IRR-Single Outflow and Multiple Inflows

I am giving formula and steps to be followed in case of single outflow and unequal multiple cash inflow :-

1--  Calculate fake payback factor= Initial cash outflow / Avg Annual CFAT     ( Avg. Annual CFAT= All CFAT/n)

2--  Find 2 discount rates from PVAF table within which such fake payback factor lies on the basis of life period.

3---    Calculate NPV at both discount rates such that you get one -ve NPV and other +ve NPV.

              * If you get both positive NPV, then from PVAF table take a higher discount rate and then you calculate NPV. If you don't get -ve NPV keep on checking higher discount rate .

               * If you get both negative NPV, then from PVAF table take a lower discount rate and then you calculate NPV. If you don't get +ve NPV, keep on checking lower discount rates.

4--Calculate IRR=  Lower discount rate + { NPV at lower rate/ NPV @ Lower Rate - NPV @ higher rate} * ( Higher Rate- Lower Rate)

For any clarification on any particular point ask me without hesitation.

Regarding two outflows:-

Suppose in 0 year ---  Purchase of machine200000

    in end of 1st year--- Purchase of small equipment for above machine50000.

So while calculating IRR , there will be no change in calculation of fake payback factor as given in above steps. Take cash outflow as Rs 250000 in step 1.

Only change will come in calculation of NPV, because you will have to calculate PV of50000. Suppose @ 10% rate its PV is45450. Then PV of all cash outflow will be245450 (200000 + 45450). Subtract with PV of all cash inflows to know NPV.

Continue with above steps as given earlier to know IRR.

can u eleborate more on point 1 by giving an example faiz

Regarding explanation of step 1 :-

Suppose Purchase of machine  Rs 200000 and working capital Rs 20000. So cash outflow will be Rs 220000.

Now if CFAT are :-   Y1= 50000 ;  Y2= 20000 '; Y3= 100000; Y4= 50000

So Avg. Annual CFAT =  { 50000 + 20000 + 100000 + 50000} / 4  = Rs 55000.

Hence, Fake payback factor =  Rs 220000 / Rs 55000 = 4

Now see PVAF table , assume project life is 8 yrs.  In 8 yrs row see where you get 4 and it fall between which two discount rates . According to table it falls  between 18% and 19%

Now compute NPV as per above steps for these two rates 18% & 19%

If both + NPV check 20 % and so on until you get -ve NPV

If both - ve NPV check 17% and so on until you get + ve NPV.

The rate at which you get one -ve NPV and +ve NPV will be taken as higher rate and lower rate in the formula for calculating IRR.

Faiz thank u so much for the example given understood how to calculate IRR by using Guess rates thank u so much

You are welcome Mr. Sivaram