IRR estimates the discount rate that makes the value of subsequent net cash flows equal to the initial investment. It is the rate that makes the NPV of the project zero. In order to calculate the IRR, we need to consider the net present value of the project at two different discount rates. The IRR is calculated based on the assumption that the cash flows received during the project are reinvested at IRR (Gallo, 2016).
Using the formula,
IRR = LR + {NPV at LR / (NPV at LR - NPV at HR)} (HR - LR)
Where,
HR = Higher Rate of Return
LR = Lower Rate of Return
Example:
Let us consider a project with following cash flows and calculate its NPV at 15 % and 20 %.
The company uses IRR to find whether the project is worth investing or not based on the estimated percentage return offered by the project. If the calculated IRR is higher than the cost of capital, the investment is expected to increase the value of the firm and accepted. In the above example, if the cost of capital is less than 18.11 %, the project is accepted else it is rejected.
NPV and IRR both provide exactly the same decision regarding acceptance or rejection of the project in case of independent projects and projects with conventional cash flows. But in case of projects with unconventional cash flows and mutually exclusive projects with substantially different initial investments or substantially different timing of cash flows, NPV and IRR give contradictory results and make it difficult to take investment decisions. Similarly, sometimes there are multiple IRRs that increase the confusion (Moyer, McGuigan, Rao, & Kretlow, 2012).
Modified Internal Rate of Return (MIRR)
MIRR is the discount rate at which the present value of a project’s cost is equal to the present value of its terminal value. The advantage of MIRR over IRR is it assumes that cash flows from the project are re-invested at the at the cost of capital. Therefore it is better indicator of project’s profitability than IRR.
MIRR is calculated by solving this equation: Initial Investment = Terminal Value / (1 + MIRR) n
Example:
Let us consider the following two projects having cost of capital of 6 %.
In the above example, we can see that on the basis of NPV, project B is desirable and project A is desirable on the basis of IRR. In such situation, we calculate MIRR for these projects,
From the calculation, we can see that MIRR suggests Project B as better option for investment like NPV. Company uses MIRR because it gives a single correct answer for comparison of projects and avoid confusions. It is superior to regular IRR because it indicates the true expected long term rate of return (Ghimire, 2011).
References
Gallo, A. (2016, March 17). A Refresher on Internal Rate of Return. Harvard Business Review.
Ghimire, S. R. (2011). Fundamentals of Financial Management. Kathmandu: K.P Pustak Bhandar.
Moyer, R. C., McGuigan, J. R., Rao, R., & Kretlow, W. J. (2012). Contemporary Financial Management (12th ed.). Oklahoma: Cengage Learning.
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Internal Rate of Return (IRR)
IRR estimates the discount rate that makes the value of subsequent net cash flows equal to the initial investment. It is the rate that makes the NPV of the project zero. In order to calculate the IRR, we need to consider the net present value of the project at two different discount rates. The IRR is calculated based on the assumption that the cash flows received during the project are reinvested at IRR (Gallo, 2016).
Using the formula,
IRR = LR + {NPV at LR / (NPV at LR - NPV at HR)} (HR - LR)
Where,
HR = Higher Rate of Return
LR = Lower Rate of Return
Example:
Let us consider a project with following cash flows and calculate its NPV at 15 % and 20 %.
Using the formula,
IRR = 15 + {465 / (465 + 281.95)} (20 - 15)
= 18.11%
The company uses IRR to find whether the project is worth investing or not based on the estimated percentage return offered by the project. If the calculated IRR is higher than the cost of capital, the investment is expected to increase the value of the firm and accepted. In the above example, if the cost of capital is less than 18.11 %, the project is accepted else it is rejected.
NPV and IRR both provide exactly the same decision regarding acceptance or rejection of the project in case of independent projects and projects with conventional cash flows. But in case of projects with unconventional cash flows and mutually exclusive projects with substantially different initial investments or substantially different timing of cash flows, NPV and IRR give contradictory results and make it difficult to take investment decisions. Similarly, sometimes there are multiple IRRs that increase the confusion (Moyer, McGuigan, Rao, & Kretlow, 2012).
Modified Internal Rate of Return (MIRR)
MIRR is the discount rate at which the present value of a project’s cost is equal to the present value of its terminal value. The advantage of MIRR over IRR is it assumes that cash flows from the project are re-invested at the at the cost of capital. Therefore it is better indicator of project’s profitability than IRR.
MIRR is calculated by solving this equation: Initial Investment = Terminal Value / (1 + MIRR) n
Example:
Let us consider the following two projects having cost of capital of 6 %.
In the above example, we can see that on the basis of NPV, project B is desirable and project A is desirable on the basis of IRR. In such situation, we calculate MIRR for these projects,
For Project A:
Terminal Value of Cash flow = 70,0001.064 + 40,0001.063 + 30,000 *1.062 + 10,000 * 1.061 + 10,000 * 1.060 = $ 1,90,322.0272
Now,
1,20,000 (1+MIRR)n = 1,90,322.0272
or, MIRR = 1.58601/3 - 1
Thus, MIRR = 16.62 %
For Project B,
Terminal Value of Cash flow = 10,0001.064 + 20,0001.063 + 30,000 *1.062 + 50,000 * 1.061 + 80,000 * 1.060 = $ 2,03,153.0896
Now,
1,20,000 (1+MIRR)n = 2,03,153.0896
or, MIRR = 1.69291/3 - 1
Thus, MIRR = 19.18 %
From the calculation, we can see that MIRR suggests Project B as better option for investment like NPV. Company uses MIRR because it gives a single correct answer for comparison of projects and avoid confusions. It is superior to regular IRR because it indicates the true expected long term rate of return (Ghimire, 2011).
References
Gallo, A. (2016, March 17). A Refresher on Internal Rate of Return. Harvard Business Review.
Ghimire, S. R. (2011). Fundamentals of Financial Management. Kathmandu: K.P Pustak Bhandar.
Moyer, R. C., McGuigan, J. R., Rao, R., & Kretlow, W. J. (2012). Contemporary Financial Management (12th ed.). Oklahoma: Cengage Learning.