NPV and IRR Calculator: Net Present Value & Internal Rate of Return

How to evaluate capital projects using NPV, IRR, and Discounted Payback

Net Present Value (NPV) and Internal Rate of Return (IRR) are the primary discounted cash flow (DCF) techniques used by corporate finance directors, investors, and operators to evaluate capital projects, equipment acquisitions, and business investments.

Because money in the future is worth less than money today due to inflation, opportunity cost, and risk, these methods discount future cash flows back to present dollars. All calculations run locally in your web browser with complete client-side confidentiality.

The Net Present Value (NPV) formula

$$\text{NPV} = -CF_0 + \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}$$

Variable definitions:

• $CF_0$ (Initial Investment Outflow): Upfront capital expenditure incurred at day zero (Time 0).
• $CF_t$ (Cash Flow at Period $t$): Net cash inflow or outflow generated at the end of period $t$.
• $r$ (Discount Rate / Hurdle Rate): The minimum required rate of return or weighted average cost of capital (WACC).
• $n$ (Total Evaluation Periods): Total lifecycle of the investment project.

Worked example: $10,000 machine investment

Consider a business evaluating an equipment purchase requiring an initial $10,000 capital outlay with a 10.0% required hurdle rate:

• Time 0 Outflow ($CF_0$): $10,000
• Hurdle Discount Rate ($r$): 10.0% ($0.10$)
• Projected Cash Inflows:
  • Year 1: $3,000
  • Year 2: $4,000
  • Year 3: $5,000
  • Year 4: $3,000

Step-by-step arithmetic:

1. Year 1 PV: $\frac{$3,000}{(1.10)^1} = \frac{$3,000}{1.1000} = \mathbf{$2,727.27}$
2. Year 2 PV: $\frac{$4,000}{(1.10)^2} = \frac{$4,000}{1.2100} = \mathbf{$3,305.79}$
3. Year 3 PV: $\frac{$5,000}{(1.10)^3} = \frac{$5,000}{1.3310} = \mathbf{$3,756.57}$
4. Year 4 PV: $\frac{$3,000}{(1.10)^4} = \frac{$3,000}{1.4641} = \mathbf{$2,049.04}$
5. Sum of Present Value Inflows: $$2,727.27 + $3,305.79 + $3,756.57 + $2,049.04 = \mathbf{$11,838.67}$
6. Net Present Value (NPV): $$11,838.67 - $10,000.00 = \mathbf{+$1,838.67}$
7. Internal Rate of Return (IRR): The discount rate where $\text{NPV} = 0 \rightarrow \mathbf{18.04%}$

Because the NPV is positive ($+$1,838.67) and the IRR (18.04%) substantially exceeds the 10.0% hurdle rate, the project creates economic value and should be approved.

Discounted payback period calculation

Simple payback ignores the time value of money. The discounted payback period tracks cumulative discounted cash flows:

• End of Year 1: $$2,727.27$ recovered ($$7,272.73$ remaining)
• End of Year 2: $$2,727.27 + $3,305.79 = $6,033.06$ recovered ($$3,966.94$ remaining)
• End of Year 3: $$6,033.06 + $3,756.57 = $9,789.63$ recovered ($$210.37$ remaining)
• Year 4 Fractional Recovery: $\frac{$210.37}{$2,049.04} \approx 0.10\text{ years}$

$$\text{Discounted Payback Period} = 3 + 0.10 = \mathbf{3.10\text{ years}}$$

The critical Microsoft Excel "NPV trap"

A frequent financial modeling error stems from a misunderstanding of Microsoft Excel's =NPV() function syntax:

WRONG:  =NPV(10%, -10000, 3000, 4000, 5000, 3000)   <-- ERRORS!

• Why it fails: Excel’s built-in =NPV() assumes the first argument in the value range occurs at the end of Period 1. If you include the initial investment inside the formula, Excel mistakenly discounts your day-zero outlay by one year!

CORRECT: =-10000 + NPV(10%, 3000, 4000, 5000, 3000)

Always keep the Time 0 cash outflow outside the Excel =NPV() function.

Frequently asked questions

What is the primary difference between NPV and IRR?

NPV expresses project value in absolute currency units (e.g., dollars added to shareholder equity), whereas IRR expresses return as a percentage yield. When comparing mutually exclusive projects of differing capital sizes, always defer to NPV.

Can a project have multiple IRRs?

Yes. If cash flows alternate between positive and negative signs multiple times over the project lifecycle (non-conventional cash flows), the polynomial equation can produce multiple mathematical IRRs. In such cases, use Modified IRR (MIRR) or NPV.

What should I use as my discount rate?

Most corporate finance teams use their Weighted Average Cost of Capital (WACC), which blends the cost of equity with the after-tax cost of debt, plus an optional risk premium for uncertain ventures.