About Internal Rate of Return (IRR) in Capital Budgeting Techniques in brief
We have two kinds of Cash Flows, i.e. Even Cash Flow and Uneven Cash Flow. We use normally two different formula each for Even Cash Flow and Uneven Cash Flow as follows.
(a) For Even Cash Flow
Initial Cash Outlay
Step 1: Calculate Payback Period = ------------------------
Annual Cash Flow
Step 2: Look at the PVIFA table for the n th period (frequency) and locate the discount factor where lies. If the discount factor match exactly with the Payback period, then that is the IRR of the project. But the PBP lies in between two discount ffactor, then we find IRR by Interpolation as follow.
PVIFA at LR - PBP
IRR = LR + ------------------------------------- x (HR - LR)
PVIFA at LR - PVIFA at HR
(b) For uneven Cash Flow
Total Cash Flow
Step 1: Find out the average Annual Cash Flow (fake annuity) = --------------------------
No of Periods (N)
I C O
Step 2: Find out the fake Payback period = -------------------
Fake annuity
Step 4: Now start trial & error using the Interest rate discount factor and find out Net Present Value (NPV). Calculate the NPV with different discount rate until there come one positive and another negative NPV. Once you find out one positive and next negative NPV, then find out IRR by interpolation by using any one of the following formula.
PV at LR - NCO
IRR = LR + --------------------------- x (HR - LR)
PV at LR - PV at HR
Or,
NPV at LR
IRR = LR + ----------------------------- x (HR - LR)
NPV at LR - NPV at HR
Note: In the meantime, it should be noted that in the Capital Budgeting- Cash Flow Principles (i.e. NCO, Annual CFAT, Terminal Cash flow) there is never a case of even cash flow. There is always uneven cash flow because of the terminal cash flow at the final year which is generally different than regular annual cash flows. Therefore, uneven case is used for IRR.