Introduction to Corporate Finance! Learn about time value of money, IRR, NPV, and other finance!

1. Fin Lecture 00: Hi, everyone. And welcome to the class. This is an introduction to finance. What we're gonna talk about today is the summary of what we're going to learn in this class and so you can get a quick head shot so you can see who's talking to you. Who's working the problems with you. We're not going over the time value of money. We do some examples together, actually. So when it says resource is available, please click that link because their RPGs that you should download and print out and so we can do the handouts together. It's a great way to learn. I haven't accounting classes well, that we do this in which is introduction to accounting, which is learning counting and less. And now you concede on my other courses. But we teach it in the way, or I teach it in a way where we print out the hand out, we do the problems together. It's a really great way to do that, so they're going to be problems like that here as well. I wouldn't learn about interest rate in the components of the interest rate, estimating the cost in default. Some of the infirm so some of this information will actually be on the C F A level one exam . So I am a chartered financial analyst, and I wanted to include some information on here so you can kind of get a few on what the CF eggs and will kind of be like. But again, this is just very introductory course when I learned about modern financial theory, which relates to correlation and diversification, Some terms we're gonna learn on a very high level is the efficient market hypothesis and the modern portfolio theory. So with that being said, let's go ahead and get started on this class. 2. Fin Lecture 02: So let's begin in a class of introduction of finance, a brief introduction in basics. So first, let's talk about the time value of money. What is the time? Value of money? It's about money today. Money today is more valuable than money tomorrow. So what does that really mean? Think about it. Would you rather receive $100 today or $100? 20 years from now, the answer is obviously $100. Today we'll show you mathematically why that is the case in other and feature lectures. But for now, the answer's obvious. Would you rather receive $100 today? Yeah, I definitely would rather to receive $100 today rather than $100.20 years from now. The very extreme example. But it's a prove a point. So why is that? Because you can earn interest on it. And that's what hopefully clicked in your mind is because you can earn interest on it. So example, I can receive $100 today or $100 a year from now. How much is the $100 worth a year from now, my bank offers an interest rate of 3% so I'm putting $100 today. I let a year pass because I put it because it put into the bank than a year from now. Will be worth 100 $3.100 dollars of my money and then $3 of interest in one year. And that's why I'd rather have the money today because I can invest it and, ERM, interest on it. So with that being said, our next lecture is interest rate dynamics. 3. Fin Lecture 03 Int Rate Dynamcis: So we talked about how you can put money into a bank and how money's worth more today than it is tomorrow, because you can put money in the bank and earn interest on it. So let's talk about interest rate dynamics. So what is an interest rate? It's the cost of borrowing or the cost that one pays for the rental bar or borrowing of funds. It impacts mortgages, student loans, credit cards and savings. Have you had any of these? Um, there's a good chance you're very familiar with interest rates, and hopefully you haven't paid tons of interest. But interest can start adding up. And if you're more interested on how if you're thinking about how to save it and you could take my personal finance class so interest rate, the money lender takes a risk and that you're usually the bank that the borrow may not pay back the loan, which is generally you or in money, let's say to buy a house the interest provides a certain compensation for bearing. That risk, coupled with the risk of default, is the risk of inflation. So when you lend money now, the price of goods and services may go up by the time you're paid back, so your money's original purchasing power would decrease. Thus, interest protects against future rises and inflation. Ah, lender, such as a bank which is pictured here, use the interest to process account costs as well borrowers. So someone like you pay interest because they must pay a price for gaining the ability to spend right now, instead of having to wait years to save up enough money. So, for example, person, our family may take out a mortgage for a house, which is pictured here alone, for which they cannot presently pay in full. But the loan allows them to become home owners, quote unquote now instead of far into the future. So I also want to point out that just because you oh, no, just because you bought the home if most of its paid by a mortgage, you do not actually own the home. So that's why I say quote unquote on homeowners because the bank actually owns that loan, and that's what we talked about during my personal finance class. Business is awesome. Ball borrow for future profit. So far, my business I may borrow to buy equipment now so that can be begin earning revenues today. Interest can thus be considered it cost for one entity. So costs for us if we're borrowing to buy a house and income for another so that bank is earning money. Interest is the opportunity cost of keeping your money as cash under your mattress as opposed to lending. So let's talk about the supplying the man interest rates are levels are a factor of supply and demand of credit. An increase in the demand for credit will raise interest rates, while a decrease in the demand for credit will decrease them. Conversely, an increase in the supply of credit will reduce interest rates. A like credit is readily available. While decreasing the supply credit will increase them. The supply of credit is increased by an increased amount of money made available to borrowers, so there's just a lot of money floating around. I can borrow a lot more money than that's an increase supply. For example, when you open a bank account, you're actually lending money to the bank depending on the kind of account you opened the bank and use that money for providing other loans and investment activities credit available to the economy's decrease as lenders decide to defer the repayment of their loans . For instance, when you decide to postpone paying this month's credit card bill until next month or even later, you're not only increasing the amount of interest you will have to pay, but also decreasing the amount of credit available in the market. So the banks providing into other loans and investment activity. So when that's part of the supply, the demand is the other loans and investment activity that people are borrowing from the bank. Eso when you don't pay off in credit card, for example, this in turn will increase the interest rates and the economy because it's lowering the supply of money. So now let's talk about the components of interest rates. 4. Fin Lecture 04 Componenets of Int Rate: So now let's talk about the components of an interest rate, so the first component is the risk free rate. This assumes no risk or uncertainty, simply reflecting the differences in timing. The preference to spend now slash pay back later versus Len now slash collect later risk free rate is usually library. We'll talk about that in our next one in our next lecture. So expected inflation expected. Inflation is them is the market expects aggregate prices to rise and the currency's purchasing power is reduced by rate, known as the inflation rate. So think about when parents or your grandparents talk about a Coke being only 20 cents 80 years ago, 90 years ago. Whatever the amount is, that is inflation. So Coke was 20 cents 80 years ago. Announcing dollar inflation makes real dollars less valuable in the future and is factored into determining the nominal interest rate. Um, so the nominal interest rate is equal the real rate, plus the inflation rate. So now on. Adding on top of that is the default risk premium. So what's the chance that the borrow won't make the payments on time or will be unable to pay what is owed. This component will be higher low depending on the creditworthiness of the person or the entity involved. So that is idiosyncratic to you as the borrower or this business. So then you have a liquidity premium. Ah, liquidity premium. Some of that investments are highly liquid, meaning they are easily exchange for cash. So some examples or U. S Treasury debt. Other securities air less liquid. And there may be a certain cause, certain loss expected if it's an issue that trades in frequently holding other factors equal So Sarah's Purvis, a less liquid security must compensate the holder by offering a higher interest rate. And then we have a maturity premiums. Sarah Despair Abyss. Also being equal a bond obligation will be more sensitive to interest rate fluctuations. The longer to mature it is. And then you add on top of the bank's profit margin, and that gives you your interest rate. So these are the five components of every interest rate that's ever provided. So now let's talk about library 5. Fin Lecture 05 LIBOR: So in an earlier lecture, I talked about library how that's approximate of the risk free rate. And so now we learn what library is. So Leiber's a benchmark rate that some of the world's leading banks charge each other for short term loans? It's important, understand short term. It stands for the Intercontinental Exchange London Interbank offered rate and serves as the first step to calculating interest rate on various loans throughout the world because it approximates the risk free rate libraries based on five currencies, the U. S dollar, the euro, pound, sterling, Japanese yen and Swiss franc and certain serves seven different maturities overnight one week and 1236 and 12 months. There are a total off 35 different library rates each business day. The most commonly quoted rate is a three month US dollar rate, and so that's what libraries it approximates. The risk free rate on DWI. Use it a lot in practice because a lot of loans are our benchmark toe library. So that being said now, you know libraries and how to approximate the risk free rate 6. Fin Lecture 06 Variable vs Fixed: So what's the difference between variable and fixed interest rates? Variable interest rates change over time. It is tied to another market. Interest rate library is the industry standard, and it's generally library plus spread. So in businesses congenitally be used for the working capital line, which we'll talk about in later lectures in in regular or in everyday life for individuals . Home mortgages can actually have variable interest rates, and that's a lot more risky. Um, and actually, ah, adjustable rate mortgages or a our EMS are adjustable rate mortgages. What partially got us into a huge debt are huge crisis back in 2008 so variable interest rates can change over time and library is the industry standard, and it's generally Leiber plus a spread. Um, it again, working capital lines for businesses are what is one thing that let him use his library. So fixed interest rates fix interest rates do not change over time. Hence the work fixed. They're used for loans that have a longer duration. So think home loans and car loans. Whole loans are generally fixed interest rate, but again there was. There are things called adjustable rate mortgages, which were more risky and caused a lot of the financial crisis they are best for risk averse borrowers. Takes interest rates are because you know how much your interest is going to be and how much your payments are going to be. So with that being said, that's the end of this lecture about the differences between variable and fixed interest rates. 7. Fin Lecture 07 Cost of Default : So now we're gonna talk about the estimating cost of default risk or estimated the cost of default risk. So what is default risk? It's a very important part of the interest rate that a sign that is assigned to a borrow is his or her default risk the risk of not being paid back. So this default risk premium one of the five components of the interest rate. So it's the only component which is unique for each and every single case, which means it's idiosyncratic eso you add on top of the other other parts of the interest rate to get your interest rate. But the default risk is the only component which is unique for each and every single case, and the banks look at default risk very carefully. So the assessment the bank needs to determine how much is going to lose if you default, and how likely is it that you will default? So how much are they gonna lose and how likely will you? How likely is it that you will default and they use this following formula that expected loss as equal to the exposure, beautiful times, the probability default, Sometimes the loss and given the default. Okay. And so now let's define the terms at the bottom of this slide. The exposure default is how much of the bank's money will be at risk if we default the total value. How likely is it that we will default? Is the probability of default? And the loss given default is the percentage of a bank's money that will be lost? Its generally never 100% somewhere between like 50 and 70%. So now let's first talk about exposure at default, so exposure at a fault. Let's do an example. The $200,000 home it's a total value that a bank is exposed to at the time of default in this case would be $200,000 each. Underlying exposure that a bank has is given an explosion er at default value and is identified within the bank's internal system. Using the Internal Ratings Board approach, financial financial institutions will often use their own risk management default models to calculate their respective e d E a. D systems, so exposure default is the total value that they will lose if you default. So now let's talk about the probability default. The earning potential is these are the things that are factored into your probability. Default your earnings potential. This works for individuals or corporations. It's reviewed under individual basis. Or if you're a corporation applying for a loan, it's the corporation. Basis is, well, the liquidity of the items that you have. So your net worth is determines your your liquidity of your network that helps determine the probability to fall just because if you need to make your monthly mortgage payment of $3000 in all your investments are tied up in some non liquid form. Um, let's say other houses. You cannot sell a part of your house that pay off another mortgage to pay off your current mortgage, for example, so liquidity. But if they're all held in equities, for example, it's easy to convert those assets. And liquidity is very high for you, Lord, in the most extreme case, all of your network there sitting in cash than converting those assets will be very, very easy because they're already in cash and you have to pay off your $2000 a month payment. For example, your credit history. So far bank are foreign corporation or for an individual. So if you're an individual, Michael score and you can see my personal finest lecture more about the fight. Go score a new credit history and an external factors like your market risk in your employment history. So market risk, if you're buying a house, is how is the housing market doing there and lost Vegas, for example? The probability of fault was probably it was a lot higher back in 2008 just because the market was bad and then employment history. So what kind of industry are you employed in? And so if you watch my intro to the stock markets there different types of industries So your secular versus your stick useless cyclical. So are you in a cyclical industry or you want a secular industry? So now we're gonna go through some time value money, examples and some handouts, and for these for this next lecture, go to the view resource is because that's where you're going to get the handouts toe complete with me and these air answers that we work together on. Um so, actually, the last thing I didn't talk about was the loss given default again that somewhere between 50 and 70% it's the amount of funds that is lost by a bank or other financial institution. When I'm borrower defaults on a loan. Okay, so again, it's never 100% it somewhere between 50 and 70%. So now you can you understand the expected lost and now let's go on to time value of money . 8. Fin Lecture 08 a Intro to TVM: so hopefully you printed out the hand out. By now, if not going pauses click. The resource is printed out. If you just want to watch the lecture. No problem with that either. So the key of time value money. So that's the time value Money intro and what's Arky? Arky is a dollar. Today is worth mawr, then a dollar tomorrow, and that is our key of time value money. So let's go through some definitions. What is the present value? So the present value is what is it worth to me today? So the worth of the value of the dollar work to me today? The future value is the worth of, um, money in the future. So let's go through an example of each of these So worked at the dollar. To me today is essentially, if somebody's willing to give me $500 in five years, how much is that worth to me today? So will bring money back in time to today in future values. If I put $100 into a savings account, how much is gonna be work to me in five years? We're looking at the future of it. Okay, so I wanted visually draw those arrows. So you think about it every time you hear those terms. So one time payment is, um what? It actually, just days. There is a one time payment. Okay. In the way we say it is a present value of a dollar, for example. So we're bringing $1 we're bringing that $1 back in time. So now an annuity payment is multiple payments. So any time you're annuity, think multiple payments. Okay, So multiple payments is essentially how much is at work to me today, and this could be feature valuable present value. In this case, we're going to stick with president value if there are multiple payments. So you're This is another year. This another year in this another year. Okay, we'll bring it all back in time. Two year zero. OK, so that's what multi annuity payment means is multiple payments and we're bringing those multiple payments back in time. In the future, values were taking multiple payments and seeing how much those multiple payments going to work for me in the future. So in a future value, what the nudie would be essentially, let's say that I put $500 into a big count every year for the next five years. How much is that worth to me? Five years from now. So annuity payment, I think multiple payments. So the type of Cashel problems, president value of a dollar means we're taking one value, and we're bringing it back in time to your zero. Okay, so I'm gonna visually draw these out, and you should as well, So taking one value, bringing that $1 this one time payment back in time. Present value. An annuity means I have multiple payments, and I'm bringing all of them back to your zero. Okay, Actually, really like this visual. So and you bring it back to time zero. That's what we call present day. So present value. So in each of this, on each of these marks or dollars, So multiple payments member, When you hear annuity, you should think multiple payments now. Future value of a dollar. What's the future value of a dollar? Okay, so now we're at time, zero. This is ah, savings account, for example, and we have some dollars here. We want to see how much it's worth in the future, so this is the future and how much is at work to me in the future. So example would be I put some money into a savings account with $100. How much is that worth? Five years from now. So again, going into the future, So future value annuity. We kind of went through that. So you have time? Zero time one time. Two times three. These are all points. So this to call that years and you're trying to figure out how much swore thin, dear four. So the example I gave earlier wise in this one would be putting $100 into a bank account every year. How much is at work to me in your four? Okay, so I'm taking the value of these amounts and bring into the future. And this is feature of our value of an annuity, which is a multiple payments. Remember when you think annuity have to think multiple payments. Okay, so this is a visualization of all of these, and these type of problems are gonna work on. It's okay if you don't really get what I just talked about because we're gonna do example together, and then you will truly understand it, and that's the only way to do it is to do examples and do multiple examples, and that's the way to understand that, so that let's go ahead and start doing the examples together. 9. Fin Lecture 08 TVM by Formula: Okay, Class. So now what we're gonna do is do a time value of money, Example together. So, first, what is the key of the time value of money? The key is that a dollar today is worth mawr, then a dollar tomorrow. So again, I just want to remind of you of that of the key. So that being said now, we're gonna learn how to solve time, value of money, problems. This is useful whenever you're trying to calculate how much something is going to be worth in the future, Um, for example, you invest some money and you want to see how much it's gonna be worth a couple of years from now, based on your savings percentage from your bank. So how we solve time, value of money problems. We use the below formulas, the first ones FB FB is equal to future value. So the future value is equal to the present value times one plus our race to the end. Power PV equals present value arias. Rate of the return and end is equal to the number of periods. The present value, which is here, is equal to the future value Times 1/1 plus are raised to the end. Power so defined here, Future value ready to return in a number of periods. So let's do an example together and you'll see how pretty simple this actually is. I am said to receive $5000.3 years. My bank is offering a 6% interest rate on savings. How much is out worth from to meet today? This is called the present value of a dollar on. And that's the type of problem this is so I'm gonna receive $5000. So this is today. You're one. You're too. And your three. So I'm gonna get $5000 three years from now. This is time period zero. So how much is out worth today? So the first thing to ask yourself is is gonna be worth less than $5000 or more than $5000 ? So, based on our key, which is why I made you write it up here that a dollar today is worth more than a dollar tomorrow. The value should be less cause we're gonna put it in. Sorry, I wouldn't put it into the bank account, and then it's gonna grow to $5000. Okay, so now let's go back and calculate how much that $5000 is worth today. So out of the two president value and future value, which one do you think we should use while we're trying to find the present value, which is how much it's worth today? So let's write down our formula. The present value is equal to the future value times 1/1, plus our races and power. Okay, so now present value is able to the future value, which is $5000 times one over one, plus our race to the end power to now let's run it out again. President value equals $5000 times 1/1. Plus, what is They are ours. The interest rate or the rate of return the rate of return is 6% here, plus 6% raise the end power. Finally, president I equals 5000 times 1/1 50000.6 race to the end power and is equal to three because it's three years from now, and that's gonna give him my present value. So what is that? So I'm gonna move over to Google sheets and calculate that out. So we have $5000. Here's $5000 and we're gonna divide that by 1.6% raise, too. The third power, so 5000 divided by that number is equal to $4198.9. So let's go back $4198. Just write that down against make sure in nine cents 0.96 if you want to be exact, so that's the present value. So today it's worth $4198.9 to me. Three years from now, it's gonna be worth 5000 if I could invest it at 6% per you. So now let's go to our second example. Our second example is I have $2000 in my savings account. My bank is offering at 6% interest rate on savings. How much will it Will it be worked to me three years from now? So let's draw this out. Time period, zero time period, one time period to in year three. Okay, so that's my little timeline here. So I have $2000 right now and I'm trying to figure out how much is gonna be worth three years from now. So how much is gonna be worth 30 years from now? This is called the future value of $1. So little grab or formula present value. I mean, the future value is equal to present value times one plus R to the end power. So future value was present value times one plus r race to the end power. So now this is fill it in future value equals the present value of 2000 times one plus our race to the end power. Future value equals 2000 times. What is our interest rate of 6% Raise the end power. Future value goes 2000 times 1.6 races the end power And is he going to three years from now? So our future value equals What? So hopefully you can calculate this out on your own? I'm gonna go ahead and move back to Google Sheets to use it. $2000. I do it all in one formula. This time, Times 1.6 Raised to the third power to see my formula there and see what 23 a 2.3 2382.3 And that's the future value. So what does that mean In less fancy terms? It means that if I am put $2000 into my bank account and my bank account is offering 6% my savings account is offering 6% interest per year than at the end of three years. Because interest is calm, pounded. I'm wanna have $2382.3. So those are 1st 2 examples of time value of money problems. And now you want understand the formula, Um, and to know how to solve time value money problems. So hopefully you have that. Now you have this forever, and you can understand time value money problems, which is very helpful whenever you're trying to your out, How much money, um, you're going to have in the future when you have a specific savings savings rate from your bank. So that being said, that's the end of this lecture 10. Fin Lecture 09 TVM by Excel: So now we're gonna do a time value money problem together. And the first thing I want to ask you is what is a key concept of the time value money again that a dollar today is worth. Make sure that dollar sign looks good. Sorry. Let me rephrase that. That a dollar today is worth mawr, then a dollar tomorrow. So how do we solve time value money problems? So previously I gave you a formula for future value formula for present value. But no one will ever actually use that in the job because that would be too time consuming . So what we use in our jobs Excel? I'm gonna use Google sheets here just because Google Sheets is free to everyone so anyone can follow along. If you don't have excel, it works exactly like it gets Excel. So when I was calculating NPV calculations at my job, it was to, uh, way wasn't except so first, we have to define the variables and equals number of periods eyes equal to your interest rate, which was our in our previous example. But from here on out, we're gonna call it I present value is equal to P V pretty self explanatory. FV is future value, and PMT is equal to your annuity payment in what annuity payment means is multiple payments and we'll explain what that means later on. So right now, I just think multiple payments So one of the variables will be unknown. So this is your ex or your unknown variable. That is the one you are solving for. So out of these five variables, one of them will be your ex because we won't know it. So that's because it's unknown. So with that being said, let's go ahead and do the first example together. I am set to receive $5000.3 years from now, my bankers offering a 6% interest rate on savings. How much is that work to meet today? This is called the present value of a dollar. We've done this one by hand, but now I want to show you how to do it in in Excel for Google Sheets. So first, what we have to do is how we solve it's going back up is we have to define the variables. Okay, So because I've done so many of these problems, I don't know you keep scrolling back up, President value future value and I and P empty. So once we define those, we can get our answer. So I'm set to receive $5000.3 years from now. So my future values 5000. My aunt is three years. My bank is offering a 6% interest rate. My eyes 6%. How much is that worth to me today? So how much did work to meteo present values? X? I'm not receiving any multiple payments. I'm receiving one lump sum payment which is called the present value of $1. So now let's figure out what the president value. So let's revolver Google sheets in type these variables. So PV f b I and in PMT So let's label him president Values are ex future value is equal to $5000. I is equal to 6% and you go to three years. PMT is equal to zero. So now that we want to solve for PB, all we have to do is happened PV year so in Google sheets and name except only type in PV because we're calculating present value and then here is gonna tell us what we need to type in. So our rate is here's I. So let's go back. Number of periods three. Self explanatory and very easy. This is, uh, next ones payment amount zero, because we're only receiving one lump sum payment in my future values here. So the total is $4198.10. So let's go. Right this down here, President values $4198.10. So quick thing you may have seen when I was looking at this is that it was negative. So you could be like, son, why is this negative? Is because we have to input the money. We have to put the money into the bank. So it's an outflow, and what we're gonna get back is $5000. That's why it's negative. That being said, we can actually go back to a previous handout, and I want you to see that we got the same exact answer. So $4198 over here, $4198.10 difference due to rounding. So it's checking our answer. So now let's go on to the next problem. Get back in a full screen here. So I'm set to receive $1000 each year. Uh, multiple payments. So this must mean something about annuity and PMT. For three years, my bank is offering a 6% interest rate on savings. How much is that worth to me today? This is called present value of an annuity. Okay, so first I want to draw this out 40. So year zero, your one you're to You're three. Okay, so I'm gonna receive $1000 each year for the next three years. How much is out work to me today? That's the question. So what did I tell you when we're solving time value, money problems, we have to define the variables. And one of them is gonna be able to our X so PV f the I. And in PMT again, I've done so many of these problems. I don't need a to do it. So our golf school back up So president value. Do we know how much our present value is? The question is, how much is it worth to me today? So that's my ex. My future value Do I know. How much am I getting? A lump sum in the future? The answer is no. So zero I we have our interest rate of 6% and three years in r p m t. So this is where we get multiple payments were getting multiple payments of $1000. So here, we're gonna put in 1000 because we're getting it three times. So now let's go to Google shapes and solve it for and get their correct answer. So again, I'm just gonna copy of paces quicker. So my present value is what I'm solving for my future value zero because I'm not receiving any lump sums. I have 6% interest rate. My three years in my PMT, which is my annuity payment, is $1000. Now I have to just solve for the president What happened? PB and it's gonna tell me exactly what I need. Input. My rate 6%. My number of periods. Three. Now my payment amount. That's 1000. And then now my future value zero. So how much is at work to me today is where $2673 is one cent. So let's move back over here. And that's my present value. That's how much that's worth to me today. So let's keep moving on. We have two more examples to do. I have $2000 in my savings account. My bank is offering a 6% interest rates on savings. How much will it be worth three years from now? This is called the future value of a dollar. We did this one by hand earlier. So we're not gonna draw that The, um, timeline out Just gonna write down the variables and then pmt So I know the president Value is 2000 because I have 2000 right now. My future value, How much? It will be work to me in three years. That's my ex. My eyes 6% in my and his three. I'm not receiving any annuity or multiple payments. So now I just have to calculate So going back over here, copy this down again to save some time. So now I have $2000. My future values my ex my I 6% Still, my aunt is three years. My pmt is yours. So now we just got a cute calculate future value So we type in F B here we put in the same information says rate, number of periods, my payment amount and in my present value. Now, if I put in $2000 it saying I get $2382.3 out So you write that down $2382 and three cents . Let's check that with our previous one. This only take a couple of seconds here and pull it back up. Hopefully, I'm right. $2382 3 cents. OK, I was right. So that's good. Um, so $2382.3. So now let's do our last example exit back into full screen here. I'm going to put $400 into my savings account each year for the next three years. My bank is offering a 6% interest rate on savings. How much will it be? Work to me three years from now, This is called the future value of an annuity. Okay, so now we hear for the next three years, my bank is offering me a 6% rate, but I put $400 in the savings each year. Okay, so that means PMT is going to be used. So future values a question mark. Present value is equal to zero. I don't have anything in there. Right now. My pmt is the goto $400 Because I wanna be putting $500 in how long my any goes. Three in my I equals 6%. So drawing out my timeline year zero your one, you're too in your three. I'm gonna put in $400 each year for three years, and I'm trying to figure out how much how much it's worth over here. So that's my future value. So now that's when you do this is through excel. Or in this case, um, Google sheets, coffee, this paste it Here, my present value Have $0 in my savings account right now. Future Valium trying to figure out my interest rate is 6% and is equal to three in my payment amount is $400. That's what I'm gonna put in each year checking it over the hole matches. So now I just gotta use the formula. The rate is 6%. The number of periods is three. My payment amount is $400. In my present values, you don't have any money, right? So three years from now it's gonna equal 1273.44 Okay, And does that make sense? It makes sense, because if I just put $400 into my savings account three times, I would equal $1200. So it's got to be more than $1200 because I'm gonna earn interest on top of that. So my interest is $73.44. So that's where I get to 12 73 44. And that's the end of this lecture. So now, um, I want you to see how we use Google sheets or Excel to figure out all these problems. So I showed you the formulas because I think it's really important. And that's how I learned it when I was in getting my graduate degree. Um, also, it's for the CF exam. We learn it like that on the CFD exam, but in actuality, in real life, when you're on the job using Excel or Google sheets most likely excel toe value capital investments and t use time by a time value of money calculations. That being said, that's the end of this lecture. 11. Fin Lecture 10 Time Value of Money Indiv Practice: Okay, so now we're gonna do individual practice. So pause this video and try to do these on your own and then compare answers to me. Okay, so hopefully you try to I try to accomplish this on your own and be very helpful if you do . If not, that's OK, too. You could just watch me do it. So now. So let's solve these problems. And for every problem we know we need to write this out. So I don't even need to read the question yet because I know that I need to write this out , and one of these is gonna be my variable. So I am set to receive $3000 fried years from now. So my future values 3000. My bank is offering a 3% interest rate. How much is that work to me today? And it's gonna be for five years from now. I have no annuity payments or multiple payments, so my present value is equal to my ex. This is called present value. The dollar, which we know. So now this is gonna become a little bit easier for you. So all we have to do is go over to Google sheets and type it in. I'm actually gonna write this out for the next four problems to save myself a little time. You. So now going back to this present value is equal to my ex. My future value is equal to 3000. My interest rate is equal to three James 3%. And as he put a 5 p.m. t equals zero. So now, solving for president very easy rate and make sure it has 3% on there. If you put in three, it's gonna make it 300% number of periods, payment amount, and then future value. So $2587.83 present value equals 2500 $87. And sorry just forgot it again. 83 cents and that's it. So now let's do this one. I am set to receive $2000 each year for five years, and my bank is offering in 3% interest rate on savings. How much is that worth to me today? Present value, future value and I pmt I know I write him in different orders every time, and I probably shouldn't do that. But you're getting the point. Now All we have to do is figure out what we're looking for. Present value is equal to X because I'm trying to figure that out. How much is at work to me today is why present values of X Future value set to receive $2000 each year each year signifies P m t. Hopefully thought about that. It's an annuity payment for five years. 3% interest rate. Future value is equal to zero. So now we just gotta figure this out again. So we go back to our handy dandy You work seat here, President. Using quit ex Future value zero I is equal to 3% state 3% and is he was five. And I know tapping back and forth, but you have the sheet in front of you. PMT was $2000. So now hopefully you already figured this out. The rain is 3% number periods. Five pmt is 2000 and then feature bicycle too. So this is work 1 $9059.41 to me. Let's go back to make sure I wrote that down correctly. $9159.41. And that's what we got. So another. Yeah, so $2000 for five years equal to $9159.41 to me today. So now it's going to the next one present value, future value and I pmt I have $4000 into my I have $4000 in my savings account today. My bank is offering a 4% interest rate. Um, how much will be worth five years from now? So I'm trying to calculate the present value. I mean, the future value payment is zero. There's no one Multiple payments on this one now feature values. My unknown. My present value is he would have 4000. My interest rate is 4%. My time periods. Five counties zero. Sure, that's right. Feature value is equal to my rate. Then I put in my number periods, my payment amount and then my present. So it's work that $4866.61. So said another way. If I put $4000 into my bank account and they're offering 4% in five years having not touched it. I'll have $4866. It's our last one will do it again. Present value, future value and I pmt. And once you do enough problems like this, he's right. Him down. It's really, really simple. And they get easier and easier. I'm gonna put $600 in my savings account each year. What does that signify your right? That's a P M T. It's an annuity payment for the next five years. My bank is offering an 8% interest rate. Um, how much will my how much will be worth five years from now? Uh, that's my ex and I have no money in my savings. Right. So now let's go back and figure out our last answer. Present value is equal to zero feature values. You go to my ex, my eyes go to 8%. My end is you gotta five years April messing it up. Pmt I'm putting $600. So now let's figure out my future value. What's my rate? 8% with my number of periods. Five payment amount 600 president about You have no money. My savings right now so I'm gonna have 3000 $519.96. So said another way, What that means if I put $600 into my bank account each year for the next five years, at the end of that's $3519.96. Just a gut check that $600 times five years it's got to be greater than $3000. The rest of that, that 519 96 is equal to my interest. So that's just a gut reasonable mistake. That being said, thank you for doing this on your own and checking your answered with me. This is a great way to learn, and I really think that this is this is the way to do it So that being said, that's the end of this election. 12. Fin Lecture 11 Capital Budgeting Group: Okay, class. Welcome to in short of capital budgeting. If you have not printed out the handout, go ahead and do so. Now. Pause. This video it's in the resource is tap. Go ahead and put it out. If you don't want to put it out and just want to go through the lecture with me, no problem without either. So what is capital budget? What we're trying to do is answer the question. Should we invest in this project Yes or no? And that's it. In simple terms, when China and determine if we're going to invest in a long term project. It also helps businesses determine which projects to invest in because every business has a limited amount of capital to employees. So they only have, let's say, a $1,000,000. And they only have. They have to decide between three different projects projects A, B and C, and they only have a $1,000,000. They only can choose, Let's say, two of those projects of which projects are they going to choose? Well, that's why there is capital budgeting, and that's what we're gonna go over today Is capital bunching and how businesses make these decisions and how you can make these decisions as well. So that being said, Let's go. Most girl that are go to the next page three different methods to determine if a project is worth it. So this is another way to say this is three different capital budgeting techniques. So the 1st 1 is the NPV. It's the difference between the present value cash inflows in the present value of cash outflows. So let's read that again. The NPV is the difference between the present value of cash inflows and the present value of cash outflows. So what already should trigger your mind is, at the time, value of money. It's taken into consideration here. Okay, the time value money is taken in consideration with NPV. The second method to determine for capital budgeting is internal rate of return. The internal rate of return is a discount rate that makes a NPV of all cash flows from a particular project equal to zero. Okay, and so that president values NPV. I r r is a short for internal rate of return, and that's what we say in business. So I R R is the discount rate that makes the NPV of all cash flows from a particular project equal to zero. And this one also takes in time value of money. It's taken into consideration here in the payback period. This is the third method. The payback appeared is the length of time required to recover the cost of an investment. So again, the payback period is the period of time, the length of time required to recover the cost of investment usually set in years. Okay, this is said in years and this does not Oops, right that again does not take into consideration the time value of money. So, out of all three of these, the best one is NPV. Okay, so let's right that, dear. The best one utilize the most. Okay, so that president values the woman who spend the most time on. I do want you to know how to calculate IR and pay back period. But again, when you work in finance, net present values the one you will use. So that's why I wanna spend the most time on it. So NPV requires a discount rate. So let's define discount rate it refers to. The interest rate refers to the interest rate used in NPV analysis to determine the present value of future cash flows. Okay, so determine the present value teacher future clash cash flows. It's the interest rate. So it's the discount rate and discounted cash flow analysis that takes into account not just the time value money, but also the risk or uncertainty a future cash flows. Okay, so discounted cash flow analysis is NPV. Right? That again, the discount rate in discounted cash flow and NPV analysis takes into account not just a time about money, but also the risk or uncertainty of future cash flows. The greater the risk or uncertainty of cash flows, the higher the discount rate. Okay, so the way to think of this is it. Let's say that you're charging someone interest. The higher the risk that person has a higher interest rate they're gonna have. That's the same exact idea here. The higher the greater the uncertainty of future cash flows, the higher the discount rate so very important. Understand? So with that being said, let's go through some examples. So we're gonna go through two examples we're gonna do together. Then the next one I'll ask you to do on your own on. And then we'll work it together, obviously at the end so you can compare your answers. So calculate the NPV of a project which requires an initial investment of 30,000 and is expected to generate a cash inflow of 15,000 each year for three years. The target rate of return or the discount rate is 8% per year. The initial investment occurred at the beginning of the first year. Okay, so this is really important here. Let's a draw it out so we can graphically see it. So you're zero your one you're too in Year three. Okay, in your zero. What happens? $30,000 initial investment in your one. What happens? We have $15,000 in your to get another 15,000 in your three. We get another $15,000. Okay, so we want to know what the NPV is. So let's go back up and re read the definition so we can really understand this. The NPV is the difference between the present value cash inflows and the present value of cash outflows. So here the cash outflows 30,000 and now we need to calculate the present value of the cash inflows. So think about that for a second pause if you need to. All we have to do is calculate the present value of this. So we know how to calculate president value now. So all we need to do is take these cash flows and bring them back to this period. Okay? Which we've done in the time value money calculations. Now we just gotta do it three times. So let's set the formula to set the formula. I'm gonna use Google Sheets. You can actually use a calculator. Okay, But I'm gonna use Google sheets because it's easier for me to see that our for you to watch . So here, we're gonna put year. Wouldn't do 012 and three. Oops. Three. And want to say, Here is the cash flow for the cash flows. $30,000 out, and then we have $15,000 in each year, and then I'm gonna make this look a little prettier here. So now we need to determine the present value, okay? And we have a discount rate of 8% per year. Okay, So 8% is our discount rate. So now let's set up a formula. Let's make this a little bit better looking and let's enough for formula. So what is the present value of this? It's 30,000. And now house. What is the present value of the? So let the formula is equal to this, which is 15,000 divided by one plus our discount rate. Okay, race to the power of one. Because this year one Okay, so I'm gonna make this now dynamic this formula dynamic so I can just drag and drop it. So here, we're gonna hold B nine because we want to hold the interest rate. So it's a Little Excel tutorial as well. And in this case, we just want to hold the d six. We don't need a hold. Now it's coffee and pace that. And these are the present value of your one cash flow your to in your three. So now, since if you were doing it by hand, I want to write it down here. So here's the present value of each of these cash flows. This is negative 30 because it already happens in your zero the next ones. 13,000 8 88 I'm not gonna write down the decimals. The next one's 12 860 and then last 1 11 907 So let's read through what the NPV is again. The NPV is the difference between the present value of the cash inflows in the present value, the cash outflows. So all we have to do now, if you read that definition has add these things together. So we Adam together, it gives us our NPV. So are NPV. Is this some of these four items? It's $8656 and 45 cents. OK, so that is our NPV. I want to also quickly show you here that you can actually do this formula in excel and not in the fact that, like we just discounted each one of these individually and that's what I did again. So all I did was discount these individually using a formula. But it is very easy to use that formula. So rewind it and watch again. We need to find out how to, like, lock the formula. If you never seen using the dollar signs, that's how you lock and accept. So that being said, I want to show you how to use the formula in excel in Google sheets, but the same exact formula to calculate the present value. So what you do is you type in NPV. You put in your discount rate 8% when you put in your cash flows here. So watch what I'm doing them. I'm using cash flow, one cash flow to and cash flow three. This occurred at the beginning of the year, so I did not put that in my calculation. So your initial investment occurs at the beginning of the of the year, then you do not include that in the formula. Now you take out the 30,000 and this is your final and PD, or this is your MPB but up with final because I'm something out to some of these two things up. Make this look a little bit better again. And look, our NPV here and our NPV here are exactly equal because they should be. When I'm using the formula and PB, So I wanted to show you how to use the MPB formula to calculate it out. So now, since my final NPV put a border around it and I'm embolden so that we calculated NPV and you know how to calculate the present value and visually, you understand it as well. So now it says, calculate the internal rate of return. So what is the internal rate of return again? We just learned it. I know I know really well, but you have to go shoot. You should go back up. The internal rate of return is the discount rate that makes the NPV of all cash flows from our particular project equal to zero. That being said, we want to use the formula in Microsoft Excel or Google Sheets. So, hero put IR, What we do is I r is equal to the cash flow amounts. So all we have to do is put in the cash little amounts. We highlight the cash little mounts here, and we have 23% as our I'm gonna put some decimals out there. So you see it 23.38% is our internal rate of return. Okay, I'm embolden. Outline it as well. And that's the only way you need to do it. We're only gonna learn how to do it by using excel or on Google sheets, because that's the way everyone does it whenever you have to do this. And it is not very barely used, its rarely used in business finance. But I want to show you here how you can calculate. So I r r and you just highlight your cash flows again. We use the initial cash flows, not the present value, because this is us calculating that present value. Okay, so that's why the highlight this formula again, we use the initial cash flows, not the president. Value the cash flows Very important, understand? So now I'm gonna show you something that they think about. So I are. Go back is 23 0.38%. Let's write that out again. Sorry. So now the question is, son, how do you know that's right. Let's check it. Okay, so it's supposed to be equal. The internal return rate of return is a discount rate that makes the NPV of all cash flows from a particular project equal to zero. Okay, so if I use my NPV calculation, it should give me in that present value of zero if I'm if my internal rate of return is correct, So let's do check. I are here. So are NPV using this discount rate using these cash inflows and then we take out our initial cash outflow. NPV using IR is equal to you. Guessed it zero. That's how we know we're correct because their NPV using RR zero. And that's how we know that our is correct and then pretty cold that see that how we could check it. Now let's calculate the payback period. The payback period. Let's go over the definition again. Is that length of time required to recover the cost of investment usually stated in years. Okay, usually stayed in years. So let's go over here and calculate. Okay, So the payback period is how many years? 30,000 and all we're trying to do is get this zero. It takes us two years to get to zero. So when I type in two years, all I did was some this up and looked at the formula. The bottom where the sun is equal to Zero Excel does that as well. For the payback period is two years. I want you to know that this valuation method exists but is very rarely used. No one does this because it has not taken a consideration time value money and it's very, very important. Okay, so let me put some borders around this, and that's our payback period, or payback period is two years. So looking at this project, the net present values $8656 are internal rate of return is 23.38%. In our payback period is two years. So now you know how to calculate them using three different capital budgeting methods. How to calculate the value of this project easier, using that present value, internal rate of return or the payback period. So that being said, let's go back down and putting the payback period is two years. Okay, so we should only invest in projects that have a NPV greater than zero. Okay, the NPV has to be greater than zero, or we will not invest in this project again. We focus on the present value because that's the one that used all the time in business finance. NPV greater than zero means that we do do this, that we we say yes to this project and we invest in this project. OK, so that present value greater than zero? Yes, we want to invest. Now we know how to calculate the internal rate of return and the payback period as well. So this is the next example on what you do on your own, and then we're gonna do it together as well. So please go ahead and start the next election, our next problem on your own. 13. Fin Lecture 12 Capital Budgeting Indiv: Okay, So hopefully try to do it on your own and it not go out and watch this video. We'll do it together. So calculate the NPV of project requires an initial investment of 60,000 and is expected to generate a cash flow of 20,000 each year for four years. The target rate of return order. The discount rate is 8% per year. The initial investment occurs at the beginning of the first year to calculate the NPV again . Since this is only the second problem we've done, let's go ahead and write this out. Make it out graphically. Okay, so you're zero your one your to your three in year four and just imagine the distance between each one of those is the same. Obviously it's not, and that's my fault. But anyways, so initial investment is $60,000 out. Okay, then we have $20,000 in each year, and I'm only gonna write 20 k here. We it's all the same. $20,000. Okay, $20,000 we will need find the present value of these. So bring them all back to your zero, okay? And that would be our NPV. So let's follow the same path that we did last time so you could do this by hand. Um, so we're trying to find the president value the present value of 60,000. 60,000 and now we're trying to find the present value of these. So I'm gonna use Google Google sheets. You can use Excel, or you can use a calculator, but I want to do it this way. So what we have here is your year zero. We have 60,000 and we have 20,000 in each year. I saved some time and just computer from my last sheet. You could do that to your four. Actually need one more year. Another 20,000 OK. And so now these are my cash flows. Non present value, right? This is just the initial cash flows and now we have the present. So what's the present value of 60,000? 60,000. Our discount rate is 8%. Okay? Actually, I'm a move my discount right up here, so it looks a little bit cleaner. Just kind of write 8%. So now what's the present value of $20,000? It's that value divided by one plus the discount rate, and I'm gonna hold it. So this case, I'm put dollar signs there raised to the first power. And again, if you don't remember this formula, it's in our time value of money, our time, value of money, lectures. So in the copy and paste this year, So all I'm doing is taking this and taking the present value. And you're one year, two year, three in your four. So my NPV is equal to the sum of my cash flows on my present value of the cash flow. $6242. 54 cents. So if I were to write it out, the present value of your one is equal to 18 518 You're too 17. 146 You're 3 15 876 in your 4 14,700 from Jungle Arrow here, 14,700. Okay, so what's my NPV is equal to 62 for two 0.54 Okay, that is my NPV. Now, even as a son, let's check it using them the formula in except or Google Sheets, I agree. Okay, so let's check on that present value. NPV is equal to our discount rate 8% and then our cash flows Capital one cash to cash for three castle for so 66,000. And I'm gonna add it into the formula here just a little. So it looks a little bit cleaner. Gonna add a $60,000 cash outflow because me 6250 to $42.54 or NPV checks. Great job, guys feel awesome. OK, so now let's calculate our i r r Okay, internal rate of return. So it says, calculate the i r. We know that our formula by r r is equal to the cash flow amounts and our i r r is 12.59%. What does IR stand for again? It makes our that present value equal to zero. So that's the way we should check this. Okay, So I r r actually, it's to our i r. Check over here. It looks cleaner. IR check. Okay, so now calculate our NPV using our i r r. I was like, Why did that not work? It's because I cooked a little too quickly. There, there we go. And then we add our initial outflow. We summit, and it's equal to zero. So does that mean our our checks? Yes, it does, because our works take off caps, lock their I our works because NPV equals zero. OK, it's our I. Our internal rate of return is 12.59% and that it is our internal rate of return. So now we calculate our internal return, and we checked it as well. So you should check your internal rate of return. So what equals zero So great, So finally willing to a pay back period its boldness. So it looks better too. So a payback period is how long does it take to recoup our initial investment? Well, after one year, we only recoup 20,000. After two years, we've recouped 40,000. After three years, we've recouped all of it. So this says that our payback period is three years and what I was looking at is a summation at the bottom. Okay, so when I was doing this are summation down here is zero. And that's how I know we've hit our payback period. for payback period is three years. So now you calculated on your own than that present value. So great job, the internal rate of return. Great job. And you checked it. Awesome. And then you calculate the payback period, which was very simple and not used very often, if ever in business finance. So again, you calculate the NPV by hand and then using the formula you, captain of the internal rate of return, using the formula in Excel and checked it with your i r. Check over here making sure the NPV zero and then you calculate the payback here. So, great job. That's the end of these examples. So again, good job. 14. Fin Lecture 13 Loan Amortization: So now we're gonna do is a loan amortisation schedule. Okay, so this is gonna build on our time value of money as well. So the goals is a complete a loan amortisation schedule and determine how much of each payment is principal versus how much for each payment is interest. This is a very valuable lesson for people because let's say that you're buying a home you're buying a car or your barring lots of money for student loans or just view borrowing money honestly alone. You wanted low how long it's going to take you to pay back and how much in each payment is principal versus interest. Whenever you are buying a home, you'll get a loan amortisation schedule. But this way you can calculate it on your own. So the example that we're gonna do together is we're barring a $200,000 we have are in $200,000 to buy a home. We have a 15 year loan with a 5% fixed interest rate. How much is our monthly payments are? Hint is think about all the variables of our time, value of money, PV FBI, and in PMT. What is my ex. Hopefully, after you think about it, your ex is your PMT. How much is my monthly payment is PMT and this is an annuity because we're making a monthly payment each month for 15 years. So now let's calculate the loan amortisation schedule. Let's go through this slowly so you can understand it. But again, you can review this lecture if you want and get a better understanding of it. I think it's a very strong, um, tool to understand I am using Google Sheets, but you could do this in myself. Excel as well. So first pause the video and set up a schedule like I have here, so I decided to set it up so you don't have to watch me type in a bunch of stuff. So the loan schedule is in the title of it, and it's a $200,000 loan. I'm gonna bold that and so right these things out for me, I'm gonna bold this as well on. And then whenever you're done, start playing the BU again, so I'm gonna keep going. So what are the terms? Are the loan term so bold that to the number of periods So let's go back to our slide 15 year loan. So because we're doing a 15 year loan, but we want to do it on monthly payments, so I'm gonna do 15 times 12. So 12 months in a year, All right out here 15 years times 12 months in a year. Give me 188 180 periods. What's my loan amount? 200,000. Make this into a dollar sign. Take out decimals. What's my interest rate annually? 5%. And then what's my interest rate monthly? So if I divide this by 12 that's gonna give my monthly interest rate and changed on 2%. So what is our monthly payment? So first I want to write down my loan terms. And now what is my monthly payment? So my present value? I currently owe 200,000 My future value. What is my future value? My future values actually a zero because I want toe nothing at the end of this right at the end of this, After I pay off my loan, I don't want only things in my future value. Zero i r 0 $200,000 Now I want to make payments. Overtime in overtime, This mountain get smaller and smaller and smaller. And after 15 years, gonna be equal to nothing. So my interest rate is gonna be point for two. In my end, number of periods is 1 80 So I want to take a step back here and say, Why is that? This needs to match the periods. Okay, So what that means is that our interest rate, we cannot use an annual interest rate and our periods bi monthly because we're using a month in time period. This is a monthly time period. We need a monthly interest rate. Okay, so we're making annual payments. We would use an annual interest rate and the annual period, so this would be 15 and this would be 5% but because we're doing it monthly, they need to match. Okay, that's a very key factor here. And R P M t equals R is our ex. So now, using the formula, we already know PMT is equal to our rate than our number of periods than our present value , and then our future value of zero. Our payment is $1581.59. Okay, so now we know our monthly payment for a house. So every month for mortgage alone, we had to pay $1581. 59 cents. Great. So now that we know this, let's bold this information. And now let's make our loan schedule. So we have a 180 periods, so I'm gonna write 180 period. So this again monthly drug list down to about 1 59 Okay, 1 74 year. When you get to 180 k only delete these last two. We have 180 periods for those you not well versed in Excel. All I did was put in one year and the formulas plus one plus one. So it just looks up to the next cell and adds one. So what's our payment? I'm gonna do a negative amount. So negative that gives me a positive payment. $1581.59. What I'm gonna do is I'm gonna lock that sell by putting dollar side in front of it. And that's just in Excel trick here. And I dragged this down all the way to. Actually, Instead of dragging down, I can just double click it and it's a little bit easier here. Just brings it all the way down to 180 so my payment is the same. But now the amount that's part of interest. The amount that's part of principal gonna change every month. And let me just ask you a question. Should the amount of interest that I'm paying every month go down? The answer is yes. Each month, as I pay off, more, more principal, the amount going to interest goes down and more of it goes the principal. So long, let's calculate our first interest. How much is the first payment of injuries going to be? So we take our interest rate of 0.42% and multiply a buyer loan amount, which is 200,000. So $833 is going to our interest in our principles that remaining so the payment subtract out. The interest is giving us our principal amount. So remaining debt would be the 200,000 and we subtract out how much came out of principle. So that's our remaining debt. So now we just gotta fill this out. Going forward. So how much is our interest for second payment? We're gonna take a remaining debt. And now, because we want this formula toe toe lock, we're gonna lock the H. We want to lock the column. When I multiply that by a monthly interest rate and we're gonna lock all of this, I wouldn't put a dollar sign in front of B and the dollar sign from the eight. Okay, When Hit, enter. And so our next game is gonna be 830. So let's just bring us all the way down and make sure that it looks right. Okay, so I did something wrong here. So what's happening is that it locked the age, okay? No, actually, we just got to keep going. So now our principle is going to be our remaining debt. Oh, sorry. Our payment. Subtract out our interest, and then remaining debt is gonna be our previous remaining debt. Subtract out payment. Okay, so now do you see that interest is actually correct. So now that we let driving these two formulas down and let's make sure this looks right, So over time our interests a mount going to interest goes down each month, the amount going to principal goes up by that corresponding amount. So this goes down. $3 goes up $3. Okay, that makes sense And are remaining debt goes down. That looks right. So our ultimate check to see if this is right on this is the fun part. Is that our last payment? It's gonna be $7 of interest, $1575 a principle in our remaining bounces. Zero. So that's how we know we did this correctly. And that's how easy it is to create your loan amortisation schedule. And the reason why this is so beneficial is because you can see here, how much goes the interest and how much goes to principal. So again, I think this is very, very valuable. I would make up loan amortization schedules next time you buy a car or buy a house because I think this is a really important tool to help you understand how much interest you're paying. So, for example, let's do a little math. You How much interest are we gonna pay over the entire life of the loan? I sum up this column put a little locked down here. I'm gonna pay $84,000 in interest over 15 years if I wait to pay off this entire house that I'm making $284,000 a payment, $84,000 of interest. And hopefully that's equals 200,000. It better or we have some done something wrong, obviously makes $200. So there we go. So over the course of 15 years over this house, at 5% interest rate, I'm paying $284,000 in cash. 84,000 of that is in the interest, okay? And so that's why you create the schedule so we can see stuff like that again. I think this is very, very important. I would do this lecture more than once if you didn't understand it and just take your time to look it through and watch it over again. That's why you have this course for life. But mainly I just want you to understand this because it's a really important point on understanding How much was the interest in how much goes to principal on a loan amortisation schedule? So now you can see how we tie this all in First, we use the time value money to determine our monthly payment, which is great using that monthly payment, we used it here. And then we use a simple math to figure out how much was off. That payment was interest. How much of that payment was principal and how much remaining debt we had. It's over when you enjoyed this lecture. This is actually one of my most fun ones because or the one I like the most, because this actually tied it all together from me when I was in grad school, so that being said, that's the end of this lecture. 15. Fin Lecture 14 MPT: So now let's talk about modern financial theory, the efficient market hypothesis and modern portfolio theory. So what is the efficient market hypothesis? It's an investment theory that states it impossible to beat the market because stock market efficiency causes existing share prices, toe always incorporate and reflect all relevant information. According to GMH, stocks always trade at the fair value on stock exchanges, making it impossible for investors to either purchase under value stocks or sell stocks for inflated prices. As such, it should be impossible to outperform the overall or beat the market. Um, so this is really important because it is the cornerstone of modern financial theory. The E. M. H is highly controversial and often disputed. So one thing that they say is, what about Warren Buffett? He is constantly beat the market over long periods of time, which by definition, would be impossible, according to GMH. Okay, so that's really important. And then what about the 1987 stock market crash when the Dow Jones industrial average dropped by 20% in a single day? So is that evidence that stock prices considerably deviate from their fair values? The reason why I mentioned efficient market hypothesis is that a lot of people, according toa this modern theory financial theory say that you should die diversify, and that is something that you should least know the basis behind. Okay, so modern portfolio theory is a theory on how risk investors can construct portfolios. MPT says. That is not enough to look at the expected risk and return of one particular stock. But by investing in more than one stock and investor can read the benefits of diversification. Chief among them is a reduction, the risk of the portfolio. So MPT quantifies the benefits of diversification, also known as not putting all your eggs in one basket. We've all heard that before, so no one there when we talk about Diane versus application, you'd be like, Son, How money should you have? I'm This is obviously for only educational purposes, so no one has in has one answer to that. People say between 20 and 30. Sometimes up to 50 stocks is a proper diversification. So to understand why that is is wise, divert diversification. But official, we have to understand correlation. Correlation shows how to securities move in relation to each other, so negative, perfectly negative correlation would be negative. One perfectly positive correlation. Be positive one and no correlation. It all would be zero. So going through some example, if we have to security, security and be and they're perfectly correlated with a plus one that they move in the same direction. So if security A moves up 10% security would as well. And then, if it went down 50% than the same would happen, the security be would go down 50%. If they're perfectly negatively correlated, they move in opposite directions by the same amounts. A magnitude security aid goes up by 45%. Security be would go down by 45%. And then if the correlation is somewhere between that. So let's say 0.8 that security a would move up by 30% security be would only move up by 80% of that, which is 24%. They're moving in the same direction, So that's what correlation is. How did these two stocks move in relation to each other and then correlation between Let's say, 50 stocks is how are these 50 socks correlated? So an index one example is a good way to do it. So that S and P 500 is an index one. If you want to learn more about index funds, a quick introduction is in my intro to stock markets, lecture or class. But let's say that we have Apple, Microsoft, Wal Mart cool. In 496 other companies, we bundle them into one portfolio, which is what the S and P 500 is. So let's say that we have $100 we buy one share of are actually treating about $200. Let's just say $200 worth of the S and P 500 so we have one small sliver of all these very large companies. So let's say that we have $200 in scenario one and we put into the S and P 500 we have $200 in scenario two and we just put it into Apple. Let's say that in scenario one Apple files for bankruptcy. Well, we're not gonna lose $200. We're gonna lose a very small percentage of that. Okay? And an example to of Apple files for bankruptcy. We lose all of our money because it's on Lee invested in Apple. And that's why they say diversification is good for you and how correlation warrants. Because let's say that Apple was into bankruptcy because of some market where technology is no longer good then Walmarts not gonna have that same reaction to that because they're not dependent. Um, on technology as much as Apple is, does that make sense? So that's what correlation is is how does or let's put on Exxon Mobil would be a better example. Let's say Exxon Mobil, which is also in S and P 500 Um, and Apple are those two companies highly correlated. One is vocus on the tech industry and the other ones in oil and gas. So the correlations probably pretty small between the two. So that being said, I want to show you, um, and related to the S and P 500 quote from Warren Buffett. He says my advice to the trustee couldn't be more simple. But 10% of your cash and short term government bonds and 90% and very law, low cost S and P 500 index fund. I suggest Vanguard. So a couple of other ones do it iShares is another one. I believe that the trust long term results from this policy will be superior to those attained by most investors, whether pension funds and institutions or individuals who employ high fee managers what he means by high fee managers actively managing to try to beat the market. Okay, And so with the S and P 500 index fund is is the 500 500 very large companies in the United States that are traded on the New York Stock Exchange or NASDAQ. And again, you'll learn more about that in my in shorted stock market class. So again, that's why being completely diversified. So if you buy into the S and P 500 we go back to this slide, uh, how many stocks I own 20 to 30 You could actually own 500 stocks by investing in the S and P 500 only one small percentage of each of those those companies so any. They're not all highly correlated to each other. Some may be correlated more than others. But again, Exxon Mobile and Apple, what is the correlation between those two? Probably not a lot. So that it concludes our lecture on, um, modern financial theory. And now you know, when people say diversification matters, What the referring to what they are referring to his modern portfolio theory. Okay, when people talk about diversification, they're referring to modern portfolio theory on. And that's what I wanted to get you to understand. Just so what I think is really important is the question when people tell you things, so if somebody says, Hey, diversification, diversification is good, it's wise that good while they'll quote you if they know what they're talking about. Correlation and then in addition to that, for example, is like an index fund S and P 500. But that said, that's the end of this lecture. 16. Fin Lecture 17 Conclusion: Okay, everyone, congratulations. You're done with this class. Wouldn't do a quick review on, then go from there. So conclusion you are done. So let's go over some key points that we learned. So they keep the time value of money and we said this several times is a dollar. Today is worth mawr than a dollar tomorrow. And if you haven't bring it out the handout please go and do so positively imprinted out Components of an interest rate are the risk free rate. So this is Leiber. The 2nd 1 is the expected inflation rate. Think Coca Cola's Remember how Coca Cola's 20 cents 80 years ago, when your grandparents talk about it now with the dollar? Next one is default risk, premium default risk premium. So not paying on time or not paying at all the next one's liquidity premium. Remember, this is if you are your investments are hard to self where your securities are hard to sell in the last ones maturity premium. So the longer the loan, the long the higher the interest rate. So think about car loans. For example, two year loan is lower interest rate than a five year loan, so a six year loan is generally a higher interest rate. A 30 year loan on a home loan is higher than a 15 year alone. So that's the maturity. Premium libraries nest is an approximation of the risk free rate. Variable interest rates change over time. Fix interest rates stay the same over time. The higher the probability to fall, the higher the interest rate. Present value is what's worth to me today. What's the worth to me today? Future values the worth to me in the future. A one time payment is a dollar. Remember the president valued in dollars, a one time payment and annuity? You remember I told you. Think multiple payments, capital budgeting answers a question of Should we invest in this project yes or no? And then that president values the difference between the present value. The cash inflows in the present value of the cash outflows. Remember, only invest if net present values greater than zero and when comparing multiple projects you want, include select the one with the NPV that has the highest NPV and highest net present values . If you're comparing multiple projects and you know only invest in projects that have a NPV greater than zero. The internal rate of return is a discount rate that makes the NPV of all cash flows from a particular project equal to zero. Remember, you can check with the NPV. Remember how we checked it with MPB? The payback period is the length of time required to recover the cost of an investment. The best capital budging technique is NPV according to loan amortisation. For each payment on a fixed interest rate loan, the amount of interest should decrease in the amount of principle should increase for each successive payment. So think back on our loan amortisation schedule that we did make sell or Google sheets. If you didn't go sheets with me, each payment, the interest goes down and the principal goes up, and that's the way it works. Um, what is that promise in a formal debt agreement that certain activities will not be carried out? It's a debt covenant. That confidence is a promising a formal debt agreement that certain activities will not be carried out according to the efficient market hypothesis. All information is priced into the market. Modern portfolio theory quantifies the benefit off. What diversification also known as not putting all your eggs in one basket. What shows how to securities moving in relation to each other? Correlation. Remember that a positive correlation move means they move in the same direction. This is a positive correlation, a negative correlation. Remember, move. They move in opposite directions and there's degrees member plus one to minus one. Remember that chart that we just went over? Negative one plus one and zero Correlation. The S and P Index fund has 500 stocks in the index fund or portfolio. Also good to know. So I just wanted to thank you again for taking the class. I really do appreciate it. Hopefully you see how much I like finance and how much I like the time value of money doing it in Excel in Loma amortization schedules actually do really enjoy all that stuff. Um, so hopefully you can see kind of my excitement, something so that being said the other courses, I offers the core for personal finance an introduction and basic. So if you already have a strong understanding, a personal finance, you don't need to take it. But if you don't. It's a really great course. It talks about the core for personal finance and then accounting in one hour brief introduction and basic. So it's very similar to this course in finance, but for account. So currently both of them are free. So hopefully you enjoy them. I may change that later on, but again, hopefully a joint. So thank you again for taking my class. It definitely appreciate it. I definitely wanted to show my appreciation so you could actually see me. Thank you. So thank you again for taking classes.