VII. ADJUSTING FOR TIMING DIFFERENCES ACROSS STUDIES AND PROJECTS: CONSTANT DOLLARS AND BASE YEAR FOR DISCOUNTING

What Are the Issues?

Individual studies follow established good practice in adjusting for the varying value of the dollar in regard to both purchasing power and opportunity cost during the span of years covered by the study; however, projects studied start and end at different times. Studies are performed at different times and span different time periods. They do not reflect differences in purchasing power and opportunity costs across the series of studies.

Constant Dollars

Studies following the practice prescribed by OMB Circular A94 of estimating all cash flows in constant dollars use constant dollars of different years. For ease in estimating, benefits and costs are often estimated at their value in the year the study is conducted; for example, if the study is done in 1995, it is likely that all cash flows will be estimated in dollars of 1995 value. Some researchers follow other appropriate practices; for example, some express results in constant dollars of more than one year, such as the year the study is conducted and the year the project started.

Net present value study results expressed in 2005 dollars do not have the same purchasing power and thus are not equivalent or additive to net present value study results expressed in 2004 dollars or any other year's dollar purchasing power. They can, however, be adjusted to purchasing power equivalents with a straightforward procedure.

Discount Rate

When using constant dollars, the fundamental principle of cash flow-based benefit-cost analysis is that all costs and benefits be adjusted for the opportunity cost of capital over time before being aggregated across time: a dollar invested or earned sooner is worth more than a dollar invested or earned later in time because of the potential for earnings at some rate during the intervening period.

Cash flows that occur at different times during the history of a project are "discounted" to a common point in time to adjust for this difference in earnings opportunity. OMB Circular A-94 simplified the rate issue by stipulating that a rate of 7% (real earnings rate, above and beyond inflation) be assumed in adjusting benefits and costs of most federal programs and projects to a common point in time. ATP has used the 7% real rate for all of its cash flow-based benefit-cost studies listed in Table 1 except the tissue engineering study.

Base Year for Discounting

The most common practice, and that used by financial spreadsheet software such as Excel, is to discount cash flows incurred in a project back to "Time Zero," or one time period ahead of the first cash flow. For example, if the first cash flow—typically the first investment—occurred in 1996, and other cash flows are entered as annual amounts, Excel discounts all cash flows back to one year before that, or 1995, in computing the net present value. The discounting process typically assumes that cash flows occur at the end of the year. The beginning of the project is the beginning of the first year, which is equivalent to the end of the previous year (Zero). This practice of using Time Zero as the base year for discounting evolved from the use of discounted cash-flow analysis in evaluating the outcomes of alternative prospective investments under consideration that year. The study was being conducted at approximately Time Zero, dollar estimates were expressed in dollar values in Time Zero, and all future cash flows were discounted back to Time Zero. In this section, we interpret the start of the project as Time Zero.

Magnitudes of net present value metrics computed using the same discounting base year (and in the same constant dollars and with the same discount rate) can be compared with each other. Selecting the project with the highest net present value would generate the maximum total net benefit from a single project. If multiple projects are feasible and independent of each other, their net present value metrics can be aggregated.

For program evaluation purposes, both prospective and retrospective analyses are done at different times in the program's history. Although, typically, studies of an individual R&D project use one time period ahead of the start of the first cash flows (i.e., Time Zero) as the base year for discounting (as Excel does), the projects analyzed in different studies most likely started in different years. The interpretation of net present value results of different studies looked at collectively becomes somewhat problematic. However, various alternatives for adjusting net present value results to a common base year have interpretation problems as well. Should project metrics be adjusted to look at the projects from the perspective of a common point in time, for example, from the time of the comparative or aggregate study, or the start of ATP, or the start of the first project among a group? Or for project evaluation purposes, is it adequate to let the base year vary as long as all studies report metrics in the same constant dollar basis and the same discount rate? To build awareness, this report attempts to illuminate those questions. Answers will depend on specific program needs to compare or aggregate net present value results from different studies.

It is important to note that although the net present value metric will change with a change in base year and/or constant dollar year, the internal rate of return and benefit-to-cost ratio will not change. They remain constant regardless of the choice of base year or constant dollar year. Furthermore, they are better measures than the net present value for assessing the efficiency of a project in regard to output per dollar of input unless investment costs are the same for all projects. However, they cannot be used to assess the total dollar value of benefits generated by a single project or project aggregate. The net present value metric provides that information, and the net present value metric requires adjustment for different base years and different constant dollar years when results are aggregated.

Examples of Effects of Constant Dollar and Base Year Differences

A comparison of reported net present values with net present values adjusted to a common constant dollar year and base year provides examples of the effects of these differences. Because one purpose of looking at the results of multiple studies would be to identify the relatively more and less successful projects among a group of basically successful ones, we also look to see whether the order of projects changes from highest to lowest net present value.

Tables 7 and 8 illustrate the effects of constant dollar and base-year differences across a number of ATP's more recent studies. Reported net present values are compared with net present values adjusted to constant 2005 dollars and then further adjusted to a common base year of 2005.

Table 7 examines the eight case study net present values reported in the component-based software study. All of these studies used a constant dollar year of 2000, but base years for discounting varied from 1994 to 1997. These variations were not enough to cause the relative order of the net present values across projects to change with the adjustment to a constant base year and constant dollar year.

Table 8 examines six cases that used a narrow spectrum of constant dollar years because the studies were all done fairly recently; however, the spectrum of base years used in discounting was broader, ranging from 1993 to 1999. The constant dollar adjustment alone was not enough to change the order of net present values. However, the additional effect of the base year adjustment was enough to cause the order of net present values across the six cases to change along with the significant change in magnitudes. The X-Ray Optics project moved from fourth position to third position, and the A-Si Detector project moved from third to fourth. The effects were greatest for projects in which the difference between the common base year and original base year for discounting were greatest; however, the revised ranking will now hold whatever common base year is used.

Table 8.   Adjusting for Timing Differences across Studies and Projects: Constant $ and Base Year (Example 2: Ranking Changes)

Figure 1 shows the formula for adjusting a reported net present value to constant 2005 dollars. The constant dollar adjustments were based on historical implicit price deflators for GDP reported for Q2 2005 in the September 2005 issue of Survey of Current Business (BEA 2005) (Tables C.1 and 1.1.9). Figure 2 shows the future value formula for adjusting reported net present values to a common 2005 base year.

Illustrating the adjustments shown in figures 1 and 2 for the Digital Video case results shown in Table 8:

1. Q2 2005 IPDGDP (Implicit Price Deflator for second quarter of 2005 published in September 2005 Survey of Current Business [BEA 2005],
   Table C.1) = 111.584
2. IPDGDPstudy (Implicit Price Deflator for constant dollar year used in study published in September 2005 Survey of Current Business [BEA 2005], Table 1.1.9) = 104.187
3. Applying the formula in Figure 1 to the reported NPV:

The adjusted NPV in constant 2005 dollars =

Applying the formula in figure 2 to adjust this NPV in constant 2005 dollars to 2005 as the base year for discounting = $177.7 million x LO^2005"1994^1' = $374 million.

Separate analyses, not shown, verified both empirically and mathematically that once all case study net present values are adjusted to a common base year, the base year can be changed again without further changing the order of the values. Magnitudes change, of course, as adjustments for opportunity costs move the base year of analysis backward or forward over time; however, the relative ordering does not change once net present values for all projects have been adjusted to a common base year.

There is little debate about the need, in theory, for constant dollar adjustments in comparing or aggregating net present value results from studies based on different constant dollar years. However, this adjustment might be considered relatively small and insignificant compared with other sources of measurement error in these studies.

The issue of the base year for discounting is more complex and controversial. The assumptions behind the discounting process are confusing to evaluators and sometimes even to others who use return on investment metrics tools. A decision on what practice to follow requires discussion and an understanding of the meaning of the discounting process for individual projects and for an aggregate of projects.

Fundamentally, the purpose of the discounting process is to force comparison of the project(s) under study to a hypothetical alternative investment opportunity with a guaranteed 7% real rate of return. For a single project, the net present value represents the magnitude of the difference in outcome (excess over or under), in constant dollars, for the project compared with a 7% federal bond taken out at the start of the project and cashed in at the end of the project study period. When multiple projects that started at different times are being analyzed together, the comparison with the alternative investment with a 7% return becomes complicated. The common base year adjustment is a mechanism for appearing to simplify the issue but it creates other interpretation issues.

The common base year and common constant dollar adjustments force a consistent base year and dollar reference for a group of projects examined collectively and compared with a 7% alternative project. However, these adjustments imply assumptions about earnings and costs of capital for individual projects prior to or beyond their individual study periods. For example, consider two projects that started in 1996 and 1998 and whose study periods ran until 2006 and 2008, respectively. To analyze the two projects together in the same study, a common practice would be to use a 1996 base year and to discount all benefits and investments from both projects to the beginning of the earliest project. This implies that a $1,000 investment at the start of the second project in 1998 actually cost less than $1,000. It cost only $873 because of an assumed earnings potential at 7% during the two-year period before the investment occurred. (Benefits likewise would be discounted back to 1996 rather than 1998 and would thus be valued at fewer dollars.)

An alternative approach would be to use 2008 as the common year for discounting. With this approach, the assumption would be that all benefits (earnings) from all projects are reinvested until 2008 at a 7% rate. Use of an interim base year, for example, 2005 or the year the study is undertaken, assumes reinvestment of benefits at 7% per year through that year. Tables 7 and 8 use this last approach of adjusting reported net present values to the year the study was undertaken, an interim point among project cash flows. Initially, each project's cash flows had been discounted to their present values as of the start of the project and reported on that basis. For this study, reported present values were first adjusted to constant 2005 dollars and then further adjusted to a common "base" year 2005 by applying future value factors for 7% and the number of years from the start of the project through 2005. Assuming cash flows are stated in 2005 constant dollars, this process is equivalent to the alternative approach of adjusting individual cash flows from each project to 2005 by discounting post-2005 cash flows to 2005 and computing future values of pre-2005 cash flows and adding them all together with 2005 cash flows. The approach used in this study in Tables 7 and 8 is more straightforward and can be implemented directly from net present values computed by Excel and those typically reported.

The following are a few considerations in the decision as to whether to adjust for differences in discounting base years for purposes of comparing or aggregating results.

• Projects are funded from different annual budgets and budget decision environments, which argues for the "floating" base year across studies as long as the base year is consistently the start of the projects evaluated. The benefit-cost calculation is then aligned with the budgetary economic events. Aggregation of results of studies with different base years poses some interpretation questions; however, this approach requires no assumption about alternative investment opportunities before and after
  the time of actual cash flows from the projects analyzed.
• Using "the time of the study valuation" for handling both constant dollars (purchasing power) and discounted value (opportunity cost of capital) has the advantage of ease of interpretation, particularly for retrospective analysis that involves aggregation across studies for program evaluation purposes. The reader understands the value of a
  dollar at the current time, which often approximates the time of the study. Using the "time of the study" as the base year assumes that all cash-flow benefits spun out of a project or put into a project are invested at the discount rate from the time they occur until the time of the study.
• Alternatively, using the start of ATP (in 1990) as the base year, or the start of the first project in an aggregate group being studied, has been considered meaningful. ATP's photonics and composites cluster studies and the component-based software study used this latter approach for analyzing a group of projects. Cash flows of all projects studied are discounted back to the start of the earliest project. As a result, in the aggregate analysis, benefits from later projects are downsized compared with earlier benefits from earlier projects. For example, consider the photonics cluster study, in which the X-Ray Optics individual case study analysis used a 1993 base year for discounting (first cash flows in 1994), the Ion Optics individual case study used 1999 as the base year for discounting (first cash flows in 2000), and the aggregate cluster analysis used 1993 as the base year. The individual Ion Optics case study showed the project to have a net present value of $143 million; however, within the aggregate cluster analysis, the Ion Optics project contributed only $95 million as a result of discounting benefits and costs back to 1993 as the base year rather than to 1999.
• The adjustment to restate project outcomes relative to a common vantage point base year, such as "time of the study" or "start of ATP," or any other point in time, can be done from previously reported metrics. The process then can be repeated over time for different base years and different constant dollar years.
  

Again, results of using a different base year have different magnitudes and different interpretations. Using the project start as the base year means that all later positive and negative cash flows are adjusted (discounted) downward at 7% compounded annual rate to compute the net financial advantage relative to the alternative safe investment made at the project start and held until the end of the project. By using some later year as the base year, for example, the year the study is being undertaken, all cash flows are adjusted upward for the equivalent of 7% annual compounded earnings on those cash flows (or lost earnings in the case of negative cash flows) until that ultimate base year. When multiple projects are examined together and cash flows are adjusted to a common "project start" or other common base year of analysis, the 7% compounding or discounting effect is extended beyond the project periods of at least some projects in the aggregate.

Using the same constant dollar year and base year for discounting, as was done in Tables 7 and 8, has the intuitive appeal that resulting dollar amount metrics can be interpreted more easily. If they are the same as the year the study is performed, dollar results have even more intuitive meaning in that they can be compared with what that amount of money will buy at that time. This concept parallels the original concept of using the project start as the base year for evaluating prospective investment alternatives under consideration that year.

Summary of Analysis of Net Present Value Adjustments

Evaluators and other users of the net present value (or net benefits) metrics resulting from cash flow-based benefit-cost studies need to recognize the effects of different constant dollar years and different base years on proper interpretation and use of these results. For purposes of presenting results of a single project case study, the traditional approach that uses the beginning of the project funding year as the base year may be adequate as long as all use the same constant dollar year and thus net present values reflect purchasing power equivalents. However, when results of different studies are presented collectively, the interpretation is fuzzy.

In instances in which multiple projects are analyzed in a single study or in which results of multiple studies are considered together to compose a minimum estimate of portfolio performance, adjustment to constant dollars and a common base year for all projects will most likely be necessary.

Adjustment to a common base year and constant dollar year after the study of an individual project is completed is relatively straightforward and may be a better solution than trying to impose a standard "fixed" base year and constant dollar year for all studies. Many practitioners are committed to the traditional concepts of base year as the "start of the project." The traditional approach provides a consistent starting point for observing the traditional metrics before considering what adjustments might be needed for comparability or aggregation with other studies.

Adjustments, particularly of the base year used in computing net present value, will require programmatic consideration of what basis makes most sense to the evaluation objective. Adjusting all study results to 1990, for example, would evaluate net benefits whenever they occurred back to the start of the ATP as if the pool of funds for them existed then and could have been invested in the interim. It does not recognize that most of the projects studied were funded out of later budgets. The cluster and portfolio analyses ATP has performed use the year the first project started as the base year. All other cash flows were discounted back to that year. This process is equivalent to computing the net present value for each project separately using that project's start as the base year and then discounting the resulting set of net present values back to the start of the first project.

Adjusting all net present value results forward to the time a collective assessment is being performed, as is done in Tables 7 and 8, reflects the assumption that the net present value reported as of the base year of each study is reinvested at the 7% discount rate until the time of the study. Equivalently, the assumption is that net cash flows generated in any year from any project are reinvested at 7% until the year the study is performed. That assumption may be a more useful than assuming that all funds for all projects were available at the beginning of ATP or the start of the first of several projects studied.

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Date created: July 11, 2006
Last updated: July 12, 2006

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