# Internal Rate of Return Definition – IRR Formula and Example

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## Internal Rate of Return Definition and Example

Internal Rate of Return Definition – “The rate at which the net present value (NPV) of an investment equals zero”.

IRR or Internal rate of return is one of the discounted cash flow method of capital budgeting. Generally, IRR is used to measure the profitability of a project or investment. In order to calculate IRR, NPV of the investment is considered as zero and then r is calculated. This r is the internal rate of return.

Internal Rate of Return Formula

Take NPV = 0, then calculate ‘r’ which is IRR here. While comparing IRR of two projects, the project having higher IRR is accepted and vice versa.

In the above formula,

C0 = Initial Investments
t = number of time period
Ct = Cash flows at the time period t
r = discount rate

Now the question arises how to calculate r? Well, hit and trial method is used. r is assumed. Now with the help of r, NPV is calculated.

• NPV = 0, IRR is equals to r
• If NPV > 0, recalculate the value of NPV by taking new value of r.
• NPV <0, calculate NPV again by taking a new value of r.

### Internal Rate of Return Example

In order to understand Internal Rate of return definition more clearly, let’s discuss a problem.

Even Cash flows –

Assume, I or C0 = 10,000, t= 6 years and Annual cash flows are 2,500. Calculate r?

I = Annual Cash flows × PVIFA (r,6)

10,000 = 2,500 × PVIFA (r,6)

PVIFA (r,6) = 10,000/2,500

= 4

From Present Value Interest Factor Annuity table PVIFA (13,6) = 4 or 3.998

Therefore, r = 13%

Uneven Cash inflows –

 r = 10% r = 6% Year CF PVIF PV PVIF PV 0 (20,000) 1.00 (20,000) 1.00 – 1 4,600 0.909 4,181 0.943 4,337 2 5,800 0.826 4,790 0.890 5,162 3 6,600 0.751 4,957 0.840 5,544 4 7,000 0.683 4,781 0.792 5,544 NPV = NPV = (1291) 588

At r = 10% , NPV is negative 1291, whereas at r = 6%, NPV is positive 588 so  total is 1879.

r = {lower discount rate + (positive NPV/ sum of both NPV) × difference of the two discount rate.

={6+( 588/1879) × 4 }

= 7.2%

### Critical Issues with Internal Rate of Return

With the help of IRR, project managers rank their projects on the basis of returns rather than their NPV. Investment or project having higher IRR are chosen and vice versa. But there are some issues with IRR as well. It does not measure the absolute size of the investment. In addition to this, it does not works with those investments that results in interim flow of cash. The worst issue with IRR is that it does not compare the projects having different time period. Cost of capital is also ignored in case of IRR.