Net Present Value (NPV) of Future Cashflows

Purpose

This calculator discounts a series of future cash flows back to today's value at a given interest rate, and sums them to give a single Net Present Value. It is useful for judging whether a project or investment's future cash flows are worth more or less than the initial outlay, once the time value of money is taken into account.

It supports cash flows at irregular periods, so Period values do not need to be consecutive.

Background

Discounting cash flows to today

Money received in the future is worth less than the same amount today, because money today can be invested to earn a return. NPV converts every cash flow in a series — usually starting with an initial outlay (a negative value) followed by a series of returns (positive values) — into today's-money terms by discounting each one at the given Interest Rate, based on how many periods away it occurs. Adding up all of these discounted values gives the Net Present Value: a positive NPV means the discounted returns exceed the initial outlay (the investment adds value at that rate); a negative NPV means they fall short.

Inputs

Interest Rate

The discount rate used to convert future cash flows to present value (for example, 5 pct/yr). A higher rate reduces the present value of later cash flows more than earlier ones, since it compounds over more periods.

Cashflow Interval

The time period between entries in the Cashflows series (for example, yr for one entry per year).

Cashflows

A table with exactly two columns in this order:

• Period (first column), for example 1, 10, 15, 25, 26.
• Cashflow (second column), the corresponding cash flow amount.

Any renamed, reordered, missing, or extra column is rejected.

Results

Net Present Value

The sum of every cash flow in the Cashflows series, each discounted back to period 0 at the Interest Rate. A positive value means the series is worth more, in today's terms, than doing nothing; a negative value means it is worth less. An NPV of (approximately) zero means the Interest Rate entered is exactly the series' own Internal Rate of Return.

Understanding the Calculation

Each cash flow is discounted according to its period from the start.

$$NPV = \sum_{i=0}^{n} \dfrac{\text{Cashflow}_i}{(1+r)^{i}}$$

where Cashflow_0 is the first entry (discounted by 1, since it occurs immediately), r is the Interest Rate converted to a rate per Cashflow Interval, and i counts periods from the first entry.

When a Period column is provided, the calculator uses those explicit period values as numeric timestamps measured in the same unit as Cashflow Interval (for example, years when Cashflow Interval is yr). These timestamps are treated as absolute times since time 0 (e.g. 0.0, 0.5, 1.75), and may be irregular — the calculator discounts each cash flow using its numeric period value directly.

$$NPV = \sum_{k=1}^{m} \dfrac{\text{Cashflow}_k}{(1+r)^{t_k}}$$

If your cash flows are listed as 1, 2, 3, ... but you intended the first entry to be time 0, supply 0, 1, 2, ... in the Period column. Using consecutive integers 1,2,3 with the period unit chosen appropriately is still equivalent to the consecutive-row model when interpreted consistently.

Example

Using the default cash flow series -40000, 5000, 8000, 12000, 30000 (one entry per year) at an Interest Rate of 5% per year, the calculator returns a Net Present Value of approximately 7,065.27 — the series is worth about 7,065 more, in today's terms, than the initial 40,000 outlay alone, at a 5% discount rate.

Raising the Interest Rate to 15% per year turns the result negative, about -4,560.23, since the later, larger cash flows are discounted much more heavily at the higher rate. At the series' own Internal Rate of Return (about 10.58% per year — see the IRR calculator), the Net Present Value comes out to (effectively) zero, exactly as expected: the IRR is, by definition, the rate at which a series' NPV is zero.

Important Assumptions and Interpretation

• With or without an explicit Period column, the first listed cashflow is treated as the timing origin (period 0 after normalization).
• NPV depends heavily on the chosen Interest Rate — always state which rate was used to discount when comparing NPV figures, since the same cash flows can show a positive NPV at one rate and a negative NPV at another.
• Comparing NPVs across cash flow series is only meaningful when they use the same Interest Rate and Cashflow Interval.
• The result is a valuation based on estimated future cash flows and an assumed constant discount rate; it is not a guarantee of actual project or investment performance.

Quick Cross-Check with FV/NFV

For the same cashflow series and rate basis, compounding NPV to horizon T should match NFV:

$$NFV = NPV \times (1+r)^T$$

To reproduce this with FV, set Present Value = NPV, Periodic Payment = 0, and Duration = T intervals.