 Hello, and welcome to the session. This is Professor Farhad, in which we would look at two CPA questions that deals with the time value of money. That's an important topic, an extremely important topic on the CPA exam. These questions are sent by one of my subscribers at farhadlectures.com. At farhadlectures.com, I covered this topic in details. So these questions are from a third party. The individual wanted to know a little bit more if I can go over them. I believe those questions are considered advanced questions, but we're going to go over them. If you can understand how we solve these problems, then you should be comfortable with the time value of money and especially computing the present value of money. The present value of money is very important because it covers bonds, leases, projected benefit obligation, notes payable. All these topics they would assume or they would require you to be very comfortable with the time value of money. How can I help you go to farhadlectures.com? I have plenty, plenty of resources. Matter of fact, before every one of my CPA FAR courses, whether it's Becker, Roger, Wiley, or Gleim, I do have lessons about time value of money before you start. You want to make sure you are comfortable with that topic. Let's go ahead and take a look at the first question. Best inventor has developed and patented a computer chip that allows telecommunication and sports event to become more efficient. BI agrees to sell the patent to the New York Jets for five annual payments of $50,000. The payments are to begin three years from today, from today, given 6% interest rate, what's the present value of the payment? What I like to do with these questions is to show it to you on a timeline. Zero is today. One, two, three, four, five, six, seven, eight, nine, ten. You may not need ten, but I'm just going to show you what's going to happen. We sold the patent today. We got rid of it today. The payments are to begin three years from now. One, two, three. So the first payments start here, and we're going to have five payments of $50,000, $50,000, $50,000, $50,000, and $50,000. The question is how much, because we need to record the present value of the payments here because we sold something, therefore we made the sale, how much do we record this payment for? That's the question. Well, how can you solve this problem? Well, there's two ways to solve this problem. First, I'm going to solve it in a way to help you understand what we are doing. So you have five payments. This looks like an annuity. The only thing is this is a deferred annuity. That's why it's an advanced question. It's a deferred annuity. So how would I solve this question? I'm going to solve it in two different ways. The first way I'm going to solve it, I'm going to assume I am at year two. If I am at year two, I am looking at an ordinary annuity with five annual payments. So N equal to five, I equal to 6%. So the first thing I'm going to find out is how much those five payments worth here at year two. Because this is what I know. This is when you learn annuity. This is what you learn. So go to your table, present value of an ordinary annuity, N equal to five, I equal to six. And the factor is going to be 4.212. I'm going to go up here and take my 50,000 multiplied by 4.212. And that's going to give me $210,600. So this annuity is worth at year two, $210,600. Now, I don't care about year two. They're asking me how much this annuity is worth. I'm sorry. How much is this amount? Not annuity now. This is a single amount. How much is this single amount worth today? All I have to do now is discount this payment two periods using 6%. So now I'm going to go to the present value of one of one payment, two periods, 6%, and the factor is 0.089. So I'm going to take my value of $210,600 at year two and discount it at 0.89. And I'm going to get $187,434. And this will be the answer because that's what they're asking me. Now, what would be the journal entry for this? If you're interested, you will debit notes receivable for that amount. You will credit sales for that amount. So your sales is for $187,434. And you have a note receivable because you're going to be receiving the money later on. Now, the difference between what you would receive, what you would receive really is in total, you're going to be receiving $250,000. Notice you're going to be receiving $250,000. The difference is it's going to be interest revenue. But the sale actually is $187,434. So this is one way to compute this. And the reason I did it this way is to illustrate the concept of an annuity. So first I worded as an annuity for year two. Then from the annuity, I discounted it using a single payment. Now, how else can you do this? Well, how else can I do this? What I would say, what I would do, I would go to the annuity table. And what I need to do, this is a, if you count the years, let me just count the years here. Let me erase everything and just keep the years. Oops. Let me just count the years. We have seven years in total. Seven years in total. What I would do is I will take the annuity of seven minus the annuity of two, and I will find the answer as well. What do I mean by this? So I'll go to the annuity table, and I would say the total period is seven. Therefore, the present value is 5.582 at 6%, 5.582. So I'm going to take 5.582, which is, this is the annuity factor for seven. But I'm going to have to take out of it two years because two years, I won't be receiving any payment. So what I would do is I will go to two years, 1.833, and I will subtract from this 1.833. And that's going to give me a factor of 3.74899. And that's my factor. Now I'll take my factor multiplied by 50,000. Let's do that. I want to double check myself as well. So if I'm going to take 50,000 times 3.74894, 187447, that's surrounding, but 187434, 187, the AME447, it doesn't matter, 434, just surrounding, rounding. So this is basically how else you can, how the other method that you can use the third payment. So take the seven, you have seven periods minus two where you don't receive anything and you will find the factor. I like to do it both ways, so this way you are comfortable with both. And so remember, remember here what they said. They said, and the reason I'm going to say this because we're going to go to the next problem. The payment are to begin three years from now. It means this is zero, one, two, three. So the payment will start three years from now. This is one, two, three. This is three years from now. Let's take a look at this question. What amount should George invest now at 12% to provide five payments of 5,000 at the end of each year starting three years from now? This is what this problem looks like. Today is zero, one, two, three, four, five, six, seven, eight, nine. So what's the present value? The payment it's going to give George 5,000 at the end of each year starting three years from now. So three years from now is one, two, three. At the end of three years, it means at the end of the year, it means the first payment George would receive is here. So the first payment that George would receive is at the end of year three, which is 5K. So George would receive 5K, 5K, 5K, 5K, 1, 2, 3, 4, 5. So this is what George is looking at from a timetable perspective. I always like to show you this because once you see this, it's easier. So be careful how the problem is given to you. If you assume the payment starts at the beginning of year three, it makes a difference versus the end of year three. Starting year three, and it's at the end of year three. Okay. Now, how do we solve this? Again, now we have eight periods, eight periods, and we're going to subtract from the eight periods, three periods that we don't receive any payments. So now n, we're going to find n equal to eight and n equal to three at interest rates. So n equal eight minus n equal three, and the interest rate is 12%. Let's find the factor. I mean, can I do it the way that I did it earlier? Sure. But I already made the point. So it's, you know, you know, you already, I already made the point. So we're dealing with 12%. First, let's find the three. Oh, let's find the eight. The eight will be someplace. Oops, this is the present value table. Be careful. So we're going to go to present value of minority, 12%, eight, 12% and eight. That's 4.968. And we're going to subtract three. And that's going to be 2.402, 2.402. Again, this is going to be rounding because it's going to be some rounding issues, but that's fine. So we're going to take, this is the factor is 4.968. Again, it's going to be a little bit of rounding. It doesn't matter. I'm just making the point 4.4.02. Now I'm going to deduct those. Again, I can do it in two steps the way I did it earlier, but this is, you know, but you don't have to do that 4.968 minus 2.402. That's going to give me a factor of 2.566, 2.566. I'm going to multiply this amount by 5K, 5,000. Let's do that. Let's get this amount multiplied by 5,000. And it's going to be 12,830. Oh, good. 12,830. It's 12,829. Again, it's because of the rounding. So that's the answer. Look, when you go to the exam, when you go to the exam day, the time value of money is critical. Why? Because if you don't know the time value of money, you won't be able to solve any bonds problem, any notes payable, any pension, any deferred taxes, any notes, long-term notes receivable, long-term notes payable, bonds. So in my courses, so when you go to sign up for my CPA course, if you sign up for Wiley or for Roger or for Becker, it doesn't matter which one you sign up for. You'll have access to everything or Glyme. The first thing I do, one of my first modules is time value of money, because if you don't know the time value of money, you cannot pass the exam. Don't even think about it. Don't even attempt the exam. If you are not 100% comfortable with that topic, I can make you 100% comfortable with my explanation, resources, multiple choice questions. Good luck. Study hard. I'm always here to help you. The CPA is a lifetime investment. Don't shortchange it.