The use of the internal rate of return in decision-making can be rather subtle and may even be misleading. At the simplest level, one often hears or reads statements (decision rules) such as: “For independent projects, accept the project if the IRR is above the required rate of return”. The logic behind such a statement is that the IRR is the rate that sets the discounted cash flow to zero, so that if the IRR is above this, then the project is a good one.
Unfortunately, this decision rule is correct only for certain cash flow profiles; for other profiles it would be incorrect and could lead to exactly the wrong decision.
The rule makes sense only if the initial cash flow(s) are negative and all other cash flows are positive, with only the one change of sign i.e. from negative to positive (zero cash flows are not considered a change of sign). For example, if you can invest $100 this year and earn $200 next year (cash profile -100, 200), the IRR is 100%, and this would in principle be a sensible and profitable investment. On the other hand, if you could earn $100 this year but have to pay back $200 next year (cash profile 100, -200), then the IRR is still 100%, but the decision to proceed would in principle not make sense or be unprofitable. Note that the IRR is the same even if the cash flow profile is reversed in sign (since the discount rate to create a zero sum for the discounted cash flows is the same for the original and for the reversed-sign cash flow profile). Thus, for the profile in which income is earned first, the decision rule would have to be reversed “accept the project if the IRR is below the cost of capital”.
The rule can also be misleading or inapplicable if the cash flow profiles change sign and if one relies on the default settings for the Excel IRR function. For example, if one could invest $100 this year to earn $120 next year (cash profile -100, 120), then the IRR is 20%. Of course, if one could delay some of the initial investment and incur the cost in year 3, then the IRR would increase. So, a cash profile of -70, 120, -30 would have an IRR of 41%. If a delay of even more investments is made so that the cash flow profile is -30, 120, -70, then the Excel IRR function will be default show a value of -29%. In other words, it appears that the ability to delay the investment (but not the return) has reduced IRR, and potentially made the project unprofitable. In fact, due to the two change of sign, there are two values for the IRR (in each case). For the latter case, the IRR function has “jumped” to a second solution (-29%) instead of showing the first solution (229%). This is because the function uses an iterative process with a default guess of 10% to initiate the iteration. However, even if one is aware of the two solutions, one no longer has a decision rule that is easy to apply. In fact, in this case, by doing an NPV analysis of the cash flows at different discount rates, one can derive the rule to apply for this particular set of cash flows: “do the project if the cost of capital is above -29% and the return requirements are below 229%”. But such rules are not clear, not least as the reverse would be true if cash flow signs were reversed.
An analysis of the properties of the IRR and its appropriate use in decision support is covered within Module A of our Certificate in Financial Modelling and Data Analysis. Participants in this course also have free access to our in-depth library of proprietary materials (such as our 80-page guide to fully understanding IRR), which can be referred to on an optional basis for those wishing to really understand the topic in depth.