The most basic economic questions that people face in their day-to-day personal and business lives involve the tradeoffs between dollars earned, spent, or invested today and those dollars they hope to earn, spend, or invest in the future. Such tradeoffs must also be considered when evaluating highway investments.
A given project will generate costs and benefits over its entire service life cycle. During construction, it will generate mostly costs. Once in service, it will generate mostly benefits, although some costs continue due to maintenance, periodic rehabilitation, and operational activities. In many cases, benefits will build over time as traffic levels increase. These benefits and costs can be presented in dollar terms for each year of the project's life cycle. Figure 1 illustrates a typical time series of costs and benefits.
Comparison of benefits to costs over the project life cycle would be a simple issue of summation except for one problem: the value of a dollar changes over time. In particular, a dollar that an individual or agency will spend or earn in the future is almost always worth less to them today than a dollar they spend or earn now. This changing value of the dollar must be understood and quantified to enable meaningful comparisons of multiyear dollar streams.
Two separate and distinct factors account for why the value of a dollar, as seen from the present, diminishes over time. These factors are inflation and the time value of resources.
FIGURE 1. Time Series of Costs and Benefits
Inflation is said to occur when the prices of most goods and services in the economy are rising by some degree over time - also referred to as - "general inflation." Economists believe that inflation is usually caused when there is more demand expressed for goods and services in the economy than there is supply of those same goods and services at current prices. To produce the goods and services needed to meet demand, firms must pay more for the inputs (including labor and raw materials) needed to produce the goods and services. For example, it might be necessary to pay overtime premiums to existing workers or pay higher wages to attract new workers. These higher costs get passed on to consumers in the form of higher prices for the goods and services produced; consumers in turn seek higher wages to pay for the higher priced goods and services, and so on, in a circular manner.
Economists usually measure inflation by comparing the price of groupings or "market baskets" of goods and services from year to year. The prices of some goods and services in the grouping will go up, the prices of others may go down - it is the overall price level of the grouping that captures the effect of inflation. A price or inflation index is constructed by dividing the price of the grouping in each year by its price in a fixed base year, and multiplying the result by 100. The change in the index value from year to year reveals the trend and scale of inflation. The Consumer Price Index (CPI) is probably the best-known price or inflation index to most Americans, but there are many others.
Just as inflation is encountered in the general economy, the costs of highway projects tend to rise over time as a result of inflation. This is because highway projects must compete for many of the same resources (such as labor or steel) that other sectors of the economy require.
FHWA measures trends in highway construction costs by a Bid Price Index (BPI, also called the Federal-Aid Highway Construction Cost Composite Index). The BPI is constructed from the unit prices for materials in actual highway project bids, compiled from reports of State awards for Federal-aid contracts of $500,000 or greater. Inflation in construction costs is measured by the changes in these unit prices from year to year. Many States produce their own highway cost indices to reflect local conditions and practices.
Engineering News-Record (ENR) publishes both a Construction Cost Index and Building Cost Index that are widely used in the construction industry. ENR also publishes various materials prices for 20 U.S. cities and two Canadian cities. Other indices include the Turner Construction Co. Composite Index and the R.S. Means Heavy Construction Cost Index.
Dollars from one year can be converted into equivalent dollars of another year (as measured by purchasing power) by using price indices to add or remove the effects of inflation (see box). Dollars from which the inflation component has been removed are known as "real," "constant," or "base year" dollars. A real dollar is able to buy the same amount of goods and services in a future year as in the base year of the analysis. Dollars that include the effects of inflation are known as "nominal," "current," or "data year" dollars. A nominal dollar will typically buy a different amount of goods and services in each year of the analysis period.
In the case of economic analysis of investments by a public agency, it is best practice to forecast life-cycle costs and benefits of a project without inflation (i.e., in real or base year dollars). Inflation is very hard to predict, particularly more than a few years into the future. More importantly, if inflation is added to benefits and costs projected for future years, it will only have to be removed again before these benefits and costs can be compared in the form of dollars of any given base year.
The essential time to consider inflation is when the project budget is being prepared, after economic analysis has shown the project to be economically viable. Future year or multiyear project budgets are appropriated in future year dollars rather than base year dollars. Failure to account for inflation in project budgets will almost always result in too few future year dollars being set aside to complete the projects (leading to public perceptions of cost overruns and mismanagement) and will hurt the agency's ability to program future projects. Also, if historical cost data are being used to develop base year cost estimates for a project, the historical cost data should be adjusted to base year dollars using an inflation index.
Formulas for Adjusting for Inflation
The use of price or inflation indices to adjust for inflation is relatively straightforward.
To remove inflation (i.e., convert data year, nominal dollars into base year, real dollars):
Dollars base year = Dollars data year x Price Index base year / Price Index data year
To add inflation (i.e., convert base year, real dollars into data year, nominal dollars):
Dollars data year = Dollars base year x Price Index data year / Price Index base year
For instance, assume that the base year for an analysis is 1999. If a highway structure cost $100,000 to build in 1992, how much would it have cost in base year 1999 dollars (all else being equal)? The answer (based on the structure price information contained in the Federal Highway Administration's Bid Price Index [BPI]) would be:
$100,000 data year (1992) x 138.3 BPI structures index (1999) / 108.4 BPI structures index (1992)
or $127,583 base year 1999 dollars. Similarly, a base year dollar can be converted to an equivalent amount of purchasing power for any other year based on the second formula.
Historical price index data can be used to adjust for inflation in years prior to and including the present. When adjusting future, multi-year project budgets to allow for inflation, the analyst should consult with a financial or economic expert to develop reasonable estimates of anticipated future price growth.
When adjusting for inflation, an index appropriate for the task should be used. For doing cost or budget estimates, this index will often be the State version of the BPI. In a few cases, the analyst may believe that a resource's cost has grown or will grow much more rapidly than the rate of inflation. For instance, right-of-way costs may soar due to real estate speculation in anticipation of a new road. In such cases, the analyst should work with experts to determine how much the real price of the resource will change over time and include this adjusted price in the economic analysis. It is good practice to consult with an economist whenever an issue arises over the appropriate treatment of inflation.
Most people have a day-to-day familiarity with inflation. They are less familiar, however, with the separate and distinct concept of the time value of resources. Yet this latter concept is the backbone of economic analysis of transportation projects and of the Nation's financial system in general.
The time value of resources is also referred to as the time value of money or the opportunity cost (or value) of resources. It reflects the fact that there is a cost associated with diverting the resources needed for an investment from other productive uses or planned consumption within the economy. This cost is equal to the economic return that could be earned on the invested resources (or the dollars used to buy them) in their next best alternative use. Equivalently, the time value of resources can be interpreted as the amount of compensation that must be paid to people to induce them not to consume their resources in the current year, but rather to make them available for future investment.
The time value of resources is measured by an annual percentage factor known as the discount rate. The discount rate has a positive value whether or not there is inflation in the economy, as illustrated by the following example.
Assume that for the next 20 years no general inflation is expected. That is, $100 would buy the same (or a comparable) market basket of goods and services in 20 years that it will buy today. In this environment, would a person expect to be able to borrow money at zero interest? Would that person lend money to someone else at zero interest? The answer to both questions, at least for most people, is "no." Money can always be invested now to earn a return (e.g., in real estate or a profitable enterprise). Alternatively, it can be spent on something a person wants now (e.g., a nicer house), as opposed to having to wait to buy it in the future.
Thus, people must be compensated for making money available even if there is no inflation. If, for example, people require at least $105 after one year as compensation for making $100 available today, then they are equating the value of $105 after one year to $100 in the present. Put another way, the "present value" of $105 one year from now is $100. The annual rate of return (5 percent in this example) in compensation for the time value of resources is the discount rate.
If an analyst knows the appropriate discount rate, he or she can calculate the "present value" of any sum of resources or money to be spent or received in the future. The application of the discount rate to future sums to calculate their present value is known as "discounting" (see box). Through discounting, different investment alternatives can be objectively compared based on their respective present values, even though each has a different stream of future benefits and costs.
Formula for Discounting
The standard formula for discounting is as follows:
PV = [1/(1+ r)t ] At
PV = present value at time zero (the base year);
r = discount rate;
t = time (year); and
A = amount of benefit or cost in year t.
The formula above is the most basic calculation of present value. The term
which incorporates the discount rate "r" is called the discount factor. Multiplying a future sum by the appropriate discount factor for that future year will yield the present value of that sum at time zero (e.g., the year in which the analysis is being done).
Of course, most highway projects generate costs and benefits over their entire life-cycles. This entire series of costs and benefits must be discounted to the present by multiple applications of the PV formula for each applicable year of the life-cycle (see formula below). These discounted values are then summed together (as represented by Σ) for each year of the life-cycle analysis period ("N") to yield an overall present value. The formula for doing this is as follows:
The present value of a series of numbers is often described as the "net present value," reflecting the fact that the discounted amount often reflects the net value of benefits after costs are subtracted from them.
As a rule of best practice, economic analysis should be done in real terms, i.e., using dollars and discount rates that do not include the effects of inflation. A real discount rate can be estimated by removing the rate of inflation (as measured by a general price index such as the CPI) from a market (or nominal) interest rate for government borrowing. The selected market rate for government borrowing should be based on government bonds with maturities comparable in length to the analysis period used for the economic analysis. Real discount rates calculated in this manner have historically ranged from 3 percent to 5 percent - the rates most often used by States for discounting highway investments (see box).
The Discount Rate Matters
The selection of an appropriate discount rate is important. For example, the present value of $1,000 of benefits received 30 years in the future is $412 when discounted at 3 percent per year, $231 when discounted at 5 percent, but only $57 when discounted at 10 percent. Thus, present values of costs and benefits 30 years in the future can be changed by more than a factor of 5 depending on the discount rate used. Due to the importance of the discount rate, care should be taken to select one that reflects a State's actual time value of resources.
The U.S. Office of Management and Budget (OMB) currently requires U.S. Federal agencies to use a 7 percent real discount rate to evaluate public investments and regulations.1 Federal agencies may use lower rates (based on inflation-adjusted Federal borrowing costs) for life-cycle cost analysis. In January 2003, OMB reported a 10-year real discount rate of 2.5 percent and a 30-year rate of 3.2 percent, based on current Federal borrowing costs. These latter rates reflect historically low costs of government borrowing.
In times of budget shortfalls, an agency may increase its discount rate to reflect the higher opportunity cost of such funds. The agency should consider, however, that the discount rate applies over the life of the project, and adjusting the discount rate to reflect short-term funding fluctuations may distort the value of long-term benefits and costs. An agency may also increase its discount rate to account for project risk. FHWA recommends, however, that risk be treated directly with risk analysis tools rather than through adjustments to the discount rate (see section on Risk Analysis, page 30).
1 This rate is adjusted occasionally. OMB has announced that significant changes in the 7 percent rate will be reflected in future guidance to Federal agencies.