HIDDEN ISSUES IN IRR
Friends, in my opinion most of the people may not aware of certain issues linked with IRR. I have decided to explore those issues. One of the major considerations of concept of IRR is, reinvestment assumption. Point of view in which we need to see IRR also makes so much difference. Another concern while calculating IRR is the rate which we obtain through using a guess option is only a reasonable approximation. Through this article, I am going to explain the following
 Finding exact IRR rate
 My interpretation on IRR and NPV rate
 Conclusion
Finding exact IRR rate
Friends consider the following example(Example1)
ABC Ltd Company is about to evaluate the project IRR. Details of project cash flows are as below Initial Cash outflow Rs.20,00,000/ Cash inflows at the Year End of Year 1 Rs.3,50,000/ Year 2 Rs.4,50,000/ Year 3 Rs.6,00,000/ Year 4 Rs.8,00,000/ Year 5 Rs.10,00,000/
We know if Net present value is equal to zero, then such rate applied will be accepted as IRR. Guessing either 15% or 14% as IRR, I have decided to calculate N.P.V . While taking present value factors using the following formula for at most accuracy in Excel Sheet
Present Value Factor = (1/(1+R))Y
In the formula R = Rate for which we need to find N.P.V
Y = Year for which we need to find N.P.V
For the purpose of further explanation, I am calculating NPV even at 16% also. Considering the above N.P.V calculation is as follows
Please Turn Page
In the above picture extracted from M.SExcel, 14.86% is obtained as explained above. Although, only two digits are shown in the picture after decimal point as every calculation was done by me with reference to answer cell where we got the actual rate (i.e. 14.86% ). In sum up, I have taken utmost care to get exact answer i.e. either for 14.86% as IRR or Rs.1617 as N.P.V. In spite of my effort I am not able to get the accurate answer, why ? . But If you have observed 14.89%, N.P.V is ZERO.
This is because change in rate is not leading to proportionate change in amount. For example when rate has been changed from 14% to 15%, change in N.P.V is Rs.57592.18/ (i.e. 6298.45+51293.73) However when we change rate from 15% to 16%, change in N.P.V is Rs.55213.61/ (i.e. 61512.066298.45). Proportionate change will happen only when cash flows(before discounting), and present value factor both are based on a same logic or formula. Such cash flows generally will not be based on same logic and will depend on project and other existing conditions. In simple we can say 14.86% as rate which will be nearer to arithmetically accurate estimated IRR rate. If we see calculation in case of 14.89%, it can be treated as arithmetically accurate estimated rate of IRR. For deriving 14.89%, I have employed option called “Goal seek” in Microsoft Excel. While using such option, I have taken rate as variable to change, NPV as target cell and target as zero.
Please Turn Page
My interpretation on IRR and NPV rate Friends consider another example (Example2) Cash inflows of the project at the end of each year are 35,000/, 25,000/, 40,000/, 30,000/ and 26,000/. And the project duration is for 5 years assuming 15% as cost of capital/investment. Calculating Present Value of cash inflows for 5 years considering rate as 15%, and 18% .


PVF @


PVF @


Cash inflow at the Year end

Cash inflow

15%

PV

18%

PV

1

35000

0.8696

30434.78

0.8475

29661.02

2

25000

0.7561

18903.59

0.7182

17954.61

3

40000

0.6575

26300.65

0.6086

24345.23

4

30000

0.5718

17152.60

0.5158

15473.67

5

26000

0.4972

12926.60

0.4371

11364.84

Total

105718.22


98799.37

In the above calculation we neither considered investment value nor reinvestment value. We have just calculated present value of cash inflows at two discount rates. If we assume total investment in the project initially as Rs.98799.37/ and no further investments, then IRR becomes 18%.
In simple 18% rate explains maximum tolerable rate (MTR) up to which such project can sustain. And if difference between cost of capital/investment and IRR is very less (i.e. 18%  15% = 3% ), then one may consider it as higher risk project. For example (Example3) consider the following table
Project

Cost of Capital/Investment

MTR

Risk Margin

Risk Based Rank

A

15%

18%

3%

2

B

16%

20%

4%

1

C

14%

16%

2%

3

In the above table, ranks are allotted based on Risk Margin. Hence this Risk Margin may also be considered as decision making factor. In general cost of capital/Investment will be same if all the projects are in the same country. However if projects are related to different countries, then cost of capital/investment may vary depending on the country.
Conclusion In my opinion, IRR calculation does not consider reinvestment. Rate which has been considered as IRR may be treated as or called as Maximum Tolerable Rate (MTR). Such MTR can be called as Internal Rate of Return or not is a point which everybody needs to evaluate again.
Thanks for your attention,
VENKATA RAVI KISHORE D
REG.NO. SRO 0214785