Businesses invest in projects to earn profits and create cash flows. The dilemma with project investments is to calculate the correct rate of return and estimate the future cash flows in terms of present value. The business entity may use several net present value methods to discount the future cash flows in present terms. For that purpose, the company would need to discount the future cash flows with a reasonable return rate. Companies finance their operations with both debt and equity; both financing options come with different costs. The combined cost of capital or practically used the weighted average cost of capital WACC then becomes the threshold rate of return in project appraisals.

In this article, we will cover how to calculate the internal rate of return (IRR). This includes the key definition, Formula, example calculation as well as advantages and limitations.

## What is Internal Rate of Return (IRR)?

Internal rate of return (IRR) is one of the capital budgeting techniques. It is the discount rate at which the net present value of future cash flows becomes zero. In other words, it offers a break-even point in discounting future cash flows for project or investment appraisals. As the WACC or cost of capital is the base to decide, any rate of return greater than WACC would be acceptable.

## Importance of Using IRR:

- It represents the discounted rate of return in present terms same the NPV method which makes the comparison easier
- The percentage term of IRR can easily be compared with WACC
- It provides the opportunity to compare different investment and project appraisals

## How to Calculate Internal Rate of Return?

The internal rate of return is calculated by taking into account two net present values (NPV) with two different discount rates. Once NPV should be positive and another one should be negative.

### IRR Formula with Linear Interpolation

The internal rate of return is the estimation of average returns on future cash flows discounted to the present value. Therefore, discounting future cash flows without a set rate of return requires a trial and error approach in IRR calculation. One method of calculating the IRR is to use the linear interpolation method. Where two rates of returns for the same cash flows are discounted for the NPV and the optimum is selected as the internal rate of return. The IRR with two rates of returns can be calculated in a three-step approach with the following formula:

**IRR formula:**

IRR = R_{L} + [N_{L} / (N_{L} – N_{H})] × (R_{H} – R_{L})

Where,

- R
_{H}= Higher interest rate, - R
_{L}= Lower Interest rate - N
_{L }= Net present value at low interest rate - N
_{H}= Net present value at high interest rate

### Three Step Approach in Calculating IRR

The calculation of IRR with linear interpolation would require a three-step approach.

**Step 1**: The first step to calculate the IRR is to select two different interest costs for the same projected cash flows. The interest costs can be calculated randomly, but to use in the formula both costs should be different. As a starting point, one interest cost can be selected above the WACC and the other below the WACC.

**Step 2**: The second step to calculate IRR is to calculate the net present values for future cash flows with both interest cost rates selected. These NPV values with a higher interest rate and the lower interest rate would then be used to calculate the IRR.

**Step 3**: The third step is to calculate the IRR using the NPVs with high-interest rates and low-interest rates with the IRR formula.

### Example Calculation of IRR

Suppose we take two interest rate costs for the same projected cash flows. The interest costs are 10% and 20% respectively.

The projected cash flows are given as:

Time Period | Cash Flow |

Time 0 | $ (200,000) |

Year 1 | $ 15,000 |

Year 2 | $ 50,000 |

Year 3 | $ 75,000 |

Year 4 | $ 150,000 |

The NPV for the same cash flows with both Interest rates can be calculated as below using the NPV formula:

Time Period | Cash flow | Discount factor @10% | Present value @10% | Discount factor @20% | Present value @20% |

(200,000) | 1.000 | (200,000) | 1.000 | (200,000) | |

1 | 15,000 | 0.909 | 13,635 | 0.833 | 12,495 |

2 | 50,000 | 0.826 | 41,300 | 0.694 | 34,700 |

3 | 75,000 | 0.751 | 56,325 | 0.579 | 43,425 |

4 | 150,000 | 0.683 | 102,450 | 0.482 | 72,300 |

Total | 13,710 | (37,080) |

From the present value table above, we can calculate the IRR by using the above IRR formula as below:

IRR = 10% + [13,710 / (13,710 – ( – 37,080)] × (20%-10%)

IRR = 10% + [13,710 / 50,790] × 10%

Hence, IRR = 12.70 %

## The IRR Interpretation

The IRR arrived with using two interest costs for the expected future cash flows can be used as a starting point in the final decision. Normally, the project or investment appraisal should be accepted if the IRR gives a higher rate of return than WACC.

When the IRR calculated is applied for the same cash flows projected investments, it may offer different results. So in absolute terms, the project or investment with a higher NPV value should be considered. Theoretically, both IRR and NPV methods offer insights on discounting future cash flows with investments. IRR offers a percentage rate of return which may not be accurate as it takes two random interest rate costs into consideration. The NPV offers absolute gain or loss in terms of present value; however, the NPV calculations also require a suitable cost of return for assessment.

## Advantages of Using IRR

Companies often compare projects and investment options to maximize profits. IRR is one such discounting method that offers insights for future project appraisals. It offers several advantages over simple project appraisal methods such as payback period analysis.

- IRR focuses on discounting cash flows in NPV terms i.e. it emphasis more on cash flows than the profitability of the project
- Takes into account the initial investment in the project and full cash flows arising over the project life
- Its percentage value offers a simpler comparison against WACC
- Comparing IRR offers a simple conclusion. However, the company may consider comparing projects with IRR and NPV analysis in conjunction.

## Limitations of the IRR

The calculation of IRR requires a trial and error approach by selecting two different interest cost rates initially. With that approach, the final result may several times result in a lower IRR than the WACC, which may not happen practically. Some other limitations of using IRR as the only project appraisal method:

- IRR considers future cash flows only, discounting to present value
- It ignores future cash flows that may arise during the project
- It may offer multiple IRRs with using different interest costs
- In absolute terms, IRR offers no precise information about the project profitability
- IRR and NPV both methods for the same cash flows can offer different results

## Conclusion

The IRR analysis is a useful investment appraisal method. It offers advanced information as compared to the simple payback period. The IRR focuses on cash flows in present value terms that emphasize company liquidity than profitability. However, the calculation of IRR can be fairly complex for the management as it requires iteration of the process with different interest rate costs. The possible IRR evaluation and NPV appraisal can be used in conjunction to arrive at a better investment appraisal analysis.