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How To Calculate Modified Internal Rate Of Return (MIRR)

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August 21, 2021
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The five key features will help to calculate the modified internal rate of return (MIRR).

  1. Overview
  2. Key Definition
  3. Formula
  4. Example
  5. Advantages and Limitations

OVERVIEW

The Internal Rate of Return (IRR) has a conventional method that assumes cash flows arising from a project to be reinvested in the same project. It discounts future cash inflows to net present value. The NPV of total cash is zero when a breakeven sets against the WACC. However, it is risky to invest cash flows in the same project, so IRR has two different calculations for costs of interest rate.

PROBLEMS WITH IRR APPROACH

IRR calculates all the cash flows associated with the project. It limits the possibilities of cash flows to different projects. It may not be correct in the cost of financing because many projects require ongoing project activities. So, it may become difficult to predict in advance. When uneven cash flows exist, it becomes difficult for IRR to calculate, resulting in multiple IRRs. However, higher IRR is the best investment option because other IRR projects offer higher NPV.

WHAT IS THE MODIFIED INTERNAL RATE OF RETURN MIRR?

The MIRR is the different cost of returns from the project’s initial investment rate and subsequent cash flows. The reinvestment is from the company’s capital. The current value is the adjusted terminal value of cash inflows with WACC. MIRR is much more flexible compared to IRR in the management of reinvestment.

HOW TO CALCULATE MODIFIED INTERNAL RATE OF RETURN?

The MIRR is calculated from the account for the time value of money. There are two simple steps to calculate MIRR.

  1. Calculate the terminal value of cash inflows.
  2. Use the MIRR formula of terminal cash flows discounted at company cost of capital.

The formula for Calculating MIRR:

  1. MIRR = (Terminal Cash Inflows / PV of Cash Outflows) ^n – 1

Here n = number of years for the project

Terminal value = Future reinvested value of cash inflows at the cost of capital

  1. MIRR = (PVR / PVI) ^ (1/n) x (1+re) -1

Here PVR = PV of return phase (PV of cash inflow)

PVI = PV of investment phase (PV of cash outflow)

Re = Cost of capital

EXAMPLE

Suppose a project with an initial investment of $ 1,000 uses a WACC of 10% to be completed in three years with cash inflows as below. However, the MIRR cash inflows calculation can be reinvested in the project. The WACC cash inflows compound rate gives modified returns. To calculate the MIRR, the total cash inflows are adjusted with WACC at the end-of-year.

YearCash flowMultiplier @ 10%Re-Invested Amount
1            400            1.100^2                       484
2            600            1.100^1                       660
3            300            1.100^0                       300
                                       1,444

As the cash outflow is at $ 1,000, we use:

MIRR = (Terminal Cash Inflows / PV of Cash Outflows) ^n-1

MIRR = (1444/1000) ^3-1

MIRR = 13%

However, if we use the second formula, we will the following present value:

YearCash flowDiscount factor @ 10%Present value
1            400            0.909                       364
2            600            0.826                       496
3            300            0.751                       225
                                              1,085

As the initial investment is $ 1,000, we use:

MIRR = (PVR/PVI) ^ (1/n) x (1+re)-1

PVR = $ 1,085

PVI = $ 1,000

Re = 10%

MIRR = [(1,085/1,000)] ^ (⅓) x (1+0.10)-1

MIRR = 13%

Both formulas will give the same MIRR result.

INTERPRETATION OF THE MIRR METHOD

According to MIRR, the cost of capital is reinvested in the form of cash inflows. However, if the project returns are less than expected, the margin of error occurs. Therefore, a higher MIRR is expected than the WACC. Even if the WACC rate changes, the MIRR can be adjusted.

MODIFIED IRR WITH DIFFERENT RATES FOR RETURN AND INVESTMENT PHASES

With different discount rates, we use a different formula for calculating the MIRR.

MIRR = (-FV/PV) ^ [1/ (n-1)] -1

FV = Future values of cash inflow (at return phase)

PV = Present value of cash flow (at investment phase)

n = Number of people

EXAMPLE

A project with initial cost of investment of $ 130,000. The project returns are as follows:

1 year = $ 50,000

2 years = $ 45,000

4 years = $ 47,000

5 years = $ 50,000

6 years = $ 42,000

(With additional investment of $ 30,000 in year 3).

Following discount rate for investment phase at 13% and return phase at 11%.

Required: Calculate MIRR for this project.

SOLUTION

Separating the table into investment and return phases:

Present value of investment phase:

YearCash flowDiscount factor @ 13%Present value
 (130,000)1.000(130,000)
3(30,000)0.693(20,790)
 Total (150,790)

The reinvested amount for the return phase:

YearCash flowFactor @ 11%Compound rateValue
1            50,000 (1+11%)^5                        1.685            84,253
2            45,000 (1+11%)^4                        1.518            68,313
3 [Outflow]   
4       47,000 (1+11%)^2                        1.232            57,909
5            50,000 (1+11%)^1                        1.110            55,500
6            42,000 (1+11%)^0                        1.000            42,000
 Total              307,975

We’ll use the formula:

MIRR = (-FV/PV) ^ [1/ (n-1)] -1

FV = $ 307,975

PV = – $ 150,790

n = 6 years

MIRR = (-307,975/-150,790) ^ (⅕)-1

MIRR = 15.35%

Thus, MIRR at different rates of return and investment phase is 15.35%.

ADVANTAGES OF MIRR

  • MIRR provides a clearer rate of return than IRR.
  • It offers a single and unique rate of return.
  • Eliminates multiple rates of return.
  • Accommodates future cash flows of project activities.
  • Indicates the same NPV.

LIMITATIONS OF MIRR

  • Requires cost of capital to compound future cash inflows that can alter with the capital structure of financing.
  • The weighted average cost is assumed and may give incorrect results.
  • Do not provide accurate profitability terms of investment appraisal.
  • It is harder to grasp compared to IRR.

MIRR VS IRR

Both calculate the cost of capital employed in a project, value of cash inflows, and assume basic cash inflows for reinvestment purposes. However, the following are the differences between MIRR and IRR:

  • MIRR calculates terminal cash flow while IRR evaluates future cash flows.
  • MIRR offers a rate of return to rank the investment options, while IRR uses a trial and error method to give multiple IRRs.
  • MIRR focuses on the reinvestment rate of WACC of the company, while IRR reinvests the cash flows at the rate of the project.
  • MIRR is more flexible than IRR.

CONCLUSION

MIRR is much superior and flexible than IRR in absolute terms of profitability. The average weighted cost of capital for project reinvestment cash inflow is much better to measure accurate appraisals. As MIRR is closer to the company WACC, the project ranking increases with a better appraisal of the rate of return.

Salman Rundhawa
Salman Rundhawa
Salman Rundhawa is the founder of Filing Taxes. Salman provides valuable tax planning, accounting, and income tax preparation services in Toronto, Mississauga, Oakville, and Hamilton.

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