Cost-Benefit Analysis Concepts and Practice Boardman Greenberg Vining Weimer Fourth Edition

Transcription

1 Cost-Benefit Analysis Concepts and Practice Boardman Greenberg Vining Weimer Fourth Edition

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3 When costs or benefits actually occur over the course of a year, a more appropriate approach is to treat them as if they occurred in the middle of that year. So, for instance, if the $100,000 in benefits and $20,000 in operating costs were distributed throughout each of the five years of the library project, one would discount these benefits and costs at times t 0.5, 1.5, 2.5, 3.5, and 4.5. If, as before, the installation costs of $325,000 occurred at the beginning of the first year of the project (t 0) and the liquidation benefit of $20,000 arose at the end of the fifth year (t 5), then the NPV of the project would be $28,562. COMPARING PROJECTS WITH DIFFERENT TIME FRAMES In principle, projects should always be compared over the same discounting period so that they have the same opportunity to accumulate costs and benefits. Projects with different time frames are not directly comparable. Suppose that a government-owned electric utility company is considering two new alternative sources of power. One is a large hydroelectric dam (HED), which would last 75 years; the other is a cogeneration plant (CGP), which would last 15 years. After considering all relevant social benefits and costs, and assuming a discount rate of 8 percent, the NPV of the 75-year hydroelectric project is $30 million and the NPV of the 15-year cogeneration project is $24 million. Is the hydroelectric project preferable simply because it has the larger NPV? The answer is no. These projects are not comparable because they have different life spans. The cogeneration project could be rolled over five times within the life of the hydro project. There are two methods for evaluating projects with different time frames: the rollover method and the equivalent annual net benefit method. They always lead to the same conclusion, as we now illustrate. Roll-Over Method Suppose that the utility decides to build the cogeneration power plant. Further suppose that in 15 years time it builds another new cogeneration plant; in 30 years it builds another one; and it builds another again in 45 and 60 years. If so, the length of these five sequential cogeneration plants will be the same as the length of the 75-year hydroelectric project. This makes the projects directly comparable. 8 The NPV of five back-to-back cogeneration power plants, denoted 5CGP, is: NPV(5CGP) = $24,000,000 + $24,000,000 $24,000, ( ) ( ) 30 + $24,000,000 $24,000,000 + = $34.94 million ( ) ( ) As this NPV is higher than the NPV of the hydroelectric project, the utility should select this option. Equivalent Annual Net Benefit Method An often easier way to compare projects of unequal lengths is to use the equivalent annual net benefit (EANB) method.the EANB of a project equals its NPV divided by the 147

4 annuity factor that has the same term and discount rate as the project itself (i.e., the present value of an annuity of $1 per year for the life of the project, discounted at the rate used to calculate the NPV): EANB = NPV a n i (10) where, a n i is the annuity factor, defined by equation (A.2). The EANB is the amount which, if received each year for the life of the project, would have the same NPV as the project itself. This process is called amortization: the cost of the project is amortized over n years. The EANBs for the hydroelectric and the cogeneration projects equal: 10 EANB(HED) = $30> = $2.407 million EANB(CGP) = $24>8.559 = $2.804 million The EANB of the cogeneration project is $2.804 million, which implies that this project is equivalent to an annuity of $2.804 million per year for 15 years. In contrast, the net benefit of the hydroelectric alternative is equivalent to an annuity of $2.407 million per year for 75 years. If one could continuously replace each project at the end of its life with a similar project, then the cogeneration project would yield net annual benefits equivalent to a perpetuity of $2.804 million per year, and the hydroelectric project would yield annual net benefits equivalent to a perpetuity of $2.407 million per year. Consequently, the cogeneration alternative is preferable, assuming replacement of both types of plant is possible at the end of their useful lives. An Additional Advantage of the Cogeneration Project In fact, if the utility chooses the cogeneration project at the beginning, then it may not be desirable to replace it with an identical cogeneration plant in 15 years.at that time a more efficient alternative is likely to be available. In contrast, if the utility builds the hydroelectric project, then it is probably locked in for 75 years.thus, the cogeneration project has an additional benefit because of its flexibility in allowing the introduction of more efficient technology as it becomes available during the 75-year period. Here it is sufficient to recognize that the shorter project has an additional benefit that is not incorporated in the EANB calculation. INFLATION AND REAL VERSUS NOMINAL DOLLARS Conventional private-sector financial analysis measures revenues, expenditures, net income, assets, liabilities and cash flows in terms of historical monetary units. Such units are referred to as nominal dollars (sometimes called current dollars). However, if you have ever listened to an older person reminisce, then you probably know that a dollar purchased more in 1986 than it does now a dollar s not worth a dollar anymore! For example, nominal per capita disposable personal income in the United States was approximately times higher in 2006 than in 1986 ($32,049 versus $13,665), but the 148

5 average person could not buy 2.3 times as many goods and services in 2006 as in The purchasing power of a dollar declines with price inflation. In order to control for the declining purchasing power of a dollar due to inflation, we convert nominal dollars to real dollars (sometimes called constant dollars). To obtain real dollar measures, analysts deflate nominal dollars. There are a number of possible deflators. Usually, the deflator is based on the market price of a basket of goods and services purchased by consumers, that is, based on consumer prices: sometimes analysts use the gross domestic product (GDP), which is broader and reflects the price of all goods and services in the economy, including the public sector. The choice of whether to use a consumer price deflator or the GDP deflator depends on whether the impacts of a project are concentrated on consumers or are much broader. In practice, most CBA studies use a consumer price deflator, especially when calculating consumer surplus. Some studies use a GDP deflator when calculating producer surplus. In the U.S. the most-often-used deflator reflecting consumer prices is the Consumer Price Index (CPI). The most commonly-used variant is the all-items CPI for all urban consumers, CPI-U, which is published by the Bureau of Labor Statistics and is summarized in Table 3 for the period Currently, the base year (when the CPI 100) is the period The CPI is expressed as the ratio of the cost of purchasing a standard basket of market goods in a particular year to the cost of purchasing the same (or very similar) basket of goods in the base year, multiplied by 100. For example, the CPI for 1980 was 82.4, which implies that the cost of a basket of goods in 1980 was 82.4 percent of the cost of a similar basket of goods in Returning to our example where average incomes increased times from 1986 and 2006, Table 3 shows that average market prices increased 1.84 times (201.6>109.6) from 1986 to Therefore, on average, people were about 27.5 percent (( )/1.84) better off in 2006 than in 1986 in terms of how much more market goods and services they could consume. 13 In order to convert amounts measured in nominal dollars for some year into amounts measured in real dollars for the base year ( ), we simply divide by the CPI for that year (divided by 100). For example, the average real income of people in 1986 measured in dollars was $12,468 ($13,665>1.096), and the average real income of people in 2006 measured in dollars was $15,897 ($32,049>2.016), again showing an increase of 27.5 percent. To convert amounts from base year dollars to, say, 2003 dollars, they are simply multiplied by the CPI for 2003 (divided by 100). Thus, the average real disposable incomes of people in 1986 and 2006, expressed in 2003 dollars, were $22,941 and $29,250, respectively. More generally, as the preceding example illustrates, to convert amounts expressed in year a nominal dollars into amounts expressed in year b real dollars, the year a dollar amounts are divided by the CPI for year a and multiplied by the CPI for year b. Fortunately for analysts in the U.S., the following government website contains an inflation calculator that does this automatically: Problems with Indices Based on Consumer Prices Although the CPI is the most widely used price index in the U.S., it is subject to a number of criticisms. Its value matters considerably to those many people who receive 149

6 TABLE 3 The U.S. Consumer Price Index (CPI) All Urban Consumers All items = 100 Year Average Annual CPI % Change Year Average Annual CPI % Change Source: ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt payments linked to it. Many pensions, for example, are adjusted each year (usually upward) according to the increase in the CPI. The return to holders of index-linked bonds also depends on the value of the CPI. Most academic economists believe that the CPI overstates the rate of increase in market prices. 14 In the mid-1990s, a commission set up by the Senate Finance Committee and chaired by Michael Boskin estimated that in the United States the CPI overestimated the increase in the cost of living by about 1 percentage point per annum, with a range between 0.8 percentage points and 1.6 percentage points. 15 As a result, people receiving entitlements linked to the CPI were, in effect, receiving more than was necessary to keep their purchasing power constant. The main reason why the CPI might be biased upward is because it does not accurately reflect consumers current purchases of goods. 16,17 This is sometimes called the commodity substitution effect. When the price of a good rises, consumers change their spending patterns and buy similar, but less expensive, products. As this switch to less expensive goods is not immediately picked up by the CPI, it overestimates the cost of living. 18 One version of this argument is sometimes called the discount stores effect. While government statisticians are visiting the same older, relatively expensive stores, consumers are switching to newer, cheaper discount stores. A similar problem occurs when pharmaceutical patents expire. Some consumers switch to new generic drugs, which are often as effective as patented drugs, but are considerably less expensive. These generic drugs did not exist previously and so are not included in the sample basket. This new goods 150

7 problem applies also to new high-tech goods, such as ipads or BlackBerry phones, which improve our quality of life and are often cheaper than older substitutes, but are also not included in the basket. A second type of problem concerns quality improvements to existing products. The CPI does not reflect changes in product quality, such as safer and more reliable cars. The U.S. government has corrected the CPI for some of these problems. In 1998, it under took some major revisions that reduced the estimated bias to about 0.65 percent per annum. 19 The downward bias in consumer price indices is probably not as large in other countries as in the U.S. For example, Allan Crawford estimates that the bias was about one-half a percentage point per annum in 1998 in Canada. 20 One reason why it was lower in Canada than the United States is that the base basket of goods has been updated every 4 years in Canada versus approximately every 10 years in the United States. Also, the Canadian index attaches a lower weight to medical services. The United Kingdom has two main consumer-focused indices: the UK Consumer Price Index (also abbreviated by CPI) and the Retail Prices Index (RPI). 21 The UK s CPI is the main measure of inflation for macroeconomic policy purposes, currently targetted at 2 percent. It is constructed in a way that is consistent across the European Union and thereby allows inflation to be compared across the EU.The RPI is the more familiar index, going back to 1947, and is used for indexation of pensions, state benefits, and index-linked gilts (short-term government bonds). The weights in the UK s CPI and the RPI are updated annually. In general, the RPI index is considerably more variable over time than the CPI index. Analyzing Future Benefits and Costs in CBA Analysts may work with project benefits and costs in either real dollars or nominal dollars. Also, they may use either a real interest rate or a nominal interest rate. Care must be taken to ensure that the units of measurement of benefits and costs are consistent with the units of measurement of the discount rate. If benefits and costs are measured in nominal dollars, then the analyst should use a nominal discount rate; if benefits and costs are measured in real dollars, then the analyst should use a real discount rate. Both methods result in the same numerical answer. 22 In the private sector, it is more natural to work in nominal dollars. Interest rates and other market data are expressed in nominal dollars; pro forma income and cash flow projections are usually made in nominal dollars; and the tax system is based on nominal amounts. However, for the analysis of public policy projects, it is usually easier and more intuitively appealing to express all benefits and costs in real dollars and to discount using a real discount rate. Returning to our library example, it makes more sense to think about the current and future annual cost savings to the library at today s prices than in future inflated prices. Similarly, it is easier to think about user benefits in terms of the number of hours of use at today s value per hour than to think about them in terms of future valuations. If one expects that user benefits will increase over time, for example, due to more people using the system or because each person uses it more often, then the projected real annual benefits will increase. This would be immediately clear if annual benefits were measured in real dollars. If, alternatively, annual benefits were expressed in nominal dollars, then it would not be immediately obvious whether increases were due to real increases in benefits or were due to inflation. 151