The Internal Rate of Return (IRR) is one of the most widely used methods for capital appraisal purposes, and there is little doubt that it’s also considered one of the most robust ones. However, because the IRR has certain limitations, you should use it in conjunction with other capital appraisal methods. Not only for the criteria to accept or reject projects, but for reasons explained below. In today’s article, we will review the internal rate of return calculation and look at a simple example.

**Definition of the Internal Rate of Return **

The internal rate of return is the discount rate which makes the costs to undertake a project equal the profits that this project will generate. In other words, the internal rate of return is the discount rate that gives a zero net present value.

If the cost of capital, i.e. the interest rate that a company borrows at, is less than the internal rate of return, you can accept the project.

**Internal Rate of Return Decision Rule**

As noted above, if the internal rate of return is lower than the cost of capital, then you should reject the project since it costs more money for the company to invest in than the expected return.

**Example**

We will use one example to illustrate how the internal rate of return calculation and approach. Let’s say that company A uses the internal rate of return to evaluate investment opportunities and decide regarding the profitability and viability of a project.

There is one potential project that Company A wishes to appraise with the following characteristics:

-An initial investment of $50,000 during the first year.

-The project will last for four years, and the cash inflows during these four years will be:

- $15,000
- $20,000
- $25,000
- $18,000

The company has a cost of capital of 15% and wishes to appraise this project and decide whether to proceed or not.

**Internal Rate of Return Calculation**

You can follow two different approaches to calculate the internal rate of return.

**Internal Rate of Return Calculation with Trial and Error**

From the IRR definition, we know that the IRR is the discount rate that makes the present value of the cash flows become $nil. Therefore, we can use a trial and error approach and increase the discount rates until we get to a nil present value.

The following table illustrates the calculations.

Time | Cash Flow | Discounted Cash Flows (10%) | Discounted Cash Flows (15%) | Discounted Cash Flows (19%) | Discounted Cash Flows (20%) |
---|---|---|---|---|---|

Period 0 | -50,000.00 | -50,000.00 | -50,000.00 | -50,000.00 | -50,000.00 |

Period 1 | 15,000.00 | 13,636.36 | 13,043.48 | 12,605.04 | 12,500.00 |

Period 2 | 20,000.00 | 16,528.93 | 15,122.87 | 14,123.30 | 13,888.89 |

Period 3 | 25,000.00 | 18,782.87 | 16,437.91 | 14,835.40 | 14,467.59 |

Period 4 | 18,000.00 | 12,294.24 | 10,291.56 | 8,976.04 | 8,680.56 |

Net Present Value | 28,000.00 | 11,242.40 | 4,895.82 | 539.77 | -462.96 |

As we can see from this table, a discount rate of 19% gives around $500 NPV, while a 20% discount rate gives a $-462 NPV. We can therefore understand that the IRR is somewhere in the middle or around 19.5%.

**Internal Rate of Return Calculation Using Two Discount Rates**

We can use another approach to calculate the internal rate of return that involves a formula (see below). The idea is that we use two different discount rates. Firstly, use a discount rate that generates a positive net present value. And then, secondly, a discount rate that will create a negative net present value. It might sound not very easy, but follow the example below, which shows you the following steps.

**Internal Rate of Return Formula**

IRR= Ra + (NPVa/(NPVa-NPVb))*(Rb-Ra)

where

Ra is the discount rate that gives the positive net present value, NPVa is the positive NPV, NPVb is the negative NPV, and Rb is the discount rate that shows the negative NPV.

Let’s proceed with a table that can illustrate what’s written above in an easier to follow way:

Time | Cash Flow | Discounted Cash Flows (10%) | Discounted Cash Flows (20%) |
---|---|---|---|

Period 0 | -50,000.00 | -50,000.00 | -50,000.00 |

Period 1 | 15,000.00 | 13,636.36 | 12,500.00 |

Period 2 | 20,000.00 | 16,528.93 | 13,888.89 |

Period 3 | 25,000.00 | 18,782.87 | 14,467.59 |

Period 4 | 18,000.00 | 12,294.24 | 8,680.56 |

Net Present Value | 28,000.00 | 11,242.40 | -462.96 |

The table above is part of the first table we looked at. We can see that a 10% discount rate gives a positive NPV, and a 20% gives a negative NPV. We can therefore use the formula above and calculate IRR as:

IRR= 10+(11,242/(11,242+462))*(20-10)=19.6%

As you can see, both methods will give the same IRR (more or less). However, most people prefer to calculate IRR by using the second approach since it involves fewer calculations.

**Limitations and Disadvantages**

The internal rate of return is a very robust capital appraisal method, but there are certain limitations. For example:

- When a project has positive cash flows, followed by negative and then followed by positive cash flows again, there will be more than one IRR (more than solution).
- IRR is not very reliable when comparing projects that have significantly different time horizons (i.e project A will last for 5 years while project B will last for 15 years).
- Due to the limitations explained above, IRR is mostly used a decision tool (accept or reject) and not as a comparison tool (project A vs project B).

**Advantages**

However, IRR has certain advantages, which make it one of the most preferred capital appraisal methods.

- It’s an easy way to decide to accept or reject projects.
- It’s a robust method that can be used to monitor how a project is performing based on the actuals vs the budgets and how that compares to the cost of capital.
- It takes into account the time value of money compared to other methods (payback period for example) that do not.