Internal Rate of Return and Modified Internal Rate of Return
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:
reinvestment of the cash flows happens at the cost of capital which is practically possible
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.
FAQs on Difference Between IRR and MIRR
1. What is the Internal Rate of Return (IRR) in the context of capital budgeting?
The Internal Rate of Return (IRR) is a financial metric used in capital budgeting to estimate the profitability of potential investments. It is the specific discount rate that makes the Net Present Value (NPV) of all cash flows (both inflows and outflows) from a particular project equal to zero. Essentially, it represents the expected compound annual rate of return an investment will generate.
2. What is the Modified Internal Rate of Return (MIRR), and what problem with IRR does it solve?
The Modified Internal Rate of Return (MIRR) is an advancement of the IRR. It is designed to provide a more realistic measure of a project's profitability by addressing a key flaw in the IRR calculation. MIRR solves the problem of the reinvestment rate assumption, assuming that positive cash flows are reinvested at the firm's cost of capital, not at the project's own IRR.
3. What are the primary differences between IRR and MIRR?
The primary differences between IRR and MIRR lie in their assumptions and outcomes:
Reinvestment Rate: IRR assumes that cash flows generated by the project are reinvested at the IRR itself. MIRR assumes they are reinvested at the firm's cost of capital or another external rate.
Realism and Accuracy: MIRR is generally considered more accurate and realistic because the firm's cost of capital is a more achievable reinvestment rate than a potentially high IRR.
Multiple Solutions: For projects with non-conventional cash flows (e.g., multiple negative flows), IRR can yield multiple results. MIRR always produces a single, unambiguous result.
4. Why is MIRR often considered a more realistic measure of a project's return than IRR?
MIRR is considered more realistic because it separates the investment and financing decisions. It uses the firm's actual cost of financing to discount outflows and a practical reinvestment rate (like the cost of capital) to compound inflows. The IRR's assumption that a company can consistently reinvest interim cash flows at the project's own high rate of return is often impractical and overly optimistic, leading to an inflated perception of profitability.
5. Can you provide a simple example of how IRR and MIRR are applied to an investment?
Imagine a project requires an initial investment of ₹50,000 and is expected to generate cash inflows of ₹20,000, ₹30,000, and ₹25,000 over three years. The firm’s cost of capital is 10%.
The IRR calculation would find the single discount rate that makes the present value of these three inflows equal to the initial ₹50,000 investment. This calculation implicitly assumes the ₹20,000 and ₹30,000 inflows are reinvested at this same high IRR.
The MIRR calculation would first find the future value of all inflows at the 10% cost of capital, then determine the discount rate that equates this future value lump sum back to the initial ₹50,000 investment. This provides a more conservative and practical return percentage.
6. What is the fundamental assumption about reinvestment in IRR, and how does MIRR's approach differ?
The fundamental and often criticized assumption of IRR is that all interim positive cash flows from a project are reinvested at the same rate as the IRR itself. If a project's IRR is 25%, the model assumes the company can find other investments that also yield 25%. MIRR's approach differs by using a separate, explicitly defined rate for reinvestment—usually the firm's cost of capital—which reflects a more plausible, average return on available investment opportunities for the company.
7. In which specific business scenarios is it more advantageous to use MIRR over IRR?
It is more advantageous to use MIRR over IRR in several key scenarios:
Comparing Mutually Exclusive Projects: When choosing between projects of different sizes or timeframes, MIRR provides a more reliable comparison because it evaluates them based on a common, realistic reinvestment rate.
Projects with Non-Conventional Cash Flows: If a project involves significant future costs (e.g., environmental cleanup), it creates non-conventional cash flows. IRR might produce multiple confusing answers, whereas MIRR will always provide a single, clear rate of return.
Capital Rationing: When a company has limited capital and must choose the most profitable projects, MIRR gives a more accurate ranking of project profitability, leading to better capital allocation decisions.
