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 Figure A-2, which shows a $60 NPV when a discount factor of 10 percent is used, to Figure A-3, which adds a discount factor of 18 percent and yields a $0 NPV.

Year	Cash Flow	PV of $1 @ 10%	Discounted Cash Flow @	PV of $1 @ 18%	Discounted Cash Flow
0	$(500)	1.000	$(500)	1.000	$(500)
0–1	225	.952	214	.915	206
1–2	225	.861	194	.764	172
2–3	150	.779	1 17	.639	96
3–4	50	.705	35	.533	26
TOTAL	$ 150		$ 60 NPV		$ 0 NPV

Figure A-3: Arithmetic of determining DCF rate of return.

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.