# IRR (Internal Rate of Return) Rule and Mutually Exclusive Investments : TIMING of CASH FLOWS issue

One of the problems with using IRR for making decision to select which project or investment among two mutually exclusive projects has a better financial feasibility is faced when two projects have different cash flow patterns, or referred to as the cash flow timing issue. This timing issue will also give rise to the conflicting results of NPV and IRR, which might lead potentially to the ranking problem.

Example 1

In the very extreme example, let’s say we have two mutually exclusive Project A (short-term) and Project B (long-term) with the timing of the cash flows displayed below.

Both projects have the SAME IRR, that is 50%, however, NPV of both projects have an extreme different gulf, which long-term project have 9.3x higher NPV compared to short-term project, under the assumption of 10% discount rate.

If we look carefully long-term project, then we see that that project doesn’t bring any cash flows in year 1 to year 4, but that project has HIGHER long-run cash flows.

Additionally, even if we pocket 150 in year 1 from short-term project, net of the investment being made -100, net of 50 and compounding that at IRR 50% a year, this will only bring 50 * (1+50%)^4 = 253, which is only 1/3 of the cash flow generated by the long-term project.

Using the above simple example, we could see that using IRR singly (without comparing it with NPV) might potentially lead to less-than-optimal decisions. In this case, NPV calculation should come first.

We might challenge the above example, since we are comparing two projects that are not apple-to-apple, meaning that those two projects do not have the same or equal project duration, one is 1 year and another one is 5 years.

However, this problematic IRR with the cash flow timing will still persist even we compare two projects with the same duration. Let’s move to Example 3 which might give more apple-to-apple comparison.

Example 2

Let’s say we have two mutually-exclusive projects with 5-year duration, with the pattern of the cash flow timing, the calculation of NPV and IRR as depicted below. The discount rate for both projects are 10%.

Here we see that we have conflicting results between NPV and IRR.

• Using NPV as the main decision criteria, Project A will be chosen.
• Using IRR as the main decision criteria, Project B will be chosen.

This conflicting results come from the fact that the cash flow pattern or timing is different between Project A and Project B.

Let me show the differential cash flow between Project A and Project B, and calculate its NPV and IRR as well, as demostrated below.

Then we can see here that the differential cash flows will give us POSITIVE NPV of 42.32 and IRR of 12.48%.

Since the differential cash flow has POSITIVE NPV, then selecting Project A over Project B will give us the optimal decision. In other words, the cash flow pattern of Project A is equivalent to Project B cash flow PLUS the differential cash flow.

By rejecting Project A, and selecting Project B, then it means we have rejected the POSITIVE NPV generated by the differential cash flows.

If we reflect the NPV profile of Project A and Project B, then we could see that as long as the discount rate is lower than IRR of the Differential Cash Flow (= 12.48%) then Project A will have higher NPV over Project B. However, if the discount rate is higher than 12.48% then Project B will have higher NPV over Project A, or this case, Project B will be preferred over Project A.

The above slope of NPV profile of Project A and Project B gives us another insight. Project A’s NPV profile has steeper slope compared to that of Project B, which means that when the discount rate is creeping northwest, then the NPV of the Project A will drop quicker than that of Project B. This comes as no surprise, since most of the cash flows from Project A comes later than that of Project B, in other words, those higher long-run cash flows will get bigger “punished” by higher discount rate.

Here, I show again the NPV and IRR if we change the discount rate to be the IRR of the Differential Cash Flows, that is 12.48%, and here we can find that at the cross-over of 12.48%, then the NPV of the Project A will be the same with that of Project B. Yet, IRR of Project B will be higher and thus, will be preferred over Project A.

In a nutshell, as long as the discount rate is 12.48% or higher, then Project B will be selected over Project A.

Source: Financial Analysis with Microsoft Excel. 7th Edition. Timothy R. Mayes and Todd M. Shank. Cengage Learning. 2015.

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