 Hello and welcome to the session. This is Professor Farhad in which we will discuss the payback method and the discounted payback method. So what is the payback method or the discounted payback method? Simply put, those methods are capital budgeting technique or tools, but they focus on the length of time. They focus on the time that it takes for a project to recover its initial cost out of its receipts that it generates cash receipts that it generates from its own project. Simply put, how long it's going to take us to recover our cost? Is it one year, two years, three years, so on and so forth? The payback method is usually evaluated or analyzed by people who are conservative. Conservative people, the first thing that they ask you when they want to make an investment is, how fast can I get my money back? How fast can I recover my initial investment? And then they would use the payback method or the discounted payback method. What's the difference between the two? One, it ignores the time value of money. The payback method ignores the time value of money. The discounted payback method uses the time value of money. Whatever we learn about the payback method, we'll apply to the discounted payback method and obviously we'll work examples illustrating both method. So when payments of cash, if we are dealing with a payback period, represent an annuity, which is simply put, an annuity means you're getting the same amount of money every period, like, you know, 2000, 2000, 2000, every period. Then it's easy to compute the payback period. You will take a look at your investment required, which is your cost, and you will divide it by your annual cash inflow, assuming the annual cash inflow is the same. Simply put, you are dealing with an annuity. Now, the best way to illustrate the payback method and the discounted payback method is to look at a couple examples illustrating the concepts. Before we proceed any further, I have a public announcement about my company, farhatlectures.com. Farhat Accounting Lectures is a supplemental educational tool that's going to help you with your CPA exam preparation as well as your accounting courses. My CPA material is aligned with your CPA review course such as Becker, Roger, Wiley, Gleam, Miles. My accounting courses are aligned with your accounting courses, broken down by chapter and topics. My resources consist of lectures, multiple choice questions, true-false questions, as well as exercises. Go ahead, start your free trial today. So the first example will be the management at Adam Company wants to install a new equipment in its manufacturing facility. The cost of the equipment is 140,000. The new equipment will generate an additional inflows of cash of 35,000. Notice we are dealing with cash inflows. And the management requires a five-year payback period. If it meets the five-year payback, we will go ahead and install the machine. Otherwise, we will not, just because it's not, it doesn't meet our payback period. Well, let's compute the payback period. It's the investment divided by the annual net cash inflows, which is 140,000 divided by 35,000. The payback period is four years. Do we accept? Well, strictly based on our criteria, we should accept because we will recover our money from this project less, shorter, earlier than what we required, which is five years. Four years is better. Three years, it's even better. Someone and so forth. Let's take a look at this example. A company is evaluating two project, project A and project B. Project A initial investment is 100,000. Project B initial investment is also 100,000. The year one cash inflow for project A is 40,000. Year two is 60,000 and no cash flow after year two. For project B, we have cash flows of 50,000 in year one, 25,000 in year two, and 20,000 year from year 10 to year 14. Which project has the shortest payback period? Well, the shortest payback period is project A because in two years, we will recoup the 100,000. For project B in two years, we would only recoup 75,000 or 75% of the money. But remember, for project B, we're going to have additional cash flows where project A, we don't have any additional cash flow. So which project has the shortest payback period? And the answer is A. Now, is A the best project? That's debatable. And that's one of the shortcomings of the payback period is the fact that it does not take into account what's going to happen after you recover your money. It doesn't evaluate all the cash flows of the project. It only goes up to, who can get me my money back first? And that's the project I'm going to accept. Sometimes the payback period will have uneven cash flows and oftentimes it's uneven cash flows and we also need to integrate the time value concept. So let's assume a project would require an initial investment of 4,000. What is the payback period and what's the discounted payback period? And this is how the cash flows are. So 1,000 in year one, 500 in year two, 1,700 in year three, 900 in year four and 1,400 in year five. So now this is uneven. So we cannot use the formula. We're going to be using the cumulative method. So what's going to happen is this. So initially we invested 4,000. That's the initial outlay. Year one, we got 1,000. That's not enough to recover. Year two, we got 500. 500 plus 1,000. We're up to 1,500. Year three, we recovered 1,700. 1,700 plus 1,500 will give us 3,200. That's not enough. In year four, we recovered 900. 900 plus 3,200 equal to 4,100. Notice in year four, we exceeded. We recovered our investment. Now we need to find out exactly when did we recover our investment in year four? Notice in year four, so simply put, it's going to take us three years plus sometime in year four. How much in year four? We will assume that the project will generate even cash flows throughout the year. Simply put, we need $800 out of the $900 in year four. So what is 800 divided by 900? It's 0.888. So if we take 0.88 times 12, 12 months of a year, we find out that it's going to take us 10.66 months. So it's going to take us three years plus 10.66 months. Well, it's been 10 months and 0.66 of a month. We can also compute what's 0.66 of a month. If we assume we have 30 days on average in a month, 30 times 0.66, that's going to give us 19.8. Let's make it 20 days. So it's going to take us three years, 10 months and 20 days to recover our money under the payback period without taking into account that time value. Let's assume we want to use the time value to discount our cash flows. We're going to be using a 10% discount. So we're going to go to the present value of a single amount one at 10% and the factors are 0.909, 0.826, 0.752, 0.683, 0.621. And if you go to your time value of money, you go to the table, period one, 10%, those are the factor year one, year two, year three, year four and year five. And I hope I copied all those correctly. And what's going to happen now? I'm going to take the amount, the inflow times, the discounted rate. It's going to give me the discounted value. I'm going to take 500 times 0.826, 0.413, 1,700 times 0.752 equal 1,278, so on and so forth. I will do the same thing to compute my payback period, but now it's called the discounted payback period. So I'm going to start with 900 and I'm going to add to it 413. I did not reach the 4,000. I'm going to add to it 1,278.40. I'm going to add to it 614.70. And notice in year four, we reached 3215. Now, if we take 3215 and add to it and 10 cent to be more specific and add to it $869.40, the discounted amount for year five, we are going to be over 4,000. In other words, we recovered our investment between year four and year five. Now, specifically, how long it took to recover the investment? Well, it took us four years up until year four. Then what do we need in year five? Well, here's what's going to happen. What's left is this. So if I take 4,000, if I need to recover 4,000, as of year four, I have 3,115. I'm just going to ignore the 10 cent for now. So if I take 4,000 minus 3,215, 4,000 minus 3,215, what's left in year five? What I need in year five is $785. Now, in year five, I'm going to be getting a discounted value of $869.40. What I'm going to do now, I'm going to take my 785 and find out how much does it represent of the total amount received in 2015. Obviously, I'm using the discounted amount. So if I take 785 divided by $869.40, and that's going to be 90.29%, 90.29%. So I need from year five, 90.29%. Now, what is 90.29%? Well, I can do it in terms of month. I can do it in terms of days. Let me do it in terms of days. If we're taking 365 days times 90.29% times 365, that's going to give me, I'm going to need 329 days. Give or take 3.56. Let's make it 330 days rounding. I'm going to need from year five, 330 days. Now, if I want to do it in terms of month, let's assume on average 30 days per month, 330 divided by 30, it's going to take approximately 11 months, approximately 11 months, which is, or if I can take 12 months times .9, it's now actually to be more specific, let's do it in terms of month. So I'm going to take 12, we said, rather than doing it by days, let's do it by month. So it's going to be 90.29 of a year multiplied by 12. So we're going to take .9029 times 12. That's going to give me 10.83 to be specific. 10 month, 10.83. Now, if I want to know exactly how many days, again, it's .83 of a month. You multiply it by 30 days and you will find out how much exactly how many days and let's do it. If I take 30 times .83, it's 24.9. It's almost 10 months plus 25 days rounding. This is how long it's going to take me. Now, notice the discounted payback is longer than the regular payback because you are factoring the time value of money. Now, let's take a look at advantages and disadvantages of the payback period starting with advantages. It's a screening tool. It's an easy way to find out whether we should accept the project or not. It tells us how fast we can recoup our cash, recover our cash. It looks for product that recoup the cash quickly. That's those are the advantages. If this is what we are looking for, the payback period is a good method. Disadvantages is it ignores the cash flows after you recover your money. So anything that happened after you recover your money, they don't take it into account. Shorter payback period does not mean it's a better investment. So we have to keep that in mind. It doesn't mean just because it's shorter. It's more desirable. And the regular payback period ignores the time value of money. What should you do now? You should go to Farhat Lectures and work MCQs through false exercises. That's going to help you understand the payback period and various capital budgeting technique. Invest in yourself. Invest in your career. It will pay you dividend down the road. Good luck. Study hard and of course stay safe.