 Hello and welcome to this session. This is Professor Farhad in which we will discuss the concept of net present value, also known as NPV. So what is net present value or NPV? It's a capital budgeting technique to evaluate long term project. What does that mean? It means when a company undertakes a project, whether they are buying a new asset, whether they are expanding the company, whether they are undergoing a major advertising campaign. They want to know whether that's a good idea or not. So you need basically a tool, some sort of a tool to judge. Well, that tool could be net present value. That's not the only tool, but that could be one of the tools, net present value. What do we do in net present value? We will compare the present value of a project cash inflow. So every project will generate positive cash, obviously. Otherwise, why will you undertake a project? We're going to discount using the present value of these cash inflows. And this is important. And that's why I keep highlighting in yellow the word the present value because here we are using the time value of money, time value. And if you don't know how to compute the time value, the present value of a single amount, the present value of an ordinary annuity, please see the prior recording because the assumption is, you know, time value. So we will compare the present value of the cash inflows from that project with the present value of the cash outflows of that project. So simply put, we bring everything to point zero. So this is a project and this project will have a positive cash, positive cash, positive cash, maybe some negative cash, some positive cash, negative, then positive. And here it will have negatives. It doesn't matter. We're going to have different negatives, different positive. We're going to bring everything, all the positives to the present value, all the negatives to the present value. Simply put, we bring everything to present value. And the difference between those two is net present value. The difference between those two is the net present value. The difference between those two cash streams is the net present value. If the answer is positive, if NPV is positive or zero, we accept the project. If NPV positive or zero, it means we are meeting our minimum required rate of return, which we'll talk about this in a moment. If the answer is negative, we don't. We will reject the project. So this is how we would use NPV to determine whether we should accept a project or not accept a project. Now let's dive a little bit deeper into this. What are the typical inflows and outflows for a project? I'm going to start with the cash outflows. Because when you start an investment, like just like your education, when you start to study for your CPA exam, when you start your college career, initially you have to invest. So the initial thing is initial investment. So usually that's the biggest cash outflow. And that's usually the first thing in a project. You have to put out some money. Then you might have to put out some money for working capital. When it's working capital, you might have to buy supplies, inventory for that project. You might incur incremental operating costs because you undertook this project, there's additional cost. That's fine. You might have to incur repairs and maintenance. All of those are considered cash outflows. So on a timeline, usually the initial investment will be a large minus at the beginning. Then the working capital will be another minus at the beginning. Then you might have to incur operating costs. You might have to incur repairs and maintenance throughout the project. So those are your typical outflows of cash. Also, you're going to have, not also you should have cash inflows. Otherwise, you will not undertake a project just to spend money. Well, yes, you do if you're the government, but we're not dealing with government, right? We're dealing with for-profit corporations. So for the cash inflows, you're going to have, it's funny, I'm going to use the red color. You're going to have positive cash. So you're going to have cash inflows, cash inflows, cash inflows, incremental revenue, okay? So what's going to happen, those are usually your largest. The reason you undertake a project, because you want to increase your revenue or sometime as a result, you're going to reduce your cost. Reducing your cost is a cash inflow. Basically, you are saving money. Also, once the project is done, remember you had to invest some working capital. That working capital is released. That's going to bring you some cash. And at the end of the project, you might be able to sell the asset itself, the equipment, whatever you are using, sell it for something that's also going to bring you cash. So notice those are the typical cash inflows. Those are the typical cash outflows. Again, what do we do with those? We bring them to present value. What does present value means? It means we discount them. To discount them, we need a discount rate. What discount rate do we use? Well, the company will decide the discount rate. But usually the discount rate is the minimum required rate of return. What does that mean? It means the company will always have some sort of a percentage. So for example, for every project, we don't accept unless we can earn 15%. Well, that's the minimum required rate of return. Now, how do they come up with this 15%? Do they pull it out of a hat? Well, they can if they choose, but usually it's the cost of capital. It's the cost of money for the company. It has to exceed the cost of money. And what's the cost of money? It's the average return on the company's long-term debt and equity. Simply put, the company will have to determine what is their cost of equity? What's their cost of debt? And they will average this and the average will be called the cost of capital. So that's one way to determine the discount rate. And you would learn about this in your finance course. For managerial accounting, that rate will be given to you. And the technical term for it is called the weighted average cost of capital. So the discount rate, again, you don't have to worry about it. I just want to give you an idea how do they come up with that 10% or 11% or 8%. Each company will have a different rate depending on their cost of capital, depending on the risk tolerance, depending on the risk of the project itself. But that number will be given to you. Now, the best way is to look at an example. Before we look at an example, most likely you are a student or a CPA candidate. And if that's the case, I strongly suggest you go to my website, farhatlectures.com for additional resources, whether you are an accounting student, taking accounting courses, or studying for the CPA exam. My resources will include lectures, multiple choice, true, false, that's going to help you do better on your CPA exam, as well as your accounting courses. Please connect with me on LinkedIn, YouTube, like this recording, connect with me on Instagram, Facebook, Twitter, and Reddit. So let's start with an example to illustrate this concept. Adam Company has been offered a five-year contract to provide component for a large manufacturer. That's fine. Adam is happy with that project. However, Adam needs to buy a special equipment to satisfy this contract. So they will need to buy a special equipment. They might need some additional capital to start the project to manufacture those components. Well, let's take a look at the data that we are giving, and we're going to compute the net present value to determine whether this is a good project or not a good project. First, we're going to start with the cost of the special equipment. We'll have to pay 165,000. We're going to have working capital required, supplies, inventory, maybe some cash committed, 110,000. In three years, we're going to have to upgrade the equipment, and that's going to cost us 40,000. Salvage value of the equipment in five years is 10. So at the end of the life of this project, we can sell this equipment for 10,000. And here's the annual cash revenues and costs. And the reason I said cash and emphasize the word cash, because when you are computing NPV, we are using cash, not net income, not accrual. So we have to be very careful. Now, usually in a problem, they will tell you what's the cash inflows per year. I am not. I'm going to give you some numbers and I want you to compute the cash inflows. So this is all the cash revenues and costs, sales revenue, 810, cost of parts sold, it's going to cost us 450, salary, shipping, and other costs 280. Therefore, we're going to compute the annual net cash inflow is 80,000. So every year, we're going to generate $80,000. Now, we have to be very careful here. Sometime, inside those costs, they may tell you we have depreciation of 10,000 or depreciation of 20,000. Remember, depreciation is not a cash outflow. You have to back out depreciation. So if they told you 450,000, including those expenses, including 50,000 of depreciation, well, guess what? Then your cash outflows only 400,000, because 50,000 is depreciation. You back it out. Just make sure you're aware of this because depreciation is not a cash expense. It's not only depreciation. Any other project, any other expense that's non-cash will have to be backed out because we are looking at a cost from a cash perspective. Now, let me show you on a timeline what this looks like before we look at the numbers. On a timeline, it looks something like this. First, we have to pay 165,000. We have to kind of commit 110,000. Those are two large negatives. Then year one, two, three, four, five. In year three, we have to commit another 40,000. We have to kind of commit 40,000. Then, let's look at the cash inflows. The cash inflows every year, we're going to get 80,000, 80,000, 80,000, 80,000, 80,000, and the salvage value is 10,000. So those are all pluses. I think I covered everything, the 10, the 40, the 110, the 65, and the cash inflows. So this is what it looks like. All you have to do now is take this information and discount it, giving a present value to determine what is the net present value of the project. Now, we need to know what is the discount rate. For the purpose of this example, we're going to go with an 11% discount rate. So how do we complete this exercise to compute the net present value? Well, we're going to start to discount everything. First, we're going to try to discount the 165,000. Well, that's easy. Why? Because we're going to have to spend the 160,000 today. Therefore, the factor is one. Why? Because there is no time value. You have to pay this money today. Therefore, we start with negative 165,000. So that's done. The 110,000, we have to spend this money now today. What's the factor? One. There is no time value. That's minus. Those both are minuses. That's done. In three years, let's start with the cash inflows. Well, we're going to have five years of cash inflows, and that's 80,000. Well, remember, this is a cash inflows. One, two, three, four, five. One, two, three, four, five. This looks like an annuity. It's the same amount we are receiving every year. It's an annuity. So what do we do? We're going to discount this 80,000 using an annuity table. And if we go to the annuity table, again, you have to know how to use this. I have, in the prior recording, I showed you how to use those tables, how to compute an annuity. The interest rate i or r equal to 11 and the period equal to five. If we go to the annuity table, whichever look in your book or in your CPA review course in the annuity table, you're going to find the factor 3.696. Now it could be a little bit slightly different if it's rounding or not. We're going to take the 80,000 times 3.696 and those positive cash flow will be 295,680. Well, we are done with the cash inflows. We are done with this part. Remember, in year three, we're going to have to pay 40,000. Well, that's going to be a negative. Do we have to pay it now? No, we have to pay the 40,000 in three years. How many times do we have to pay it only once? Therefore, we're going to go, again, 11% n equal to three and we're going to go to the present value of a dollar. So it's going to be a different table than the annuity table. So you go i equal to 11, the interest rate equal to 11, n equal to three, you will find the factor 0.731. You will take 40,000 times that factor and the present value of it is only negative 29,240 because we're discounting to the present. So we are done with the 40,000. We have the salvage value, 10,000. Again, the 10,000 we're going to receive the 10,005 years from now. Again, we'll go to the table, i equal to 11%, or r equal to 11%, n equal to 5, the present value of one dollar of a single amount. We only receive this 10,000 once and the factors happens to be 0.593. We'll take 10,000 times this factor and this will give us 5,930. What else do we have left? The working capital released. Remember, we spent, we, we, we committed this money here. Once the project is done, we're going to get back the money. Well, when we get back the money, we're going to get it only once using the same factor as the salvage value because we're going to get it in five years and only once and that factor is 0.593. And that's going to give us 65,230. We counted for everything. Now we are ready to determine whether this project has a negative zero or positive. And the answer is it has a positive NPV. What does that mean? It means we will accept this project because it has a positive NPV. The project is accepted. Adam will buy this asset and we'll start to manufacture the parts for this company. What should you do now? Go to Farhat lectures and work additional MCQs, additional true, false exercises that's going to help you learn how to compute net present value. Net present value is a very powerful tool because you would learn how to utilize the time value of money in a business context. Invest in yourself. Good luck. Study hard and of course, stay safe.