Thanks William. I may be wrong, but to my knowledge IRR assumes that the cash is re-invested immediately at the same rate. This may not be so, as finding an investment for the same rate may not be practical always. If this is wrong... why would people use Modified IRR? Anyway I'll let you decide that. You can check out this article from McKinsey Quarterly http://www.mckinseyquarterly.com/Corporate_Financ...
Jose Paul Martin
· 1 year ago
Please note that this post is a combination of two previous posts that I worked on - IRR and IRR Tables. Hope you enjoy it.
William Little
· 1 year ago
Found your article on IRR very interesting.
Just one comment - Weaknesses: para 3, IRR can also produce misleading results because, as classically defined, it assumes that the cash returned from an investment is reinvested at the same percentage rate, which may not be realistic. ...
The definition of IRR does NOT assume that cash is reinvested - if reinvestment takes place then that is a different problem to solve. IRR measures the rate of return of the "project balance". The "project balance" is the cash employed by the project and varies over time as the interest in the project accumulates and as cash is added or returned.
It has been established throughout the literature that NPV is a better metric than IRR when assessing or comparing cash flow projects.
William Little
· 1 year ago
Further to my contention that the classic IRR problem does NOT assume that the benefits are reinvested immediately at the same rate, I offer the following discussion.
Internal rate of return problems may be visualised by examination of the cash flow (CF) or in combination with reinvested CFs. May I demonstrate using your example of CF and a hurdle rate of 10%.
Case (a). For IRR and no reinvestment. Your example, CF1 is (-1000, 300, 300, 300, 300, 300), in thousands of dollars which gives an IRR = 15.24% and NPV @ 10% = $137,240. The same results as you. Here the benefits are ejected from the project as they occur - no reinvestment. This could be Bond interest payments or a company paying dividends.
Case (b). For IRR with a reinvestment of 15.24% the same as the unreinvested IRR of (a). Reinvested CF2 is (0, -300, -300, -300, -300, 1732.35). Add CF1 and CF2 to get the reinvestment CF3 (-1000, 0, 0, 0, 0, 2032.35) which gives an IRR = 15.24% and NPV @ 10% = $261,930. Here the IRR is the same as (a) but we have a larger NPV.
Case (c). For IRR with a reinvestment of 10%, the same as the hurdle rate. Reinvested CF4 is (0, -300, -300, -300, -300, 1531.53). Add CF1 and CF4 to get the reinvestment CF5 (-1000, 0, 0, 0, 0, 1831.53). IRR = 12.87% NPV @ 10% = $137,240 Here the IRR is smaller than (a) but we have the same NPV.
Case (d). For IRR with a reinvestment of 3.55%. Reinvested CF6 is (0, -300, -300, -300, -300, 1310.51). Add CF1 and CF6 to get the reinvestment CF7 (-1000, 0, 0, 0, 0, 1610.51). IRR = 10.00% NPV @ 10% = 0 The smallest acceptable reinvestment rate is 3.55%.
Example (a) is the classic IRR problem where the benefits are consumed or paid out as they occur as in the case of an interest paying Bond.
Here (b),(c), and (d) are examples of modified rate of return (MIRR) where the benefits are kept within the project. They would be used with an appropriate reinvestment rate and hurdle rate.
My point is that benefits can be paid or reinvested at an appropriate rate but each particular problem should be modelled by describing its CF which may have several components and then calculating its IRR and NPV.
Since IRR is the rate of return on the "project balance" and NPV a measure of "value creation" then when comparing or assessing projects, NPV is normally the basis for selection and decision.
All Comments
Just one comment - Weaknesses: para 3,
IRR can also produce misleading results because, as classically defined, it assumes that the cash returned from an investment is reinvested at the same percentage rate, which may not be realistic. ...
The definition of IRR does NOT assume that cash is reinvested - if reinvestment takes place then that is a different problem to solve.
IRR measures the rate of return of the "project balance".
The "project balance" is the cash employed by the project and varies over time as the interest in the project accumulates and as cash is added or returned.
It has been established throughout the literature that NPV is a better metric than IRR when assessing or comparing cash flow projects.
Internal rate of return problems may be visualised by examination of the cash flow (CF) or in combination with reinvested CFs.
May I demonstrate using your example of CF and a hurdle rate of 10%.
Case (a). For IRR and no reinvestment.
Your example, CF1 is (-1000, 300, 300, 300, 300, 300), in thousands of dollars which gives
an IRR = 15.24% and NPV @ 10% = $137,240. The same results as you.
Here the benefits are ejected from the project as they occur - no reinvestment.
This could be Bond interest payments or a company paying dividends.
Case (b). For IRR with a reinvestment of 15.24% the same as the unreinvested IRR of (a).
Reinvested CF2 is (0, -300, -300, -300, -300, 1732.35).
Add CF1 and CF2 to get the reinvestment CF3 (-1000, 0, 0, 0, 0, 2032.35) which gives
an IRR = 15.24% and NPV @ 10% = $261,930.
Here the IRR is the same as (a) but we have a larger NPV.
Case (c). For IRR with a reinvestment of 10%, the same as the hurdle rate.
Reinvested CF4 is (0, -300, -300, -300, -300, 1531.53).
Add CF1 and CF4 to get the reinvestment CF5 (-1000, 0, 0, 0, 0, 1831.53).
IRR = 12.87% NPV @ 10% = $137,240
Here the IRR is smaller than (a) but we have the same NPV.
Case (d). For IRR with a reinvestment of 3.55%.
Reinvested CF6 is (0, -300, -300, -300, -300, 1310.51).
Add CF1 and CF6 to get the reinvestment CF7 (-1000, 0, 0, 0, 0, 1610.51).
IRR = 10.00% NPV @ 10% = 0
The smallest acceptable reinvestment rate is 3.55%.
Example (a) is the classic IRR problem where the benefits are consumed or paid out as they occur as in the case of an interest paying Bond.
Here (b),(c), and (d) are examples of modified rate of return (MIRR) where the benefits are kept within the project. They would be used with an appropriate reinvestment rate and hurdle rate.
My point is that benefits can be paid or reinvested at an appropriate rate but each particular problem should be modelled by describing its CF which may have several components and then calculating its IRR and NPV.
Since IRR is the rate of return on the "project balance" and NPV a measure of "value creation" then when comparing or assessing projects, NPV is normally the basis for selection and decision.