# Net Present Value Analysis: A Primer for Finance Officers.

This article demonstrates how to use a decision tool called net present value (NPV) analysis to evaluate a project's long-term financial costs and benefits.

A traditional analysis of a project's long-term costs and benefits simply adds together each year's cost or benefit so that the total cost is the sum of the costs in each year, and the total benefit is the sum of the benefits in each year. Subtracting the total cost from the total benefit calculates a project's total net benefit.

The flaw of the traditional method of analysis is that it assumes that dollars in future years have the same value as dollars today and can simply be added together. Although a traditional analysis gives dollars in the future the same value as dollars today, governments, and society as a whole, implicitly place a lower value on future dollars than current dollars, a concept known as the time value of money. One simple example that proves this is a savings bond. A \$100 savings bond that matures in 10 years represents \$100 in the future, however, it is worth much less than a \$100 bill today.

Governments also place a higher value on dollars today rather than dollars in the future. Many governments are willing to pay an interest cost to borrow money to finance capital projects. Instead of paying an interest cost to borrow money, a government could have saved money year by year to meet future capital needs. The fact that a government chose to spend its revenue on current rather than future needs (and pay an interest cost down the road) proves that it places a higher value on current rather than future needs.

Since traditional analysis gives a mistakenly high value to dollars in the future, it may provide poor information. In traditional analysis of capital projects, money in the future is given the same value as money today; but as proven above, money in the future is given a lower value than money today. Thus, traditional analysis may provide an estimate that is inconsistent with a decision-maker's criteria. Net present value analysis closely matches the criteria that governments implicitly use when making long-term decisions--meaning that it gives a lower value to dollars in the future.

Instead of simply adding together each year's cost or benefit, net present value analysis first converts the value of future costs and benefits to their actual value today. This is like converting the value that is written on the face of a savings bond to its actual value today. After converting each year's future value to a present value, the net benefits for each year are summed to calculate the total net benefit.

To convert future dollars to present dollars, net present value analysis uses a number called a "discount rate." A discount rate reflects a government's cost of borrowing or a community's preference for present versus future consumption. Although there is no standard government discount rate, the interest rates in the nation's financial markets are a good source for determining a discount rate.

How to Do a NPV Analysis

Net present value analysis involves four basic steps.

* The first step is to forecast the benefits and costs in each year.

* The second step is to determine a discount rate.

* The third step is to use a formula to calculate the net present value.

* The final step is to compare the net present values of the alternatives.

Step 1: For each alternative, forecast the benefits and costs in each year. To begin, forecast the total benefits and total costs in each year. A typical forecast of costs and benefits might look something like Exhibit 1. In this example, the government would incur large upfront costs but enjoy a stream of benefits in later years.

Making accurate forecasts of future costs and benefits can be the most difficult step in net present value analysis. Analysts should follow five general rules when forecasting costs and benefits.

1) Forecast benefits and costs in today's dollars.

2) Do not include sunk costs.

3) Include opportunity costs.

4) Use expected value to estimate uncertain benefits and costs.

5) Omit non-monetary costs and benefits.

Forecast benefits and costs in today's dollars. It is important to treat inflation consistently throughout a net present value calculation, so all forecasts of future costs and benefits should be made in today's dollars, i.e., real dollars, and discounted at a real discount rate.  When a forecast is made in "real" dollars, future costs and benefits are not increased to include the effect of inflation. In other words, if a benefit of \$100,000 is forecast for the fifth year of a project, that \$100,000 will have the same buying power as \$100,000 today.

As an alternative to making forecasts in real dollars, it is also possible to make all forecasts in nominal dollars and discount them at a nominal discount rate. However, forecasts in real dollars are easier to make and understand than forecasts in nominal dollars. It is easier to make forecasts in real dollars because inflation does not complicate the forecast. For example, if an analyst forecasts the future revenues of a swimming pool in nominal dollars, the forecast for each year must take into account both the number of users of the pool and the effect of inflation. If the same forecast is made in real dollars, only the number of users (or real increase in revenue) needs to be projected. It is also easier to understand forecasts in real dollars. Excluding inflation from the forecast makes it clear that an increase in costs or benefits is an actual increase, and not simply an increase due to inflation. 

Do not include sunk costs. A sunk cost is a cost that already has occurred and will remain the same regardless of what decision is made. An example of a sunk cost is the cost of conducting a survey to determine resident interest in an outdoor pool. The cost of the survey is a sunk cost because it will remain the same regardless whether a pool is built. Since a sunk cost will remain the same regardless of what decision is made, this cost should be ignored in an analysis.

To see how including sunk costs can lead to bad decisions, suppose a county government is considering demolishing its 52-year-old high school and building a new facility on the same site. The year before the county had spent \$1.2 million to meet an Environmental Protection Agency (EPA) deadline for asbestos removal. Opponents of the new facility argue that the old building should not be abandoned since the county had just poured \$1.2 million into it to bring it into compliance with EPA regulations. However, this argument could justify renovating the building forever since each new renovation could be justified by the money that has been "invested" in the building already. The \$1.2 million for asbestos removal is a sunk cost and should be ignored because it cannot be recovered regardless of the decision that is made. If the cost of renovating and expanding the old building is \$4.3 million and the cost of demolishing the old building and building a new facility is \$3.4 million, the county would save \$900,000 b y selecting a new facility. In other words, including the sunk cost of the asbestos removal would lead the county to spend \$900,000 more than it has to for a high school facility of equal quality.

Include opportunity costs. When forecasting costs, it is important to include opportunity costs. The opportunity costs of a proposed project are the potential benefits that are lost by selecting it. For example, if a city were considering building a public pool on vacant city-owned property, the city would lose the potential revenue it would generate by selling the land to a private developer. This potential tax revenue loss is the opportunity cost of the pool, and it should be included as a cost of the pool.

If opportunity costs are not included as costs, then some proposals may appear to be better just because they use existing government resources. To show how this can lead to bad decisions, suppose a small city government is considering two proposals for a community center. One proposal is to use a vacant city-owned building downtown (that could be sold for \$2.3 million). A second proposal is to purchase vacant land in a residential area. If the opportunity cost of using the city building were ignored, the costs and benefits of both proposals in the first year would look like the top box in Exhibit 2.

Note that the total cost of proposal A (\$0.7 million) appears to be \$1 million less than the total cost of proposal B (\$1.7 million). However, if the opportunity cost is included, the costs and benefits look like the bottom box in Exhibit 2.

Since the building could be sold for \$2.3 million, its value to the city government is \$2.3 million. Therefore, using this building for a community center entails an opportunity cost of \$2.3 million. Including this opportunity cost shows that the initial cost of proposal A is \$1.3 million more than proposal B.

To discover opportunity costs, first consider all of the government resources that are used by the proposed project-land, employee time, facilities, etc. This would include "hard" costs requiring out-of-pocket expenditures and "soft" costs such as employee time. Second, determine the value of each of these resources to the government or the greatest benefit that the government would obtain by using each resource in another way, then record this benefit as a cost of the proposal.

Use expected value to estimate uncertain benefits and costs. Many times it is difficult to estimate the benefits or costs because they are dependent on an unpredictable environment or because the result of a project is uncertain. However, it is still possible to make an estimate by using the technique in Exhibit 3. To estimate an uncertain benefit or cost:

1) list the possible scenarios;

2) estimate the probability of each scenario;

3) estimate the benefit (or cost) in each scenario;

4) multiply the probability of each scenario by the benefit (or cost) in the scenario to get an expected value; and

5) add the expected value for each scenario to get the expected benefit (or cost).

Omit non-monetary costs and benefits. It is possible to put a monetary figure on intangible items. In fact, it is not uncommon for public policy studies to put a monetary value on human life. However, there are two reasonable arguments for only including monetary benefits and costs in the net present value calculation: 1) the analysis is easier to perform--nonmonetary benefits and costs such as human life and happiness are difficult and time-consuming to quantify and 2) the overall analysis may be more accurate if non-monetary benefits and costs are left out of a net present value calculation. When a non-monetary cost or benefit is included in a net present value analysis, there is the tendency to consider these non-monetary factors twice. First, they are quantified in the net present value calculation. Then, after the net present value formula recommends a specific option as the best alternative, decision makers tend to not completely trust the recommendation so they reconsider the importance of non-monetar y factors such as the human lives saved or the political ramifications. For this reason, it may be better to separate monetary and non-monetary considerations and have a clear picture of the monetary payoff and then compare it to the non-monetary considerations. Omitting non-monetary costs and benefits also may make an analysis more accurate because it would remove the danger of over or undervaluing non-monetary costs and benefits.

Step 2: Determine the discount rate. The discount rate converts the stream of future costs and benefits into their value today. For a private firm, the discount rate is simply the rate of return on an investment with a similar risk as the proposed project. Unfortunately, there is no consensus on how governments should determine their discount rate. The author prefers to use a different discount rate for projects that are primarily financed with taxes and projects that are primarily financed with bonds.  Tax-financed projects should have a discount rate that is different from bond-financed projects because tax financing displaces private consumption, whereas bond financing mostly displaces private investment.

Using this method, projects that are financed by taxes are given a discount rate equal to the real, long-term interest rate. The real long-term interest rate is like an "exchange rate" that reflects society's preference for exchanging present for future consumption. By using this discount rate, a government's decisions to forgo current expenditures for future expenditures match society's preferences. For example, if society highly values forgoing current spending for spending in the future, then this preference will be reflected by a low interest rate. Government discount rates also should be low to reflect this preference.

For projects that are financed by bonds, the discount rate is set equal to the real interest rate on the government's bonds of similar maturity. This interest rate reflects the opportunity cost of the private investment dollars which would have gone to other uses.

A convenient source of forecasts of long-term interest rates and inflation is the Congressional Budget Office publication, Economic and Budget Outlook: Fiscal Years 2002-2011, which is updated annually. This publication is available at www.cbo.gov.

The following example shows how to calculate a real discount rate using the method shown in Exhibit 4. Using a forecast inflation rate of 2.6 percent and a forecast 10-year Treasury bond rate of 5.7 percent, the real discount rate for tax-financed projects would be:

(1+0.057/1+0.026)-1=0.030=3.0%

Assuming that the government's bond interest rate is 5.3 percent and the forecast inflation rate is 2.6 percent, the real discount rate for bond-financed projects would be:

(1+0.053)/1+0.026)-1=0.026=2.6%

It is important to remember that the formulas above calculate real, not nominal, discount rates. Thus, they should be used with forecasts of costs and benefits made in real (or current) dollars. If a real made in real (or current) dollars. If a real discount rate is used, care should be taken when comparing this rate to the rate used in other governments because other governments may be using a nominal discount rate. To compare a real discount rate to a nominal discount rate, use the formula in Exhibit 5 to convert a real discount rate to a nominal discount rate.

Step 3: Calculate the net present value of each alternative. Use the diagram in Exhibit 6 to calculate a net present value for each alternative. First, combine the benefits and costs in each year to produce a net benefit for that year. Second, plug the net benefit of each year into the formula below it. Third, solve the formula to calculate the net present value for the alternative. (Although the diagram in Exhibit 6 only extends out to a six-year period, it could be extended to any length of time.)

Step 4: Determine which alternative has the highest net present value. After calculating a net present value for each alternative, determine which alternative has the highest net present value. If only monetary costs and benefits were included in the calculation, then consider whether the non-monetary costs and benefits justify selecting another alternative. For example, if the government determines that three capital projects offer approximately the same NPV (e.g., new bus, new train, road widening), then other non-monetary factors may tip the balance in favor of one proposal. Such factors might include improved service to the public or environmental benefits.

Example of a net present value analysis. To show an example of a net present value analysis, suppose a small city is considering building a set of public baseball diamonds on vacant land owned by the city. The Recreation Department presents two proposals. Proposal A is to build the entire park in the first year. Proposal B is to build half of the park in the first year and expand the park in the sixth year at a higher cost. Both proposals generate revenue from concession sales. Since the baseball diamonds would be located on city property, an opportunity cost of \$1 million is included as the initial cost of both proposals. Exhibit 7 shows the forecasts of the costs and benefits of both proposals.

Assuming a discount rate of 3 percent and that both options have a life of eight years, the net present value calculation for Proposal A would look like Exhibit 8. The net present value calculation for Proposal B would look like Exhibit 9. This analysis shows that Proposal B has the best net present value, i.e., lowest costs.

Limitations of NPV Analysis

The main limitation of net present value analysis is the difficulty of accurately forecasting future costs and benefits. In particular, benefits are often non-tangible (but real) improvements to the community. Programs can have unanticipated costs or generate less revenue than expected. Another limitation of net present value analysis is that there is no universal discount rate or standard method of setting a discount rate. Because there is no standard in this area, net present value analysis is vulnerable to manipulation through selecting a high or low discount rate, however, both of these weaknesses may be addressed by conducting a sensitivity analysis.

Other Analysis Tools

Net present value analysis is just one of many useful analysis tools. A new publication from the GFOA, Decision Tools for Budgetary Analysis, provides practical, step-by-step procedures for using 12 analysis tools including:

* decision tables;

* expected value tables;

* weighted score tables;

* decision trees;

* breakeven analysis;

* activity-based costing;

* net present value analysis;

* return on investment analysis;

* cost-benefit analysis;

* fiscal impact analysis;

* cost-effectiveness analysis; and

* sensitivity analysis.

This publication is the third in the GFOA Budgeting Series that shows how to implement the recommended practices of the National Advisory Council on State and Local Budgeting. It is available from GFOA for \$15 member/\$20 nonmember. Contact GFOA at 312/977-9700 or Publications @gfoa.org for more information.

R. GREGORY MICHEL is Manager in GFOA's Research and Consulting Center in Chicago, Illinois. He holds a master's degree in Public Policy from the University of Chicago.

NOTES

(1.) It is also possible to make all forecasts in nominal dollars and discount them at a nominal discount rate. In either case, inflation should be treated consistently.

(2.) There are also advantages to making forecasts in nominal dollars and using a nominal discount rate. If a forecast is made in nominal dollars, the analyst knows the actual number of dollars that will be spent or received each year. This is important for budgeting and financing decisions. Forecasts in nominal dollars also make it easier to recalculate the analysis at a future date because the forecasts are made in terms of the value of a dollar in each year rather than the value of a dollar in the year that the analysis was made. Finally, nominal discount rates can be easily compared to other governments that use nominal discount rates.

(3.) The Government Finance Officers Association dots not have a recommended practice on setting a discount rate.
``` A FORECAST OF A PROJECT'S COSTS AND BENEFITS
Now Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Benefits \$ 0 \$32,000 \$47,000 \$47,000 \$47,000 \$47,000 \$47,000
Costs -\$950,000 -\$40,000 -\$ 5,000 -\$ 5,000 -\$ 5,000 -\$ 5,000 -\$ 5,000
Year 7 Year 8 Year 9 Year 10
Benefits \$47,000 \$47,000 \$47,000 \$500,000
Costs -\$65,000 -\$ 5,000 -\$ 5,000 -\$ 5,000
INCLUDING VS. IGNORING OPPORTUNITY COST
Proposal A--Use City Building
Ignoring Opportunity Cost
Land purchase cost \$0.0 m
Construction cost \$0.7 m
Total cost \$0.7 m
Including Opportunity Cost
Opportunity cost of building \$2.3 m
Construction cost \$0.7 m
Total cost \$3.0 m
Proposal B--Purchase Land
Land purchase cost \$0.5 m
Construction cost \$1.2 m
Total cost \$1.7 m
Land purchase cost \$0.5 m
Construction cost \$1.2 m
Total cost \$1.7 m
AN EXAMPLE OF FORECASTING BENEEITS
WHEN IT IS DIFFICULT TO PREDICTTHE
THE FUTURE
Step 1 Step 2 Step 3 Step 4 Step 5
List possible Estimate Estimate Calculate
scenarios probability benefit expected benefit
Recession 10% X \$ 50 = \$ 5
Moderate growth 70% \$100 \$70
High Growth 20% \$200 + \$40
\$115
PREFERRED METHOD OF CALCULATING
A GOVERNMENT DISCOUNT RATE
For tax-financed Real long-term = (1+Forecast 10 year Treasury bond/
projects: interset rate 1+ Forecast CPI) - 1
For bond-financed: Real bond Local government's bond interest rate
projects: interest rate for a bond with smilar naturity
(1 + as the life of the project/
1 + Forecast CPI)
```

REAL TO NOMINAL CONVERSION FORMULA

( 1 + Real discount rate ) X ( 1 + Future CPI) -1 = Nominal discount rate
``` CALCULATING THE NET PRESENT VALUE
Now Year 1 Year 2
Benefits \$X \$X \$X
Costs -\$X -\$X -\$X
Net Benefits () () ()
[down arrow] [down arrow] [down arrow]
Net Present = Value ( ) (/[(1 + r).sup.1]) (/[(1 + r).sup.2])
Year 3 Year 4 Year 5
Benefits \$X \$X \$X
Costs -\$X -\$X -\$X
Net Benefits () () ()
[down arrow] [down arrow] [down arrow]
Net Present = Value (/[(1 + r).sup.3]) (/[(1 + r).sup.4]) (/[(1 + r).sup.5])
Year 6
Benefits \$X
Costs -\$X
Net Benefits ()
[down arrow]
Net Present = Value (/[(1 + r).sup.6])
1. Forecast the benefits and costs
2. Determine the discount rate (r)
3. Calculate the NPV
FORECASTED COSTS AND BENEFITS
OF BOTH PROPOSALS
Proposal A Now Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
Benefits \$0 \$0 \$25k \$25k \$25k \$25k \$25k \$25k
Costs -\$1,000k -\$3,000k -\$40k -\$40k -\$40k -\$40k -\$40k -\$40k
Net Benefit -\$1,000k -\$3,000k -\$15k -\$15k -\$15k -\$15k -\$15k -\$15k
Proposal B
Benefits \$0 \$0 \$15k \$15k \$15k \$15k \$ 15k \$25k
Costs -\$1,000k -\$1,500k -\$20k -\$20k -\$20k -\$20k -\$1,700k -\$40k
Net Benefit -\$1,000k -\$1,500k -\$ 5k -\$ 5k -\$ 5k -\$ 5k -\$1,685k -\$15k
Proposal A Year 8
Benefits \$25k
Costs -\$40k
Net Benefit -\$15k
Proposal B
Benefits \$25k
Costs -\$40k
Net Benefit -\$15k
Opportunity cost of land Construction costs Maintenance costs
```

CALCULATING THE NET PRESENT VALUE OF PROPOSAL A

NPV = (-\$1,000k/)+(-\$3,000k/[(1+0.03).sup.1])+(-\$15k/[(1+0.03).sup.2])+(-\$1 5k/[(1+0.03).sup.3])+(-\$15k/[(1+0.03).sup.4])+(-\$15k/[(1+0.03).sup.5] )+(-\$15k/[(1+0.03).sup.6])+(-\$15k/[(1+0.03).sup.7])+(-\$15k/[(1+0.03). sup.8])

-\$4,003k = (-\$1,000k/)+(-\$3,000k/(1.03))+(-\$15k/(1.06))+(-\$15k/(1.09))+(-\$15k/(1 .13))+(-\$15k/(1.16))+(-\$15k/(1.19))+(-\$15k/(1.23))+(-\$15k/(1.27))

CALCULATING THE NET PRESENT VALUE OF PROPOSAL B

NPV = (-\$1,000k/)+(-\$1,500k/[(1+0.03).sup.1])+(-\$5k/[(1+0.03).sup.2])+(-\$5k /[(1+0.03).sup.3])+(-\$5k/(1+0.03))+(-\$5k/[(1+0.03).sup.5])+(-\$1,685k/ [(+0.03).sup.6])+(-\$15k/[(1+0.03).sup.7])+(-\$15k/[(1+0.03).sup.8])

-\$3,910k = (-\$1,000k/)+(-\$1,500k/(1.03))+(-\$5k/(1.06))+(-\$5k/(1.09))+(-\$5k/(1.13 ))+(-\$5k/(1.16))+(-\$1,685k/(1.19))+(-\$15k/(1.23))+(-\$15k/(1.27))
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