Executive Summary

Net present value (NPV) and internal rate of return (IRR) are two very practical discounted cash flow (DCF) calculations used for making capital budgeting decisions.

NPV and IRR lead to the same decisions with investments that are independent.

With mutually exclusive investments, the NPV method is easier to use and more reliable.
Introduction
To this point neither of the two discounted cash flow procedures for evaluating an investment is obviously incorrect. In many situations, the internal rate of return (IRR) procedure will lead to the same decision as the net present value (NPV) procedure, but there are also times when the IRR may lead to different decisions from those obtained by using the net present value procedure. When the two methods lead to different decisions, the net present value method tends to give better decisions.
It is sometimes possible to use the IRR method in such a way that it gives the same results as the NPV method. For this to occur, it is necessary that the rate of discount at which it is appropriate to discount future cash proceeds be the same for all future years. If the appropriate rate of interest varies from year to year, then the two procedures may not give identical answers.
It is easy to use the NPV method correctly. It is much more difficult to use the IRR method correctly.
Accept or Reject Decisions
Frequently, the investment decision to be made is whether to accept or reject a project where the cash flows of the project do not affect the cash flows of other projects. We speak of this type of investment as being an independent investment. With the IRR procedure, the recommendation with conventional cash flows is to accept an independent investment if its IRR is greater than some minimum acceptable rate of discount. If the cash flow corresponding to the investment consists of one or more periods of cash outlays followed only by periods of cash proceeds, this method will give the same accept or reject decisions as the NPV method, using the same discount rate. Because most independent investments have cash flow patterns that meet the specifications described, it is fair to say that in practice, the IRR and NPV methods tend to give the same accept or reject recommendations for independent investments.
Mutually Exclusive Investment
If undertaking any one of a set of investments will change the profitability of the other investments, the investments are substitutes. An extreme case of substitution exists if undertaking one of the investments completely eliminates the expected proceeds of the other investments. Such investments are said to be mutually exclusive.
Frequently, a company will have two or more investments, any one of which would be acceptable, but because the investments are mutually exclusive, only one can be accepted. Mutually exclusive investment alternatives are common in industry. The situation frequently occurs in connection with the engineering design of a new installation. In the process of designing such an installation, the engineers are typically faced at a great many points with alternatives that are mutually exclusive. Thus, a measure of investment worth that does not lead to correct mutually exclusive choices will be seriously deficient.
Incremental Benefits: The Scale Problem
The IRR method’s recommendations for mutually exclusive investments are less reliable than are those that result from the application of the NPV method because the former fail to consider the size of the investment. Let us assume that we must choose one of the following investments for a company whose discount rate is 10%: Investment A requires an outlay of $10,000 this year and has cash proceeds of $12,000 next year; investment B requires an outlay of $15,000 this year and has cash proceeds of $17,700 next year. The IRR of A is 20%, and that of B is 18%.
A quick answer would be that A is more desirable, based on the hypothesis that the higher the IRR, the better the investment. When only the IRR of the investment is considered, something significant is left out¾and that is the size of the investment. The important difference between investments B and A is that B requires an additional outlay of $5,000 and provides additional cash proceeds of $5,700. Table 1 shows that the IRR of the incremental investment is 14%, which is clearly worthwhile for a company that can obtain additional funds at 10%. The $5,000 saved by investing in A can earn $5,500 (a 10% return). This is inferior to the $5,700 earned by investing an additional $5,000 in B.
Cash flows  
Investment  0  1  IRR (%) 
A  −$10,000  $12,000  20 
B  −15,000  17,700  18 
Incremental (B−A)  −$5,000  +$5,000  14 
Figure 1 shows both investments. It can be seen that investment B is more desirable (has a higher present value) as long as the discount rate is less than 14%.
We can identify the difficulty just described as the scale or size problem that arises when the IRR method is used to evaluate mutually exclusive investments. Because the IRR is a percentage, the process of computation eliminates size; yet, size of the investment is important.
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