# Internal Rate of Return (IRR)

The IRR is used when the cost of the investment and the annual cash flows are known and the unknown rate of earnings to be determined.The IRR is described as that rate which equates the present value of the future cash flows with the cost of the investment which produce them. IRR method is also called yield on investments, marginal efficiency of capital, time adjusted rate of return, rate of return and so on.

The IRR is the discounted rate that equals the aggregate present value of CFAT (cash flow after tax) with the aggregate present value of cash outflows required for a new investment. The project will be accepted only if IRR is higher than cost of capital.

1. IRR method considers the time value of money.
2. IRR method discloses the maximum rate of return the project can give.
3. IRR method considers and analysis all cash flows of entire project.
4. IRR method ascertains the exact rate of return the project earns.

1. IRR method is difficult to understand, complications due to trial and error method.
2. The important drawback of IRR is that it recognizes the cash inflows generated by project is reinvested to internal rate of project, but NPV recognizes such cash inflows are reinvested to cost of capital of the organization.
3. Single discount rate ignores the varying future interpret rate.

### Calculation Of IRR

For even case

First, find out factor

Factor = Net Cash Outlay(NCO)/Cash flow after tax(CFAT)

Factor is also known as payback period.

After finding out the factor, locate the factor in the line of annuity table at given year from row side, if the factor lies exactly in any percentage then that percentage is known as IRR.If the factor does not lie exactly then take two percentage corresponding one higher and another lower and interpolate it.

By interpolation,

IRR= LR + (Factor at LR- Required rate)/(Factor at LR- Factor at HR) x (HR-LR)

where, LR = lower rate and HR = higher rate.

For uneven case

First find out factor

Factor = NCO/Average CFAT

where, average CFAT= Total sum of CFAT/Total life of the project

After finding the factor, locate the factor in the line of annuity table at given year from row side, if the factor lies exactly in any percentage then that percentage is known as IRR. If the factor does not lie exactly then take two percentages corresponding one higher and another lower and interpolate it.

By interpolation,

IRR= LR +(TPV at LR – NCO)/(TPV at LR- TPV at HR)x (HR-LR)

Note: For even case one TPV must be higher than NCO whereas another should be lower than NCO.

#### Decision Rules Of IRR

If projects are independent

* Accept the project which has higher IRR than cost of capital(IRR> k).

* Reject the project which has lower IRR than cost of capital(IRR

If projects are mutually exclusive

* Accept the project which has higher IRR

* Reject other projects

For the acceptance of the project, IRR must be greater than cost of capital. Higher IRR is accepted among different alternatives.