 Hello, and welcome to this session. This is Professor Farhad. In this session, we would look at applications and plenty of examples of the time value of money. This topic is covered in introductory course, as well as advanced accounting. Simply put, by the time you are done this session, you should be very familiar how to analyze, review, look at time value problems. This topic is also covered on the CPA exam, both FAR, and I believe the BEC also covered the time value of money. As always, I would like to remind you to connect with me on LinkedIn, if you haven't done so. YouTube is where you would need to subscribe. I have 1,600 plus accounting, auditing, finance, and tax lectures. This is a list of all the courses that I cover, including many CPA questions. If you like my recording, please like them, share them, put them in playlists, subscribe, connect with me on Instagram, and on my website, you will have additional resources to complement your accounting education and or your CPA exam, where you have resources such as practice exercises to reinforce and study to pass your certifications and exams. A prerequisite for this session, it's an important prerequisite, is the time value of money. In the description below, you can find a link to explain all the concepts that I'm gonna be practicing today. So if you are confused, it means you have to go back to the link and view the lectures, the present value of a single amount, the future value of a single amount, the present value of an annuity, and the future value of an annuity. In this session, I'm going to apply them. I'm going to work examples that apply those concepts. So let's get going. Let's take a look at the first example. How much money would you have to deposit today if you wanted to have 60,000? Four years from now, the annual rate is 9%. It's always a good idea to see if you can draw this picture on a graph, draw it on a graph. So how much money you would have to deposit today? So simply put, they're asking us, how much today? How much do we have to invest today? So we will have $60,000. $60,000 is the future value. Today is the present value. And we're looking at n equal to four in four years from now, and this money invested at 9%. So simply put, what they're asking us, what is the present value today of a $60,000 invested for four periods at 9%? All I have to do is find the present value factor. It's of a single amount. Take 60,000 multiplied by that present value factor. So what I need to do, I need to go to the present value table, the present value of one, a single payment. And in this situation, four periods and the interest rate is 9%. And I'm going to find the factor to be 0.7084. So that's the factor. So I'm going to take my 60,000, my 60,000 multiplied by 0.7084. And I will need to invest today $42,504. And this money will grow at a rate of 9% for four ends, four periods grow to be $60,000. So this is what I just did. I found the present value. Assume you are saving for a trip around the world when you graduate in two years. If you can earn 8% on your investment, how much money would you have to deposit today to have 15,000 when you graduate? So simply put, the trip will cost you 15,000. The question is how much you will need to invest money today for two years, earning 8%. Obviously you will need less than 15,000. Basically the same concept. How much money do we need today? So the present value is how much money do we need today? The future value, I need to have 15,000. Here the period, I'm looking at two years and I can earn, wow, 8%, that's pretty good investment. I don't know where you're gonna find this, but we're gonna go with this. Same exact concept, how much money will I need today? I need less than 15,000. So I'm gonna go and I only have to deposit this money once, so it's a single payment. So I have to go to my present value of one, which is the same table that we used a minute ago. Here my period is two years, my period is two years and the interest rate I'm gonna be earning is 8%. My factor is 0.8573. So I'm gonna take my 15,000 multiplied by 0.8573 and I will need to invest today, 18,000, $12,500 and $59.50. So the present value is 12,859.50. If I invest this money for N equal to two, I equal to 8%, this money will grow to be 15,000 and I can take my vacation around the world and hopefully by that time, the coronavirus will be cleared up. So don't take this vacation now, maybe in two years hopefully we'll be out of the world. So this is how some application of the, of the present and future value. Let's work more exercises. Let's take a look at this exercise. Would you rather have $463 now or $1,000 10 years from now, assuming you can earn 9%. So this is where now we're going into the area of decision-making. Now they're giving you two options and you want to find out if both options, which one is better, okay? So would you take $463 now or $1,000 10 years from now, you would like to earn 9%. So how can I solve this problem? Well, to solve this problem, I have to find out what happened if I can solve this problem in two different ways. Let me start with the future value concept. So if I have, if somebody gave me $463 today, if I can invest it for 10 periods at 9%, how much, how much would my future value be? The answer is if my future value more than $1,000, I will take the $463. Why? Because I can invest it and make more than $1,000. To find out, I have to go to the table, the future value table and equal to 10, I equal to nine. So I'm gonna say, okay, if I take this money today, let me choose this option first. If I take this money today, invest it for 10 period and look and I'm looking at the future value of one because I'm gonna get this money only once. And I'm gonna, I like to earn 9% and the factor is 2.3674. So I'm gonna take this amount times 2.3674. And I need to find out how much will that money be worth? And if it's more than $1,000, I will take the 463 times 2.3674. And that's gonna give me almost 1096. 1096, guess what? I will take the 463. No, thank you, you can keep your $1,000 for later. Another way to solve this problem also, here's what you are giving. It's the same problem, so I will take the 463, but here's how you can look at it. Here's what you are told. Will you take this today or this is in the future? Given an equal to 10, I equal to nine. The other way to do it is to find the present value of the $1,000, okay, this is the future value. So I need to ask myself, what if I took this $1,000 and discounted at present value? In other words, multiplied by the present value factor and equal to 10, I equal to nine. Obviously the present value factor, it's gonna be the reciprocal of this, but let me go ahead and go to the table and show you. So if I take the $1,000, this is my, now I'm dealing with my present value, present value of one and equal to 10, I equal to nine and it's gonna be 0.4224, 0.4224. And that's worth $422.40. No thank you, I will take my 463. Okay, so I will not accept the thousand, doing the present value because it's worth more for me today. I will take the 463 and run away with that option because that's my best option. Let's take a look at number D. Assume that a college parking sticker today costs $90. That's the day. If the cost of the parking is increasing at a rate of 5% per year and it has been increasing if you're in a college, I can tell you that's true. Well, it's increasing just like the tuition. How much will the college parking sticker cost in eight years? Basically what the riskiness is, you have $90 today. How much this $90 will be worth and equal to eight, I equal to five. So it's a single amount. I'm finding the future value. Well, I'm gonna have to go to the future value of a dollar and equal to eight. So this is the future value. And equal to eight, I equal to five. And the factor is 1.447. What does that mean? It means I can take my $90 multiplied by 1.4775. And let me do this, $90 times 1.4775. Let me get the calculator. 90 times 1.4775. And that's gonna give me $132.98. Wow, that's gonna be an expensive parking sticker. Hopefully they'll make it for two years. So that's the how we solve this problem. So basically you have to take the information that you are giving and convert this into something that's useful, okay? Let's look at E. Assume that the average price of the new home is $158,500. If the cost of the new home is increasing at 10% per year, how much will the new home cost in eight years? That is true. In the US, the cost of the home has been increasing by 10%. So same exact concept. I'm taking something, the value of a home, and I am finding the future value giving n equal to 8, i equal to 10%. So 158,500, so I'm gonna have to go to the future value, future value of a single amount, future value of a single amount given, maybe I wanna buy a house in eight years, so I wanna see how much I need, I will need money, and n equal to 8, i equal to 10, and the factor is 2.1436. So it's 158,500 times 2.1436. It's gonna more than double 2.1436. Let's see, that's nuts, in a sense that homes are increasing at that rate, but that's reality times 2.1436, because your wages don't increase that fast. So the home will cost $339,760. 339,760, wow. Yes, because think about it. If your earnings are not growing by 10%, if your earnings are not growing by 10%, it's gonna be hard for you to buy this home because the home is growing, the price of the home is growing at a faster rate. That's why I said it's crazy, and usually your earnings don't grow by 10%, especially with inflation very, very low lately. At least we're talking in 2020 during the coronavirus outbreak. Who knows what's gonna happen next, okay? Let's take a look at this. An investment that will pay you $10,000 in 10 years, and it will also pay you $400 at the end of each of the next 10 years, year one through year 10. If the annual rate is 6%, how much you would be willing to pay for this investment? This looks like a bond problem. This looks exactly like a bond situation, although it doesn't say it's a bond, but basically this investment is a bond. And what would happen is this. In other words, how much will you pay for a bond or for this investment if you're gonna get the following? Here's what the deal is. Let me take a look at it on a graph. Here's the deal. We have 10 years, and in 10 years, they're gonna give you $10,000 as one shot. Then one, two, three, four, five, six, seven, eight, nine, 10. Then for the next 10 years, you're gonna be getting $400, $400, $400, $400 and eight, nine, I hope those are 10. So simply put, the interest rate for this, they're assuming you can earn 6% and equal to 10. Now we have two problems. We have two separate problems. First, let's find how much this 10,000 worth separately. So first you find, doesn't have to be first, but I'm gonna start with the $10,000. You're gonna take the 10,000 and discount the 10,000 to the present value separately. So let's do that. So I'm gonna take, go to the present value of one because I'm only getting this 10,000 once. My interest rate is 6% and the period is 10. So my factor is 0.5584. So I'm gonna take this 10,000, multiply it by 0.5584. In this $10,000 by itself, I'll pay for it 5,584. So if I buy this investment, pay 5,584, let it sit, it's gonna give me 10,000 10 years from now assuming 6%. So this is part of the solution. Now what else am I getting? I'm also getting those $400 and this looks like an annuity to me, okay? So I'm gonna take this annuity, $400. Again, I equal to 6% and equal to 10, which is the same thing that you used for the other one. Then I have to multiply it by the factor but going to which table to the present value of an annuity, annuity. Notice I'm going to table B3. I don't know what table is that in your textbook but it's a different table. Therefore, I'm looking at I equal to 6 and equal to 10 and I need to find the factor and the factor happens to be 7.3601. I'm gonna go to the $400, multiply it by 7.3601 and that's gonna give me 2,944. I will add both of these numbers and I'll pay for this investment today, $8,528. So this is the price of the investment. So this is the price of the bond. This looks exactly like a bond because a bond pays you the par value. So basically put, this is the par value and those are the interest payment because you're getting two things. You're getting the par value as well as the interest payments, okay? Let's take a look at one more, okay? The college student, that should be familiar to you. A college student is reporting in the newspaper as having won $10 million in Kansas City Lottery. However, as it's often the custom with lotteries she doesn't actually receive the entire 10 million now. Instead, she would receive $500,000 at the end of each year for the next 20 year. If the annual interest rate is 6%, what's the present value of this investment? So somebody won $10 million. The question they're asking us is this, you're not gonna get the $10 million, that's the sticker price basically to tell you you won $10 million, but what's gonna happen? The way they're gonna pay you this $10 million is $500,000 times 20 years, which is equal to 10 million in total. But is it really worth 10 million? Not really, because you're not getting the 20 million today. If you're getting, if you are getting the 20, I'm sorry, if you are getting the 10 million today, yes, it's worth 10 million, but that's not the case. They're paying you half a million, half a million, half a million, half a million for the next 20 years. And assuming you can earn an interest rate of 6%, how much is that lottery winning really worth? So this is what we're looking at here. We're looking at something like this. One, two, three, four, five, six, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and this is 20. So all of those are one, through, two, three, four, all the way till 20. You guys got the point, right? So now what's gonna happen is they're gonna pay you every year half a million. 500K, 500K, 500K all the way. In total, yes, they will pay you in total $10 million, but is it really worth 10 million? And the answer is no, it's not worth 10 million. If you're getting the 10 million now, here, let me put this in a different color. If you're getting the 10 million here right away, if they're paying you today the 10 million, then you want 10 million, but that's not the case. They're gonna pay you 10 million and half a million for the next 20 years. So how much is that price really worth? Well, we have to use an interest rate of 6% and equal to 20, and it looks like an annuity. Therefore, we have to take the half a million multiplied by this factor and I equal to 6% and equal to 20, going to the annuity table. Let's go to the table and find out the amount, N equal to 20, present value of an annuity, N equal to 20, I equal to 6%, 6% is right here, and the factor is 11.4699. So it's half a million times 11.4699. So the true value or the present value of all these payments is 5,734,950 dollars. So this is what they really want. This is what they really want in today's money, 5,734,950, and that's not bad. That's still not too bad. But remember this individual, I do remember one time one of our clients actually won the lottery where I used to work. One of our clients at the CPA firm and basically on the return, all what they had is this annuity. So there was a simple return that said they would report the winning from the lottery and they'll pay their taxes. So what I'm trying to tell you here is it's not only that you want this money, but if you have to pay taxes on this money, so simply put, let's assume you have to pay taxes on this money and let's assume you get $500,000 a year and let's assume now the interest rate depending on your rate. And in this situation, you're around 30, 32%. Let's assume you're in the 30% tax rate. You're gonna keep 70% of this. Therefore what you really want per year net is 350. And that's not too bad for the one nothing, but it's not the 10 million that you were promised up front. So after you pay the taxes, you're left with 350,000. Yeah, I'm not complaining. But I still remember an actual, we had an actual client. That's all what they had. They didn't even invest the money. They didn't even have anything. It was a simple, the simplest return I saw in my life. All what this individual wanted is get the money and spend it. They didn't even invest. I still remember it. It was just amazing. Anyhow, in the next session, I would look at additional exercises. I would look at additional exercises. As always, like my recording, subscribe. If you have any questions about these exercises, email me, stay motivated and stay safe during those coronavirus days. Visit the website.