 Hello and welcome to this session. This is Professor Farhad in which we will discuss the internal rate of return or IRR What is the internal rate of return? Well, it's a tool to find out the rate of return So the first thing I want you to pay attention to it's you are looking for a percentage a rate of return For a project for for the purpose of what of capital budgeting So simply put a company might want to expand they want to buy a new equipment They want to buy a piece of land. They want to make an investment. They want to spend money on advertising They want to find out if they do so. They're gonna have to put out some money today And they're expecting some return down the road. They want to know what percentage is the rate of return on that project now IRR could be used to supplement something called net present value or MPV Now on the prior session, we looked at net present value and the net present value gives us a dollar answer So when we computed NPV, we said for example NPV is 42,000 dollar. That was the answer or NPV equal to 16,530 dollars. That was the answer NPV tells you whether the project is acceptable or not based on a dollar amount IRR It's gonna tell you what is the rate of return on that project Specifically the internal rate of return the rate of return that the company is earning NPV they give you a rate They give you a required rate and they want to find out under this required rate of return with this project be positive NPV or negative NPV IRR basically they're they're answering the same questions except IRR tells you exactly how much you are getting for that project MPV all what it tells you you are earning more than the required rate of return, but you don't know what is the IRR What is how much is the project earning all what you know? It's earning more because NPV is of MPV is positive another way to say it is IRR is the rate That's going to give you the present value of the discounted cash inflows Equal to the present value of the discounted cash outflows simply put when you discount your inflows You're gonna have you're gonna get to a number and that number is X and When you this when you discount your outflows, that's number gonna be X as well So those two are equal to each other So if your discounted cash inflows were a thousand your discounted cash outflows are a thousand and the rate of return That's gonna give you this same number is called the IRR. So simply put another way to say it You remember net present value have to be positive and IRR the net present value is zero Why the net present value is zero think about it if your cost if your discounted cost equal Which is the negative cash the outflow of cash equal to the inflow of cash then you have NPV equal to zero So another way to say NPV I'm sorry another way to say what IRR is IRR is when NPV equal to zero, okay? What does that mean? Let's put it in a formula when you take your future cash inflows You multiply them by a present value factor, which you should know this number You should know when you are undertaken a project you should be able to estimate your future cash inflows That's part of capital budgeting And you're gonna look at your initial investment or outflow at period zero Those two should equal to each other also the initial investment is known Well good now we have three factors. We have the future cash inflows We have the inflows. We have the outflows all what we are missing is the present value factor Now what we can do is we can rearrange the formula to find what's the present value factor? Well, the present value factor is the investment cost whatever cost we did Divide by the future value of cash flows and that's gonna give us the present value specifically not the present value It's gonna be an annuity because it's gonna involve a future assuming most likely it's gonna be an annuity It could be only one payment, but that's easy to compute So most likely it will be a future value of an annuity because you have a future cash and you will cash inflows more than one So what does that mean? It means let's go ahead and apply this formula to find out how to find the IRR Then we will discuss specifically how the IRR differ from NPV. They they don't really differ But how does it differ in a sense? What is the purpose of the NPV? What is the purpose of IRR? The best way to illustrate this is to work an example with some numbers Before we look at an example, please I would like to remind you you're most likely a student or a CPA candidate and that's great you need to go a step further go to farhatlectures.com and Take a look at my material resources lectures multiple choice through false exercises That's gonna help you with your accounting courses as well as your CPA preparation I don't replace your CPA review course I'm gonna help you do better in your CPA Preparation if you have not connected with me on LinkedIn, please do so take a look at my LinkedIn recommendation Like this recording if you're watching it's helping you like it connect with me on Instagram Facebook Twitter and Reddit So let's take a look at this example Adam company can purchase a new machine at a cost of 104 320. That's the cost simply put That's the initial investment and it's today that will save $20,000 per year in cash operating cost the return is positive cash $20,000 for the next for the next 10 year the machine has has a useful life of 10 years now bear in mind I just want to I want to emphasize this On the CPA exam or in your accounting course depending on how much your teacher wants to test you IRR it's not easy to compute unless you have some clean numbers the way I'm giving you But IRR would need either IRR would need would need either a financial calculator an excel sheet or some sort of a Financial program, but I'm gonna use some simple numbers to illustrate the point because that's all what we need to do here So let's use what we learned about earlier and what we said earlier is we take the inflows of cash Multiply them by the present value factor It's there should equal to the you should equal to the cost to the investment cost or the investment same thing Let's let's use this formula if we rearrange and we put the present value factor Equal to the cost. This is the cost or the investment required Divided by the annual cash inflows simply put we divide we divide by inflows of cash Both sides of the equation. So let's do that when we do that will take one or four three twenty Which is the cost or the investment divided by the inflow of cash and that's gonna give us five point two one six Now, what does that mean? Is this the answer? No, that's not the answer. This is the present value annuity Factor now, what do I need to do once I have the present value annuity factor I need to go to the time value tables and notice it's five point two one six And we are looking at a ten-year investment now we're gonna go to the present value annuity factor and it should be in your textbook somewhere and The period is on this side. So we're gonna choose ten now We don't know what the interest rate what we're gonna do But we know the answer is five point two one six five point two one six And you're gonna go across to come up with the closest factor to five point two one six Now for my example, it's gonna be a clean cut. So it's gonna be a clean cut It's gonna be five point two one six one and you look at you look on the top and the IRR equal to 14% Now we find what the IRR is but let's assume the IRR was five point three the factor was five point three Five point three is between five point four and five point two, right? So the rate is in between 13 and 14 and that's why you would need to find the calculator But this example keep it simple now on the CPA exam if they gave you anything It will be straightforward in a sense. It's computable. You can compute it They don't expect you to do usually it's it's done by trial and error And I'm gonna show you what does it mean when you do it in a trial and error, but this number is clean cut Now what are the rule for IRR? If IRR is greater than the required rate of return you accept the project if the IRR is less than the required rate of return You would reject now. What does that mean? Well, the best way to illustrate this is to go to an Excel sheet and show you how the numbers work and show you what what I mean But what I mean by if IRR is greater than the required rate of return or lower So let's go to the Excel sheet. So this is the Excel sheet for this Exercise and let me just review. So you see what I'm looking at here We have the cost we have the cash flow year 1 year 2 year 3 all the way till year 10 We have okay, let me show you what I did. So I took I took the annual cash inflows And we already know it's 14% we already know the answer, but let's assume. We don't know the answer We don't know what IRR is. We already know the answer. Let me first show you how the answer work What is IRR because we already computed the answer and I'm gonna show you if you don't know the answer What would happen? So what we did is this we took the 20,000 and since we know the IRR is 14% We discounted the 20,000 one period at 14% we did the same thing for period to 20,000 Year three another 20,000 so on and so forth So I took all of those discounted cash flows and I add them up This is the present value of the future cash inflows Then I took them and I subtract them from the cost and notice MPV equal to 2.3 assume This is zero two dollars and 30 cents. This is just simply simply put you're just gonna rounding. This is this is a rounding issue So notice The answer is zero the answer is zero. Okay What does that mean? It means this project because we don't know all what they told us is the cost is 103 104 320 that's all what we are told the cost or the investment and it's gonna give you 20,000 for the next 10 years what we did is we find out this project is earning 14% now the question is this becomes so this is the IRR Now is 14% an Acceptable IRR. Well, the answer is well it all depends on the required Rate of return. What is the required rate of return? It means how much the company wants to earn? Let's assume the company wants to earn 15% the company has a required rate of return of 15% Would this be an acceptable IRR? Well, let's test it. Let's test it if the company requires 15% of that's the required rate of return. Then we're gonna switch to MPV Remember the MPV gives you a rate that tells you this is the rate that the company wants to earn So if the company wants to earn 15% let me discount everything at 15% I'm changing this to an MPV problem. If I do 15% here Notice what's gonna happen. Now. I have a negative MPV Why because the company wants to earn 15% and we know from our computation a minute earlier That the internal rate of return of this project is 14. Well, guess what the required rate So the IRR 14% is less than 15. We would reject because this project is not Earning us the required rate of return, which is we want to earn 15. This project is earning We want to earn 14. We want to earn 15. This project is earning 14 Let's assume the required rate of return is less than 14% I'm gonna make it 13 for the sake of illustration. Notice what's gonna happen when I do 13 when I do 13% MPV is positive What does that mean if my required rate of return is 13? This project is earning me 14% Well, that's good. That's unacceptable So all what IRR gave us is what it gave us exactly what this project is earning But it answered the same thing as MPV. Okay. I if IRR is is is Acceptable MPV is is acceptable if IRR is not acceptable. The MPV is not acceptable Simply put illustrated in this problem is 14% is basically what gives us MPV equal to zero 14% will give us MPV to zero Okay, if 14% MPV to zero if we if you're required rate of return of the company wants to earn more than 14% Don't take this project because if you discount your cash flows based on 15% That's gonna be negative if your required rate of return is anything less than 14 Let's assume 10 if you discount those based on 10 the MPV will be positive The IRR is acceptable and PV is acceptable. So basically the answer the same Question in a different way IRR tells you exactly The project is earning 14% whether that's acceptable or not it all depends on your required rate of return NPV on the other hand at this count your rate based on a given rate of return and the answer would either be a negative or a Positive MPV positive or zero MPV you accept a negative MPV you would reject Let's go back to the slides and discuss advantages and disadvantages of IRR The advantages are it uses the time value of money, which is good when the time value of money is used That's good because it's taken into account the time value and also consider the cash flows for the entire project Now the disadvantages is this it's difficult to calculate if the numbers are not straightforward You'd have to use a financial calculator Excel or some sort of a software again That's not really a disadvantage But the point you want to know is it's a little bit complicated and when you have when cash flows Which is between negative and positive you might have different answers multiple answers Also, you want to consider all the cash flow for the project, but the effort to do so that's a disadvantage You might not be able to do so all cash flows must be either positives or negatives Otherwise it will not work You'll have multiple answers of the cash flow switching and here it assumes all the cash flow is immediately Reinvested at IRR, which is not reasonable when you're undertaking a project, but those are the assumptions that we do so remember NPV tells you whether tells you whether the rate used given exceeds the hurdle rate tells you whether the rate You are using is greater than the rate you want to earn if that's the case NPV is positive you're gonna have a positive NPV But an NPV the rate is given the rate you are using is already given it tells you whether that rate is higher or lower But it doesn't tell you what is the required rate of return not the required the IRR IRR Gives you the rate of return it tells you what is the percentage for the project When the NPV equal to zero, so that's the difference between them Okay, NPV you're already given a rate and you're discounting everything based on that rate and you're hoping the NPV is positive If the NPV is positive, it means the rate giving Exceeds the hurdle rate. What's the hurdle rate? It's the rate that the company wants to earn That's all what it tells you it tells you it's a greater It doesn't tell you what the rate exactly is for this project. It tells you it's a greater than the hurdle rate The IRR gives you exactly the rate Where NPV equal to zero it means it's breaking even that's basically they're both telling you the same thing If the IRR if the project is acceptable under IRR giving our assumption The the project is acceptable under NPV and vice versa So just want to let you know they both supplement each other What should you do now go to farhatletures.com work MCQs through false Exercises that's gonna help you do better in your course on your CPA exam invest in yourself. Good luck study hard And of course stay safe