How can we determine internal rate of return (IRR)?

Refer 

 

http://www.investopedia.com/terms/i/irr.asp

The IRR can be found either by using trial-and-error technique with interpolation or with the aid of a sophisticated financial calculator or a computer.
Here we demonstrate the trial-and-error approach. 
In my opinion, use of interpolation method is better in the absence of advanced calculator or computer.

IRR can be reach through the following process:

First find out Present Value:

PV = FV / (1+r)n

• PV is Present Value
• FV is Future Value
• r is the interest rate (as a decimal, so0.10, not10%)
• n is the number of years

And let's use the formula:

Example: Alex promises you $900 in3 years, what is the Present Value (using a10% interest rate)?

• The Future Value (FV) is $900,
• The interest rate (r) is10%, which is 0.10 as a decimal, and
• The number of years (n) is 3.

Use the formula to calculate Present Value of $900 in3 years:

PV = FV / (1+r)n PV = $900 / (1 +0.10)3 = $900 /1.103 = $676.18 (to nearest cent).

 

Example: try that again, but use an interest rate of6%

The interest rate (r) is now6%, which is 0.06 as a decimal:

PV = FV / (1+r)n PV = $900 / (1 + 0.06)3 = $900 / 1.063 = $755.66 (to nearest cent). Net Present Value (NPV)

Now we are equipped to calculate the Net Present Value.

For each amount (either coming in, or going out) work out its Present Value, then:

• Add the Present Values you receive
• Subtract the Present Values you pay

Like this:

Example: You invest $500 now, and get back $570 next year. Use an interest Rate of10%.

Money Out: $500 now

You invest $500 now, so PV = -$500.00

Money In: $570 next year

PV = $570 / (1+0.10)1 = $570 /1.10 = $518.18 (to nearest cent)

And the Net Amount is:

Net Present Value = $518.18 - $500.00 = $18.18

 

So, at10% interest, that investment has NPV = $18.18

But your choice of interest rate can change things!

Example: Same investment, but the interest Rate is 15%

Money Out: $500 now

You invest $500 now, so PV = -$500.00

Money In: $570 next year:

PV = $570 / (1+0.15)1 = $570 /1.15 = = $495.65 (to nearest cent)

Work out the Net Amount:

Net Present Value = $495.65 - $500.00 = -$4.35

 

So, at15% interest, that investment has NPV = -$4.35

It has gone negative!

Now it gets interesting ... what Interest Rate would make the NPV exactly zero? Let's try14%:

Example: Try again, but the interest Rate is 14%

Money Out: $500 now

You invest $500 now, so PV = -$500.00

Money In: $570 next year:

PV = $570 / (1+0.14)1 = $570 /1.14 = $500 (exactly)

Work out the Net Amount:

Net Present Value = $500 - $500.00 = $0

 

Exactly zero!

At14% interest NPV = $0

And we have discovered the Internal Rate of Return ... it is 14% for that investment.

Because14% made the NPV zero.

Internal Rate of Return

So the Internal Rate of Return is the interest rate that makes the Net Present Value zero.

The rate of return wher all inflows are equal to outflows is IRR.
 

The discount rate often used in capital budgeting that makes the net present value of all cash flows from a particular project equal to zero. Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. As such, IRR can be used to rank several prospective projects a firm is considering. Assuming all other factors are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

Calculating IRRThe simplest example of computing an IRR is by using the example of a mortgage with even payments. Assume an initial mortgage amount of $200,000 and monthly payments of $1,050 for30 years. The IRR (or implied interest rate) on this loan annually is4.8%. Because the a stream of payments is equal and spaced at even intervals, an alternative approach is to discount these payments at a4.8% interest rate, which will produce a net present value of $200,000. Alternatively, if the payments are raised to, say $1,100, the IRR of that loan will rise to5.2%.The formula for IRR, using this example, is as follows:

• Where the initial payment (CF1) is $200,000 (a positive inflow)
• Subsequent cash flows (CF2, CF3, CF N) are negative $1050 (negative because it is being paid out)
• Number of payments (N) is30 years times12 =360 monthly payments
• Initial Investment is $200,000
• IRR is4.8% divided by12 (to equate to monthly payments) =0.400%

 

 

Different method are available to determine the internal rate of return, also called economical rate of return, that have mentioned below Payback Period Net Present Value: NPV=PvB-PvC,  Internal rate of Return Mostly, the last one is used in determing the IRR for a project.
it can be defined"the rate at which NPV becomes Equal to zero that is NPV=0.
And we use hit and trial technique to find out that value of r which makes NPV equal to zero

step
1- create the the cash flow chart of the project on yearly basis.
step
2- calculate the npv at WACC. 
step
3- calculated npv=A and discount factor i.e WACC should be marked as =a step4 - calculate npv at a higher discount rate.
suppose if a=10 then calculate at20 step
5- marked the npv=B and discount factor=b apply the formula = a+((A/(A-B))*(b-a))  

In simple terms, it is the rate (a percentage) of growth a project is expected to generate.
So if you invest $500 in a project and it generates $550 in year1.
Your IRR is10% [(550/500)-1] For detailed explanation you see this website: http://www.mathsisfun.com/money/internal-rate-return.html