Foundations of Financial Management: An Analysis (part 47)

“Develop success from failures. Discouragement and failure are two of the surest stepping stones to success.” 

– Dale Carnegie

The Capital Budgeting Decision (part C)

by

Charles Lamson

Selection Strategy

In both the internal rate of return and net present value methods covered in last post, the profitability must equal or exceed the cost of capital for the project to be potentially acceptable. However, other distinctions are necessary---namely, whether the projects are mutually exclusive or not. If investments are mutually exclusive, the selection of one alternative will preclude the selection of any other alternative. Assume we are going to build a specialized assembly plant, and four major international cities are under construction, only one of which will be picked. In this situation we select the alternative with the highest acceptable yield or the highest net present value and disregard all others. Even if certain locations provide a marginal return in excess of the cost of capital, assumed to be 10 percent, they will be rejected. In the table below, the possible alternatives are presented.

Among the mutually exclusive alternatives, only Bangkok would be selected. If the alternatives were not mutually exclusive (for example, much-needed multiple retail outlets), we would accept all of the alternatives that provide a return in excess of our cost of capital, and only Singapore would be rejected.

Applying this logic to Investments A and B in the prior post and assuming a cost of capital of 10 percent, only Investment B would be accepted if the alternatives were mutually exclusive, while both would clearly qualify if they were not mutually exclusive.

The discussion to this point has assumed the internal rate of return and net present value methods will call for the same decision. Although this is generally true, there are exceptions. Two rules may be stated:

1. Both methods will accept or reject the same investments based on minimum return or cost of capital criteria. If an investment has a positive net present value, it will also have an internal rate of return in excess of the cost of capital.

2.  In certain limited cases, however, the two methods may give different answers in selecting the best investment from a range of acceptable alternatives.

Reinvestment Assumption

It is only under this second state of events that a preference for one method over the other must be established. A prime characteristic of the internal rate of return is the reinvestment assumption that all inflows can be reinvested at the yield from a given investment. For example, in the case of the aforementioned Investment A yielding 11.17 percent, the assumption is made that the dollar amounts coming in each year can be reinvested at that rate. For Investment B, with a 14.33% internal rate of return, the new funds are assumed to be reinvested at this high rate. The relationships are presented in Table 5.

Table 5 The reinvestment assumption---internal rate of return ($10,000) investment)

For Investments with a very high IRR, it may be unrealistic to assume that reinvestment can occur at an equally high rate. The net present value, depicted in Table 6, makes the more conservative assumption that each inflow can be reinvested at the cost of capital or discount rate. 

Table 6 The reinvestment assumption---net present value ($10,000 investment)

The reinvestment of assumption under the net present value method allows for a certain consistency. Inflows from each project are assumed to have the same (though conservative) investment opportunity. Although this may not be an accurate picture for all firms, net present value is generally the preferred method.

Modified Internal Rate of Return You should also be aware that there is a recently developed methodology that combines the reinvestment assumption of the net present value method (cost of capital) with the internal rate of return. This process is termed the modified internal rate of return (MIRR). The analyst searches for the discount rate that will equate the future value of the inflows, each growing at the cost of capital, with the investment.

In terms of a formula, we show:

The terminal value of the inflows is equal to the sum of the future value of each inflow reinvested at the cost of capital. MIRR is the modified internal rate of return discount rate that equates the terminal (final) value of the inflows with the investment. As an example, assume $10,000 will produce the following inflows for the next three years:

The cost of capital is 10%.

First, determine the terminal value of the inflows at a growth rate equal to the cost of capital. The assumption is that the inflows will come at the end of each period.

To determine the modified internal rate of return, we calculate the yield on the investment. The formula to help determine yield is Formula 2. PV is the investment value and FV is the terminal value of the inflows.

We go to Table 2 from last post for three periods and a tabular value of .641. We see the yield or modified internal rate of return is 16 percent. Had we computed the conventional internal rate of return used throughout these posts dealing with the capital budgeting decision, the answer would have been approximately 21 percent, which is based on reinvestment at the internal rate of return.

The modified internal rate of return, using the more realistic assumption of reinvestment at the cost of capital, gives a more conservative, perhaps better, answer. For that reason, you should be familiar with it. However and the balance of these posts covering the capital budgeting decision, when the internal rate of return is called for, we will use the traditional internal rate of return rather than the modified internal rate of return because of the former's wider usage. 

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 358-361*

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