When a capital expenditure is proposed, the project must be evaluated and the economic consequences of the commitment of funds determined before referring it to a budget committee for review or to management for approval. How are the economic consequences described best? This is done in two steps:
First, set up the project in a standard economic model that can be used for all projects, no matter how dissimilar to each other they may be.
Benefits – costs = cash flow
To describe the formula in accounting terminology:
Benefits:
Projected cash revenue from sales and other sources
Costs:
Nonrecurring cash outlays for assets, plus recurring operating expenses
Cash flow:
Net income after taxes plus noncash charges for such items as depreciation
Thus, if the model were stated in a conventional accounting form, it would appear as:
Add:
Cash revenues projected (benefits)
Less:
Cash investment outlay and cash expenses (costs)
Total:
Cash flow
The "benefits less costs" model is usually developed within the framework of the company’s accounts and supported with prescribed supplementary schedules that show the basis of the projection.
Comparing Costs and Benefits
It should be apparent that in setting up an economic model, the conventional accrual accounting concept, net income after taxes, has been abandoned. The established criterion is cash flow—net income after tax plus noncash charges.
The second step is to adjust the cash flow into relevant financial terms. The cash flow projected for each year over the life of the proposal has to be translated into financial terms that are valid; that is, the annual dollar cash flows must be translated into a common dollar value in a base year. This concept must not be confused with attempts to adjust for changes in the purchasing power of the dollar.
The calculations assume no significant erosion in the purchasing power of the dollar. Should this occur, the time-adjusted common dollar concept may require adjustments for the diminished real value (purchasing power) of future dollar payments. The common dollar value concept used in capital budgeting adjusts for time value only. This is achieved through the development of the concept of discounting and present value that will be examined in the next section. An examination of how a simple two-step model is developed will illustrate the rationale of this approach.
In the first step, we set up the economic model: Benefits minus costs equals cash flow. To complete this model, we need to identify in detail all economic benefits and costs associated with the project. Benefits typically take the form of sales revenues and other income. Costs normally include nonrecurring outlays for fixed assets, investments in working capital, and recurring outlays for payrolls, materials, and expenses.
For each element of benefits and costs that the project involves, we forecast the amount of change for each year. How far ahead do we forecast? For as long as the expenditure decision will continue to have effects: that is, for as long as they generate costs and significant benefits. Forecasts are made for each year of the project’s life; we call the year of decision "year 0," the next year "year 1," and so on. When the decision’s effects extend so far into the future that estimates are very conjectural, the model stops forecasting at a planning horizon (ten to fifteen years), far enough in the future to establish clearly whether the basis for the decision is a correct one.
We apply a single economic concept in forecasting costs: opportunity cost. The opportunity cost of a resource (asset) is what the company loses from not using it in an alternative way or exchanging it for another asset. For example, if cash has earning power of 15 percent after taxes, we speak of the cash as having an opportunity cost of 15 percent. Whenever an asset is acquired for a cash payment, the opportunity cost is, of course, the cash given up to acquire it. It is harder to establish the opportunity cost of committing assets already owned or controlled. If owned land committed to a project would otherwise be sold, the opportunity cost is the aftertax proceeds from the sale. The opportunity cost of using productive equipment, transportation vehicles, or plant facilities is the incremental profit lost because these resources are unavailable for other purposes. If the alternative to using owned facilities is idleness, the opportunity cost is zero. Although opportunity costs are difficult to identify and measure, they must be considered if we are to describe the economic consequences of a decision as accurately as possible. An understanding of this concept of opportunity cost is probably the most critical to this economic analysis and is generally quite foreign to the manager.
At the end of the first step, we have an economic model for the project’s life showing forecast cash flows for each year. In the second step, we convert the results into financial terms that are meaningful for decision making. We must take into account the one measurable financial effect of an investment decision left out in step 1: time. Dollars shown in different years of the model cannot be compared since time makes them of dissimilar value. We clearly recognize that if we have an opportunity to invest funds and earn 15 percent a year and we have a choice of receiving $1,000 today or a year from now, we will take the $1,000 today, so that it can be invested and earn $150. On this basis, $1,000 available a year from now is worth less than $1,000 today. It is this adjustment for time that is required to make cash flows in different years comparable; that is, discounting.
This time value of funds available for investment is known as the opportunity cost of capital. This should not be confused with the cost of raising capital—debt or equity—or with the company’s average earnings rate. Like the opportunity cost of any resource, the opportunity cost of capital is what it will cost the company to use capital for an investment project in terms of what this capital could earn elsewhere.
The opportunity cost of capital is alternatively referred to as the minimum acceptable rate of interest, the marginal rate of interest, the minimum rate of return, the marginal rate of return, and the cost of capital. Whatever the term used, and they are used loosely and interchangeably, it reflects the rate the corporation decides it can be reasonably sure of getting by using the money in another way. It is developed through the joint efforts of management, which identifies relevant opportunities, and the controller, who translates management’s judgment into a marginal rate.
Another simple economic concept must be introduced: incremental cost, sometimes called differential cost or marginal cost. By definition, it is the change in cost (or revenue) that results from a decision to expand or contract an operation. It is the difference in total cost. In performing the capital budgeting analysis, we deal with incremental costs (revenues) only. Sunk or existing costs are not relevant to the evaluation and decision.
Determining Present Value
Discounting is a technique used to find the value today or "present value" of money paid or received in the future. This value is found using the following formula:
Future dollar amount × discount factor = present value
The discount factor depends on the opportunity cost of capital expressed as an interest rate and a time period. Present value of $1 at 10 percent illustrates how discount factors are usually displayed. The discount factors are grouped according to the annual interest rate, expressed as the present value of $1.00, and then listed according to the year the amount comes due. The table should be read this way: When a dollar earns 10 percent per year uniformly over time, a dollar received at the end of the second year is equivalent to (worth) about 86 cents today.
To adjust the model’s results for the time element, we discount both the positive and negative cash flow forecasts for each period at the company’s marginal rate of return to determine their present value. This discounting process makes the forecasts equivalent in time. We can now add the present values of these cash flow forecasts to derive the net present value (NPV). The NPV is a meaningful measure of the economic consequences of an investment decision since it measures all benefits and all costs, including the opportunity cost of capital.
When the NPV of a proposed investment is determined, we are ready to decide whether it should be accepted. This is done by comparing it to the economic consequences of doing nothing or of accepting an alternative. The general rule followed in comparing alternative projects is to choose the course of action that results in the highest NPV.
Arithmetic of determining net present value (NPV) illustrates the cash flow forecasts and time-value calculations for a typical proposal to invest in a new project when the alternative is to do nothing, that is, to maintain liquidity rather than invest. A discount rate of 10 percent is assumed as the company’s marginal rate.
The proposed project will cost $500 in year 0, and cash operating expenses thereafter will be $200 per year for four years. Assume the cash benefits will be positive but decline over the four years and total $1,450. The cash flow is negative in the year of investment but positive in the succeeding years, and there is a net positive cash flow over the life of the project of $150 before discounting. When the cash flow forecasts are made equivalent in time by multiplying each annual cash flow by the present value of the dollar for each period, the time-adjusted cash flow is determined, and the NPV is found to be $60. The proposed investment is better than doing nothing because all costs are covered, the 10 percent opportunity cost of the corporation’s funds is realized, and in addition, the project will yield an additional $60 return.
Arithmetic of determining net present value (NPV) indicates an NPV of $60. Depending on the cash flow and/or the discount rate, the NPV could be negative or zero. If the NPV were zero, the company would have projected earnings exactly equal to its marginal rate of 10 percent. If there were no alternative projects, and the only alternative were to do nothing, the project with the NPV of zero would be accepted because the company would earn its marginal rate of return. (As explained later, the NPV of zero would yield the discounted cash flow rate of return, that is, 10 percent.) If the NPV were negative because of an inadequate cash flow, assuming the same 10 percent marginal rate required by management, it would mean the project would earn less than 10 percent, and it would be rejected.
A number of evaluation methods are employed in capital budgeting; however, after critical examination of all methods, only the arithmetic developed in this simple model will be used to examine three methods used in evaluating capital budget proposals: (1) cash payback, (2) net present value, and (3) discounted cash flow rate of return (DCF-ROR)—sometimes referred to as the "internal rate of return."
Cash payback is commonly used by business managers evaluating investment opportunities, but it does not measure rate of return. It measures only the length of time it takes to recover the cash outlay for the investment. It indicates cash at risk. In our model there are costs of $500 committed in year 0. To determine payback, we merely add the unadjusted cash flow for each year and determine how many years it takes to get the outlay back. In the first two years $450 is recovered, and by the end of the third year $600 is recovered. By interpolation we find cash recovery to be approximately 2.3 years. It is obvious that the rational manager does not commit a large sum of money just to recover it. He expects a rate of return commensurate with the risks and his alternative use of his funds in alternative investments (opportunity cost). In our example, the calculation of payback reveals a relatively short exposure of funds and cash flow continuing beyond the payback period. It is interesting information in overall project evaluation, but it is not conclusive. Our model will automatically throw off payback as a by-product as we calculate the crucial time-adjusted NPV of the investment and DCF-ROR.
A version of cash payback is the cash bailout method. This approach takes into account not only the annual cash flow as shown in Figure A-2 but also the estimated liquidation value of the assets at the end of each year. If the liquidation value of a highly specialized project is zero, then cash payback and cash bailout are the same. But if it is assumed in our example that the liquidation value of the investment at the end of year 1 will be $275, the cash bailout would be one year (cash flow $225 plus liquidation value $275 = $500 original cash commitment).
We consider NPV as described a valid basis for determining the economic consequence of an investment decision. Many business economists use it as their sole criterion for the go-no-go decision for investment. We recognize this method as paramount throughout our analysis but prefer using it in conjunction with other measures rather than as the sole criterion.
Calculating Rate of Return
We are now ready to examine the concept of DCF-ROR. It is completely different from the return on investment (ROI) commonly used in business. The conventional ROI is computed for an accounting period, generally on the accrual book figure; investment is taken at original cost, although it is sometimes taken at half original cost; no adjustment is made for time value when looked at in the long run.
We are talking about a very different ROR on investment: The DCF-ROR is the interest rate that discounts a project’s net cash flow to zero present value. Let us expand Arithmetic of determining net present value (NPV)., which shows a $60 NPV when a discount factor of 10 percent is used, to Arithmetic of determining DCF rate of return, which adds a discount factor of 18 percent and yields a $0 NPV.
The DCF-ROR is 18 percent. By definition, the DCF-ROR is the rate of return on the project determined by finding the interest rate at which the sum of the stream of aftertax cash flows, discounted to present worth, equals the cost of the project. Or, stated another way, the ROR is the maximum constant rate of interest the project could pay on the investment and break even. How was the 18 percent determined? By trial and error.
Many analysts use the NPV method exclusively; some use the DCF-ROR; others use the two methods to complement each other. Using NPV, positive or negative dollar values are determined with the cost of capital as the benchmark. Excess dollar PV is evaluated and a judgment is made. The DCF-ROR approach ignores the cost of capital in the calculation and determines what the ROR is on the total cash flow. The result of this approach on our example is to convert the $60 NPV into a percentage. It works out to 8 percent on top of the 10 percent that had been calculated for the NPV. Many businesspeople prefer working with the single figure of 18 percent for evaluating a project against a known cost of capital, instead of describing a project as having an NPV of $60 over the cost of capital. The two methods complement each other, and under certain circumstances one may give a better picture than the other.
Let us reexamine this special DCF-ROR to see what distinguishes it from the conventional ROR. It is time-adjusted to base year 0, so that all dollars are on a common denominator basis; it is calculated absolutely on a cash flow basis; the investment is a definite time-adjusted value; the ROR is determined at a single average rate over the total life of the investment. Certain implications of this statement require explanation.
The DCF-ROR is calculated over the full life of the project, and the accountant’s yearly ROI cannot be used to test the success/failure of the new investment. If the planned life of a project is ten years, and if it can be segregated from other facets of the operation, the DCF-ROR has meaning only when the full economic life of the project is completed. However, in this case it is possible to monitor results on a year-to-year basis by examining the actual dollar cash flow and comparing it with the projected cash flow.
The one thing that disturbs business managers most with the DCF-ROR concept is the underlying mathematical assumption that all cash flows are reinvested immediately and constantly at the same rate as that which yields an NPV of 0. In our example in Figure A-3, 18 percent was used as the discount factor as a constant. Another case could just as easily have indicated a 35 percent ROR, with the implicit assumption that the cash flow was reinvested at 35 percent. But if the earning experience indicates a cost of capital of 10 percent, how can we reconcile the assumption that we can continue to earn 35 percent on the incremental flow?
Even though a company’s average earnings reflect a cost of capital of 10 percent, the demands on incremental new investment may well have to be 18 to 35 percent to compensate for investments that fail to realize projected earnings. Opportunities to invest at 18 percent or 35 percent are not inconsistent with the average earnings of 10 percent. However, if it is felt that a projected rate of return of 18 percent, in our example, is a once-in-a-lifetime windfall and no new opportunities can be found to exceed the average 10 percent rate, then we are in trouble with our DCF-ROR concept. The reinvestment rate will not stand up. In this situation we have to combine both NPV and ROR to explain the situation in this way: The 10 percent ROR of this project covers the opportunity cost of money and throws off an additional $60 cash flow. If other projects of the same magnitude can be found so that the total cash flow generated can be reinvested at the same rate, there would actually be an ROR on the project of 18 percent (the DCF-ROR). The lack of other good investment opportunities is a constraint on the full earning capacity of the project.
We have examined three methods of evaluating investment opportunities. Cash payback evaluates money at risk. Present value measures the ability to cover the opportunity cost of an investment on a time-adjusted basis of money and indicates by an NPV whether the project under consideration will yield a "profit" or a "loss." The DCF-ROR is an extension of the NPV concept and translates it into a single ROR that, when compared with the opportunity cost of capital, gives a valid basis for evaluation.
Since NPV and DCF-ROR concepts take into account the opportunity cost of capital through the discounting technique, it may be stated as a principle that all projects under consideration where this opportunity cost is covered should be accepted. This proposition is both theoretically and practically sound, but three factors need to be considered: How do you determine the minimum acceptable ROR (the opportunity cost of capital) to select the proper discounting factor? How can you assume no constraints on the supply of capital so that all worthwhile projects can be accepted? How do you take risk into account when examining indicated results? These questions are examined in the next three sections.
Using Cost-of-Capital Guidelines
How do you determine the minimum acceptable ROR (cost of capital) used in discounting? The cost of capital concept used here is not the same as the cost of borrowing. This is probably the most critical factor in the evaluation process. It is a unique and personal rate to each company. There is no guide to look to in other companies. Two companies looking at a potential investment, say an acquisition, may place two completely different values on it. To Company A, with a minimum required ROR of 10 percent, the investment could be attractive, while to Company B, with a required ROR of 25 percent, the investment would be totally unacceptable. The difference is centered in the cost of capital to each company, its opportunity ROR—the rate that can be expected on alternative investments having similar risk characteristics. An example of the arithmetic involved in reaching this conclusion can be seen when we modify Figure A-2 to include both a 10 percent and 25 percent discount factor and assume that both Companies A and B are the sole potential bidders for an investment with an asked price of $500 and a net cash flow of $150 (see Figure A-4).
The investment is very attractive to Company A but completely unacceptable to Company B—it would realize less than its objective of 25 percent. If Company A were in a position to know the cost of capital of Company B, it would know that Company B would not bid at all for this investment. Company A would know that it would be the sole bidder.
If a company has successfully earned 25 percent on the capital employed in it, an investment opportunity, to be attractive, would have to yield at least that rate. The 25 percent represents the cost of capital to that company, and an investment opportunity offering only 15 percent would be rejected. A second company with a 10 percent cost of capital would find the same 15 percent potential attractive and accept it. Thus the same 15 percent opportunity investment is attractive to one and unattractive to the other. Both companies analyzing the identical situation reach different logical conclusions.
Cost of capital is always considered to be the combined cost of equity capital and permanent debt. We evaluate economic success/failure of a project without regard to how it is financed. Yet we know that money available for investment is basically derived from two sources: debt, with its built-in tax saving so that its cost is half the market price for money (assuming a 50 percent tax rate), and equity, which has as its cost the opportunity cost of capital of the owners.
It is necessary at times to break down the combined cost of capital into its components of cost of debt capital and cost of equity capital to put it in terms understandable to the businessperson who commonly measures results in terms of return on equity. To illustrate this cost of capital concept, we will assume that a corporation is owned by a single individual whose investment objectives are clearly defined. The total capitalization of the company is $100, made up of $30 permanent debt capital and $70 owner’s equity capital. If preferred stock was outstanding at a fixed cost, it would be treated the same as debt. The aftertax interest rate of the debt money is 2.75 percent. The aftertax dollar return on the combined debt and equity capital of $100 under various operations would appear as shown in Figure A-5.
To restate these dollars as rates of return on the investment of $100, $30 debt, and $70 equity, the percentage return on capital would be as shown in Figure A-6.
If the company has been earning an average of $10 on the total investment of $100, and the cost of debt is $.825, the earning on owner’s equity is $9.175. Stated as a rate of return, the $10 earned on $100 is 10 percent return on the total investment (combined cost of capital), and because of the leverage built into the capital structure with long-term debt, the $9.175 earning on equity yields a return on equity of 13.11 percent (cost of equity capital). When there is a 30 percent debt structure and the average cost of debt is 2.75 percent after taxes, we can readily convert return on total investment into return on equity by reading our table. It is quite simple to create similar tables for each company and its debt/equity ratio (e.g., with a 50/50 ratio and debt cost of 2.75 percent, a 10 percent return on total investment yields a 17.45 percent return on equity capital). If there is the opportunity to invest the company funds in alternative situations or reinvest the funds in the business and continue to earn at least 10 percent on the combined debt/equity funds, we would describe this as the opportunity cost of capital. This is the critical rate used in discounting: The discount rate used to determine NPV and the benchmark for comparing DCS-ROR are based solely on the combined cost of capital. The ROR to the stockholders can be derived and compared with their opportunity cost, that is, the ability to invest their funds elsewhere and earn at least the same rate.
Evaluating Profit Projects
Evaluating components of aninvestment program for a company is complex at any time. There are many categories of investment: (1) revenue-producing projects, (2) supporting facilities projects, (3) supporting services projects, (4) cost-savings projects, and (5) investments required to comply with public authority that will yield no return. Each must be evaluated to determine its incremental consequence.
When a project is isolated from the rest of the operation, evaluation is relatively clear. But sometimes a planned major investment embraces several auxiliary projects which, evaluated by themselves, are not very meaningful. When this occurs, it is necessary to construct a master model that includes all of the projects. Some of the auxiliary projects may not come into being for several years after the main investment is made, and may or may not produce a new positive cash flow. The master model in simple form may take on the appearance shown in Figure A-7 if individual projects of the types (a), (b), and (c) above are assumed (the figures do not add up—only format is demonstrated).
If the three projects are interrelated, they should be projected as a single entity. In our example, (a) is assumed to be a major facility that to be successful needs (b) added in three years as supporting facilities; (b) would have no basis for existence if (a) were not created. Project (c) may possibly be identified as a new computer/information system that will produce only costs, but would not exist if (a) and (b) were not created. All costs and all benefits for all corollary investments need to be projected as far into the future as possible to get a true evaluation. Investment evaluations that are made of a project with all the certainty of a DCF percentage can be grossly misleading if the supporting investment of satellites is not taken into account. Actually, these are not separate investments. There is only one—Project abc. The evaluation has to be of the new single entity. The postaudit can be of only the conglomerate single entity (abc).
Projects of the cost-savings category are generally easiest to identify and evaluate. There are relatively clear-cut choices: Invest $40,000 today for new labor-saving machines that will reduce labor costs $12,000 per year; the machines will last eight years, and quality of performance will be unchanged. Determine the NPV and/or DCF-ROR and accept/reject. Such investment opportunities constantly arise, but it is almost impossible to project them as part of a master project. As a result, such investments are evaluated as isolated investment opportunities that may occur in three years, or eight years, or never. When they occur, if of major proportions, they affect the potential return on the total investment.
A cost-incurring project, such as spend $100,000 to prevent air pollution or be closed up, is one of the few black-and-white decisions a manager faces. Ideally it would be expensed. It may have to be capitalized and written off and in addition have annual related operating expenses. This nondiscretionary investment falls into the same general category as a support project. The cash flow is always negative and must be included as an integral part of the master investment. A large enough commitment may sharply reduce the original projection, and a revision may be necessary.
On the basis of the techniques for evaluating planned capital investment, it is now possible to move to the methods of selecting among projects. As noted previously, in theory, selecting among projects is easy. Invest in anything that, when discounted at the appropriate marginal rate, will yield a positive NPV. Practically, for many reasons, there are constraints on capital in the minds of most managers. Let us look at the project selection problems that are involved for projects under consideration in a particular risk category when there is a limit on capital.
We have selected the NPV method as the best approach to analyze proposed projects of varying lives. Comparing projects under the DCF-ROR method can be misleading because of the different life factor and the reinvestment factor inherent in each ROR. Excess NPV avoids this difficulty. When the various projects are converted into a profitability index, selection is further facilitated. The profitability index is the ratio of the NPV to investment. For example:
In selecting projects when a limit is imposed upon the amount available for investment, we look for the combination that will maximize combined NPV without exceeding the imposed limit. We know that we have reached this goal when we can no longer increase the combined NPV by substituting one project for another and still satisfy the constraint.
A way to achieve a satisfactory combination of projects is through trial and error. As a guide, we can use the profitability index (see Figure A-8). However, such ratios are not foolproof. This is illustrated where there are three possible projects requiring a total of $1,500 in initial outlays, but where $1,000 is the imposed limit.
The choice is between investment in A + C (cash outlay $1,000) or investment in B + C (cash outlay $900). Since A + C have a combined greater NPV than B + C ($1,500 vs. $1,200), A + C should be selected even though C’s ratio (1.25) is less than B’s ratio (1.40). Such differences are common. The profitability index must always be used judiciously. When there are numerous projects to choose among, the combining process becomes more difficult.