Internal rate of return (irr)

Internal rate of return (irr) is defined as that discount rate which equates the present value of future cash flows of a security to its market value.

Irr is viewed as the average annual rate of return that investors earn over their investment period assuming that cash flows are reinvested at irr.

In other words, it is a discount rate that makes net present value of a project is zero. The IRR is a total initial cash outflow and discounted cash inflows are equal to zero.

What is formula for Internal rate of return (irr)?

The Internal rate of return (irr) formula is as follows:

IRR = (Cash flows)/(1+r)ⁿ – initial investment

0 = CF₀ + CF₁ /(1+irr) + CF₂ /(1+irr)² ++CF₃ /(1+irr)³ + …….+CF_n /(1+irr)ⁿ

Where,

n = Each period

CF₀ = Initial investment/ outlay

CF₁ , CF₂, CF₃, CF_n = Cash flows

NPV = Net present value

IRR = Internal rate of return

This can be explained with the help of example:

Suppose Mr. Rishi invested Rs. 20,000 now in an asset that offers a cash flow of Rs. 3,000 one year from now and Rs. 23,000 from two year now . Mr. Rishi wants to know the irr of the investments. For this you must find out the discount rate that equates the present value of cash inflows to Rs. 20,000 , the value of initial investment .

	0 Time	1st year	2nd year
Cash flows	20,000	3,000	23,000

Now we solve the following equation for r which denotes irr and get 15%

20,000 = 3,000/(1+r) + 23,000/(1+r)_²

r = 15%

Thus Mr. Rishi’s IRR is 15% Which implies that Mr. Rishi earn on an average 15% on the investment per annum.

Now, lets assume that when he receive Rs. 3,000 , he reinvested @10% , which is actually less than what was expected to be earned before investment. The reason is that the cash flow is reinvested at 10% which is less than his expected IRR.

Further, if he had chance to reinvest Rs. 3,000 @15% , he would receive Rs. 26,450 at the end of 2nd year , and the internal rate of return (irr) of the investment would be equal to exactly 15% as calculated below:

= (26,450/20,000)^1/2 -1 = 0.15 or 15%