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# Internal Rate of Return (IRR) on Investment Concept & Modelling

Updated: Apr 27, 2018 This is the third article on key financial models and calculations in modern finance and investment analysis for the capital budgeting process. As mentioned in the previous article, because capital is limited in its availability, capital projects are individually evaluated using both quantitative analysis and qualitative information.

There are 6 main tools in use;

1. Net Present Value (NPV)

2. Internal Rate of Return (IRR)

3. Modified Internal Rate of Return (MIRR)

4. Profitability Index (PI)

5. Payback

6. Discounted Payback

Internal rate of return (IRR) is a financial metric used in cash flow analysis, primarily for evaluating investments, capital acquisitions, project proposals, programs, business case scenarios as well as capital budgeting to estimate the profitability of potential investments. Internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.

The higher a project's internal rate of return, the more desirable it is to undertake. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and be undertaken first.

IRR is sometimes referred to as "economic rate of return" or "discounted cash flow rate of return." The use of "internal" refers to the omission of external factors, such as the cost of capital or inflation, from the calculation. One popular use of IRR is comparing the profitability of establishing new operations with that of expanding existing ones. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand a previously existing one. While both projects are likely to add value to the company, it is likely that one will be the more logical decision as prescribed by IRR.

IRR is all about cash flow stream and there should be a negative and positive cash flow values to be able to calculate it accurately. Timing, interest rate and reinvestment rates support an investment decision. However, IRR alone would not be suitable to give accurate information and therefore variations kicks in. This article emphasises several IRR issues and we will review it accordingly.

# So, What is Internal Rate of Return (IRR)

Internal Rate of Return estimates the profitability of potential investments. Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. There are several different IRR interpretations and formulas. Therefore, I will explain two simple IRR definitions and then MIRR and XIRR respectively.

Definition 1- IRR is the Discount Rate That Brings NPV to Zero

For any IRR calculation, negative and positive cash flow values required; there should be at least one negative and one positive cash flow to complete the calculation. The first number in the cash flow series is typically a negative number that is assumed to be the project's initial investment.

A higher IRR figure generally indicates less risk. This is because IRR shows just how high inflation rates or risk probabilities have to rise in order to eliminate the present value of this investment.

Simple IRR calculations have limited value for evaluating and comparing investment proposals. The reason behind this verdict is simple because some months have 31 days while others have 30 or fewer, the monthly ­periods are not exactly the same length, therefore, the IRR will always return a slightly erroneous result when multiple monthly periods are involved.

Definition 2- IRR is the single interest rate for financing costs and for reinvestment earnings that sets the total gains exactly equal to total costs

In this definition IRR result assumes the use of funds to pay investment costs brings additional costs, either borrowing costs or opportunity costs. Also, incoming returns are reinvested, earning additional gains.

The meaning of IRR magnitude is difficult to interpret because IRR can differ from the actual financing and earnings rate for returns. Therefore, a new Modified Internal Rate of Return (MIRR) metric has been developed to the real financing cost rate and real earnings rate for returns.