# Internal Rate Of Return

Internal rate of return is that rate at which the sum of discounted cash inflows
equals the sum of discounted cash outflows. In other words, it is that rate which
discounts the cash flows to zero. It can be stated in the form of a ratio as follows:

Cash outflows

Thus in case of this method, the discount rate is not known but the cash outflows and inflows are known. For example, if a sum of $800 invested in a project becomes $1,000 at the end of a year, the rate of return comes to 25% calculated as follows:

COF = CIF / (1 + r)

Where,

800 = 1000 / (1 + r);

1 + r = 1000 / 800;

1 + r = 1.25;

r = 0.25 or 25%.

In case if the return is over number of years, the calculation would take the following pattern:

In case of conventional initial investment:

Where,

In case of non-conventional cash flows (i.e., when there are a series of cash outflows and inflows)

= (EQUATE)

__Cash inflows__= 1Cash outflows

Thus in case of this method, the discount rate is not known but the cash outflows and inflows are known. For example, if a sum of $800 invested in a project becomes $1,000 at the end of a year, the rate of return comes to 25% calculated as follows:

COF = CIF / (1 + r)

Where,

COF | = | Cash outflow |

CIF | = | Cash inflow |

r | = | Internal rate of return |

800 = 1000 / (1 + r);

1 + r = 1000 / 800;

1 + r = 1.25;

r = 0.25 or 25%.

In case if the return is over number of years, the calculation would take the following pattern:

In case of conventional initial investment:

Where,

CF | = | Cash inflows |

COF | = | Cash outflow (initial) |

r | = | Internal rate of return |

n | = | last year of the project |

In case of non-conventional cash flows (i.e., when there are a series of cash outflows and inflows)

= (EQUATE)

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**Accept/Reject Criterion:**__A project would be qualified to be accepted if IRR exceeds the cut-off rate__pre-determined by the management. Generally the cut-off rate would be the cost of capital of the company.

__While evaluating two or more projects, a project giving a higher IRR would be preferred.__

**Method of calculation:**

IRR is calculated according to two methods on the basis of Tabular values as follows:

- Where cash inflows are uniform: IRR can be calculated locating the Factor in Annuity Table II. Factor is calculated as Initial investment / Cash inflow per year.
- Where cash inflows are not uniform: IRR is calculated by trial calculations in an attempt to compute the correct interest rate. Cash inflows are to be discounted by a number of trial rates. The first trial rate may be calculated on the basis of factor calculation which is done when cash inflows are uniform. But in this case, factor is calculated by dividing the initial investment by average annual cash inflows. In case the PV of cash inflows exceeds the PV of cash outflows, a trial rate higher than the first trial rate will be used and this process will continue will the two flows are more or less set off each other and this rate will be the IRR.

**Example:**Let us calculate the IRR of an equipment which requires an initial investment of $6,000. The annual cash inflow is estimated as $2,000 for 5 years.

**Solution:**Annual cash inflows are uniform. So, factor = $6,000/$2,000= 3. This factor of 3 should be located in Table II in the line of 5 years. The discount percentage would be somewhere between 18%($3.127 PV of annuity $1) and 20% ($2.99 PV of annuity of $1). By exact interpolation, we can find out the exact rate. But in this case, we can straight away take IRR as 20% as $2.99 is closer to factor 3.