 Hello, and welcome to the session in which you would look at the time value of money concept. This topic is extremely important, whether you are an accounting student or a finance student. On the CPA exam, you cannot pass the exam, I can assure you, FAR or BEC, unless you have a good understanding about the time value of money. The reason is simple. When it comes to the FAR section of the exam, there are many accounts such as bonds, notes payable, leases, the third income taxes, account, long term notes receivable. They use this concept and the assumption is, is you have a good understanding of this concept. On BEC, we have the finance section and they expect you to know the time, the concept of the time value of money. So whether you are an accounting student or a CPA candidate, I strongly suggest you have a strong understanding about this topic before sitting for the exam. 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If you haven't done so, take a look at my LinkedIn recommendation. Share this recording. Share it with other. Connect with me on Instagram, Facebook, Twitter and Reddit. The time value of money concept is extremely important. So let's go ahead and dive into it and I'm going to explain it from scratch, from zero. So what is the idea behind the time value of concept? Simply put, a dollar received today is not the same as a dollar promised in the future. Well, what does that mean? It means if you give me a dollar today, that dollar is not the same. If you give me the same dollar a week from today. Now why? It doesn't have to be a week. It could be a month, a year, it doesn't matter. Why that's the case? Well, one reason is inflation. What is inflation? Let's assume rather than a dollar, two dollars. You gave me two dollars. Two dollars today, I can buy, I can still buy easily a cup of coffee from a place called Wawa, okay? Easily buy a cup of coffee. Maybe a year from now, the way inflation is going, where prices are going up, if you gave me the same two dollars, I walk into Wawa, it's the same exact two dollars, I cannot buy the same cup of coffee. Why? Because of inflation, prices went up, I lost my purchasing power. So a dollar today is worth more than a dollar a year from now, or two years from now, or three years from now. So that's what we mean by inflation. The other thing is risk. Well, if you give me the dollar today, I know I have it in my hand. A year from now, you may not exist. I don't know whether you're going to give me that dollar or not. So giving those two factors, inflation and risk, the same dollar is not worth the same. So investors need a way to compare a dollar worth today to a dollar worth into the future. Because if I'm going to invest with you, if I'm going to give you money, whether lend you money or invest money in your company, I need to compare a dollar today to a dollar into the future. I need to compare, what is my dollar worth today? If I give you my dollar today, how much would you need to give me in the future? So my dollar equal to my dollar in the future. So that's what we're trying to do. So what we do is we use something called the present value or discounting or the time value concept. So this is where the time value concept. So if I'm going to give you a dollar today, let's assume I'm the lender, I want to get my money in the future, but I want to have the same principal amount that I gave you. I want to have the same amount. If I'm going to give you a dollar today, I'm going to, I want to receive equal value. How do I compute this? How do I compute it? This is where I would come. This is where I would use the present value or the discounting. Now on accounting, we have many uses of this. For example, when we're measuring the fair value of a company at level three, we use discounted cash flow because we don't have observable market value. So simply put, we're looking at a company and there's no value and we need to value the company today. We need to find the fair value. What we do is we look at their future cash flow. They're going to be making 100,000, 100,000, 100,000 and 100,000. That's what we projected. Then we need to know how much is the value of the company today. What we do is we discount those 100,000 to the present value to find out what's the value of the company using discounted cash flow. When we discount cash flow, this is what we would learn in this chapter. Using interest rate, we discount the value, find the present value. Same concept applies when we deal with long-term liabilities, bonds, leases, notes. They are recorded at the present value of the payments. Same thing with long-term receivable. They are recorded at the present value of the receipts. So these are the uses. That's why you cannot pass the exam without knowing, understanding very well the time value of money, starting with the concept of interest. What is interest? Interest is the cost of money. You want to buy something from the store, you give the money, they give you something in return. You want to buy money? That's fine. They will give you the money, but you have to pay them interest for that. So if you borrowed $10,000, which we call the principal amount from your bank, and you repaid $10,500 a year later, the difference between the principal, the difference between what you borrowed, called the principal, we're going to say P, and the amount repaid, the $10,500 is $500, and we call this interest. So $500 is the difference, and $500 is the interest. Now we can express the interest as a percentage. So if you paid $500 for borrowing $10,500 divided by $10,000, we can say that your interest is 10, a 5%. Now how do banks determine that interest? How do they say we're going to charge you five interests? Well it depends on two factors, usually, your risk, how risky are you? I'm going to give you this money. Well if you're too risky, I mean I'll give you anything altogether. But what is your level of risk? Now for individuals, that is reflected in your credit, in your credit score, each one of us has a credit score, and companies they also have what's called ratings. So it depends on your rating, on your risk. The higher your risk, the higher the interest rate, because they want to be compensated. If I'm going to give you money and you're a risky individual, I want to be compensated for my risk. If I want to be compensated for my risk, I'm going to charge you higher interest rate. The second factor is time. The longer I'm lending you this money for, the higher interest rate I'm going to be charging you. So simply put, higher rate, if I charge you higher rate, you're going to have higher interest payment, higher interest cost. If the amount is larger, given everything else is equal, you're going to pay more interest. The longer time it takes to repay that loan, the larger is the interest amount. So make sure you know the relationship between those three. Basically, if they're common sense, if I charge you higher interest rate, you're going to pay more in interest. If the amount that you borrowed is larger, you're going to pay a larger amount of interest, giving the same interest rate. And the longer the loan, the more interest you will pay. Let's dive a little deeper into the interest. And we're going to say we have two types of interests. We have simple interest and we have compound interest. And it's very important that you understand the difference between those two. Simple interest is computed on principle only. Remember, we have a principle and we have interest. It's only computed on principle only. And here's the formula for it. Interest equal to the principle, which is what we borrowed times the interest rate or what we invested. It doesn't matter whether we borrowed or we invested times time. So p times i times n. To remember the formula interest, it's pin. Your pin for your debit card, right? Pin for your debit card. So if you borrowed $10,000 for three years at 5%, here's what's going to happen. Time is three, period is three. The interest rate is five. The principle is 10. If we use pin, 10,000 times 5%, times three will equal to 10,000 or 1,500. If you borrowed now $10,000 for three months, so notice the difference for only three months, not three years at 5%, you have to be careful with the time. Now we have to prorate the time. We have 10,000 times 5%. The time is not three. The time is three divided by 12. I did this on purpose to kind of show you, you multiply it by three divided by 12. What do I mean by three divided by 12? Three divided by 12, it means I have three out of 12 months in the year. Therefore, three divided by 12 is the proper time, not three. So be careful whether you are giving a yearly or less than a year. Always if the interest rate is for less than a year, it will be prorated just like this one. For example, if it's six months, six out of three, 60, six out of 12. If it's daily, for example, if it's for 40 days, you divided 40 divided by 365, if you are told to use 360, you would use 360. So simply put, the simple interest rate here is we took 10,000 times 5%, 10,000 times 5%, 10,000 times 5%, so we only use the principal amount and we earned in total 1,500 and the bank paid 1,500 if you're going to look at it from a bank perspective. Compounding interest is different. Compounding interest is when you would compute the interest on both the principal and the interest and we're assuming here the interest is not taken out. It means the interest stayed at the bank like a CD and will compound interest where you don't take the money out, you don't withdraw it. And for our purposes in intermediate accounting or any other course, the assumption is it's compounded, it's not taken out, okay? So let's take a look now at this $10,000 if it's compounded, the same $10,000 that we invested for three years. Here's what's going to happen. The first year, it's going to earn 5%. It's going to earn $500. We're going to have at the end of the year, $10,500. The second year, we're going to start with $10,500 because we did not take the money out and this is the idea of compounding. It's going to earn 5%. We're going to earn $525. Again, we're going to keep this money and we're going to add the $525 to the $10,500. Now we have $11,025. We're going to take this $11,025 multiplied by 5%. We're going to have $551.25. We're going to add this amount to the principal and we're going to have now $11,576 and to be specific, 25 pennies. In total, we earned $1,576, which is how much more? Which is $76.25 more than the simple interest. Now you're talking it's not that much of a difference in a three-year period. But if you take those numbers and add zeros to them, then you're talking in millions and billions in terms of interest and this is how you should be thinking about. Now there is a formula to compute the compound rate and it goes something like this. 1 plus i raised to the nth power, which is to come up with the future value factor for any particular period at i interest rate. For example, here, if we want to use our example, 1 plus, which is 1 plus, our interest rate is 0.05. And if you want to compute this for three years, because we'll go up to three years, because think about it. If you're computing compounding, you don't want to keep adding the principal, adding the interest to the principal, it takes a long time. Therefore, what you can do is you can use this formula and basically we're going to take 1.05 raised to the third tower. And that's going to give us 1.157.625 if we multiply this by $10,000. And we know that we would receiving 11,576, which is how much we would receive for this loan. Let me keep the calculator up because we will need it anyway. So let's see. Yeah, we'll need it. So for example, if you want to do this computation for five years, 1.05 raised to the fifth power in five years, you multiply it by $10,000. And you will have $12,762, so on and so forth. So this is how you will compute the compounding rate. Let's talk more about the compound interest. Well, interest is expressed in terms of annual rate. So they would say the interest is 10%. But the period doesn't have to be a year. So although they tell you it's 10%, but the compounding can occur less than a year. Remember, compounding is when you earn interest on the interest in the principal on both. And what happened is you can compound the interest throughout the year. When that happens, you have to convert the annual rate into a compounding rate. And how do you do that? You will take the annual rate and you'll divide it by the number of periods. And you have to determine the proper number of periods. Now, because you have the period is less than a year, you will take the number of periods times the compounding period. Let's take a look at an example to illustrate this concept. Let's assume we invested this $10,000 at 5% compounded semiannually. Remember the $10,000 earned us $500 in the prior example. Now it's compounded semiannually. It means we have two periods. Why? Because the year have two periods semiannually, two, six months. And the rate now, we're going to divide the rate by two. So annual rate divided by the number of period. The number of period is two. It's 2.5%. The number of periods, which is one year times two equal to two, two compounding period. Therefore, here's what's going to happen. We're going to have this money. We're going to start with $10,000. The first six months, it's going to earn $250. After a six month later, we're going to have $10,250. And this $10,250, it's going to earn, again, 5%. And it's going to earn $256.26. So notice, if we add them up, it's going to add up to $506.26. It's more than the $500 if the interest was compounded only once. So here's how we convert. If you are told a 12% compounded over five years, if the interest rate is compounded annually, the period is five, five years, interest rate is 12%. Why? Because it's compounded annually. If you are told 12% over five years compounded semi-annually, the interest rate is not 12, the interest rate is 6%. Why? Because you have to divide it by two. So the interest rate 12 divided by two semi-annually. And the number of periods, we have five years, but we have two periods. And each year, the period equal to 10. If you are told the interest rate is compounded for this example, semi-annually, sorry, quarterly, 12 divided by four, the interest rate is three. And quarterly, we have four quarters in a year times five years and equal to 20. If you are told it's monthly, well, monthly means the interest rate is one, because 12% divided by 12 equal to 1%, divided by 12 month. And we have 12 month in a year times five years equal to 60. So you have to be very careful adjusting I and adjusting N when you are doing this computation. This is very important. I just want to make sure I emphasize this enough. You have to know how to do those computation. You have to know how to do this. Now, notice the interest rate is $506, which is more than the $500. So you would earn more. The more it's compounded, the better off you are. Now, we can compute what you actually earned. You earned 5.06 because you earned $506.26 and you invested $10,000. So notice, we call this 5.06 is the effective rate. You effectively earned not $5, not 5%, you effectively earned 5.06. So the 5% that we quoted invested at compounded semi-annually is called the nominal or the stated rate, but you effectively earned 5.06. Now, the more the compound occur, the higher is your return. The higher is the effective rate. And to compute the effective rate, basically you will take 1 plus i raised to the N tower minus 1. So let's assume we're going to go back to this $10,000 investment. How can we compute this? Well, if it's compounded annually, easy, 10,000 times 10%. Now, what happened if it's compounded semi-annually? Well, let's find the effective interest rate using this formula. Now, this is how we compute the effective interest rate. 1 plus, they have to be careful, the interest rate here has to be adjusted. Rather than 10%, it's going to be 5%. So it's going to be 0.05 because it's semi-annually equal to 1.05 raised to the second power minus 1 will give us 0.1025. That means you would earn 10.25%, 10.25%. So you will earn rather than 1,000. If you invested $10,000, if the compounding was semi-annually, the effective rate is 10.25. Therefore, you will earn rather than 1,000. You will earn 1,025. Let's assume it is compounded quarterly. So the rate is 10% but compounded quarterly. Well, compounded quarterly means what? Well, quarterly it means four times a year. If we take 10% divided by 4, it's going to be 2.5. So the interest rate that we're going to be using 2.5. So let's do this computation. 1.025, 1 plus the i raised, we're going to raise this to the number of periods. Quarterly means four periods, minus 1. And that's going to give us 10.38, which is 10.38%. 10.38% will give you a return of 1,038. Notice the more this money is compounded. So on a timeline, it looks something like this. This is what we're saying on a timeline. If it's compounded annually, it's only one period. If it's compounded semi-annually, it means you earn the interest for this period. You stop, you add the interest to the principle, then you will earn the more interest on both the original principle and the interest. If it's compounded quarterly, 1, 2, 1, 2. So 1, 2, 3, 4. So after 1 quarter, you would stop, earn the interest, add it to the principle, and earn interest on the principle and the interest. Quarterly 2, you would stop. The second quarter, you do the same thing. You will add the interest to the previous interest and at the principle, so on and so forth. And that's why you will earn more. Now, if this was compounded monthly, we could also do it monthly, same thing. It's gonna be monthly 10.47, 10.47% which is you will earn 1,047 dollars. Actually, you can compute this daily. If you want daily, you would earn an effective rate of 10.52 and you will earn in total 1,052 dollars. Again, very important to understand. The more it compounded, the more, if you are investing, the more is the return, but if you are paying, for example, if you have a credit card and it's most credit cards, they compound daily, it means every day that goes by, the interest added to the interest and they compute the interest based on the previous interest, so on and so forth. And that's why it becomes fit, it becomes quickly, it goes quickly out of control. So this is the compound interest, simple versus compound, compound interest. This is important, this is important stuff that you will need to know for the CPA exam as well as for your intermediate accounting course. At the end, I'm gonna remind you, keep your CPA review course. I'm a useful addition to that course. I can help you understand the material better in a different way. Your risk with me is one month of subscription. That's all what your risk is. You pass your CPA exam once in your lifetime. Invest in yourself, study hard, good luck and stay safe.