Calculating Intrinsic Value using Discounted Cash Flow (DCF) Analysis | Finance + Investing 2020 | Skillshare

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Calculating Intrinsic Value using Discounted Cash Flow (DCF) Analysis

teacher avatar Finance + Investing 2020, I teach Finance to make you money

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

20 Lessons (1h 10m)
    • 1. Introduction

      1:43
    • 2. 1a, b, c, d: What is Intrinsic Value?

      5:07
    • 3. 2a: Projecting Future Cash Flows

      6:16
    • 4. Projecting Future Cash Flows Example

      2:12
    • 5. 2b: Calculating Terminal Value

      2:58
    • 6. Terminal Value Example Calculation

      1:27
    • 7. 2c: Calculating the Discount Rate

      5:20
    • 8. Discount Rate Example Calculation 1

      2:09
    • 9. Discount Rate Example Calculation 2

      5:56
    • 10. Summary of Chapter 2

      3:02
    • 11. 3a: Why is FCF Projected

      2:08
    • 12. 3b: Which Discount Rate should be used?

      5:02
    • 13. 3c: Which growth rate should be used?

      2:31
    • 14. 3d: Adjusting for debt and applying a margin of safety

      3:00
    • 15. 3e: The Pros and Cons of DCF

      3:20
    • 16. 3f: Further Example Calculations

      7:53
    • 17. Chapter 3 Summary

      1:32
    • 18. Bonus Video:

      0:53
    • 19. 4a: Creating an Intrinsic Value Calculator

      6:18
    • 20. 4b: Final Words

      1:33
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About This Class

In this course I will teach you how to calculate intrinsic value using DCF analysis. This is one of the most powerful stock and asset valuation methods in the world. It is a cornerstone tool for value investing, and it has for many years remained the method of choice for the best investors, including the likes of Warren Buffett. I made this course as I myself couldn't find a comprehensive guide as to how to actually perform an intrinsic value calculation. In that manner, I attempted to make it as easy to follow as possible, to cater to people from all skill ranges. I hope you enjoy the course, and that you learn a skill which can help you earn money from investing. I also greatly appreciate your feedback, so please do let me know if there is any way that i can improve the course in the future. 

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Transcripts

1. Introduction: Hello and welcome to this course on intrinsic value calculations using discounted cashflow analysis. The course is divided into three main chapters. In the first chapter, we will go over what intrinsic value is. I will define it and then I explain it in simple terms. I will then explain where and when the intrinsic values used. Before describing why we should care about it. I then talk about what creates value for business in the context of DCF. In chapter two, I will explain the inner workings of DCF. I will give you the steps of calculating it before explaining each step and walking through it to make it easier to understand. I will also derive the DCF formula and give you a simpler version to make it easier to use. We will then do a plenty of example calculations so that you can learn by seeing. Moving on to chapter three, I will give you some additional things to keep in mind when calculating intrinsic value. And we'll talk about why free cashflow is projected, which discount rate should be used, what growth rate should be used, and how we can improve the accuracy of our calculations. At the end of each chapter, I will summarize what you have learned as simply as possible, which will make it easier to retain the information for future reference. I will also attach a transcript of all the key info in this course as a document which can be found any attachments section of the course. Finally, as a bonus lesson, that'll teach you how to build your own intrinsic value calculator within Google Sheets. I hope that you enjoy this course and that you learned something useful. 2. 1a, b, c, d: What is Intrinsic Value?: Chapter 1A and 1B, what is intrinsic value? Let's start with the definition. Intrinsic value can be defined as the true, inherent, and essential value of an asset independent of its market price. Well, what does this actually mean? Another way of thinking about the value of an asset is that the value is what it is worth or what the buyer receives when buying the asset. Therefore, there's clearly a distinction between an asset's value and its price. A good way of highlighting this difference is the idea that prices what you pay value is what you get. Chapter one, see, what is intrinsic value used for and why do we care about it? As investors, we want to find assets which can help us earn a lot of money. However, the return that we will earn from buying an asset depends a lot on how much we paid for the asset. If we paid too much money, even if the asset increased a lot in value, we will not realize most of this value increase. So much money was spent on getting the answer. Therefore, as investors and particularly its value investors, we should aim to buy assets at a price which is below its intrinsic value. As we are there for getting more of a good thing that we paid for. Good way of highlighting this is that as investors, we aim to buy a dollar worth of value for $0.60. Intrinsic value calculations are simply the method of choice for figuring out what is and isn't a fair price to pay for an asset. The diagram here demonstrates this. If we bought an asset in the red section, we would be able to see a greater return than if we bought into blue section. The goal of this course is simply to help you estimate where this value curve is to help you buy or when stalks enter the undervalued section. Another reason why we should care about intrinsic value is that it can be used to evaluate whether or not the management of a company is working to benefit the shareholders of the company, or if they are instead using their positions to benefit themselves. The primary aim of the management of a publicly owned company should be to create value for the shareholders. However, certain things like mergers and acquisitions may actually destroy value for shareholders. Particularly if shares are issued while it's benefiting the management that started the action. Therefore, intrinsic value can be used to see if value increased or decreased after the merger. Which will then let the shareholders know if the management is truly acting in their best interests. This is important as good management is one of the most important things for a company to possess. But this begs the question of what actually creates value for business? Well, there are many types of value and there are also many ways to measure it. For example, the book value of a company, the dividend it pays, and it's cache can all be thought of as ways to measure the value of a company. However, as you know, this course will focus on one method of valuing companies called discounted cash flow analysis. This method estimates value by projecting how much cash the business will generate in the future before finding the value of this cash today. Therefore, in the context of DCF analysis, value for business is created by how much cash the company can produce or put differently, how much money it can earn minus the costs necessary to earn this money. So, to summarize Chapter one, intrinsic value can be thought of the worth of the asset that is purchased. This is not to be confused with the price of the asset. As investors, the goal is to buy assets when the intrinsic value of it exceeds the price. Intrinsic value is also useful to see if the management of a company is acting in the best interests of the shareholders of that company. In this course, we will focus on the valuation method called Discounted Cash Flow Analysis, also known as DCF. In this context, value is created by the cash generating ability with accompany. Let's now move on to chapter two. 3. 2a: Projecting Future Cash Flows: Chapter two, how does discounted cashflow analysis work? And the next few videos, I will walk you through how to calculate intrinsic value step by step. We will begin with the easiest, most central concept before moving to the more complex ideas later on, I will also show you the equations for each respective step before finally combining all the equations into the proper discounted cashflow formula, which would make it easier to follow and understand. After I have explained each step of the process, I will do several mini examples to illustrate each point before combining all of the steps in several more example calculations at the end of this chapter. This is so that you can easily learn by seeing how the method actually works in practice, as opposed to simply staring out the formula. Along the way. I will also be updating the formula to the point which we have covered so far. And I will give you step-by-step checklist for calculating intrinsic value on your own. This is because I've divided the calculation process into three main steps to introduce the idea and the simplest way possible. But for now, let's get right into it. Chapter to a projecting future cash flows. To calculate intrinsic value, we must first estimate how much cash the acid will generate from now until an infinite point in time. This process of estimating how much cash the asset will produce is divided into two steps called the growth stage and the terminal value stage. During the growth stage, the asset grows at a high rate, which lasts anywhere from one to ten years. We manually calculate each cashflow during this time, which is what I will teach you to do. Now. On the other hand, during the terminal value stage, which I will cover in the next video. Cashflows are projected from the first year after the growth period until an infinite point in time in the future. When we are projecting cashflows, we use something called free cash flow or FCF. We'll go over what this is in greater detail in a later video. But for now you can simply think of it as the cash available to shareholders. So to get into it, in order to calculate cash during the growth stage, we must begin by finding the present cash flow, which is how much money the asset has generated in the last 12 months. Before multiplying this cash by suitable growth rate at which it is expected to grow. This can be written as the following. Future cashflow is equal to Present cashflow multiplied by one plus the growth rate to the power of n years. In the simplified form, this can be rewritten as the term on the right, with FCF being free cashflow and G, the growth rate. However, since we are calculating cash flows for several years during the growth period instead of just one year, which is what this formula shows us. He must instead find the total amount of cash which will be generated out as opposed to the cash within one year. To do this, we simply sum up the cash flow for each year that we are protecting. This can then be written as this next formula. This is a key point of discounted cashflow analysis and it is important that you understand what this formula at the bottom tells us. If you look closely, this is a future cash flow during the growth period. We are there. Then calculating the cash generated when in year one and year three and onwards, where each term here is equal to the equation at the top. Finally, we simply sum up each cashflow for the years to figure out how much cash the company generates during the growth period. The number of years into the future that we project these cashflows, meaning how long do we continue summing up cashflows for each year is called the length of the growth period. The better the financial health of the company, the longer the growth period. Slow growth companies typically have a growth period of one to three years. Medium growth, 47, I'm high-growth, eight to ten years. However, no growth period should ever exceed ten years. This is because projecting cashflows estimating how much cash will be generating the future beyond ten years becomes too inaccurate for it to be significant. This can be summarized in the following table, which shows the company type and the length of the growth period from slow growth, medium growth to high-growth companies and the respective years they grow out. Let's now move on and summarize what we have covered so far in this first video. So the first step in calculating intrinsic value is to project future cash flows. The formula we derived on the previous slide in order to do these calculations has been added into the full discounted cash flow formula. As you can see. Essentially, what I mean by this is that I have substituted the equation we found previously into the entire the real discounted cashflow formula. And as you can see, there's also a few blanks left. But throughout the next few videos, we will fill in these blanks and expand the steps table in order to arrive at the entire formula with a list of things to calculate intrinsic value. But for now, let's use what we have learned in order to do some practice calculations in estimating future cashflows using this formula. At the top. 4. Projecting Future Cash Flows Example: Okay, we're now in Google sheets. At the very top of the screen you can see the formula that we found in the previous video. We will now practice using this formula to actually calculate cashflows. So to begin with, Let's go over some basic assumptions we will need in order to do the calculations. Let's start with the present cash flow, which is this term here. In this example, we will use $25 thousand as the free cash flow generated in the last 12 months. Then the next term we need is one plus the growth rate, which in this case will be 1.06, meaning we have a 6% growth rate. Furthermore, the number of terms we will project into the future will be for this example, 5-years. So let's begin simply by listing out the number of years. We will calculate the cashflows into the future, which as you remember here is five. We will then do the projecting. So in the first year, you can see that it's simply FCF multiplied by one plus G. So I can take the FCF and multiply it by one plus G. In the next year, it is simply e to the power of two. So I will multiply the president cashflow by this, the growth rate to the power of two. Moving on, I will repeat the same formula here. And simply change this to the power of three and to the power four, and then to the power of five. So as you can see, we have now calculated how much cash the asset will generate in each year into the future. I know that this is quite a simple calculation. However, it is very important to understand in order to be able to properly do the entire DCF calculation. So let's now move on to the second step in calculating intrinsic value. 5. 2b: Calculating Terminal Value: Chapter to be calculating terminal value. As you remember, the terminal value stage estimates the cashflow every year from the first year after the growth period until an infinite point in time. Therefore, we use a different growth rate from the growth stage, called the perpetual growth rate. As the asset cannot grow at a rate as high as seen during the growth stage forever. The perpetual growth rate can be anywhere in between the average rates of inflation and the average GDP growth rate. Meaning that for most countries it is usually around two to 4%. What this means is that we expect the cash that the asset is producing after the growth stage to continue growing at a rate of two to 4% per year until an infinite point in time. So the first step in calculating the terminal value is to multiply the free cash flow in the last 12 months of the projected period. Ie, if the growth period is four years long, you take the free cash flow in the fourth year before multiplying this by the perpetual growth rate plus one. This can be written as terminal value is equal to free cashflow in the last 12 months and the growth period multiplied by one plus e perpetual growth rate. However, this is only half of the terminal value equation. To do the other half, we simply take the difference between something called a discount rate, which is, which I will discuss later, and the perpetual growth rate. We then divide the formula you see on the screen by the difference between the discount rate and the perpetual growth rate to arrive a terminal value. Therefore, the entire equation can be written as free cashflow in the nth period multiplied by one plus the growth rate divided by the difference between the discount rate and the perpetual growth rate. If we substitute the terminal value equation we just found here into the DCF formula, we have so far, we find that we get the following, following formula. So here you can see the Intrinsic Value formula as we have found it so far. Here's the growth period stage. So in the previous video, and here's the terminal value stage. Now also have two of three steps needed to calculate intrinsic value. Step three, we'll complete the formula by filling in the missing question marks at the bottom. As for now, let's use what we just learned to practice calculating terminal value using this formula here. 6. Terminal Value Example Calculation: Let's now calculate the terminal value of the asset that we were working on previously. So as you can see here at the top is again the formula. So what we need first is a free cashflow in the last 12 months of the growth period. So if I go back to the growth period calculation we've worked on earlier, we can see that since the growth period is five years long, what we want is the fifth year cash flow. So the first thing we need is to simply substitute this value into our formula here. Child put it in here. So this is the FCF term. Moving on, we need the perpetual growth rate for this example will be 2%. We then also need the discount rate, which will be 11% for this example. So to do the first part of the calculation, which is the top part of the terminal value clause, was simply multiply the FCF and by one plus the perpetual growth rate. This gives us this figure, which is the top row. Then we will find the difference between R and G, just simply R minus G. Before dividing the top by the bottom. This then gives us this figure, which is the result for the intrinsic value of the asset. I mean terminal value of the asset. 7. 2c: Calculating the Discount Rate: Chapter to see calculating the discount rate. We have so far projected cash flows from the present until an infinite point in time. However, we must do one additional step called discounting, in order to adjust each year's cashflow to something called the time value of money. Essentially, the time value of money states that a dollar today is worth more than a dollar a year from now. As the dollar today can be invested to earn interest. So the cashflow that the ass, so we'll produce five years from now, is worth less than the cashflow that the company will produce one year from now. As we will have to wait four more years to get the cashflow in the fifth year. In which time if we had them money now, it could have been invested to earn interest. Therefore, each cashflow that we have calculated will of course, need to be adjusted for the fact that we won't get it until many years in the future. As the further into the future the cash flow, the less valuable it is. So to adjust each year's cashflow by the time value of money, we simply have to divide each cashflow by an interest rate at which the cache could have grown had we had the money today. This interest rate is called the discount rate. We do this because in order to figure out the present value, we can simply rearrange the equation we derived earlier to find the future value. If you remember in step one, we use the formula shown here. Future values equal to present value multiplied by one plus the growth rate to n years. In order to project the cash flows that the company would generate in the future. Well, if we want to get the present value, we can simply divide by this term, one plus the growth rate to n years on both sides of the equation, which will give us an equation for the present value. This can be seen here. This works is we are assuming that we don't know the present value as this is the intrinsic value we are trying to figure out. And that we do know the future value as this is the cash that we have projected in step one. Should now be clear why we divide by interests rates, also called the discount rate. In order to get the present value of money by adjusting for the time value of money. It should also be clear that to get the correct discount rate each respective year, we simply increase the power of the discount rate to how many years into the future the cash flow will occur. So for example, if we were discounting the cashflow three years into the future, we would simply raise the discount rate to the power of three. After dividing each year's cash flow by the discount rate, we have calculated the present value of each cashflow. So to get the total present value for the acid, also called the intrinsic value, we simply add up all of the present values during both the growth stage on the terminal value stage. If we take the idea of discounting and added to the formula we have covered so far, we will arrive at the complete discounted cash flow formula. As you can see here. If we can find a way to combine the discount rate term simply by putting it in here, we get the complete DCF formula, which you can see here. So this is the entire formula with all the steps that we have covered included in it is actually a rewritten version of the original DCF formula. However, I personally find this one to be easier to use. So we will use it for the remainder of the course. Now that we have the formula, and it's also recap the three steps we have found so far before going in to some more example calculations. So step one, I'm calculating intrinsic value is to project future cash flows, which is the top part. The first three terms during or however many terms there are during the growth period. And the second step in calculating intrinsic value is to use the last term we figured out, the growth period. If you calculate the terminal value claws up in the top right. Finally, the third step is to divide each projected cashflow by one plus the discount rate to how many years into the future the cashflow occurred. This will then give us the present value of the each year's cashflow. So to arrive at the intrinsic value, we simply add up each term, as you can see in the formula. In order to get the intrinsic value of an on a per share basis, we simply divide the total intrinsic value by the number of shares outstanding. Let's now continue with the examples that we were worked out in the last two steps to find the total intrinsic value. Using the formula. 8. Discount Rate Example Calculation 1: Let's now complete our example calculation of intrinsic value by discounting each cashflow that we have calculated. So to begin with, we need to find the free cashflow which reprojected, which we can find simply by copying what we calculated previously and pasting it in there. We'll then do the same with a terminal value, and we figured out, put that into the formula. Now you find a discount rate, which we will use, which if you remember from the terminal value equation, was 11%. So the discount rate in the first year, as you can see, is simply one plus the discount rate. Moving on to the second year, we must take this to the power of 2 third year, it does this to the power of three, as you see here. Simply continue this process for all of the cashflows, increasing the power, but sorry, increasing it by an additional power each time. We then come to the terminal value clause, which we must also discount since the chairman of value comes after the end of the growth period, it is simply the first year after the growth period. So if it's the fifth, the terminal value is increased to this power of six. Ok, we now have the discount rate and all the free cash flows. So all we have to do with simply, as you can see, divide the cache by the discount rate. So we divide this by that. We can then drag this formula over so that in every row and calculates this divided by that. Finally, in order to arrive at a figure for the intrinsic value, we simply sum up the cash flow for every single year. As you can see here with the plus sign in between. This then gives us this number, which is the intrinsic value of the asset. 9. Discount Rate Example Calculation 2: In this next example, we will be practicing calculating intrinsic value using real life numbers. So we will be calculating the intrinsic value of Apple in this example. Just as a quick disclaimer, however, I am not giving you any advice on whether or not you should purchase or sell Apple stock. This is purely for educational purposes. Now let that is out of the way. Let's get right into it. To begin with, we will simply enter apples ticker symbol here, which is AAPL. Then we can put in Apple's current cash flow, which I have down here. That is, how much cash Apple earned in the last 12 months. We can then use a function which in Google sheets, which is the Google Finance command, in order to get us some more information about Apple's price and shares outstanding. So to do this, we simply write in Google Finance and we select the ticker. And in quotation marks we write price. This will then give us the price of a single share of Apple stock. We can then repeat the same thing, but for to find Apple's shares outstanding, where the command is simply shares in between quotation marks. Now, let's go through some more assumptions that we need in order to calculate the value. So the discount rate we will be using will, for the first example BY 12%. Growth rate we will use will then be 5%. This is the growth rate during the growth stage. As a reminder, the perpetual growth rate will be 2.5%. So as always, the first thing we will do is protect the free cash flow for the next few years. It will take the current cashflow and multiply it by one plus the. Now multiply it by the growth rate to the power of one. And then next year we will change this to the power of two, the year after, to the power of three, and thereafter to the power four, and then to the power of five. So we have now projected how much cash Apple will produce each year in the next five years, assuming a 5% growth rate. So let's now calculate the terminal value stage using what we found here. So the first step is to find the free cash flow in the last 12 months, which is of course this. We then multiply it by one plus the perpetual growth rate. To get us this figure. We then find the difference between the discount rate and the perpetual growth rate, which gives us 10%. And therefore the terminal value is simply that divided by that. Okay, let's now calculate the discount rates we need for each year. So in the first year, the discount rate is simply one plus 12%. In the second year, it is this to the power of 2, third year this to the power of three. And the fourth year this to power of four. And the fifth year this to the power of five. And as you remember, we simply pretend as if the terminal value is the sixth year. So we simply take this to the power of six. Okay, let's now calculate the present value of all of the cashflows. Simply divide the free cash flow by the discount rate. And then we drive better over. We then do the same thing for the terminal value stage. We now have our figures, and now we must simply sum up all the president cashflows before adding the growth stage to the terminal value stage. This gives us the total intrinsic value of Apple Stokes. However, if you want to find this on a per share basis, simply divide it by the shares outstanding. This tells us that assuming the assumptions we heard, an Apple currently has an intrinsic value per share of a $153. Suggesting in his quite overvalued. However, this of course depends a lot upon the growth rates we have selected. As you all know, apple is quite a high growth companies. If he were to instead change this to a 20% growth rate, you can see that the intrinsic value would increase accordingly. However, for now we'll stick to the basic assumptions we had originally. We can then calculate the intrinsic value to price ratio simply by dividing the intrinsic value per share by the price per share. This gives us a ratio and telling us what every dollar paid for an Apple share will get us in value. So as you can see, it doesn't meet our condition that for every dollar we pay, we should get more than $1 in value. So we could argue that right now, Apple Share is quite overvalued. 10. Summary of Chapter 2: Let's now summarize Chapter two. So I'd like to walk you through my variant of the equation once more. As I know that this is quite a complex idea. So I'd like you to understand all of it in detail. To begin with. Remember that intrinsic value is the present value of all future cash flows out of a company. Therefore, the first step is simply, is to simply estimate how much cash the acid will produce in the future. We do this by multiplying the current cash flow that the company generated in the last 12 months by a suitable growth rate. We continue this process for anywhere from one to ten years, depending on how strong the company is. High-growth companies have longer growth periods. This process is represented by the top row of the first three parts of the equation, which you can see here. After we've estimated cash flows during the growth period, we use the data to calculate the terminal value, which is the amount of cash which the company will generate from the first year after the growth period ends until it infinite point in time. To do this calculation, we take the last cashflow that we calculated during the growth period and multiply by one plus e perpetual growth rate. Or the perpetual growth rate, is the rate at which the cache will grow forever. After we have that figure, we divide it by the difference between the discount rate and the perpetual growth rate. Where the discount rate can be thought of as the interest rate we use to adjust the cash for the fact that we wrote receive it until many years into the future. We now have a figure for terminal value, which can be seen here. The next and final step is to calculate the discount rate for each year. This is to adjust for the time value of money as we won't receive the cashflow until many years in the future. We do this suggesting simply by dividing the cashflow in each year by a discount rate corresponding to that year. Because future value is equal to present value multiplied by one plus the growth rate to the power of n, which rearranged gives us present value equals the future value divided by one plus the growth rate to the power of N. So once we have divided each year's cashflow, including the terminal value by the discount rate. We must simply sum up all the present values to arrive at a figure for the intrinsic value of the company. This can be seen in the formula here. The bottom row represents the discounting of each cashflow. In order to figure out the intrinsic value per share, we simply divide the value for the entire company as a whole by the number of shares outstanding. Let's now move on to chapter three. 11. 3a: Why is FCF Projected: Chapter three, additional points about DCF analysis. Three, a y is FCF or free cashflow projected. When calculating intrinsic value, we're trying to figure out the present value of all the money that a company will ever earned for its shareholders. Why then do we not project metrics like net income or revenue? The reason is that not all of this money is available to shareholders. For example, with the revenue There are many expenses to pay for, such as the cost of goods sold or debt repayments. On the other hand, earnings are not commonly used for two reasons. One is due to the accrual accounting or sales revenue can be recorded without any cash having yet exchanged hands. Another reason is that it is easier to manipulate, manipulate earnings as there are different methods of calculating charges like depreciation. Therefore, you using free cashflow instead of earnings. We are getting a more accurate picture of the cash that the company actually has instead of the income that it reportedly has. As a result, free cashflow represents both the money that an investor can receive and dividends and the money that the investor can receive via, via reinvestment into the firm, which will generate more value in the future. The same cannot be said about earnings or revenue. Fcf can be found either by Googling the ticker symbol of the stock followed by FCF. For example, AAPL space FCF. Or it can be found by using the following formula. Fcf equals sales revenue minus operating costs plus taxes minus required investment and operating capital. This can also be written as free cashflow equals net operating taxes. Net operating profit after taxes, minus net investment in operating capital. 12. 3b: Which Discount Rate should be used?: Chapter three B, which discount rate should be used? There are three discount rates which are most commonly use. These are the risk-free rate, the weighted average cost of capital, and the required return. The risk-free rate is the interest rate that you will earn from buying US backed treasury bones. The Weighted Average Cost of Capital is the average cost that a company must pay to all its security holders in order to maintain its assets. The required return can be thought of as the return that the investor wants to earn in order to justify their risk in buying the asset. But which of these three interest rates should we actually use when discounting? As I've already explained, the discount rate is used to find the present value of money in the future by dividing it by rate at which the money could be expected to grow until that point. Therefore, the risk-free rate is often used as a discount rate as we can compare how our money could be growing outside of the investment without any risk. To then compare it to the growth rate we are getting. For example, if you are forecasting ten years into the future, you would use the ten year risk-free rate and 5-years, the five-year risk-free rate. As it is then easy to see how much the money could be worth had I receive it today instead of five years from now. However, as at the time of the making of this course and 20-20 US interests rates are so low that I would advise you not to use them as a discount rate. As discounting with interest rates lower than 1% has no discernable effect when adjusting for the time value of money. Additionally, since the interest rates are below the perpetual growth rate, the terminal value formula will yield a negative result, which of course won't work. So when discounting, I'd advise you to stick away from the first discount rate, the risk free bond rate. And this then brings us onto the second Coleman, newly used discount rate, the weighted average cost of capital. As I mentioned, the WACC is the rate that accompany must pay to retain its assets through its security holders. However, I would again recommend that you do not use the weighted average cost of capital as a discount rate due to some assumptions in its calculation which don't make sense. For example, the WACC is calculated using the capital asset pricing model or CAPM m, which uses beta, a measure of how much the price of a stock varies from the market average. That's reevaluate the asset's riskiness. Therefore, using WACC, the more volatile the stock price, meaning, the more it changes, the riskier the acid and the less valuable the intrinsic value. This clearly doesn't make any sense as the price of a stock is not, does not reflect its riskiness. Instead, highly volatile stocks may even be preferable as they can be bought more often, I've argued in prices for more reasons as to why you shouldn't use the weighted average cost capital as a discount rate. See the link and the attachments session of this course. We then arrive at the discount rate which I would encourage you to use, which is the investor's own required return. When buying an asset, investor exposes himself to a lot of risk. In order to compensate for this risk, the investor should choose a return that he wants to earn each year, which will make, assuming the risk worthwhile. This is because for the investment to make sense, risk should be correlated with return. Hence, the higher the risk of the asset, the higher the required return should be. This is because buying high-risk assets with no potential for high returns is clearly foolish. Because of this, any required return over the risk-free rate is in theory acceptable as every investment will be more risky than us bones. However, Coleman discount rates typically range from ten to 12% as the risk-free rate would ideally exceed the interest rate. Interest, which could be earned simply by owning an S and P 500 Index, which is also quite a low-risk investment as otherwise the investor could earn equally well simply by buying an index fund. One thing to note, however, is that the higher the discount rate is, the lower the intrinsic value. So higher discount rates are in fact more conservative. Therefore, to summarize, the investor must choose a discount rate individually, which is equal to the rate that he wants to earn each year. This rate should not be below roughly 9%. As otherwise, the investor could make a safer investment simply by buying US stock indexes. 13. 3c: Which growth rate should be used?: Chapter 3C, which growth rate should be used? One of the most common methods of finding a growth rate is to simply average the company growth rate for the last few years before using this rate for the next few years as well. However, within this, there are few points to consider. Some of the average growth rates will be either far too high, are far too low to make any sense, especially when an averaging highly volatile companies. So as a remedy to this, we can use a range of acceptable growth rates which may apply for all assets. For example, if the growth rate where below 5%, I would recommend you to use 5% as the growth rate because any lower results won't keep up with inflation. And the long-term. On the other hand, if the growth rate of the last few years was over 20%, you should use 20% as the growth rate. In between these two, however, you should simply use whatever growth rate the previous year's average arrives dot. So if you have a growth rate of 7%, use 7%. What I've just mentioned can be summarized in the following table. This of course, only applies to the growth stage of the formula, which is the period of time when the asset earns excess returns compared to the market as a whole. During the terminal value stage, however, we must use a different growth stage. Growth rate. This rate must be somewhere between the average inflation rate and the average GDP growth rate. This is because if it were to be above the GDP growth rate, the asset would eventually become larger than the economy as a whole, which is of course impossible. Whereas if the perpetual growth rate we're below the inflation rate, the asset would eventually cease to exist as all the cash would be destroyed by inflation. Therefore, the perpetual growth rate changes depending on where in the world you are. Although it is usually between two to 4%. Well, this can be summarized in the following way. For example, in the United States, the long-term inflation rate is 3.22%, whereas in Canada, the inflation rate is 2.2%. So valuing assets depends also quite significantly on where in the world you are valuing it. 14. 3d: Adjusting for debt and applying a margin of safety: Chapter 3D, adjusting for debt on applying a margin of safety. Since all intrinsic value calculations are but an indicator of value, not a precise figure, it is always better to be conservative in order to compensate for any errors in the calculation. One way of adjusting intrinsic value calculations to make them more conservative is to subtract long-term debt from the company's intrinsic value. This ensures that the company is able to pay off all its long-term obligations with the cashflow. As if you recall, free cash flow is used to repay both creditors and share holders. Therefore, subtracting debt, we are left with only the cash that is available as value to investors, which is a more accurate figure than the money that is available to both investors and creditors. For example, assume a company's intrinsic value, so a $100 million and it has debt of $20 million. If there are 2 million shares outstanding, each share that isn't adjusted to debt will have a value of $50. However, only 40 of these dollars will actually be realized as value for the investor. Therefore, in adjusting for, you would only buy the asset if the price were below $40 instead of $50, which would ensure that you're getting more for your money. Another way of adjusting intrinsic value figures is by applying something called a margin of safety. The margin of safety is simply a percentage, which is multiply it by the estimated intrinsic value in order to make it more conservative. For example, if I estimated the intrinsic value of an asset to be a $100 and I applied a margin of safety of 15%, my estimated value would fall to $85. Therefore, I would only buy the asset if you were under $85 as opposed to under a $100. In doing so, we not only assure that a good price is being received, but we also give a little leeway to allow for Q generous assumptions in my growth rate by discount rate and my perpetual growth rate. This is because as it is impossible to compute our precise figure for intrinsic value, it is better to lower the estimate and therefore lower the risk that you are buying at a too high price. Coleman margins of safety typically ally in the ten to 15% range. Ideally, the two methods described here would be used in tandem for all intrinsic value calculations in order to make them more conservative. This couldn't be done by first subtracting a debt, then applying a margin of safety. Remember that it is always better to underestimate intrinsic value than two overestimated. 15. 3e: The Pros and Cons of DCF: Chapter three, the pros and cons of DCF analysis. In order to fully understand what intrinsic value means and what it can do for you. And it's important to have a good understanding of the advantages and disadvantages of the method. This is so that you do not make any misstep things in your assumptions which could potentially impair the results are in calculations. To begin with, let's cover some advantages of using discounted cashflow analysis. A ECF is one of the only actual intrinsic value models. Most other alternatives are relative measures of value, meaning they have to be compared to other businesses within the same sector to gauge whether or not it is an attract deal. For example, valuation metrics like price to earnings or price-to-book lose their merit if the entire sector is over or undervalued. By DCF focuses on free cashflow as opposed to other earnings based metrics. This is beneficial as it is harder for companies whose accounting tricks to inflate their cash accounts. So it is, it is more likely to represent the actual financial position of the company. We will now move on to the limitations. So just kinda cashflow a, the model may become less accurate simply due to the large number of assumptions necessary to calculate value. For example, it is unlikely that the company will even grow at the growth rate predicted by the analyst. Even small deviations from the actual growth rate can be magnified in the terminal value. Making the estimate inaccurate be even more unlikely, is that the company will grow in perpetuity. Most companies eventually shut down after awhile. For example, the average life expectancy of S and P 500 companies is 61 years. See, another drawback is that the model is so sensitive to changes in its inputs, even small, very small changes in things such as particularly the perpetual growth rate and the discount rate, can have massive changes in the final intrinsic value result. What does all this tell us? Due to the aforementioned reasons, DCF calculations should never be used as an absolute value. Instead, the result should be used as an estimation of whether or not the price is fair. It is an indicator of the value of the stock compared to its price. Because of this, using the method should always be the final step in picking a stock. As it doesn't tell you whether or not the stock is good. It's simply indicates whether or not the current price is fair. Another consideration to make is that intrinsic value results should always be rounded. For example, if the value is $17.693, we should round it to either 18 or $20. This is so that we acknowledge the fact that no intrinsic value calculation can be entirely accurate, especially null to such precise figures. Therefore, in rounding, it'll be easier to use. The value has an indicator instead of an absolute failure. 16. 3f: Further Example Calculations: This example calculation, we will be doing another calculation using real-life numbers. We will be calculating the intrinsic value of Microsoft. So to begin with, we can enter MSFT, the ticker symbol, into the assumptions box. In this example, we will be looking at some of the considerations I gave you earlier on. As you can see here, we have the total debt and the margin of safety as additional parameters within the assumptions box. I will use these to adjust the intrinsic value failure in order to show you how you can make it more conservative. If you look up here, you can also see that I have three different discount rates this time the Weighted Average Cost of Capital, the US boundary, and the required return. We will play around with the different discount rates in order for you to see more easily how vastly the intrinsic value figure can change by using different discount rates. So let's get right into it by filling in the assumptions box first. If we go down, we find Microsoft's total cashflow in the last year to be roughly $45 billion. We can then use a Google Finance command in order to find Microsoft, Microsoft's courage sharp price. You can then use a similar command in order to find Microsoft's did the number of shares of Microsoft currently outstanding? Let's then input the total depth dot microsoft house. We can then enter our margin of safety is 15%. Believe the discount rate for now and our growth rate as 1.05%. So if as in 5% plus one is 1.05, the perpetual growth rate will be 2.5% in this example. Let's now start by projecting the free cash flows. As always, we'll take the present cashflow. We will multiply it by the growth rate to the power of one. To make this more quick, I will simply copy paste a Form Labs. We'd go and edit it accordingly. So we can now change this one to two. We can change this to three. And we can change this to four. And then we can change this to five. This will now give us the future cashflows from Microsoft from generating the next five years, assuming a 5% growth rate. Let's think calculate the terminal value. As always, the FCF editor is the last 12 months during the protection period. That's in this case, it's the fifth year's cashflow. We then multiply this figure by one plus the perpetual growth rate to get the top part of the terminal value formula. Moving on, we take the difference between RNG, which as you know, is, is it bottom part terminal value formula, which is this minus this. So to begin with, we will use the required return is the discount rate in the first example. We can then calculate the terminal value by dividing this by this. Let's now do the discount rates. As always, the first term is one plus the discount rate, which is this. We then take this and we square it. And then we increase it to the power of each year into the future where the cashflow is occurring. And as always, the terminal value is simply can be thought of as the year after that last year during the growth stage. In this case, the terminal value is E6 year. So we will take the discount rate and increase it to the power of six. We can then figure out the term, the present value of all the cashflows by taking a terminal value and dividing it by the discount rate. And doing the same thing for deep growth stage and cash flows. We can then sum up all the growth stage cashflows. If we add the present value of the terminal value to the present value of the growth stage, we get the present value for the company as a whole. However, I'd now like to show you a few things we can do in order to adjust the figures as you remember. So let's first start by doing our debt adjustment. As you remember, this is simply taking the total intrinsic value of the company and subtracting the total debt, the sun leaves us with this figure. We can then adjust the figure for margin of safety adjustment by taking this the adjusted figure for intrinsic value and multiplying it by one minus the margin of safety. This gives us this figure. If we then divide that by the total number of shares outstanding, we see that the intrinsic value, each share of Microsoft is currently around $73. Assuming we didn't adjust for the debt or the margin of safety, you would find that the current intrinsic value per share is roughly $98. As you can see, there's quite a big difference between these two numbers in terms of the price we would be willing to pay. Let's now calculate an intrinsic value to price ratio simply by dividing this by the price of each share. This then tells us that for each dollar of shares we buy in Microsoft, we get roughly thirty-five cents of value. And in this sense, Microsoft can be seen to be overvalued as we're getting less value than we paid for. Let's now have a play with a different discount rates in order to see how they impact the total figure. Let's test the weighted average cost of capital as our discount rate simply by pasting it in. As you can see immediately, intrinsic value changes to a $176, which is almost a 100, which is more than a $100 over the previous figure. This clearly shows you that simply by a 3.5% difference between the required return on the Weighted Average Cost of Capital. There has been a huge difference in the intrinsic value per share of Microsoft. Another thing you should note is that the higher the discount rate is more conservative, meaning the lower the intrinsic value figure is. This is why I using higher, higher discount rates is usually preferable. Let's now see what happens if we use the US baud rate, then the discount rate category. As you can see, we get a negative value for the intrinsic value. This, this is because the interest rate is so low that it's less than the long-term perpetual growth rate, meaning that during the terminal value stage, we get a negative result for the terminal value, which is why the result is negative. This should reiterate wide recommend you not to use the US bond rates as a discount rate at least as of 2020. I hope this demonstration made it clear to you the importance of adjusting for debt and adjusting with a margin of safety. And I hope it also made it clear how even small changes in the parameters within the calculation can lead to large changes in the overall intrinsic value. 17. Chapter 3 Summary: Let's now summarize Chapter three. Using DCF reproject free cashflow as this is the money that is actually available to investors. I recommend you to use the required rate of return as the discount rate. As this measures how much you have to be compensated to assume the risk of buying an asset. It also makes more sense and using the risk-free rate or the Weighted Average Cost of Capital. Due to the reasons I mentioned earlier. To make intrinsic value calculations more reliable, you should subtract total debt from the calculated value, and you should then apply a margin of safety at least 15%. The benefits of intrinsic value include the fact that it is one of the only actual intrinsic value calculation tours. Unlike relative measures. It also uses free cashflow instead of a more subjective measure. And it is widely applicable in many areas, including real estate, business ventures. And stops. The disadvantages of intrinsic value or several, including the large number of assumptions necessary. The fact that no companies will grow into perpetuity, and that the model is very sensitive to small changes in the inputs. 18. Bonus Video: : Chapter for a building your own DCF model calculator. In the next video, I will teach you how to build an intrinsic value model calculator within Google Sheets upon simply entering some basic information, such as the ticker symbol and free cashflow. The spreadsheet will calculate intrinsic value for us. All the things we need it to do can be seen here. In building this calculator, it'll be much quicker to value assets in the future, is we don't need to use the formula every time. If you don't want to make it, learn to make your own intrinsic value calculator. And you simply wish to use the one that I've already built. You can find it in the attachments section of this course. As for now, let's get right into it. 19. 4a: Creating an Intrinsic Value Calculator: In the table here, left side, you can see nearly a repeat of the list you saw on the previous slide about what we need the calculator to do for us. It will check the items off as we start building. What do you see here is simply a blank template with different categories for all the sections we need. And then calculator. We will now program all of the cells within the spreadsheet. So that's simply by inputting some data. The spreadsheet we'll calculate the value for us, meaning we don't have to do anymore equations in the future. So let's start right from the beginning in the top-left. Assuming we have AAPL, Apple as the ticker, We can write in a Google Finance command here, select the ticker and right price in order to get the price of the stock. Can then do the same thing but for shares outstanding. Okay? We can now, in this section we can input some drop-down lists in order to make it easier to find the things we won't. So for the discount rate, we can go to data and data validation can then press list of items for writing down some suitable discount rates. We can now do the same thing for the perpetual growth rate. Okay? So now as you can see, we have a drop-down menu where we can select the growth rate and the different parameters we want to use. Now, let's now start with the terminal value. So as always, we will simply select the free cashflow for the first for the last 12 months of the growth period multiplied by one plus the perpetual growth rate here. We will then divide this figure by the difference between R and G. This then gives us the total terminal value figure. Let's now calculate the free cash flows for each year will take the current free cashflow. Free cash flow in the trailing 12 months. We will multiply it by the growth rate to the power of one. And as always, we simply increase the power for each year into the future. Okay, so now when the data is input, it will project a free cashflow for us. Okay, let's now do the discount rate. The first year as always, it's 11 plus the discount rate. And the second year it's this squared, 30 years, this cube. Fourth year, it's this hour four. And then the fifth years this to the power of five. Now also do the discount rate for the terminal value stage by taking this to the power of six. And then do the present value by dividing the terminal value by the discount rate. And over here we can do the present value by dividing the free cash flow by the discount rate. Dragging along the formula. Can then sum up this row before adding them both up here. Okay? And then we will subtract the total debt. And then we will multiply it by 0.85, which is the 15% margin of safety. This will then give us our adjusted figure for intrinsic value. And simply divide this by the shares outstanding to get intrinsic value per share. And then we divide this by the price per share to get intrinsic value to price ratio. Now if we input the data about Apple, let's assume that there's $50 billion of total, sorry, a free cashflow. I'm 25 billion of total debt and the growth rate is 10%. We can see assuming this information, apples intrinsic value is a $185. So as you can see, immediately calculates intrinsic value for us. And if we change any of the parameters, they to change instantly. So you could come with any asset and all you have to do is simply enter the ticker symbol here, the free cashflow for the last month and the debt, and then it will calculate it for you. So we have now completed all the things on the table. 20. 4b: Final Words: Chapter four B, final words, congratulations on completing the course has been my pleasure to walk you through intrinsic value, starting with the basics and ending at a point where you hopefully have enough understanding to know how the Intrinsic Value calculation works. If used correctly, the method can prove vital in any instance when you are looking to investor cash. My hope is that with what you've learned in this course, you will able to become a better investor. And i, you will realize the importance of the distinction between value and price. If there's anything you want to ask me, I'll do my best respond to any queries within the comments section of this course. I've also attached a mini-project for you guys to complete if you want to. It can be found in the attachments section in this course. Using the information in the attachment and the parameters I've given you, calculate the intrinsic value of the asset. Make sure to give me your answer so I can let you know if you did it right or not. As for now, thank you so much. I'm watching my first course. Be sure to leave a positive review. You enjoyed it. I created this course as I felt that when I myself was learning about intrinsic value, there weren't any complete courses which walk through each step. Because of this. I tried to make this as easy as follow for everyone, from people with no experience about intrinsic value to those who are skilled at using it. As a result, I would love to receive feedback from the viewers about anything I can do to improve the course and the future in order to make it better over time. You're feedback is greatly appreciated. Goodbye.