NPV Calculator

Net present value converts a stream of future cash amounts into a single number expressed in today's money. Each entry in the list is divided by (1 plus r) raised to the power of its period index, so a flow arriving in year 4 at a 10 percent discount rate is worth 1.10 to the fourth power, or about 1.4641 times less than the same amount today. This calculator applies the end-of-period convention: the first number in the comma-separated list is discounted one full year, the second two years, and so on, and the initial investment is treated as an outlay at time zero that is not discounted. The profitability index shown alongside NPV is the total discounted inflow divided by that outlay, so a PI of 1.48 means each dollar committed returns about one dollar forty-eight cents in present-value terms. The discount rate carries almost all of the judgment. Corporate users normally supply a weighted average cost of capital, which for listed non-financial firms has commonly sat in the 7 to 12 percent range, while venture-stage or highly uncertain projects are screened at 20 percent or more. Two structural caveats matter for a quick screening tool like this one. First, NPV is extremely sensitive to the rate: a project that clears at 8 percent can turn negative at 12 percent, so the number should always be recomputed across a band of rates rather than trusted at a single point. Second, a finite list of flows implicitly assumes the asset is worth nothing after the last entry, which understates long-lived assets unless a terminal value is added as the final figure.

Discounting is far older than the acronym NPV. Simon Stevin published interest and discount tables in his 1582 Tafelen van Interest, giving merchants a printed way to value a future sum in present terms rather than recomputing the arithmetic by hand. The economic reasoning was formalized by Irving Fisher, whose The Rate of Interest (1907) and The Theory of Interest (1930) argued that the value of any asset is the discounted stream of income it is expected to yield, and who framed investment choice as a comparison of that value against cost. John Burr Williams applied the idea systematically to securities in The Theory of Investment Value (1938), setting out the dividend discount model that remains the basis of modern valuation. Moving discounted cash flow from theory into corporate routine took another generation. Joel Dean's Capital Budgeting (1951) is generally credited with introducing discounting to American industrial practice, which until then relied heavily on payback period and accounting rate of return. Adoption was slow while the arithmetic had to be done with printed present-value tables and a slide rule; the spread of financial calculators in the 1970s, and then the spreadsheet function that computes NPV directly from a cell range, made a list-based calculation like this one trivial. Survey work on chief financial officers published in 2001 by John Graham and Campbell Harvey found that roughly three-quarters of the 392 firms they polled used NPV always or almost always.