What is Net Present Value (NPV)?

Net Present Value is the sum of all future cash flows discounted to their present value, minus the initial investment. A positive NPV means the investment is expected to generate more value than it costs when accounting for the time value of money. A negative NPV means the opposite. NPV > 0 is the fundamental criterion for accepting an investment.

What is the Internal Rate of Return (IRR)?

IRR is the discount rate that makes the NPV of a cash-flow series equal to zero. It represents the annualized expected return of the investment. If the IRR exceeds your required rate of return (hurdle rate), the investment is generally worth pursuing. IRR is calculated numerically - this calculator uses Newton-Raphson with a bisection fallback.

Which discount rate should I use?

Use your Weighted Average Cost of Capital (WACC) for corporate projects, or your personal required rate of return for individual investments. A common starting point for stock-market investments is 7–10% annually. For risk-free benchmarks, use the current 10-year Treasury yield.

What is the payback period?

The payback period is the number of periods it takes for cumulative cash flows to turn positive (i.e., when you have recovered your initial investment). It is a simple risk indicator - a shorter payback period is less risky - but it ignores cash flows after payback and the time value of money. Use it alongside NPV and IRR.

Why might there be multiple IRRs?

When a cash-flow series has more than one sign change (e.g., it goes negative, then positive, then negative again), the NPV equation can have multiple roots - each is a valid IRR. This is the "multiple IRR problem." In these cases, NPV is a more reliable decision criterion than IRR.

NPV & IRR Calculator - Net Present Value & Internal Rate of Return

Period (years)

Cash Flow ($)

Discount Rate	NPV
5.0%	$21,204.76
7.5%	$13,242.59
12.5%	-$402.04
15.0%	-$6,269.06

Discount Rate

NPV

5.0%

$21,204.76

7.5%

$13,242.59

12.5%

-$402.04

15.0%

-$6,269.06

Understanding NPV and IRR

Net Present Value (NPV) and Internal Rate of Return (IRR) are the two most important metrics in capital budgeting. NPV tells you the absolute dollar value an investment creates above your cost of capital. A positive NPV means the investment is worth pursuing. IRR tells you the percentage return the investment generates. Compare it to your hurdle rate to decide.

How NPV is calculated

NPV sums all future cash flows discounted to today's dollars using the formula: NPV = Σ CF_t / (1 + r)^t. The discount rate r reflects the opportunity cost of capital (what you could earn in an alternative investment of similar risk). The higher the discount rate, the less future cash flows are worth today.

The multiple IRR problem

When a project has unconventional cash flows (outflows in the middle of the project or multiple phases), the NPV equation can have more than one solution, meaning there are multiple valid IRRs. This calculator detects that situation and warns you. In such cases, rely on NPV rather than IRR for your decision.

MIRR - Modified Internal Rate of Return

MIRR solves the multiple-IRR problem by making explicit assumptions about reinvestment rates. Traditional IRR implicitly assumes positive cash flows are reinvested at the IRR itself - an often unrealistic assumption. MIRR instead assumes positive cash flows are reinvested at the cost of capital (or a specified reinvestment rate), producing a single, unambiguous result.

The formula: MIRR = (FV of positive flows / PV of negative flows)^(1/n) − 1

Where FV is computed at the reinvestment rate and PV at the finance rate.

Worked example

Year	Cash flow	PV at 10%
0	−$100,000	−$100,000
1	+$40,000	+$36,364
2	+$50,000	+$41,322
3	+$60,000	+$45,079

NPV at 10% = −$100,000 + $36,364 + $41,322 + $45,079 = +$22,765 (positive -> accept the investment).

IRR ≈ 23.4% (the discount rate at which NPV = 0). Since 23.4% > 10% hurdle rate -> accept.

Discount rate selection guide

The discount rate represents the opportunity cost of capital - what you could earn on an alternative investment of similar risk. Common choices:

WACC (Weighted Average Cost of Capital): used for corporate capital budgeting. Reflects the blended cost of debt and equity financing.
Risk-free rate + risk premium: for personal or project-level investments. Start with the current 10-year Treasury yield and add a premium for the specific risks of the project.
Next-best alternative rate: if the alternative is a 7% index fund, use 7% as the minimum acceptable return. Any NPV-positive project at that rate beats leaving the money invested.