BUS601: Financial Management

The time-adjusted rate of return, also called the internal rate of return, equates the present value of expected after-tax net cash inflows from an investment with the cost of the investment. It does this by finding the rate at which the net present value of the project is zero. If the time-adjusted rate of return equals or exceeds the cost of capital or target rate of return, a firm should consider the investment further. If the proposal's time-adjusted rate of return is less than the minimum rate, the firm should reject the proposal. Ignoring other considerations, the higher the time-adjusted rate of return, the more desirable the project.
Calculators and computer software with time-adjusted rate of return functions are readily available. Present value tables also can approximate the time-adjusted rate of return. To illustrate, assume Young Company is considering a USD 90,000 investment expected to last 25 years with no salvage value. The investment yields a USD 15,000 annual after-tax net cash inflow. This USD 15,000 is referred to as an annuity, which is a series of equal cash inflows.
The first step in computing the rate of return is to determine the payback period. In this case, the payback period is six years (USD 90,000/USD 15,000). The second step is to examine Table A.4 in the Appendix (present value of an annuity) to find the present value factor that is nearest in amount to the payback period of 6. Since the investment is expected to yield returns for 25 years, look at that row in the table. In that row, the factor nearest to 6 is 5 92745. which appears under the 16.5 percent interest column. The third step is to multiply the annual return of USD 15,000 by the 5-92745 factor; the result is USD 88,912, which is just below the USD 90,000 cost of the project. Thus, the actual rate of return is slightly less than 16.5 percent. The rate of return is less than 16.5 percent but more than 16 percent because as interest rates increase, present values decrease because less investment is needed to generate the same income.

A broader perspective:
Caterpillar, Inc.

The preceding example involves uniform net cash inflows from year to year. But what happens when net cash inflows are not uniform? In such instances, a trial and error procedure is necessary if present value tables are used. For example, assume that Young Company is considering a USD 200,000 project that will last four years and yield the following returns:

The average annual cash inflow is USD 290,000/4 = USD 72,500. Based on this average net cash inflow, the payback period is USD 200,000/USD 72,500 = 2.76 years. Looking in the four-year row of Table A.4 in the Appendix, we find that the factor 2.77048 is nearest to the payback period of 2.76. In this case, however, cash flows are not uniform. The largest returns occur in the later years of the asset's life. Since the early returns have the largest present value, the rate of return is likely to be less than the 16.5 percent rate that corresponds to the present value factor 2.77048. If the returns had been greater during the earlier years of the asset's life, the correct rate of return would have been higher than 16.5 percent. To find the specific discount rate that yields a present value closest to the initial outlay of USD 200,000, we try out several interest rates less than 16 percent. The rate of return is found by trial and error. The following computation reveals the rate to be slightly higher than 12 percent:

Since the cost of capital is not a precise percentage, some financial theorists argue that the time-adjusted rate of return method is preferable to the net present value method. Under the time-adjusted rate of return method, the cost of capital is used only as a cutoff point in deciding which projects are acceptable and should be given more consideration.

No matter which time value of money concept is considered better, these methods are both theoretically superior to the payback period and the unadjusted rate of return methods. However, the time value of money methods are more difficult to compute unless you use a business calculator or a microcomputer spreadsheet program. In reality, no single method should be used by itself to make capital-budgeting decisions. Managers should consider all aspects of the investment, including such nonquantitative factors as employee morale (layoff of workers due to higher efficiency of a new machine) and company flexibility (versatility of production of one machine over another). The company commits itself to its investment in a capital project for a long time and should use the best selection techniques and judgment available.

Too often, in capital project selection decisions, investments in working capital are ignored. The next section shows how to incorporate this factor into the analysis.

An accounting perspective:

Use of technology