A return-based alternative to IRR evaluations.

CAPITAL

A dilemma often faced by healthcare financial managers is whether to describe a potential investment project to organizational decision-makers in terms of the projects' internal rates of return (IRR) or to use the net present value (NPV) method. The IRR represents an intuitively

appealing method of measuring investment value, but a number of conceptual and methodological problems associated with IRR measurement would seem to argue the use of the NPV method. Unfortunately, while the NPV measure is theoretically valid, it lacks the intuitive appeal of the IRR in communicating the value of investment alternatives. This article details an alternative method of measuring return that incorporates all the intuitive appeal of the conventional IRR, but few of the shortcoming associated with that measure.

In the November 1986 issue of Healthcare Financial Management, John J. Carroll and Gerald D. Newbould describe the quandary healthcare financial managers often encounter with respect to capital budgeting decisions. Is it better to present investment projects to administrative decision-makers using the easily understood internal rate of return (IRR) measure, and risk an inaccurate assessment of the projects under consideration, or should the investment proposals be presented in terms of the more trustworthy net present value (NPV) measure, and risk that the significance of the evaluation will be lost on many decision-makers?

Fortunately, neither course of action is necessary. The conundrum described by Carroll and Newbould is easily resolved by turning to a third measure of project evaluation known as the marginal return on invested capital (MRIC).

The MRIC method is a "modified" internal rate of return measurement, and alters the traditional calculation methodology used to produce the IRR.(a) Using the MRIC measure avoids the "multiple rates of return" problem and eliminates the conflict in ranking mutually exclusive projects that many analysts associate with return-based measures of project evaluation. Moreover, the MRIC calculation easily can accommodate increases and decreases in capital costs over time, allowing different inflation expectations and changing risk preferences to be incorporated within a simple analytical framework. The marginal return on invested capital is mathematically defined as:

|Mathematical Expression Omitted~

* CCFt = The capital cash flow required by the project in period t. Capital funds represent the amount of new capital external to the project that the organizational sponsor must contribute to finance the project.

* OCFt = The operating cash flow generated by the project in period t. Operating funds represent excess cash flow generated by the project that is available for investment in other projects maintained by the sponsor.

* k = The opportunity cost of capital used to: 1) discount capital funds to the project's initial period (i.e., t = 0), and 2) compound operating cash flows forward to the horizon date specified by the analyst (i.e., t = n). The MRIC framework requires k be set equal to the organizational sponsor's marginal cost of capital (MCC). This ensures that the discounted and compounded cash flows maintain the same level of risk as the original cash flows, a property known as "risk equivalence".

* n = The analyst's horizon period, represented in the MRIC framework as a time period greater than or equal to the point at which the longest project under consideration generates or consumes its final cash flow.

* MRIC = The marginal return on invested capital.

At first glance, the equation may appear to be a formidable barrier to the MRIC. By breaking the procedure down into its component parts, however, it is really quite easy to apply this method. In general, the analyst using the MRIC does nothing more than:

* Separate the project's periodic cash flows into capital flows (i.e., those required to fund the project) and operating flows (i.e., those generated by the project),

* Identify the horizon period of the project, which represents a future time period greater than or equal to the point at which the longest project under consideration generates or consumes its final cash flow,

* Discount capital flows to the origin at the project sponsor's cost of capital, and compound operating flows to the horizon period (also called the terminal period) at the sponsor's cost of capital,

* Total the discounted value of all capital flows, and total the compounded value of all operating flows, and

* Determine the rate of return that equates the discounted and totaled capital flows in period zero with the compounded and totaled operating flows in the terminal period.

Exhibit 1: Project A annual net cash flows

                                         Year
                            0         1         2         3

Cash inflow                ---      $100      $100      $100
Cash outflow             ($100)     (50)        0         0
Net cash flow            ($100)     $50       $100      $100

A simple example illustrates this procedure. Consider the capital project shown in Exhibit 1. Notice that this is a three-year project, and the project requires an external capital contribution of $100 in Year 0 and $50 in Year 1. Accordingly, these two cash outflows represent the project's capital flows, while the $100 cash inflows in Years 1 through 3 represent the project's operating cash flows. Finally, assume that the project sponsor's risk-adjusted capital cost is 10 percent annually.

Given this information, Exhibit 2 details each step in the calculation of the MRIC. First, the project's capital flows and operating flows are identified. Second, the horizon period is determined (set equal to Year 3 in this example). Third, all capital flows to the project's origin are discounted at the 10 percent cost of capital, and all operating flows are compounded forward in time at the 10 percent cost of capital to the project's horizon period. Fourth, all discounted capital flows are totaled, and then all compounded operating flows are totaled. Finally, the MRIC is determined as that rate of return that equates $145 (the sum of the discounted capital flows in Year 0) with $331 (the sum of the compounded operating flows in Year 3, the project's horizon period). In this particular example, the MRIC is 31.7 percent. In contrast to the traditional IRR, the MRIC calculation method can be performed using nothing more that a hand-held calculator with an exponential key. By breaking the problem down into its component steps, the methodology requires no more advanced financial knowledge than a basic understanding of the time value of money. Given this simplicity, it is very easy to program each step of the MRIC procedure within an electronic spreadsheet to accelerate the calculation of the MRIC for projects extending over many years. Dealing with multiple rates of return

As Carroll and Newbould noted, the conventional IRR measure suffers from a number of conceptual and computational problems. In contrast, the MRIC procedure contains few of these limitations. The first problem noted by Carroll and Newbould is that real-world projects often produce multiple IRR solutions, which in turn leads to difficulties in interpreting project returns and, in some cases, erroneous investment decisions.

The multiple IRR problem frequently occurs when negative net cash flows occur in more than one period of a project's life. This often results when significant periodic maintenance and/or upgrade expenditures are required during the life of the project, or when a major expenditure is necessary to terminate the project. As an illustration, consider the cash flows of the project in Exhibit 3. These particular cash flows were used by Carroll and Newbould to demonstrate how the conventional IRR measure can yield multiple rates of return. This cash flow pattern produces one IRR of 17.56 percent, and a second IRR of 9.62 percent. Should a healthcare agency with a 10 percent marginal cost of capital accept the project? The conventional IRR measure offers an ambiguous answer to this question. The MRIC procedure, however, provides a clear, definitive solution. Exhibit 4 details each of the steps necessary to obtain the project's marginal return on invested capital, where the net cash outflows in Years 0, 4, and 5 represent capital flows and the net cash inflows in Years 1, 2, and 3 represent operating flows. Because the project's MRIC (10.02 percent) is slightly greater that the sponsor's cost of capital (10 percent), the project should be accepted.

Dealing with mutually exclusive projects

A second problem with the conventional IRR measure deals with the ranking of mutually exclusive projects, where acceptance of a given project from a set of many projects means rejection of all remaining projects in the set. As Carroll and Newbould point out, this ranking problem can occur if individual projects in the set of investment proposals under consideration possess vastly different lives, show significant timing differences in the receipt and/or expenditure of cash, or are markedly different in size, as measured by the magnitude of cash inflows and outflows associated with each project.

Consider the set of the two projects shown in Exhibit 5. Both of these projects require the same initial cash outlay, but Project Alpha extends for only one year, while Project Beta has a four-year life. At a 10 percent cost of capital, the NPV evaluation method suggests that Project Beta should be selected, while the conventional IRR indicates that Project Alpha is preferred.

Exhibit 3: Project B annual net cash flows

                                          Year
                        0       1       2       3       4       5

Net cash flow        ($524)   $493    $316    $133    ($47)  ($407)
Exhibit 5: Project Alpha and Beta annual net cash flows

                                     Year                      NPV
                     0        1       2       3       4         10%      IRR

Project Alpha     ($300)    $360     $0      $0      $0       $27.27     20%
Project Beta      (300)       0       0       0    524.60      58.31     15%

At this juncture, the healthcare financial manager faces a classic capital budgeting dilemma: Is it better to present these investment alternatives in terms of their respective NPVs, and simply ignore their rates of return? Or should the IRR for each project be presented, with the knowledge that this information most certainly provides a faulty ranking of the projects?

This choice can be avoided completely by calculating the MRIC. The MRIC procedure consistently provides rates of return that consistently rank projects in the same order as the NPV, and offers the intuitive appeal of a return-based index that specifies each project's investment value. Consider the MRIC evaluation of Projects Alpha and Beta shown in Exhibit 6, and recall that the NPV evaluation favored Project Beta. Notice that Project Alpha's MRIC is only 12.4 percent, while Project Beta's MRIC is 15 percent.

The MRIC index suggests that Project Beta is the appropriate choice, in conformity with the NPV ranking of these two projects. Alternation of the investment horizon used to evaluate Projects Alpha and Beta can affect the value of the MRIC obtained for each project, however, it will never affect the relative ranking of these mutually exclusive projects. The MRIC of Project Beta will always exceed that of Project Alpha, regardless of the horizon period chosen by the analyst.

Another conflict that can occur between NPV and conventional IRR project rankings arises from differences in the timing of cash flows. For example, consider Projects Slow and Fast, whose annual net cash flows are shown in Exhibit 7. Project Fast has its most substantial cash inflows occurring in the early years of the project, while the largest cash flows for Project Slow occur in the final two years of its life. As a result of this cash flow timing disparity, the conventional IRR calculation ranks these projects in opposite order from that of the NPV.

Once again, this apparent conflict can be resolved by the MRIC index. Exhibit 8 provides the calculation of the MRIC for Projects Fast and Slow, where the project sponsor's cost of capital is again taken as 10 percent. Project Slow's MRIC is 23.7 percent, and Project Fast's MRIC is 21.7 percent. The MRIC procedure confirms the superiority of Project Slow, which is consistent with the NPV ranking of these projects shown above.

A final difficulty arising from the need to rank projects--the problem of disparity in project sizes--is more troublesome for all return-based measures, including the conventional IRR and MRIC procedures. This problem occurs whenever competing projects exhibit substantial differences scale, such as Projects Small and Large shown in Exhibit 9. In this case, no return-based measure can provide an index of project ranking consistent with the NPV. This occurs because all return-based procedures make a relative comparison between a given project's capital funds and operating cash flows.

Since the relative distance between $100 and $1,000 for Project Small is much larger than the relative distance between $100,000 and $200,000 for Project Large (i.e., $100 x 10 = $1,000, while $100,000 x 2 = $200,000), Project Small yields a significantly greater IRR value. In most cases, analysts recommend the use of an incremental IRR procedure to accommodate this problem.(b) The incremental IRR, however, requires paired project comparisons to provide a return-based ranking index consistent with the NPV. Unfortunately, evaluating paired comparisons within a set of n competing projects requires |n X (n - 1)/2~ separate incremental IRR calculations, substantially increasing the complexity of the analysis. In this instance, the NPV technique still maintains an advantage over the set of return-based measures of project evaluation.

Exhibit 7: projects Slow and Fast annual net cash flows

                                     Year                     NPV
                   0       1       2      3      4      5      10%      IRR

Project Slow    ($400)    $60    $125   $200   $260   $375    $319      30.3%
Project Fast     (400)    300     250    125     70     70     265      43.6%

Changing capital costs

Carroll and Newbould observed one final problem with the conventional IRR calculation: It forces decision-makers to hold constant the cost of capital over time. In cases where inflation expectations and/or investor risk preferences vary over the life of investment projects, and these changes can accurately be forecast, the conventional IRR measure constrains project evaluation to a single number. Carroll and Newbould suggested that this limitation only can be resolved by abandoning the IRR evaluation in favor of the NPV framework. Once again, however, the MRIC provides a return-based index of project value that easily accommodates changing capital costs over time. Consider Project Change shown in Exhibit 10. Notice that the annual capital cost faced by the project's sponsor changes in each year of the project's life. Incorporating these annual capital costs within the MRIC framework simply requires adjusting the annual interest rates used to discount capital flows to the project's origin, and compound operating flows forward to the project's horizon period. These capital cost adjustments are incorporated in the determination of the project's MRIC, shown in Exhibit 11.

In this case, the project's MRIC is 13.6 percent, and the project sponsor's average cost of capital over the three-year life of the project is:

|cube root of |(1.09) X (1.10) X (1.11)~~ - 1 = 10%

Since the project's MRIC exceeds the sponsor's average capital cost over the three-year life of the project, the analyst would recommend acceptance of Project Change.

Conclusion

The conventional IRR index of capital project returns contains many well-known shortcomings that render it unsuitable for many real-world investment analysis applications. In cases where the IRR produces an invalid measure of project returns, many experts, including Carroll and Newbould, recommend that a return-based evaluation of project value be replaced with an NPV-based index of project value. While the NPV measure is more robust and theoretically satisfying, it lacks the intuitive appeal of a return-based measure in communicating investment value to organizational decision-makers.

As this article has described, use of an alternative return-based measure, the MRIC, can overcome most of the shortcomings associated with the traditional IRR measure. The MRIC index is quite simple to use, and it provides an accurate return-based index of capital project value in almost all capital budgeting circumstances.

Exhibit 9: Projects Small and Large annual net cash flows

                                   Year            NPV
                              0            1        10%         IRR

Project Small              ($100)       $1,000      $809        900%
Project Large            (100,000)     200,000     81,818       100%
Exhibit 10: Project Change annual net cash flows and capital costs

                                            Year
                           0          1             2          3

Net cash flow          ($5,000)    $2,200        $2,200     $2,200
Cost of capital            9%        10%           11%        12%

a. A technical presentation of the MRIC framework is made by W.R. McDaniel, D.E. McCarty, and K.A. Jessell in "Discounted Cash Flow with Explicit Reinvestment Rates: Tutorial and Extension," The Financial Review, August 1988, pp. 369-385. b. The incremental IRR procedure is described by R.A. Brealey and S.C. Myers in Principles of Corporate Finance, 4th rev. ed. (New York: McGraw Hill, 1991) William F. Kennedy, PhD, is an associate professor of finance at the University of North Carolina, Belk College of Business Administration, Department of Finance and Business Law, Charlotte, North Carolina.

D. Anthony Plath, PhD, is an associate professor at the University of North Carolina, Belk College of Business Administration, Department of Finance and Business Law, Charlotte, North Carolina.