NPV Calculator

Background.

Pay $10,000 today and collect $3,000, $4,000, $5,000 and $3,000 over the next four years, and you end up $5,000 ahead in plain dollars. Whether that is a good deal depends on what the $10,000 could have earned in the meantime. Discount the four receipts at 10 percent a year and they are worth $11,838.67 today, so the net present value is $1,838.67: the project beats a 10 percent alternative by that much, measured in today's money. Discount at 20 percent instead and the same receipts are worth less than the $10,000 they cost. Somewhere near 18 percent the answer crosses zero, and that crossing point is the internal rate of return.

Net present value is the standard yardstick of capital budgeting for this reason. It converts a stream of money spread across years into one figure in today's currency, and the sign carries the decision: positive means the cash flows earn more than your discount rate, negative means less, at whatever level of risk the rate reflects.

The first number in your list is period 0, money that moves today, and it is not discounted. Every later number is treated as arriving at the end of period 1, 2, 3 and so on. That is the textbook form, NPV = CF₀ + Σ CFₜ ÷ (1 + r)ᵗ, and it is how the CF0 register on a financial calculator such as the HP 12C or TI BA II Plus works. Excel's NPV() function works differently: it treats its first argument as a period-1 amount, so passing it the whole series, outlay included, pushes every flow one year later than it happens. On the example above, that mistake shrinks the answer to $1,671.52, understating it by $167.15.

Nothing enters the sum that is not in your list. Taxes, inflation, salvage value and anything beyond the last year count only if you have built them into the cash flows.

What is npv calculator?

Net present value is the sum of every cash flow in a series after each has been converted to its value today by dividing by (1 + r) raised to the number of periods until it arrives. Outflows enter as negative numbers and inflows as positive ones, so the total is a net figure in today's currency. The discount rate r is the return you could earn elsewhere on money of similar risk, which makes NPV a comparison rather than a forecast: a result of zero means the project earns exactly r, a positive result is the amount by which it beats r, and a negative result is the shortfall. Because each project's NPV is a sum in today's dollars, the NPVs of independent projects can be added together, which ratios such as the internal rate of return and the profitability index do not allow. A positive NPV can also be read as a price: it is the most you could pay on top of the stated cost and still earn exactly your rate, so a machine with an NPV of $1,838.67 at 10 percent would still break even at that rate if it cost $11,838.67.

How to use this calculator.

1. 01Type the cash flows in order, starting with period 0. Separate them with a comma and a space, a semicolon or new lines; thousands separators are fine, so -10,000, 3,000, 4,000 reads as three values.
2. 02Make money you pay out negative and money you receive positive, including any later outflows such as a mid-life refit or decommissioning cost.
3. 03Keep every period the same length. The rate applies per period, so yearly flows need an annual rate and monthly flows a monthly one.
4. 04Enter the discount rate as a percentage: a company's weighted average cost of capital for a corporate project, or the return you could realistically earn elsewhere at similar risk for a personal decision.
5. 05Check that the number of periods entered matches what you meant to type; a count one short usually means two values ran together.
6. 06Run the same flows at a lower and a higher rate. If the NPV changes sign inside the range of rates you consider plausible, the decision depends more on the rate than on the project.

The formula.

NPV = Σ CFₜ ÷ (1 + r)ᵗ, summed from t = 0 to n. CFₜ is the cash flow at the end of period t, r is the discount rate per period written as a decimal (10 percent is 0.10), and n is the last period you entered. At t = 0 the divisor is (1 + r)⁰ = 1, so the opening cash flow passes through unchanged.

The divisor grows geometrically. At 10 percent the discount factors 1 ÷ (1 + r)ᵗ for years one to four are 0.9091, 0.8264, 0.7513 and 0.6830, and by year 20 a dollar is worth under 15 cents today. That is why long projects are so sensitive to the rate: raising r trims the near years slightly and the distant years heavily.

The present value of future cash flows shown beside the NPV is the same sum taken from t = 1 onward, so NPV equals that figure plus the period-0 entry. The rate must be above −100 percent, because at −100 percent the divisor becomes zero; the input itself accepts −50 to 100 percent. A negative rate makes later money worth more than money today, which is unusual but has occurred, for example on some government bonds in the late 2010s.

Three assumptions sit inside the formula. Every flow lands at the end of its period, so income that actually arrives through the year is discounted slightly too much; valuation analysts sometimes use a mid-year convention, t − 0.5, to correct for that, and it is not applied here. Periods are equally spaced, so irregular dates need a date-based method such as Excel's XNPV. And one rate applies to every period, so a project whose risk or financing changes over time is approximated by a single average rate.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Brealey, R.A., Myers, S.C., and Allen, F. — Principles of Corporate Finance, 13th edition. Chapter 5 develops the NPV rule, the CF0-undiscounted convention, and the comparison with IRR.
2. [2]Bodie, Z., Kane, A., and Marcus, A.J. — Investments, 12th edition. Covers discounted cash-flow valuation and the role of the required rate of return in present-value analysis.
3. [3]CFA Institute — CFA Program Curriculum, Corporate Issuers topic area, covering capital budgeting and the net present value decision rule.
4. [4]Microsoft Support — NPV function. Defines NPV for equally spaced future cash flows, states the end-of-period convention, and explains that a time-zero cash flow is added separately.
5. [5]Microsoft Support — Go with the cash flow: calculate NPV and IRR in Excel. Explains the discounted-cash-flow relationship between NPV and IRR and the timing convention for periodic cash flows.
6. [6]Federal Reserve Economic Data (FRED) — benchmark interest-rate series commonly used to anchor discount-rate assumptions in present-value analysis.