Capital budgeting results

Selection Strategy

In both the internal rate of return and net present value methods, 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 consideration, 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 other 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.

Mutually Exclusive Alternatives |
IRR |
Net Present Value |

Bangkok | 15% | $300 |

Beijing | 12 | 200 |

Mexico City | 11 | 100 |

Cost of capital |
10 |
− |

Singapore | 9 | (100) |

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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 discussion 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 percent internal rate of return, the new funds are assumed to be reinvested at this high rate. The relationships are presented in Table 12-7.

**Table 12-7** The reinvestment assumption—internal rate of return ($10,000 investment)

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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 method, depicted in Table 12-8, makes the more conservative assumption that each inflow can be reinvested at the cost of capital or discount rate.

**Table 12-8** The reinvestment assumption—net present value ($10,000 investment)

The reinvestment 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 of an alternative 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. Here is the formula:

As can be seen in this equation, the MIRR is the discount rate that equates the future value of inflows with the value of the original investment. As an example, we will return to the cash flow stream from our NPV valuation of Investment B. Notice in the MIRR spreadsheet shown in Table 12-9 that for each of the cash inflows, we have calculated a future value in Column E. As an example, in line 6 we calculate the future value of the $1,500 inflow by assuming it is reinvested for four years at the 10 percent cost of capital. Specifically, $1,500 × 1.464 = $2,196.15, the value in cell E6. The sum of these future values ($18,383.15) in cell E11 represents the numerator in Formula 12-1.

Since we now know both the future value of the cash inflows and the present value of the outflows (the investment), we can use Excel’s **RATE** function to find the MIRR. Being careful to enter a zero for the **pmt** argument in the **RATE** function, we find that the MIRR is 12.95 percent.

Excel also offers an **MIRR** function that produces the same result, shown at the bottom of Table 12-9. The list of value arguments in the **MIRR** function are the same as those used in Excel’s **IRR** function, but a finance rate and reinvestment rate must be entered also. In most instances, including our example, these rates are the same.

Recall that the conventional internal rate of return for Investment B was 14.33 percent. The modified internal rate of return, using the more realistic assumption of reinvestment at the cost of capital, gives a more conservative, and more theoretically correct, answer. For that reason you should be familiar with it. However, both NPV and IRR are used more often by financial analysts than is the MIRR. Therefore, we will end our discussion of MIRR here and continue the analyses in this chapter using IRR where an internal return measure is needed. The MIRR indicates that when you have an IRR higher than the cost of capital, the MIRR will be smaller than the IRR. In the case of Investment A, the difference between the 11.17 percent IRR and the 10 percent cost of capital is small, and while the MIRR would fall below the cost of capital, it would not decline as much as Investment B.

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**Table 12-9** Calculating MIRR for Investment B

Capital Rationing

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At times management may place an artificial constraint on the amount of funds that can be invested in a given period. This is known as **capital rationing**. The executive planning committee may emerge from a lengthy capital budgeting session to announce that only $5 million may be spent on new capital projects this year. Although $5 million may represent a large sum, it is still an artificially determined constraint and not the product of marginal analysis, in which the return for each proposal is related to the cost of capital for the firm, and projects with positive net present values are accepted.

A firm may adopt a posture of capital rationing because it is fearful of too much growth or hesitant to use external sources of financing (perhaps there is a fear of debt). In a strictly economic sense, capital rationing hinders a firm from achieving maximum profitability. With capital rationing, as indicated in Table 12-10, acceptable projects must be ranked, and only those with the highest positive net present value are accepted.

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