# Discounting

Cost-benefit studies examine the future benefits and costs of a program or policy as well as current benefits and costs. Discounting provides a way to compare the dollar value of costs and benefits received in different time periods to present values. This document describes the purpose of discounting, explains how it is used in cost-benefit analysis (CBA), and provides information on selecting discount rates.

### The purpose of discounting

Discounting is a technique that translates future costs and benefits into present-day values to account for the time value of money. The *time value of money* is the concept that money is worth more today than in the future because people prefer to spend now rather than later and because today’s dollar can be invested for a profit. Discounting differs from accounting for inflation because the time value of money applies even in the absence of inflation. When used appropriately, discounting future dollars provides a more accurate assessment of an initiative’s economic impact.

### Selecting a discount rate

Selecting an appropriate discount rate is important because different rates can produce very different cost-benefit results and therefore affect policy recommendations. A high discount rate has the power to reduce sizable future benefits and costs to very small present values. A lower rate reduces future values less, making the value of future benefits and costs closer to current dollar values.

The following example demonstrates how discount rates affect cost-benefit findings and the resulting policy recommendations. Consider a hypothetical investment that costs $45,000 and generates $6,000 in benefits each year for 10 years. Table 1 shows the net present value of the investment using three discount rates: 0, 3, and 7 percent. When discounting with a 0 percent rate (i.e., not discounting future benefits), the value of future benefits stays at $6,000 each year, and the program’s benefits outweigh its costs by $15,000. When discounting with a 3 percent rate, the program’s benefits outweigh its costs by $6,181. With a 7 percent rate, the program’s costs outweigh its benefits by $2,859, suggesting it is not worth the investment.

**Table 1: Discounting with Rates of 0, 3 Percent, and 7 Percent**

The discounting formula section below provides the formula underlying the calculations in Table 1.

The federal Office of Management and Budget (OMB) recommends both 3 and 7 percent discount rates. The 3 percent rate is the rate of return for the average consumer. At that rate, the average consumer is willing to substitute present for future consumption; that is, the average consumer is equally happy with either $100 today or $103 a year from now. The 7 percent rate is OMB’s estimate of the average rate of return for private investments.

It is common to use a discount rate of 3 to 5 percent when evaluating social programs. The Washington State Institute for Public Policy and the Urban Institute—two organizations that have conducted many CBAs of criminal justice initiatives—use 3 and 5 percent rates, respectively.

### The discounting formula

The formula for discounting is:

- PV, or present value, is the value at time=0
- FV, or future value, is the value at time=n
- i is the discount rate
- n is the number of years in the future that the future value will be received

Using this formula, the present value of the future benefits of the hypothetical investment referenced in Table 1, using a 3 percent discount rate, is:

PV = $6,000/1.03^{1} + $6,000/1.03^{2} + $6,000/1.03^{3} + $6,000/1.03^{4} + $6,000/1.03^{5} …$6,000/1.03^{10 }= **$51,181**

The net present value (NPV), which equals the present value minus the initial investment, is:

NPV = $51,183 – $45,000 = **$6,181**

### Discounting in Excel

Microsoft Excel discounts future benefits and costs using the financial function “NPV,” which calculates the present value of future cash flows given a defined discount rate. Despite its name, the NPV function does not calculate net present value, as it does not account for the initial investment. When using the function, subtract the initial investment from the discounted benefits to calculate the net present value.

The syntax for the NPV function is =NPV(rate,value1,value2, …).

To practice, type or copy and paste the following formula in Microsoft Excel to calculate the present value of a $6,000 benefit that accrues each year for 10 years, using a 3 percent discount rate:

=NPV(0.03,6000,6000,6000,6000,6000,6000,6000,6000,6000,6000)

The answer ($51,181) represents the discounted future benefit. To calculate the net present value, subtract the cost of the initial investment ($45,000) from the discounted future benefit ($51,181). The result ($6,181) is the net present value.

**For more information on Discounting, please see the Cost-Benefit Analysis and Justice Policy Toolkit. **