# MIRR

Published on :

21 Aug, 2024

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Edited by :

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Reviewed by :

Dheeraj Vaidya

## MIRR (Modified Internal Rate of Return)

MIRR or Modified Internal Rate of Return refers to the financial metric used to assess precisely the value and profitability of a potential investment or project. It enables companies and investors to pick the best project or investment based on expected returns. It is nothing but the modified form of the Internal Rate of Return (IRR).

In capital budgeting, Modified Internal Rate of Return allows entities to compare the viability or return of an investment or project with others. Unlike IRR, which overstates the attractiveness of any investment and misleads investors about expected higher returns, MIRR offers an accurate estimate of the ROI investors can expect.

##### Table of contents

- MIRR is a financial measure used by firms and investors to calculate the cost and profitability of a new investment or project. It is simply a tweaked form of the Internal Rate of Return (IRR).
- It rates investments and projects based on the opportunities they provide and eliminates capital budgeting errors caused by IRR.
- Unlike IRR, which misleads investors into expecting bigger returns, MIRR provides a precise assessment of the ROI investors can expect.
- It ranks investments based on their opportunities and eradicates all issues arising due to multiple IRRs for the same period.

**How To Calculate MIRR?**

MIRR depicts the ROI in a clearer, more accurate, and realistic manner using evaluation parameters. It calculates both the cost of the investment (capital) and the interest earned on the funds to be reinvested. It assumes the reinvestment rate as the company’s positive cash flows, while the finance cost as negative. Modified Internal Rate of Return, thus, deals with the capital budgeting mistakes caused by IRR.

Organizations work on calculations, estimating revenues, profits, or expenditures. The **MIRR calculator** provides more precise returns, allowing managers to better control the expected reinvestment rate from future cash flows. Therefore, it helps avoid capital budgeting mistakes and exaggerated expectations.

Before we go into the calculations for the Modified Internal Rate of Return, let us look at the three approaches used in the computations:

**Discounted Approach**– All negative cash flows are discounted to the current investment and added to the initial cost.**Reinvestment Approach**– All positive and negative cash flows (except the first one) are compounded to the end of the project tenure, and IRR is calculated on the same.**Combination Approach**– It is the hybrid method where the above two are merged and applied. In this approach, all negative cash flows are discounted back to the current investment, and all positive cash flows are compounded for the IRR to be calculated.

**MIRR Formula**

The **MIRR formula** used by firms and investors in capital budgeting is as follows:

Where,

- FVCF = Future cost of the positive cash flows after deducting the reinvestment rate or cost of capital:

*FV = ∑ *

Here, C_{i} is the positive cash flow, and RR is the reinvestment rate

- PVCF = The present cost of the negative cash flows after deducting the finance cost of the firm:

*PV = C**₀** - ∑ *

Here, C_{0} is the negative cash flow, and FR is the finance rate

- n is the number of years

Calculating Modified Internal Rate of Return manually using the formula could be difficult and result in errors. Therefore, financial firms and stock dealing companies use spreadsheet applications like Microsoft Excel to assess the return on investments. The **MIRR Excel** function is:

= MIRR (value_range, finance_rate, reinvestment_rate)

Where,

- Value range = The range of cells containing cash flow values from each period
- Finance rate = The cost of capital of the firm or interest expense during negative cash flows
- Reinvestment rate = Compounding rate of return on the reinvested positive cash flow

**Examples**

Let us consider the following **MIRR example** with calculations to understand the concept better:

#### Example #1

A company made an initial investment of $1,000 for a project, expecting returns in cash worth $300, $600, and $900 for three consecutive years. The cost of capital and the reinvestment rate was 12%. Hence -

FV = 300 * (1+0.12)^{2} + 600 * (1+0.12)^{1} + 900

= (300 * 1.25) + (600* 1.12) + 900

= 375 + 672 + 900

= 1947

PV = 1000

Using Modified Internal Rate of Return formula:

= 24.87%

#### Example #2

A company invests $1,800 and evaluates the return worth $500 to be consistent for the next three years with an additional profit of $500 at the end of the third year. What is the difference between the IRR and Modified Internal Rate of Return of the project if the reinvestment rate is 10% and IRR is 12%?

FV = 500 * (1+0.10)^{2} + 500 * (1+0.10)^{1} + 1000

= 605 + 550 + 1000

= 2155

PV = 1800

= 6.18%

The difference between the IRR and Modified Internal Rate of Return is equal to = (12 – 6.18) %

= 5.82%

**IRR vs MIRR - Which Is Better?**

Both IRR and Modified Internal Rate of Return are interrelated terms when considering a new investment or project. However, a few things make one option better than the other. Let us look at them:

IRR | MIRR |

Overstates the returns expected on an investment | Provides an exact estimation of the returns |

Can result in capital budgeting errors | Resolves issues that arise in capital budgeting because of multiple IRRs |

Calculates reinvestment rate, accounts, and cash flows | Calculate returns based on the assumed respective stage-wise current reinvestment rates that apply |

Assumes reinvestment of cash flows at the same rate, i.e., IRR | Assumes reinvestment of positive cash flows at the cost of capital |

Discounts the growth from the initial investment | Consider financing the initial expenses at the finance cost |

Works like the inverted compounding of the growth rate | Helps managers expect a realistic return and plan their objectives accordingly |

Sometimes provides two solutions that cause ambiguity or misunderstanding | Always offers a single solution |

Assumes the growth rate to remain constant from project to project | Assumes the rate of reinvested growth to vary at different stages in a project |

**Uses Of MIRR**

The regular IRR exaggerates the returns on investment, giving investors false hope. On the other hand, MIRR assesses different costs to conclude the returns one can expect from an investment. Thus, it prevents investors and firms/business managers from being misled. Besides this, there are multiple other financial aspects with which Modified Internal Rate of Return can help:

- Ranks investments of similar size based on the opportunities they provide
- MIRR higher than the expected return suggests an attractive investment or project and vice versa
- Modifies IRR of an investment or project and calculates the difference between the reinvestment rate and the investment return
- Eradicates all issues arising due to multiple IRRs for the same period
- Keeps room for adjustment of the assumed growth rate of the reinvestments at different stages of project accomplishment
- Offers the liberty to add any reinvestment rate and make the calculations based on that

### Frequently Asked Questions (**FAQs**)

**What is MIRR?**MIRR or Modified Internal Rate of Return is a financial metric used to precisely analyze the profitability of a new investment or project. Given the assessment characteristics it considers, it gives businesses and investors a clearer, better, and more realistic image of the ROI. It is computed by considering the investment cost and the interest earned on the cash to be re-invested.

**What is the difference between IRR and MIRR?**Calculating IRR involves deducting the growth from the initial investment made. As a result, it is based on the inverted compounding of the growth rate. On the other hand, MIRR allows companies to compute returns based on the assumed stage-by-stage current reinvestment rates.

**Why is MIRR calculated?**MIRR is the modified form of the Internal Rate of Return (IRR), which is known for overstating the attractiveness of any investment. IRR misleads investors, making them expect higher returns. Modified Internal Rate of Return offers an accurate and reliable estimate of the ROI investors can expect.

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