Net Present Value (NPV) Calculator

Period (t)AmountActions

What Is Net Present Value (NPV)?

Net Present Value (NPV) measures how much value an investment adds today after accounting for the time value of money and your required return. It discounts each future cash flow back to its present value and then subtracts the upfront cost. A positive NPV indicates the project is expected to create value above your hurdle rate; a negative NPV suggests it falls short.

\( \displaystyle \text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^{t_y}} – C_0 \)

Here, \(C_0\) is the initial investment at \(t=0\), \(CF_t\) is the cash flow at period \(t\), and \(r\) is the annual discount rate (your required return). The term \(t_y\) converts the period index into years (e.g., for quarters \(t_y=t/4\), for months \(t_y=t/12\)).

Variables & Assumptions

  • Initial Investment \(C_0\): The cash outflow today. Enter as a positive number; the tool treats it as an outflow.
  • Cash Flows \(CF_t\): Net inflows or outflows at each future period (revenue minus costs, including capex, operating costs, taxes, and changes in working capital).
  • Discount Rate \(r\): The annual return you require given the project’s risk. Many use WACC for core projects or a risk-adjusted hurdle for riskier ones.
  • Timing: Assumes end-of-period cash flows (ordinary annuity). If they occur at period starts (annuity due), shift periods by one or multiply PVs by \((1+r)^{\Delta t}\).
  • Period Unit: Choose years, quarters, or months. We convert the exponent so an annual \(r\) is applied consistently.
\( \displaystyle PV_t = \frac{CF_t}{(1+r)^{t_y}}, \quad t_y = \begin{cases} t & \text{(years)}\\ t/4 & \text{(quarters)}\\ t/12 & \text{(months)} \end{cases} \)

Why NPV Is the Decision Workhorse

  • Accounts for time value of money: Cash today beats the same nominal amount later.
  • In real currency units: NPV tells you how much value is created (or destroyed) in dollars, not just a rate like IRR.
  • Clear accept rule: For independent projects, accept if \( \text{NPV} > 0 \).
  • Ranks mutually exclusive options: When you must choose one, prefer the highest positive NPV.

Worked Examples

Example 1: Annual Cash Flows

A project costs \(C_0=\$10{,}000\). Required return \(r=10\%\) (annual). Annual inflows: \(CF_1=\$3{,}000\), \(CF_2=\$4{,}000\), \(CF_3=\$5{,}000\).

\( \text{NPV} = \frac{3000}{(1{+}0.10)^1} + \frac{4000}{(1{+}0.10)^2} + \frac{5000}{(1{+}0.10)^3} – 10000 \)

Compute each present value, sum them, and subtract \(10{,}000\). If the result is positive, the project beats your 10% hurdle rate. Verify this above by selecting Years.

Example 2: Monthly Cash Flows

Suppose \(C_0=\$12{,}000\), \(r=12\%\) (annual), and you expect \(CF_t=\$1{,}200\) at the end of each month for 12 months. With months selected, the exponent becomes \(t_y=t/12\):

\( \text{NPV} = \sum_{t=1}^{12} \frac{1200}{(1{+}0.12)^{t/12}} – 12000 \)

Note we still use an annual \(r\) but scale exponents by months. If cash flows occur at the beginning of each month, shift each \(t\) back by one (or multiply by \((1+r)^{1/12}\)).

Best Practices, Uses, and Pitfalls

How People Use NPV

  • Capital budgeting: Rank and select projects, equipment replacements, or product launches.
  • Real estate underwriting: Evaluate rehab or development projects with uneven cash flows and a terminal value.
  • Valuation sanity checks: Model discrete initiatives even when a full DCF is overkill.

Common Pitfalls to Avoid

  • Mixing real and nominal: If cash flows include inflation, use a nominal rate. If they’re real, use a real rate.
  • Ignoring working capital: Include initial working-capital investments and the recovery at project end.
  • Forgetting taxes and depreciation: Use after-tax cash flows; depreciation affects taxes via shields.
  • Wrong timing assumption: End-of-period vs. beginning-of-period matters—be consistent.
  • Terminal value mistakes: If you expect a sale or residual value, include it as a final \(CF_n\) and discount properly.

Choosing a Discount Rate

Your discount rate should reflect opportunity cost and risk. For core corporate projects, many use the firm’s WACC. For riskier or non-core initiatives, increase \(r\) to reflect uncertainty. If cash flows are volatile or economy-dependent, perform sensitivity tests (e.g., \(r=8\%\), \(10\%\), \(12\%\)) and scenario analysis on key drivers such as prices, volumes, and costs.

NPV FAQ

Is a higher NPV always better?

For independent projects, any NPV > 0 adds value. For mutually exclusive projects, choose the highest positive NPV subject to strategic and capacity constraints.

How does NPV compare to IRR and Payback?

IRR is the discount rate that makes NPV = 0; payback ignores time value beyond a cutoff. NPV directly measures value in currency and is the most reliable rule.

Can I model uneven or negative cash flows?

Yes. Enter any combination of inflows and outflows by period. The calculator discounts each one individually and aggregates the result.

Bottom Line

NPV translates future expectations into today’s dollars, letting you compare opportunities on equal footing. Use the calculator to test rates, timing, and scenarios. If the NPV is positive, the project is expected to beat your required return and create value.

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