Certified Financial Analyst with 15+ years of experience in capital budgeting and investment valuation.
The **Net Present Value Calculator** helps evaluate the profitability of a projected investment or project. It determines the present-day value of all expected future cash flows, minus the initial investment cost. A positive NPV indicates a profitable project. This simplified model uses an annuity for cash flows. Input any three variables (Initial Investment, Annual Cash Flow, Discount Rate, or Project Term) to solve for the missing one, or calculate NPV if all four are entered.
Net Present Value Calculator
Net Present Value (NPV) Formula Variations
This simplified model uses the Present Value of Annuity (PVA) factor to represent the cash flows:
Let $C₀$ = Initial Cost, $CF$ = Annual Cash Flow, $R$ = Discount Rate (decimal), $N$ = Term in Years.
Formula Source: Investopedia – Net Present Value
The Present Value of Annuity (PVA) Factor is: $PVA_{Factor} = \left[ \frac{1 – (1 + R)^{-N}}{R} \right]$
The core equation is: $NPV = -C₀ + (CF \times PVA_{Factor})$
C₀ (F) = (CF × PVA Factor) - NPV
CF (P) = (NPV + C₀) ÷ PVA Factor
R (V) — Solved Iteratively
N (Q) — Solved via Logarithms
Variables Explained
- F (Initial Investment – C₀): The cost incurred today to start the project. Entered as a positive value.
- P (Annual Cash Flow – CF): The constant, equal cash inflow (or outflow) received each period.
- V (Discount Rate – R): The rate used to discount future cash flows. Represents the opportunity cost or cost of capital.
- Q (Project Term – N): The lifespan of the project, measured in years (periods).
Related Calculators
- Internal Rate of Return (IRR) Calculator
- Discounted Cash Flow (DCF) Calculator
- Payback Period Calculator
- Present Value of Annuity Calculator
What is Net Present Value (NPV)?
The **Net Present Value (NPV)** is a measure used in capital budgeting to determine the present value of all the cash flows expected from a project, subtracted by the initial cost of the project. Simply put, it converts future money into today’s money and checks if the value you gain from an investment exceeds the value you initially spend.
The NPV rule dictates that projects with a **positive NPV** should be accepted, as they are expected to increase shareholder wealth. Projects with a **negative NPV** should be rejected, as they are expected to result in a net loss in today’s dollars. An NPV of zero means the project returns exactly the cost of capital.
How to Calculate NPV (Example)
Scenario: Initial Investment ($50,000), Annual Cash Flow ($15,000) for 5 years, Discount Rate (10%).
- Convert Rate to Decimal (R):
$$R = 10\% \div 100 = 0.10$$
- Calculate the PVA Factor:
$$PVA_{Factor} = \left[ \frac{1 – (1.10)^{-5}}{0.10} \right] \approx 3.7908$$
- Calculate Present Value of Cash Flows:
$$PV_{CF} = \$15,000 \times 3.7908 \approx \$56,862.00$$
- Final Result (NPV):
$$NPV = PV_{CF} – C_0 = \$56,862.00 – \$50,000 = \$6,862.00$$
Frequently Asked Questions (FAQ)
Any NPV greater than zero is considered acceptable, as it signals that the project is expected to generate a return higher than the discount rate (cost of capital). A higher positive NPV is generally better.
How does the Discount Rate affect NPV?The discount rate is inversely related to NPV. A higher discount rate means future cash flows are worth less today, thus reducing the NPV. The discount rate often reflects the company’s weighted average cost of capital (WACC).
Can NPV be used for non-constant cash flows?Yes. The standard (unsimplified) NPV formula calculates the PV of each year’s unique cash flow individually. This calculator uses a simplified model where cash flow is constant (an annuity) for the entire term.
What is the relationship between NPV and IRR?The Internal Rate of Return (IRR) is the discount rate that makes the NPV of a project exactly zero. If the IRR is higher than the project’s discount rate (R), the NPV will be positive.