**This writing puts to rest all arguments made against IRR in comparison with NPV.**

- One must understand how IRR is computed before its comparison with NPV. Note that IRR is an approximation. Input to calculate IRR requires that one provides ‘the amounts’ and ‘the corresponding points of time.’ When we calculate monthly or annual IRR, we do huge approximations. The thousands of cash inflows and outflows happening at different points of time are assigned to one particular point of time (typically starting or ending or mid of year) in a say, year, which is technically mathematically incorrect. So, for all practical purposes, alternate positive and negative cash flows are intrinsic to business and IRR is designed to take into account that.
- When we want to calculate IRR in ‘% per year’, we sum up all cash inflows and outflows for a year. It is not necessary to do so for a year and we can choose a different period. The result won’t mislead. IRR is an interpretation of the returns from a business. The returns from a business are never uniform in reality but they fluctuate with time. So IRR has utility only in terms of approximate barometer of returns and it doesn’t capture precise reality.
- Take a cash flow of an investment in which you invest Rs. 100 in a business and it returns Rs. 5 each year. You, say, exit the investment after 10 years. The IRR here is 5%. You can easily compare it with all available options at the outset and this facility is not there with NPV.
- As the number of years increase, the NPV would be more. Should this affect decision? Do all investment options have same period of entry and exit of investment? No. Then how would compare them when there is different period involved? IRR is the solution. Not only this but the various business options require that you put the money in and take it out at ‘different points of time in economy’ though the ‘period’ may be same. NPV can’t factor in this can mislead you.
- When we sum up all cash inflows and cash outflow and calculate net cash flow, we have option to change this period so that there is only one negative cash flow. For example, make net cash flow biannual or semi-annual to take of fluctuations of positive of negative sign. Here, if rb is biannual IRR, (1+r)
^{1/2}-1 is the annual IRR. - Many a time or most of the times, NPV and IRR don’t contradict in what has been deduced.
- The most serious lacuna of NPV is that there is nothing to compare it with. Suppose you calculate NPV of two businesses at 16% discounting rate. NPV1 of business B1 is more than NPV2 of business B2. But depending upon what is the ‘amount of investment’, you would be misled to think that business B1 is better. Think of two businesses with same NPV of Rs 100 but churning of Rs 1000 crores in one and just Rs 1000 in another. It doesn’t make sense!!!
- In the same way there are two real IRRs r1 and r2 for a cash flow, you may reach the same NPV, say NPV1, for some another case of business with two real discounting rates d1 and d2. Where is advantage of NPV in averting mathematical trauma that IRR suffers?
- There are ways out sign changes for cash flows. For a multiple positive and negative cash flows business, you may choose to keep the highest negative cash flow NCF1 as it is. Take some approximate discounting rate d1 and merge other major nearby negative cash flows NCF2 , NCF3 into NCF1. Now you would have only one negative cash flow. Compute the IRR r1. Change the discounting rate d1 to recalculate r1 such that d and r very close using iterations.
- The realness of IRR can be tested. In one the above examples where 100 Rs. is invested, the IRR of opposite cash flow from the perspective of the business is also 5% (and not -5%). This is absurd. But for this and every other cash flow you test the reality (being a real number, I mean) of IRR. Recalculate the IRR ‘of investor’ with Rs. 1 advantage, i.e. Rs 99 investment and same 5 Rs. return. This should increase investor’s IRR (it does). For the business, advantage of Rs 1, i.e. investment of 101 by investor and same return to investor, i.e. Rs. 5 should also result in increase in the IRR (but it doesn’t) and we can discard that. Thus we can test whether the IRR is real or game of complex numbers.
- Suppose you calculate the NPV of cash inflows NPVi and NPV of cash outflows NPVo for a business. Assume that you have made projections for 15 years. If we find that the ratio NPVo/NPVi is 1.20. Would this imply that there is 20% return? A big no! The 20% return is over ’15 years’ and not in one year. Note that what NPV tells is about project life cycle in value terms for whole life and what IRR tells is return in percentage every year. Thus IRR further helps to know the better entry and exit points of an investment as NPV talks only about worth of business at the end. If your actual returns (IRR) ra have more than expected returns re at the outset and if there no better future, you can exit. Thus, IRR helps in intermediate decisions.

In conclusion, for all practical purposes, all disadvantage of IRR can be done away with which is not possible with NPV. I will address the rest of issues in next comment. Please feel free to ask further questions. Please watch the videos and see the speech note on basics of IRR on r/StartupPhilosophy where all this has been verbally narrated.