Introduction
You must have come across the term MIRR. MIRR is an acronym for Modified internal rate of return and is a commonly used finance term in capital budgeting and valuation of loans. MIRR is a measure to rank a particular investment’s alternative options in capital budgeting. MIRR is a modification of the Internal rate of return (IRR), which solves the issues revolving around IRR.
Before diving further into this topic, let us first understand what MIRR is:
Definition of modified internal rate of return:
Modified Internal rate of return (MIRR) is a revised version of the Internal rate of return (IRR). MIRR calculates a reinvestment rate and accounts for even or uneven cash flows. It assumes that the positive cash flows are reinvested at the firm’s cost of capital and the financing cost as the discount rate for the firm’s negative cash flows, whereas the traditional internal rate of return (IRR) assumes cash flow from a project is reinvested in IRR itself. The MIRR thus more accurately reflects the cost and profitability of a project
The major difference between IRR and MIRR is that IRR assumes that cash flow is reinvested at the same rate at which they were generated, whereas, In MIRR positive cash flow is reinvested at the reinvestment rate.
An investment should be considered/undertaken if the MIRR is higher than the expected return. If the MIRR is lower than the expected return, the project should be rejected. Between two projects the one with higher MIRR should be considered.
How do you calculate MIRR?
To calculate the MIRR formula of a project we need to know three things:
- a) Future value of a firm’s positive cash flow discounted at the reinvestment rate.
- b) Present value of a firm’s negative cash flows discounted at the cost of the firm.
- c) The number of periods
Mathematically, the calculation of MIRR is expressed using the following formula:
MIRR = n(FVCF/PVCF) -1
FVCF- Future value of positive cash flows discounted at the reinvestment rate
PVCF- Present value of negative cash flows discounted at the financing rate
n – the number of periods
MIRR is tedious to be performed by manual calculation, calculating it in spreadsheets is fairly easy. In applications like MS excel, it can be calculated using the following function
=MIRR (cash flows, financing rate, reinvestment rate).
MIRR Example:
There are two mutually exclusive projects X and Y and we have to decide which one is more profitable than the other.
Project X has a life of 3 years with a cost capital of 12% and financing cost of 14%
Project Y has a life of 3 years with a cost of capital of 15% and financing cost of 18%
The estimated cash flow is as follows:
Calculating the future value of positive cash flows discounted at the cost of capital.
Project X: 4,000 x (1+12%) x1+5,000=9,480
Project Y: 3,000x (1+15%) x1+1500=4,950
Calculating the present value of negative cash flow discounted at the financing cost:
Project X: -1,000+(-2,000)/ (1+14%) x1= -3,000
Project Y: -800+(-700)/ (1+18%) x1 = -1,500
Calculating the MIRR of each project
Using the formula:
MIRR = n(FVCF/PVCF) -1
Project X: MIRR = 3(9,480/3,000) -1 = 0.467
Project Y: MIRR = 3(4,950/1,500) – 1= 0.488
Therefore, Project Y should be undertaken as it has a higher rate of return
Let us now talk about some of the advantages and disadvantages of MIRR:
Advantages of MIRR:
- MIRR can be used to assess projects with inconsistent cash flow
- MIRR takes into consideration, the practically possible reinvestment rates
- MIRR can be used to calculate project sensitivity as it measures variation between the cost of capital and financing cost.
Disadvantages OF MIRR:
- MIRR demands computing an estimate of the cost of capital, which can be flawed as it is not subjective and can vary depending on the assumptions made.
- MIRR does not quantify the various impacts of different investments in absolute terms, it may also fail to produce optimal results in case of capital rationing.
How MIRR solves the multiple IRR problems
MIRR improves on standard IRR by adjusting for differences in assumed reinvestment rates of initial cash outlays and subsequent cash inflows.In a project with different periods of positive and negative cash flows, the IRR produces more than one solution which creates ambiguity. MIRR solves this problem by providing only one solution.
Conclusion:
MIRR is excellent to assess projects with a mix of positive and negative cash flow. It can also be used to compare the different investment projects of unequal sizes. MIRR also solves the issues associated with IRR having multiple solutions for the same project. It helps an individual to make a definite investment decision.
MIRR also provides flexibility, allowing the project managers to change the assumed rate of reinvested growth from stage to stage in a project. If there are a series of investments at different times having different interest rates, then MIRR can offer more accurate results compared to IRR.
To sum it up, although MIRR has certain disadvantages like its complexity, and assumptions considering the cost of capital. But its clarity and its ability to produce a single solution make it an attractive option for measuring investments.
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