Internal Rate of Return

The Internal Rate of Return is the rate which equates the Present Value of Cash Inflows with the Present Value of Cash Outflows of an investment. It is the rate at which the Present Value of the proceeds and the outlays are equal. In other words, it is the rate at which the Net Present Value is (PV of Cash Outflows – PV of Cash Inflows) is zero.

As you know we use the following formula to find the Present Value of Cash inflows:

FV1 [1 / (1 + r)1] + FV2[ 1 / (1 + r)2] +

………… ………………………………………………….+ FVn[1 / (1 + r)n]

Since PV of Cash Outflows (Co) is also known, we may use the following equation to find out r:

{FV1 [1 / (1 + r)1] + FV2[ 1 / (1 + r)2] +

……… …………………………………………….+ FVn[1 / (1 + r)n]} – Co = 0

The IRR, or internal rate of return, is defined as the discount rate that makes NPV = 0. Like the NPV process, it starts by identifying all cash inflows and outflows. However, instead of relying on external data (i.e. a discount rate), the IRR is purely a function of the inflows and outflows of that project. The IRR rule states that projects or investments are accepted when the project’s IRR exceeds a hurdle rate. Depending on the application, the hurdle rate may be defined as the weighted average cost of capital.

Example:

Suppose that a project costs Rs. 10 million today, and will provide a Rs. 15 million payoff three years from now, the FV of a single-sum formula will be used to solve for r to compute the IRR.

IRR = (FV/PV) 1/N -1

= (15 million/10 million) 1/3 – 1

= (1.5) 1/3 – 1 = (1.1447) – 1

= 0.1447, or 14.47%

In this case, as long as the hurdle rate is less than 14.47%, a ‘go’ signal will be given to the project.