## IRR Examples (Internal Rate of Return)

The following IRR example

Internal rate of return is the rate which is used by management to take capital budgeting decisions while evaluating the profitability of prospective projects. It is calculated by equating the Net Present value to zero.

The formula to calculate the internal rate of return is:

Here N is the number of years of cash flows of the project & CF is the cash flow

### Examples of Internal Rate of Return (IRR)

The calculation for IRR can either be done manually by hit and trial method or by using the calculator or excel function of IRR. Below are some of the examples of Internal Rate of Return

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#### IRR Example #1 – Project with Equal Cash Flows

Let’s consider a firm taking up a solar energy project i.e. replacing all its electrical power needs with solar power. The firm needs to make an initial cash outflow or investment of $100,000 for purchasing and installing the solar panels. Assuming that the project generates a cash inflow of $30,000 for the first 5 years in the form of saving electricity bill payments as per below table i.e. a total of $150,000 cash inflow. The calculation for IRR would be simply based on the above formula, which in this case comes out to be 15%. We can interpret this as an annualized profit of doing the project while also having considered the present values of future cash flows.

**Solution:**

The calculation of Internal Rate of Return can be done as follows-

**Internal Rate of Return=15%**

#### IRR Example #2 – Project with Uneven Cash Flows

Let’s reconsider the above example, with slightly higher overall cash inflow of $155,000 but unevenly distributed in different years due to maintenance costs in the first 4 years. The cash flows are as per below table. The IRR for this setup comes out to be 14% which is lower than the above example even when the overall cash inflow is more in this case. This illustrates that not only a project’s cash flows but also their timing play an important role when considering the present values of future cash flows for evaluating.

**Solution:**

The calculation of Internal Rate of Return can be done as follows-

**Internal Rate of Return =14%**

#### IRR Example #3 – Mutually Exclusive Projects

Let’s consider a situation where the management needs to choose any one project in between the two prospective projects as they are mutually exclusive. Assuming that a manufacturing company plans to increase its product line offering and has two options: product A and product B, out of which only one can be implemented due to limitations of the production facility. The cash flows of the two projects are as per below table. The investment for both the projects are the same but the cash inflow is different, Product A gives the bigger cash flows in the early years while B gives the bigger ones in the later years. The IRR of the project appears to highlight Product A as the more desirable one.

**Solution:**

The calculation of IRR can be done as follows-

**Internal Rate of Return =29% and 26%**

However, if there are other constraints that need to be considered as the cost of capital then the results might change. Let’s take a look at different scenarios with varying cost of capital and their results with the NPV method.

It is evident here that if the cost of capital is equal or below 10%, Product B is more desirable contradicting the results found by IRR. This happens because at lower interest rates the present values of cash flows appearing at the later stages are less penalized than at higher interest rates.

This discrepancy in the IRR method can be addressed by calculating incremental IRR i.e. finding the IRR of the extra cash flow of one project over the other. Like in this case as per below table:

**Incremental IRR =11%**

As per the above calculated incremental IRR of the differential cash flow of ‘A’ over ‘B’, we can conclude that if the cost of capital or interest rate is more than 11%, then choose ‘A’ otherwise ‘B’.

#### Example #4 – Multiple IRR

To understand this scenario let us consider a project which requires investment not only at the initial stage but also in the middle or the end. Assuming a mining company taking up a coal mining project which requires digging up the land to access the coal under it, here the company will have to invest money for digging in the beginning and then once the coal starts coming out there will be cash inflows for 5 years straight by selling it, then finally once all the coal has been extracted it needs to restore the land to its original condition by filling up soil which would again require some investment.

**Solution:**

The calculation of Internal Rate of Return can be done as follows-

The cash flows of the project are as per below table:

Since the IRR for this project gives two values: -6% & 38% it is difficult to evaluate the project using this method as it is unclear as to which IRR should be considered. Hence it is more convenient to use NPV over IRR to evaluate such projects that change the direction of cash flows more than once.

Based on the above examples we can say that on one hand IRR is a simple method and is easily interpretable while also considering the time value of money on the other hand sometimes it gives ambiguous results like in the case of multiple IRRs where other methods like NPV seem to be more appropriate and reliable. So depending on the nature of the project and its cash flows the IRR method provides an easy and quick way of evaluating.

**For the detailed calculation of IRR, you can download the Excel template here – IRR Examples Excel Template**

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