Difference Between IRR and MIRR

IRR Formula 

In the above equation,

Ct = Cash flows in the period 

r = Rate of return

t = Time period 

NPV = Net Present Value 

Example of IRR

Vin and Paul have opened their dream mechanic shop after a failed stint in racing career. As they are cash strapped having squandered away their fortune, they are hesitant in purchasing a new machine. They are not sure if that is the best use of company funds.

Book numbers indicate that with a new Rs.1,00,000 machine, Vin and Paul will be able to meet the new order which may generate revenue of Rs. 20,000, Rs. 30,000, Rs. 40,000 and Rs. 40,000.

Minimum rate calculation follows starting from an approximate rate of 8% -

Since NPV has come out to be a positive number as opposed to zero, the internal rate estimation has to be increased.

Let the revised approximate rate be 10%. 

Vin and Paul will have an internal rate of return to the tune of 10%. They will have to compare it with other investment options to determine whether the equipment should be purchased.

Modified Internal Rate of Return 

Modified internal rate of return is similar to IRR, which also takes into account the capital cost as reinvested rate focusing on the positive cash flow of a firm. Financing cost is taken as the discount rate for a negative cash flow of a firm.

Investment should be undertaken if MIRR is found to be higher than that of expected return. If it comes out to be less than expected return, the particular project will not be viable. 

MIRR, as an effective investment performance indicator, finds frequent usage in commercial real estate as well as finance. The set of cash flows in MIRR can be categorised into – (i) initial investment in a given time, and (ii) amount of accumulated capital when the holding period ends.

MIRR formula 

In the above equation,

MIRR= Modified Internal Rate of Return 

FV = Positive cash flows future value at reinvest rate (r)

PV = Negative cash flows present value at finance rate (f)

n = Number of periods

Example of MIRR

Twinkle Kumar works for an interior designing firm and is entrusted with calculating MIRR for two competing projects to determine which one should be selected.

Project A

Total life = 3 years 

Cost of capital = 12%

Cost of financing = 14%

Project B

Total life = 3 years 

Cost of capital = 15%

Cost of financing = 18%

Projected Cash Flow of Project A and B:

Positive cash flow future value that is discounted at cost of capital:

Project A

4000 X (1 + 12%)1 + 5000 = 9480

Project B

3000 X (1 + 15%)1 + 1500 = 4950

Negative cash flow present value that is discounted at cost of financing:

Project A

-1000 + (-2000) / (1 + 14%)1 = -3000

Project B

-800 + (-700 / 1 + 18%)1 = -1500

MIRR = (Positive cash flow future value / negative cash flow present value) (1/n) – 1

Hence, 

Project A

{9480 / (3000)} 1/3 – 1 = 5.3%

Project B

{4950 / (1500)} 1/3 – 1 = 10.0%

It follows that Twinkle Kumar should report that Project B should be taken up due to its higher MIRR compared to Project A.

Difference between IRR and MIRR

The Difference Between IRR and MIRR Have Been Elucidated Below. 

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Pointing the Key Differences Between IRR and MIRR – In Points 

The Points that are given below are the Main Points of difference between IRR and MIRR:

• Internal Rate of Return abbreviated as IRR implies the method of calculating the discount rate after considering the internal factors (this is done excluding the cost of capital and the inflation rate). While, MIRR implies the method of capital budgeting, which calculates the rate of return taking into the account cost of capital. This is used to rank the various investments of the same size.

• The internal rate of return is equal to NPV. 

• IRR is taking the principle of interim cash flow as the basis. This is reinvested at the project’s IRR. Unlike IRR, under MIRR, cash flows (excluding the initial cash flows) are being reinvested at the rate of return.

• The accuracy rate of MIRR is more than IRR, this happens as MIRR measures the true rate of return.

So, We Can Say- 

The decision criterion which is decided to keep the capital budgeting methods as the main- MIRR delineates better profit as compared to the IRR, because of the two major reasons:

1. reinvestment of the cash flows happens at the cost of capital which is practically possible

2. multiple rates of return fail to exist in the case of MIRR. Hence, MIRR is better regarding the measurement of the true rate of return.