Net Present Value (NPV): How to Discount Cash Flows and Read the Answer

By the end of this article, you will be able to determine whether a project that costs money now and pays money later is worth undertaking. You will understand the discount factor, where it comes from, how to compute NPV in a single SQL line, the errors that can arise when using that line, and how to present a result that hinges on an assumption you choose.

The quickest way to start is to apply the method to a real project. Consider any project with an initial cost and several years of expected returns. Divide each future year's cash flow by 1.10 raised to the number of that year, sum all the results, and then subtract the initial cost. If the result is positive, the project outperforms a 10% required return.

The essence of the concept can be expressed in one line: a dollar received in five years is not equivalent to a dollar today. NPV reduces every future amount to its present value and then sums them all together, including the initial negative outflow. This reduction is the core idea behind NPV, so the rest of the article builds upon it.

The original graphic features five vertical bars representing years one to five, with the height of each bar indicating the expected cash flow for that year. The bars grow progressively taller from left to right, from $150,000 in year one to $190,000 in year five. Each bar is divided into two parts: the solid colored portion at the bottom represents the present value of that cash flow, discounted at 10%, while the pale hatched section on top represents the value lost due to waiting.

The solid portions decrease steadily from left to right, from approximately $136,364 to $117,975, while the pale caps increase from a thin sliver in year one to a thick block in year five. A dashed line connects the tops of the solid portions, sloping downward as the bars increase in height, illustrating the fundamental principle that a payment made further in the future is worth less due to the compounding effect of discounting.

At the top right of the graphic, a legend pairs a pale swatch with the term "waiting" and a solid swatch with "today." Every number in this article has been verified through computation in SQLite, and you can independently verify each row using a calculator. The project presented in this article involves a $500,000 upfront investment and five years of additional cash flows amounting to $850,000.

To determine whether this project exceeds a 10% required return, the following steps are taken: 1. Establish the cash flows for each year: Year 0: -$500,000 (initial investment) Year 1: $150,000 Year 2: $160,000 Year 3: $170,000 Year 4: $180,000 Year 5: $190,000 2. Identify the discount rate, which is 10%. 3. Calculate the discount factor for each year by raising (1 + rate) to the power of the year: Year 0: 1.0000, Year 1: 1.1000, Year 2: 1.2100, Year 3: 1.3310, Year 4: 1.4641, Year 5: 1.61051 4.

Divide each cash flow by its corresponding discount factor to obtain the present value: Year 0: -$500,000, Year 1: $136,364, Year 2: $132,231, Year 3: $127,724, Year 4: $122,942, Year 5: $117,975 5. Sum the present values, including the initial investment as a negative number, to obtain the NPV: -$500,000 + $136,364 + $132,231 + $127,724 + $122,942 + $117,975 = $350,000 6.

Interpret the NPV result: A positive NPV indicates that the project generates more value than the required return of 10%, while a negative NPV suggests it fails to meet the required return. In this case, an NPV of $350,000 indicates that the project exceeds the 10% required return by $350,000.