Question

What is the problem with using the Internal Rate of Return capital budgeting method when deciding between two mutually exclusive projects? Discuss and illustrate your explanation with a graph.

Answer 1

The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the “discounted cash flow rate of return” (DCFROR) or the rate of return (ROR). In the context of savings and loans the IRR is also called the “effective interest rate. ” The term “internal” refers to the fact that its calculation does not incorporate environmental factors (e.g., the interest rate or inflation).
The IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.
IRR figures are commonly used to evaluate the desirability of investments or projects. The higher a project’s IRR, the more desirable it is to undertake the project. Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first. A firm should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital.However, investment may be limited by availability of funds to the firm and/or by the firm’s capacity or ability to manage numerous projects.

Net present value (NPV) and internal rate of return (IRR) are two of the most widely used investment analysis and capital budgeting techniques. They are similar in the sense that both are discounted cash flow models i.e. they incorporate the time value of money.However, NPV is an absolute measure i.e. it is the dollar amount of value added or lost by undertaking a project. IRR, on the other hand, is a relative measure i.e. it is the rate of return that a project offers over its lifespan.

Mutually exclusive projects are projects in which acceptance of one project excludes the others from consideration. In case of mutually-exclusive projects, an NPV and IRR conflict may arise in which one project has a higher NPV but the other has higher IRR. The conflict either arises due to relative size of the project or due to the different cash flow distribution of the projects.

Sometimes investors come across mutually exclusive projects, which means that if one is acceptable, then the other is not. Building a hotel or a commercial complex on a particular plot of land is an example of a mutually exclusive project. In such situations, knowing whether they are worth investing in is not enough. The challenge is to know which investment is the best. The IRR method will give a percentage interpretation value, but that is not enough. This is because IRR ignores the economies of scale.The IRR method ignores the actual dollar value of benefits.
For example, ​​​​​one should always prefer a project value of $1,000,000 with an 18% rate of return over a project value of $10,000 with a 50% rate of return. It can be clearly seen that the dollar benefit of the former project is $180,000, whereas that of latter project is only $5,000. There is no comparison as to which is more worthwhile.However, the IRR method will rank the latter project, with a much lower dollar benefit - first, simply because the IRR of 50% is higher than 18%.

When comparing two mutually exclusive projects, the NPV and IRR may provide conflicting results. It may be so that one project has higher NPV while the other has a higher IRR. This difference could occur because of the different cash flow patterns in the two projects.

For an example, there are two mutually exclusive projects A & B. Initial investment for both of them is $5000.
Project A cash flows are :- Year 1- $2000, Year 2- $2000, Year 3- $2000, Year 4- $2000, Year 5- $2000.
Project B has a cash inflow of $15000 in the 5th year.
NPV of Project A & Project B are $2581 & $4318 respectively. However, the IRR of Project A is 29% & that of Project B is 25%. We have assumed a discount rate of 10%. Hence, Project A has higher IRR, while Project B has higher NPV.

Here, the project with a higher NPV should be chosen because there is an inherent reinvestment assumption. The IRR inherently assumes that any cash flows can be reinvested at the internal rate of return. This assumption is problematic because there is no guarantee that equally profitable opportunities will be available as soon as cash flows occur. The risk of receiving cash flows and not having good enough opportunities for reinvestment is called reinvestment risk. NPV, on the other hand, does not suffer from such a problematic assumption because it assumes that reinvestment occurs at the cost of capital, which is conservative and realistic.

In our calculation, there is an assumption that the cash flows will be reinvested at the same discount rate at which they are discounted. In the NPV calculation, the implicit assumption for reinvestment rate is 10%. In IRR, the implicit reinvestment rate assumption is of 29% or 25%. The reinvestment rate of 29% or 25% in IRR is quite unrealistic compared to NPV. This makes the NPV results superior to the IRR results. In this example, project B should be chosen.

Hence, IRR, as an investment decision tool, should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in. IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR. IRR does not consider cost of capital, hence, it should not be used to compare projects of different duration.

When two mutually exclusive projects differ in size, or differences exist in the timing of their cash flows, their NPV profiles will cross when plotted on a graph. This point at which they cross is defined as the crossover rate, which happens because one project’s NPV is more sensitive to the discount rate caused by the differences in the timing of cash flows. When evaluating mutually exclusive projects with crossing NPV profiles and the cost of capital is less than the crossover rate, the NPV and IRR results will conflict, with respect to the decision in which project to accept or reject. Because the NPV method uses a reinvestment rate close to its current cost of capital, the reinvestment assumptions of the NPV method are more realistic than those associated with the IRR method. Hence, the project with higher NPV needs to be chosen.

In the graphical illustration of the above given example, the two NPVs of the projects A & B, have a crossover point at 8.9% discount rate. Discount rate is plotted on the X axis, NPV plotted on the Y axis in terms Since the crossover rate of 8.9% is closer to the previously considered discount rate or the cost of capital i.e. 10%, the results obtained from the NPV method of project appraisal of the two mutually exclusive projects A & B, are to be considered rather than their IRRs.