Difference between IRR ie Internal rate of return and ARR ie Annual rate of return?

Question

The terms are commonly used for viability analysis of new projects to go ahead with.

Answer 1

The first and main difference is that an ARR is for one year only. While an IRR can be computed for a period of 1 or more years. =)

Second, we usually use IRR when making projections of expected income of a proposed project. On the other hand, when we speak of ARR, we usually refer to historical data (computation of rate based on income already earned, not income forecasted. Just a matter of point of view).

ARR is actually a form of IRR, although for one year only.

To make things simple:

Let's say you invested 100 today for a project expected to provide income of 40 after a year. To get the ARR, we simply divide 40 by 100. The ARR then is 40%. Your project earned 40% after one year. At this time, the IRR is also 40%.

Another example. Let's say you invested 100 today for a project expected to provide income of 40 EVERY YEAR FOR 5 YEARS. At the end of the first year, the ARR is 40% (40/100). At the end of the second year, the rate is no longer 40% because now you have 140 to begin with! The computation of ARR is 40/140, which is 28.57%. At the 3rd year, 22.22% (40/180), and so on.

It would be tedious to compute the yearly rate of return, so mathematicians (I guess) invented a way to compute just one rate -the Internal Rate of Return. This involves a complex computation for someone who has not studied about the time value of money. It involves the process we call Interpolation. The cost of investment, the income per year, and the no. of years are the factors needed in computing IRR. You better look for books or other resources to learn about this.

Based on my computation, the IRR is somewhere between 28% and 29%.

Answer 2

ARR is used to label the kind of percentage it is.

IRR of return is a method of calculating the return on investment, the result of which could be stated in either an ARR, or a monthly rate of return.