 each, period 5 = +40,000 (30k + 10k salvage). Discount rate = 10%. Calculate NPV and IRR.

Result: NPV comes out positive, and IRR exceeds 10%, so the project is attractive. The manager can present both NPV (dollar value added) and IRR (rate of return) to stakeholders.

2. Real Estate Rental Property Analysis

Scenario: An investor buys a rental property for $250,000. After accounting for rent, expenses, and taxes, the property generates $18,000 net cash flow per year. After 10 years, the investor plans to sell for $320,000. The investor's required return is 8%.

Using the calculator: CF₀ = -250,000, CF₁–CF₉ = +18,000 each, CF₁₀ = +18,000 + 320,000 = 338,000. Discount rate = 8%.

Result: The calculator shows NPV, IRR, and ROI. If NPV is positive and IRR exceeds 8%, the investment is conceptually attractive. The investor can also compare this to other properties or investment options.

3. MBA / Finance Course Homework

Scenario: A student is given a textbook problem: "Project A requires $50,000 upfront and returns $15,000 per year for 5 years. Project B requires $50,000 upfront and returns $10,000 in year 1, $15,000 in year 2, $20,000 in year 3, $20,000 in year 4, and $25,000 in year 5. Both have a 12% discount rate. Which project has higher NPV? What are the IRRs?"

Using the calculator: Enter Project A cash flows, calculate NPV and IRR. Then clear and enter Project B cash flows, calculate again. Compare results.

Result: The student verifies homework answers, builds intuition about how cash-flow timing affects NPV, and sees how IRR can differ even when total undiscounted inflows are the same.

4. Small Business or Side Hustle Launch

Scenario: An entrepreneur is considering launching an online course. Upfront costs (production, marketing, platform setup) are $8,000. Expected revenue is $3,000 in month 6, $4,000 in month 12, $4,500 in month 18, and $3,500 in month 24. The entrepreneur's opportunity cost (what they'd earn doing something else) is 15% annually.

Using the calculator: Convert the annual discount rate to a monthly rate (roughly 15%/12 ≈ 1.25% per month, or use annual periods). Enter cash flows, calculate NPV and IRR.

Result: If NPV is positive, the project is expected to beat the 15% opportunity cost. If IRR is above 15%, it's attractive. The entrepreneur can also test sensitivity: "What if revenue is 20% lower? Still positive NPV?"

5. IT Infrastructure Upgrade Decision

Scenario: A company is deciding whether to invest $200,000 in new servers and software. The upgrade will reduce downtime and improve efficiency, saving $60,000 per year in costs for 5 years. Salvage value is negligible. The company uses a 12% hurdle rate.

Using the calculator: CF₀ = -200,000, CF₁–CF₅ = +60,000 each. Discount rate = 12%.

Result: NPV and IRR are calculated. If NPV is positive, the upgrade is worth it. The IT director can also compare this project to other capital requests using NPV and PI (profitability index).

6. Comparing Two Investment Projects

Scenario: A firm has two mutually exclusive projects. Project X has a low initial cost and modest returns (NPV $50k, IRR 18%). Project Y has a high initial cost and large returns (NPV $90k, IRR 14%). Discount rate is 10%.

Using the calculator: Calculate each separately. Compare NPV and IRR side by side.

Result: Project Y has higher NPV (more absolute value created), but lower IRR (lower percentage return). In this case, NPV rule says choose Project Y. The calculator helps illustrate this classic IRR vs NPV conflict and why NPV is the better decision criterion when projects differ in scale.

7. Energy Efficiency or Sustainability Investment

Scenario: A facility manager evaluates installing solar panels for $75,000. The panels will save $12,000 per year in electricity costs for 10 years, plus there's a $10,000 tax credit at year 1 and $5,000 salvage value at year 10. Discount rate is 6%.

Using the calculator: CF₀ = -75,000, CF₁ = +12,000 + 10,000 = +22,000, CF₂–CF₉ = +12,000 each, CF₁₀ = +12,000 + 5,000 = +17,000.

Result: The calculator shows whether the solar project has positive NPV and acceptable IRR. This helps justify the investment on financial (not just environmental) grounds.

8. Startup Investment or Venture Capital Modeling

Scenario: An investor considers a $500,000 investment in a startup. Expected exit in year 5 is $2,000,000 (with no intermediate cash flows). The investor's required return for high-risk ventures is 25%.

Using the calculator: CF₀ = -500,000, CF₁–CF₄ = 0, CF₅ = +2,000,000. Discount rate = 25%. Calculate NPV and IRR.

Result: The IRR is the annualized return implied by 4x money in 5 years (roughly 32%). Since 32% > 25%, and NPV is positive, the investment clears the hurdle (conceptually). In practice, the investor would also consider risk, dilution, and qualitative factors, but the calculator provides a baseline quantitative check.

1. Mixing Time Units (Periods and Rates)

Using monthly cash flows with an annual discount rate (or vice versa) without converting. Solution: Make sure your discount rate matches your period length. If cash flows are monthly, convert your annual rate to a monthly rate (roughly annual rate / 12, or use the exact formula (1 + r_annual)^(1/12) − 1).

2. Forgetting the Sign of Initial Investment

Entering the initial cost as a positive number when it should be negative (an outflow). This flips the NPV and makes interpretation nonsensical. Solution: Always enter investments, costs, and expenses as negative cash flows at the appropriate period.

3. Misinterpreting ROI as Annualized

Treating a multi-year total ROI (e.g., 40% over 5 years) as if it were 40% per year. Solution: ROI is total return unless otherwise specified. To annualize, use CAGR or IRR, which account for compounding over time.

4. Comparing IRR Across Projects Without Context

Choosing a project with a high IRR (say, 25%) over one with a lower IRR (15%) without considering scale. A small project with 25% IRR might add $10k of value, while a large project with 15% IRR adds $100k. Solution: Use NPV as the primary metric when projects differ in size or timing. IRR is a supplement, not a replacement.

5. Ignoring NPV When Discount Rates Differ

Relying solely on IRR when different projects or scenarios have different risk levels (and thus different appropriate discount rates). Solution: Calculate NPV with the appropriate discount rate for each project. NPV directly tells you value added at your required return; IRR does not.

6. Overconfidence in Cash-Flow Forecasts

Treating estimated future cash flows as certainties and making decisions based on a single NPV or IRR value. Real-world cash flows are uncertain. Solution: Run sensitivity analyses (vary discount rate, cash flows, timing) and scenario tests (best case, worst case, most likely). The calculator's NPV curve is a great starting point for sensitivity.

7. Using Payback Period as the Sole Criterion

Rejecting a project with a 5-year payback but excellent long-term returns in favor of a 2-year payback with poor total value. Solution: Use payback as a rough screening tool, but rely on NPV and IRR for the final decision.

8. Ignoring Non-Cash Factors (Depreciation, Taxes)

Forgetting that depreciation creates a tax shield (reduces taxable income, thus reduces taxes paid, which is effectively a cash inflow). Solution: Use the Depreciation mode to calculate tax shields and incorporate them into your cash-flow projections for a more accurate NPV.

9. Assuming IRR = Profitability Without Checking NPV

Accepting a project because IRR > hurdle rate, without checking if NPV is positive. In some unusual cash-flow patterns, IRR can be misleading. Solution: Always check both NPV and IRR. If they conflict, trust NPV.

10. Not Accounting for Opportunity Cost

Using an arbitrary discount rate (say, 5%) when your actual opportunity cost or required return is higher (say, 12%), making bad projects look good. Solution: Choose a discount rate that reflects your true alternatives, risk, and cost of capital. For corporate projects, WACC is often appropriate; for personal investments, consider your next-best alternative return.

1. Run Sensitivity and Scenario Analyses

Don't rely on a single NPV or IRR. Vary key assumptions—discount rate, cash-flow amounts, timing—to see how results change. The calculator's "NPV vs Discount Rate" chart is a built-in sensitivity tool. For broader scenarios, create "optimistic," "base," and "pessimistic" cash-flow forecasts and calculate NPV for each.

2. Understand the NPV vs IRR Decision Rule

When projects are mutually exclusive and differ in scale or timing, NPV and IRR can give conflicting rankings. In such cases, NPV should take precedence because it directly measures value added in dollar terms. IRR is useful for communication and screening, but NPV is the gold standard for accept/reject decisions.

3. Use MIRR for More Realistic Return Estimates

IRR assumes all interim cash flows are reinvested at the IRR itself, which may be unrealistic. MIRR lets you specify separate rates for financing (borrowing) and reinvestment, often yielding a more conservative and realistic return estimate. Use MIRR when presenting to stakeholders who want a single percentage return but with fewer assumptions.

4. Incorporate Tax Shields and Depreciation

For capital-intensive projects (equipment, vehicles, real estate), depreciation reduces taxable income and thus saves taxes. Use the Depreciation mode to calculate annual tax shields, then add those back into your cash-flow projections for NPV analysis. This can significantly improve a project's NPV, especially in high-tax environments.

5. Choose an Appropriate Discount Rate (WACC, CAPM, or Opportunity Cost)

The discount rate is subjective but critical. For corporate projects, WACC (Weighted Average Cost of Capital) is common. For personal investments, consider your opportunity cost—what return could you earn elsewhere with similar risk? For risky ventures, add a risk premium. A well-chosen discount rate makes NPV a much more reliable decision tool.

6. Use Profitability Index to Rank Projects Under Capital Constraints

When you have limited capital and multiple positive-NPV projects, you can't accept them all. The Profitability Index (PI = PV of inflows / initial investment) shows "bang for your buck." Rank projects by PI and select the top ones until your budget is exhausted. This maximizes total NPV under a capital constraint.

7. Compare to Industry Benchmarks and Historical Performance

An IRR of 12% might sound good, but if your industry average is 20%, it's below par. Conversely, 12% in a low-risk, stable industry might be excellent. Use the calculator to understand the numbers, but interpret them in context—industry norms, historical returns, and macroeconomic conditions.

8. Combine Quantitative and Qualitative Factors

NPV and IRR are quantitative tools, but investment decisions also hinge on strategy, competitive advantage, brand, talent, and timing. A project with modest NPV might be worth doing for strategic reasons (market entry, learning, customer relationships). Conversely, a high-NPV project with major execution risk might be too risky. Use this calculator to inform your decision, not make it for you.

9. Document Assumptions and Present Results Clearly

When presenting NPV/IRR analysis to stakeholders, be transparent: "We assumed 10% discount rate, 5-year horizon, and $50k annual cash flows. If cash flows are 20% lower, NPV is still positive but falls to $X." Clear documentation builds trust and invites constructive feedback, making your analysis more robust.

10. Revisit and Refine Over Time

Investment analysis isn't a one-time exercise. As projects progress, update your forecasts, recalculate NPV/IRR, and track actual vs projected cash flows. This "post-audit" process helps you learn from experience, refine future estimates, and build a track record of realistic forecasting—valuable for both personal and corporate decision-making.