### IRR (TIR) Calculation and its use on Project investment analysis Given the interest in our previous article «IRR, NPV or Payback to evaluate my investment projects?«, We will expand on these two topics of great interest to anyone who is to invest in a project or managing the convenience of investments in business and How to calculate them?

We’ll begin with the project IRR or Internal Rate of Return on Investment. For those unfamiliar with finance, let’s start with the premise that if the IRR is greater than the weighted average cost of capital for the project (WACC) or your yearly interest rate, it can be classified as economically feasible; subject to risks and changes in economic flows of operation. How to calculate the IRR? As we can see in the graph above, the basic principle is that the more expensive is my cost of capital (WACC), less economic value at the beginning of the project we will have, the latter is what should be of high interest for you in any project, have the project NPV as large and positive as possible. The IRR is precisely that mark or point where our economic value at the beginning of the project NPV, taking all economic flows (positive or negative) to the start time of the project (in financial terms: discounting) will make NPV equal to ZERO. ZERO profit on the interest rate (IRR). That is, how much interest our project is capable to pay. If your project has an IRR of 8% and your WACC is 10%, invest your money somewhere else.

I present you two options to calculate the IRR: via iteratively with the mathematical formula or formula via excel. Let’s start by knowing the mathematical formula. Since the IRR is derived from the formula of value of money over time, as shown in the image above, the IRR formula is not linear hence not possible to get its roots or IRR values that makes it zero. Someone, perhaps you, with mathematical knowledge would know what it means: there may be more than one solution to the equation to bring it to zero or function roots. Complex mathematical procedures are required to define the equation roots. To wrap it up, in terms of investment and decision making: once the roots are defined use the criterion of the smallest positive value of those roots as the project IRR. Another option to get to one of the roots (IRR value) is iterating IRR values in the formula until the value of NPV is zero. We can prepare the analysis with values of 0.5%, 1%, 2%, 3%, 4%, 5% ……. 25% and observe how the VPN value changes. You can see NPV diminishing as we increase the value of IRR, NPV tends to be zero. It is important to start from 0.5% or less, taking into consideration that there are many solutions to the equation. Thus eliminate the risk of not observing a much lower value of IRR than our WACC. On the other hand, it is of personal criteria to stop the iterations when the IRR does not take the VPN to zero (e.g. Iteration in IRR = 18% and my VPN is 350) and has exceeded considerably the project WACC (continuing with the same example think in a WACC of 13%), then it can be defined that the project itself is profitable or economically feasible (IRR> WACC). Of course, you still need to calculate the IRR or state that is greater than your WACC.

Note that in the case of analysis of more than 3 economic flows, it is recommended to make use of data sheets analysis to ease the iteration process calculation.Thinking on this fashion, a faster way to get an approximation of our IRR is with excel, a tool with automatic calculations on your PC or any other mathematica software (e.g maple, mathlab). Although anyone can install the MS Office validate the results using the method explained above formulation and make sure of what it is «behind the screen» is right! Not the case for maple or mathlab. On the other hand, if we have confidence in the millions of dollars that Microsoft invests in its programs, let’s get right to the calculation. To calculate the IRR, we use the formula: “=IRR(flows cells range)”, including the negative value for the initial investment. Make sure that the range of flows are the final value of the operations of the period to include in the range of assessment and the investment is at the beginning of the range; e.g.: calculate operational flows after tax and also make sure what language was the one used to install your software because that can change the formula name to use.

Recommendations on the use of the IRR value:

• Don’t use it to compare mutually exclusive projects or projects with different periods of evaluations
• If the project under analysis’ IRR is greater than it’s WACC: the project is economically feasible. If by any chance they are equal or IRR lower than WACC, invest the money somewhere else.
• The IRR is not the only criterion to evaluate a project. Bear in mind: the VPN, the Period of return on investment and finally and most important: the risks of changes in your financial flows to which your investment is exposed.
• Do not forget to perform a sensitivity analysis of your calculation and your overall project.