*NPV Definition: The sum that results when the discounted value of the expected costs of an investment are deducted from the discounted value of the expected returns.*

The Net Present Value (NPV) benefit is a calculation that measures the net benefit of a project in today’s dollar terms, taking into account that over time money today is more valuable than money in the future (discounted time value of money).

The NPV savings calculation consists of two financial concepts:

• The “net” part of the NPV savings calculation is the difference between all costs and all benefits (savings and other gains).

• The present value portion of the NPV calculation takes into account the time value of money; so that adjusts to expenditures and returns, as they occur over time, can be evaluated equally.

When examining a project investment decision, and knowing that money has a time value, future payments need to be higher than investments made today in order to be equivalent to today’s dollars.

This time value accounts for the fact that:

• Money typically inflates over time, meaning that a dollar invested today will be worth less in the future because of inflation.

• A dollar invested today could earn interest over time, so the investment needs to make up for the lost opportunity. As the investment could earn interest elsewhere at the organizations weighted average the cost of capital, this is often called opportunity cost.

**NPV Defined**

The NPV calculation evaluates a set of costs and benefits over time in order to account for the time value of money. The cash flows are the amounts and timings of the various investment costs and benefits, and these are brought into a common term, today’s dollars, so that the net benefit can be quantified and compared if necessary to competing investment opportunities.

Using an IT project as an example, let’s say that a company invests $100,000 in a new application and that the application requires $25,000 annually thereafter in maintenance and support costs. From this investment, the company expects to save $200,000 each year. An analysis of this investment over three years would yield the following negative (costs) and positive (benefit) cash flows:

The cash flow from this investment is shown as the Net Benefit, which is the Total Benefits minus Total Costs: a cash flow of -$100,000 initially (year 0), with $175,000 in year 1, year 2 and year 3.

The NPV Savings calculation seems intimidating when expressed as a formula; however, when demonstrated in practical terms it is quite intuitive. Mathematically NPV calculation is represented by the formula:

In this formula, the " I "s represent the net benefits for each year, the subscript "0" represents the initial net benefit, the subscript "1" represents the year one net benefit, and so on. The exponent in the denominator is also equal to each year of the analysis, up to n, the number of years in the analysis term. The discount rate is r and is held constant through the analysis period.

To put the calculation in practical, step-by-step terms, we will use the calculation applied against our example cash flows. The net present value calculation, using a cost of capital/discount rate of 7%, takes the initial costs and ongoing costs and benefit cash flows to create a single net cost or savings figure. For the example set of cash flows in the above table, the net benefits are as follows:

Initial = I(0) = - $100,000

Year 1 = I(1) = + $175,000

Year 2 = I(2) = + $175,000

Year 3 = I(3) = + $175,000

The initial expense of $100,000 is not discounted because it is already in today’s dollars terms. However, Year 1 through Year 3 need to be adjusted to be brought into today’s dollar terms and is calculated as follows:

NPV Year 1 = $175,000 divided by (1+ .07) = $163,551

NPV Year 2 = $175,000 divided by (1+.07) squared = $152,852

NPV Year 3 = $175,000 divided by (1+.07) cubed = $142,852

The total NPV savings is the sum of the initial expense and the three-year NPV analysis, represented as:

NPV Savings = - $100,000 + $163,551+ $152,852 + $142,852 = $ 359,255

As shown, the net benefits from later years are discounted more in today’s dollar terms such that they mean less in the overall analysis. As a result, the total NPV savings is only $359,255 compared to the cumulative benefits of $425,000 when the discount rate is not considered.

The higher the discount rate is and the further into the future that a cash flow will occur, typically the lower the present value of that cash flow will be. Because the net present value calculation increases the impact of current costs and near term savings while reducing the impact of future costs or benefits, the following holds true:

• Projects with high initial costs and savings that grow slowly over time yield lower NPV savings values;

• Projects with low initial costs and greater initial savings yield higher NPV savings calculations.

**The Bottom-Line**

The NPV Savings is one of the most popular and accurate methods used to assess business investment viability. NPV uses discounted cash flow to accurately quantify the net benefits from a project.

However, the NPV calculation usually cannot be used alone to determine whether a project is viable. As an example, a project may yield a substantial $100M NPV savings over a three-year period, but the required initial investment of $10M may be so risky for the company that it is not considered a prudent risk. As well, a project might have a large NPV benefit but has a long payback period and derives much of its benefits through huge gains in outgoing years.

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