**The internal rate of return (IRR)**For an investment plan it is the rate that corresponds to the present value of the anticipated cash inflows with the initial cash outflows. On the other hand,

**the modified internal rate of return, or MIRR,**It is the real IRR, where the reinvestment rate does not correspond to the IRR.

Each business makes a long-term investment in several projects with the objective of obtaining benefits in future years. Out of the various plans, the company has to choose one that generates the best result, and the returns are also according to the needs of the investors. In this way, the capital budget is used, which is a process of estimating and selecting long-term investment projects that are aligned with the basic objective of investors, that is, the maximization of value.

IRR and MIRR are two capital budgeting techniques that measure the attractiveness of the investment. These are commonly confused, but there is a fine line of difference between them, which is presented in the following article.

### Comparative graph

Basis for comparison IRRMIRRSense | The IRR is a method of calculating the rate of return considering internal factors, that is, excluding the cost of capital and inflation. | MIRR is a capital budget technique, which calculates the rate of return using the cost of capital and is used to classify various investments of equal size. |

What is it | It is the speed at which the NPV is equal to zero. | It is the speed at which the VAN of the terminal inputs is equal to the output, that is, the inversion. |

Assumption | Project cash flows are reinvested in the project's own IRR. | Project cash flows are reinvested at the cost of capital. |

Accuracy | Low | Comparatively high |

### IRR definition

The internal rate of return, or also known as IRR, is the discount rate that produces the equality between the present value of the expected cash flows and the initial capital outlay. It is based on the assumption that interim cash flows are at a rate similar to that of the project that generates it. In IRR, the net present value of cash flows is equal to zero and the rate of return is equal to one.

Under this method, the discounted cash flow technique is followed, which considers the temporary value of money. It is a tool used in the capital budget that determines the cost and profitability of the project. It is used to determine the viability of the project and is a primary factor for investors and financial institutions.

The trial and error method is used to determine the internal rate of return. It is mainly used to evaluate the investment proposal, in which a comparison is made between the IRR and the cut-off rate. When the IRR is greater than the cut-off rate, the proposal is accepted, while, when the IRR is lower than the cut-off rate, the proposal is rejected.

### MIRR definition

MIRR expands to the modified internal rate of return, it is the rate that equals the present value of the final cash inflows to the initial cash outflow (at or zero). It is nothing more than an improvement over the conventional IRR and overcomes several deficiencies, such as the multiple IRR that is eliminated, addresses the problem of the reinvestment rate and generates results, which are in conciliation with the net present value method.

In this technique, interim cash flows, that is, all cash flows, except the initial one, are taken to the terminal value with the help of an adequate rate of return (usually the cost of capital). This is a specific cash inflow in the last year.

In MIRR, the investment proposal is accepted, if the MIRR is greater than the required rate of return, that is, the cut-off rate and is rejected if the rate is lower than the cut-off rate.

## Key differences between IRR and MIRR

The points given below are substantial with regard to the difference between IRR and MIRR:

- The internal rate of return or IRR implies a method to calculate the discount rate considering internal factors, that is, excluding the cost of capital and inflation. On the other hand, MIRR refers to the capital budget method, which calculates the rate of return taking into account the cost of capital. It is used to classify various investments of the same size.
- The internal rate of return is an interest rate at which the NPV is equal to zero. Conversely, MIRR is the rate of return at which the VAN of the terminal inputs is equal to the output, that is, the investment.
- The IRR is based on the principle that interim cash flows are reinvested in the project IRR. Unlike MIRR, cash flows apart from initial cash flows are reinvested at the company's rate of return.
- The accuracy of MIRR is more than IRR, since MIRR measures the true rate of return.

### Conclusion

The decision criterion of both methods of capital budgeting is the same, but MIRR defines a better gain compared to the IRR, due to two main reasons, that is, first, the reinvestment of cash flows at the cost of Capital is practically possible, and secondly, it is multiple. Return rates do not exist in the case of MIRR. Therefore, MIRR is better with respect to the measurement of the actual rate of return.