In this podcast, Motley Fool senior analyst John Rotonti discusses how investors can value a company using the discounted cash flow model, the fundamental way to determine if you’re getting a bargain or paying too much when you buy any stock.

John discusses:

How to pick a discount rate for investments.

The key difference between fair and intrinsic value.

How to project free cash flows.

Have an investing question for John? Call 703-254-1445, leave a voice mail, and he may answer your question in an upcoming episode.

To catch full episodes of all The Motley Fool’s free podcasts, check out our podcast center. To get started investing, check out our quick-start guide to investing in stocks. A full transcript follows the video.

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**John Rotonti: **The next step is pretty easy. Don’t try to be a hero. You have to pick a tax rate, get some good industry-level data, see what the average taxes that the company you’re valuing has paid over the past five years or so, see what ways that tax rate has been trending, has it been trending up? Has it been trending down? Understand what is driving the change in that tax rate, take a tax rate run it out year 1 to year 10.

**Dylan Lewis:** I’m Dylan Lewis and that was Motley Fool analyst John Rotonti. Today we’re continuing John’s series on navigating major financial statements with a breakdown of how to build and understand a DCF or discounted cash flow model. I will confess that I’ve built exactly one DCF in my entire life. It was for college finance class and honestly, I may never make another one. Even if you’re like me, this conversation is for you because throughout John’s overview of modeling cash flows, he provides mental models and the questions you need to ask yourself when you’re looking at companies. Understanding how those inputs affect the company’s path forward will make you a better investor, even if you never opened and Excel spreadsheet. Before I turn things over to John, we also want to know what investing questions you have. Give us a call at 703-254-1445, and leave us a voice mail with your name, city, and whatever questions you may have, he may answer it on an upcoming show. That number is 703-254-1445. Now, here’s Professor John Rotonti. [MUSIC]

**John Rotonti:** Hello Fools, John Rotonti again. Today we’re going to talk about valuation. In particular, a discounted cash flow valuation also called a DCF for discounted cash flow. The first thing we need to understand is the definition of intrinsic value, the definition of fundamental business value. When I say intrinsic value, I mean the estimated business value based on the company’s fundamentals. Fundamental business value, intrinsic business value, they mean the same thing. The definition of intrinsic value is the present value of future free cash flow that a company will generate. Why present value? Present value because everything in corporate finance is pretty much based off present value. Present value says that a dollar today is worth more than a dollar in the future because you can invest that dollar today and earn some interest on it.

What we’re going to be talking about in a second is estimating a company’s free cash flows far out into the future. We need to convert those far out into the future free cash flows to their present value. This is one of the primary pillars, foundational pillars of corporate finance and valuation, this idea of present value. The definition of intrinsic value, which is what we’re talking about when we’re talking about valuing a business, is the present value of future free cash flows. If we said that a different way, it would be that the intrinsic value of our business is all of the estimated future free cash flows of the business from now until the end of the life of that business discounted back to their present value. I just said the same thing in two different ways. The three primary things you need to know about a discounted cash flow model are DCFs are based on the size of the free cash flow, number 1, the timing of the free cash flow, number 2, and the riskiness of the estimated free cash flow, number 3. DCFs are based on the size of the cash flow, the timing of the cash flow, and the riskiness of the cash flow. What do we mean by size? Well, $10 billion in free cash flow in any given year is worth more than one million dollars in free cash flow. Size matters, Fools, when you’re doing DCFs, size matters. Timing. We just talked about the present value concept. Well, timing, $10 million in free cash flow one year from now is worth more than $10 million in free cash flow 10 years from now.

I want to say that again because the further out you get, the lower the present value of those free cash flows are. Then the third thing is the riskiness of those free cash flows. We incorporate the riskiness of a business into our discounted cash flow models with something called a discount rate. A discount rate is also sometimes referred to as a hurdle rate, a discount rate is also sometimes referred to as a cost of capital or a weighted average cost of capital. For the purposes of this podcast, discount rates, hurdle rate, cost of capital, and weighted average cost of capital or WACC, all means the same thing. The discount rate is what we divide or discount those future free cash flows back to present value. To bring future free cash flows back to present value, we need to do a simple division and we need to divide by a discount rate. The more risky we believe a business is, the higher the discount rate we want to use. The less risky a business is, the lower the discount rate we want to use. Riskiness of the business is incorporated into the DCF model through the discount rate. Now, this is incredibly important. Think of the discount rate as your required rate of return. There’s a fifth synonym, we have discount rate, we have hurdle rate, we have cost of capital, we have weighted average cost of capital, and this give you a fifth one, required rate of return. This is a personal decision, this is you, I’m talking to you the individual Fool out there.

If you deem the business risky, then you are going to require a higher rate of return to invest in that business. Therefore, you’re going to use a higher discount rate. If you deem the business less risky then you may require a lower rate of return to invest in that business. Let’s put some numbers around this. The stock market has historically returned on a nominal basis before inflation 9-10 percent per year on average. Most investors want to beat the stock market by a little bit and so their required rate of return for the average risk level business is going to be slightly higher than 9-10 percent. Because the stock market, they can get 9-10 percent on average over time just investing in an index fund. If they’re going to take on the extra risk and put in the extra time and effort to pick individual stocks then they’re going to probably try to beat the market by a little. If the stock market has returned about 9-10 percent on average per year over a long period of time, then maybe you want to discount stocks at 10-11 percent for your average medium-risk level business.

But we’re living in weird time right now Fools because interest rates until two weeks ago were set at the zero bound. Interest rates were at near historical record lows. Because interest rates are so low, because the interest rate you could get investing in a US treasury bond, or the interest rate you’re going to get investing in a highly rated corporate bond is so low. Stock investors were willing to lower their required rate of return so very few investors were using the 10-11 percent required rate of return or the 10-11 percent discount rate we just discussed. Because interest rates are so low, they lowered their discount rates, they lowered their required rates of return to somewhere around 6-8 percent, let’s say. But that’s a personal decision. But if you were valuing **PepsiCo** or **NextEra Energy**, low-risk businesses or lower-risk businesses, you may want to use a lower discount rate, something in the 6-8 percent range. If you were investing in a start-up, early in its lifecycle, unproven hasn’t proven at scale yet, not earning any money, burning through cash, not self-funding, highly reliant on capital markets to grow because it’s not self-funding, then you’re going to use a higher discount rate. You’re going to have a higher hurdle rate. You’re going to have a higher required rate of return to put your dollars in that company. These interest rates, these required rate of returns, these discount rates, this is the assets, Fools. If you’re investing in a company that is highly dependent on commodity prices and so it doesn’t really have a control over its key input costs or if you’re investing in a company that operates in a highly cyclical, highly commoditized industry, prone to boom and bust cycles, then you’re going to have a higher required rate of return. You’re going to use a higher discount rate in all likelihood, but that’s a personal decision.

Now it’s getting more important. Discount rates and free cash and present values of free cash flow move in the opposite direction. The higher the discount rate, the lower the present value of future free cash flows, and the lower the present value of future free cash flows, the lower your estimate of intrinsic value will be. Let’s take the opposite. The lower your discount rate, the higher the present value of future free cash flows will be, and the higher the present value of future free cash flows will be, the higher your estimate of intrinsic value will be. Discount rates and intrinsic values are inversely related Fools, the higher the discount rate you use, the higher your required rate of return, the lower your estimate of intrinsic value will be. The lower your discount rate you use, or the lower your required rate of return, the higher your intrinsic value will be. If you model out of business, which will get to in a second, you do a DCF, you estimate out the free cash flows from now until the end of the life of that business, and the only thing you change in the model is the discount rate at which you bring those future free cash flows back to present value if the only thing you changing the model is that one Excel cell in the XL model if the only thing you change is the discount rate, the higher you put that cell, the higher you put that discount rate, the lower your intrinsic value will be. Literally, you can go into Excel, change the discount rate in that one cell, and hit “Enter” and your intrinsic value will drop. I guarantee it. It’s just math.

If you go into that cell and you put in a lower discount rate in that cell in Excel, your intrinsic value will increase after you hit Enter in that model. Let’s get into the model. We separate a discounted cash flow model into two parts, the forecast period also called the projection period, and then the terminal value period. The forecast period or projection period is the period in which we are actually putting in our assumptions for what we think revenue will be in each year of that forecast period. Most models that I’ve seen have a forecast period of anywhere from 5-10 years. Why do they stop at 10 years? Two reasons I would say. One is because our crystal ball goes pretty dark after 10 years. It’s really hard to estimate what a company’s sales and margins are going to be 10 years from now, much less three-year from now. That’s the first reason. The further out your projection period is, the further out your forecast period is, the less conviction you’re going to have in your assumptions on those far-out years because our crystal ball oral just goes dark.

The other reason is because the best most proper way I think to do a free cash flow model is to make your projection period as long as you think the company can maintain its competitive advantage. This is called a CAP, C-A-P or Competitive Advantage Period. This is the amount of time measured in years that you believe a company can maintain an excess return spread. What do we mean by an excess return spread? It means the amount of time measured in years that you think a company can generate a return on invested capital, which is a measure of profitability and performance. It’s the amount of time measured in years that you think a company can maintain a return on invested capital that is higher than its cost of capital. The best way to do a DCF is to set your projection period or your forecast period to the number of years and this is just an educated guess at best that you think a company can maintain its competitive advantage. Meaning the amount of time measured in years that you think a company can generate a return on invested capital that is higher than its cost of capital. But most DCF models’ for 10 years. For the purpose of this, we’re going to use 10-years. This is the second part of the DCF. In the terminal period, we’re using a mathematical formula which is called a perpetuity to estimate the cash flows from year 11, the very next year after our projection period. Because remember for the purposes of this podcast, we’re using a DCF of 10-years for the forecast period.

The terminal value or the terminal period calculates the free cash flows from year 11 into perpetuity. That’s the only way we can do it. Because we just don’t know what a company is going to look like in year 30 or 40 or 50 or 100 if it’s going to be around that long. There are companies around that long, IBM. There are definitely companies around that long but we can’t estimate our sales and margins in year 100. We use this mathematical shortcut because it’s the best option that we know of today. What happens in the projection period? You have year 1, year 2, year 3, year 4, year 5, year 6, year 7, year 8, year 9, year 10. That means we need to estimate how fast we think the company is going to grow its revenue in year 1. One year from now. How fast we think it’s going to grow its revenue in year 2, how fast in year 3, how fast in year 4, how fast in 5, 6, 7, 8, 9, and how fast in year 10. This revenue rate should fade down as you get to year 10, as you get to the last year of your projection period. So all we do is take the revenue that we currently have, multiply by one plus the growth rate that we think it’s going to grow at one year from now, and you get an estimate of revenue one year from now. Then you take revenue one year from now, multiply by one plus what we think the revenue growth rate will be two years from now, and you get estimate revenue two years from now. Then you take our estimated revenue two years from now, multiply by one plus your estimate of what you think revenue growth will be in Year 3, and you get estimate revenue growth three years from now and on and on until you get to your 10, which is the last year of our projection period. That’s it. Now, you have modeled out revenues for the next 10 years.

The next slide down in a traditional DCF is the EBIT margin or the operating margin. We talked about EBIT margins on financial statement analysis when we talked about the income statement. Now you need to estimate what you think the EBIT margin will be in Year 1, in Year 2, in Year 3, 4, 5, 6, 7, 8, 9, and 10. Maybe you think this company has a lot of margin expansion opportunities as it scales up and achieves economies of scale and unlocks that operating leverage. So maybe you have operating margins slightly increasing every year from Year 1, through Year 10. Maybe you think margins are going to remain pretty stable because it’s a pretty stable industry, market shares don’t shift that often. The players in the industry are rational about their pricing, they don’t get into pricing wars, and maybe the industry has been around a long time that you think pricing is going to remain stable. That’s fine. You just pick a operating margin or EBIT margin for Year 1 and run it out across the next nine years, Year 10. Maybe you think this company is in secular decline, maybe you think it’s got a weakening competitive advantage, maybe you think competition is going to take share. In that case, the company may have to sell stuff at a discount to maintain growth, they may have to gift stuff away and they have to discount items.

In that case, you think operating margins, EBIT margins may decline slowly, well not so slowly, over the next 10 years. In either of the three cases, you have now estimated an operating margin that you think the company can achieve for each of the next 10 years. Remember, we just estimated, these are all estimates, all of them. We just estimated right before that, what we thought revenue would be in each of the next 10 years. Now you literally take the operating margin that you just estimated in Year 1, multiply it by the revenue that you just estimated in Year 1 and you get your operating income or your EBIT in Year 1. Then you take the revenue that you’ve estimated in Year 2, multiply it by the operating margin that you estimated in Year 2, and you have operating income estimate for Year 2. Then you take the revenue you estimated for Year 3, multiply it by the operating margin you estimated in Year 3, and you get your estimated operating income in Year 3, and you do that on and on, every year through year 10.

The next step is pretty easy. Don’t try to be a hero. You have to pick a tax rate. Just pick, gets some good industry-level data, see what the average tax is, that the company you’re valuing has paid over the past five years or so. See what ways that tax rate has been trending. Has it been trending up, has it been trending down. Understand what is driving the change in that tax rate, see what the industry-level tax rate is with the average peer tax rate is. Pick a tax rate, run it out, Year 1 to Year 10. Keep it the same unless you think there’s going to be some major change to the corporate tax rate at some point over the next 10 years. Honestly, just don’t be a hero, just pick a tax rate and run it out every year for the next 10. Then you take the operating income in Year 1, multiply it by the tax rate in Year 1, and you get this all important number called NOPAT, N-O-P-A-T. Just net operating profit after-tax. It’s just your operating income after tax, NOPAT. Then you do the same thing for Year 2. Take your operating income Year 2, multiply by the tax rate Year 2, and you get your NOPAT Year 2. Do the same thing Year 3, 4, 5, 6, 7, 8, 9, 10. Next line down. We’re almost at free cash flow. Literally, one more line and we’re at free cash flow. We have NOPAT, after-tax operating income. Now we need to subtract reinvestment into growth. If you remember from our financial statements and analysis podcasts, we defined free cash flow as the amount of excess cash flow leftover after a company has reinvested to maintain and grow its business. So from NOPAT, we have to subtract total reinvestment that we think the company is going to make in Year 1, Year 2, Year 3, all the way through Year 10.

What is included in that reinvestment? Changes in working capital from one year to the next. Capital expenditures, property, plant, and equipment acquisitions, those are the three big ones. R&D was already included in NOPAT, so that is already included in your operating income. So you subtract from NOPAT, you subtract what you think reinvestment will be. Remember, working capital changes, CapEx and acquisitions, and you get free cash flow. Now we have free cash flow Fools, model out in an Excel model from Year 1 to Year 10, these are estimated free cash flows in Year 1 to Year 10. Now, you have to pick your discount rate or your required rate of return, let’s say you pick eight percent. Let’s say that’s your required rate of return because interest rates are still so low, and now you just need to discount the free cash flow in every year, Year 1 to Year 10 by your discount rate. The way you do this, is you take the free cash flow in any given year, so free cash flow Year 1 as your numerator. Free cash flow Year 1 is your numerator. You divide by one plus your discount rate raised to the year. This is your y. You divide your free cash flow estimate for Year 1, divide that by 1 plus 0.08, raised to the y. That gives you the present value of that free cash flow for Year 1. Then you do the same thing in Year 2. You take your estimated free cash flow Year 2, divide that by 1 plus 0.08 and raise that to the two, to get the present value of that free cash flow. Then for Year 3, you take your estimated free cash flow Year 3 as your numerator, divide that by 1 plus 0.08 raised to the three. Now you have the present value of that one, you do that all the way to Year 10. For Year 10, it would be your estimated free cash flow Year 10, divide that by 1 plus 0.08 raised to the 10. Now you have calculated the present value of the estimated free cash flows from year 1-10. Now you sum those up. You literally add them. Add present value from Year 1, present value of free cash flow Year 2, present value of free cash flow Year 3, present value of free cash flow Year 4, on and on until you get the present value of free cash flow Year 10. You add those up, and now you have the sum of the present value of the free cash flows for your projection period, Year 1 through Year 10.

Now, we just use a perpetuity formula, to calculate the free cash flows you think the company’s going to generated from Year 11 until the end of time using a perpetuity. How do you do that? You need to come up with a terminal growth rate. Remember, we estimated how fast you thought revenue was going to grow Year 1, how fast you thought it going to grow year two, how fast you thought it was going to grow year three, and on and on. I told you to fade that growth rate down by the last year of your forecast period. Your terminal growth rate can’t be set higher than global GDP. Why? Because if a company grows faster than global GDP into perpetuity than that one company will eventually become bigger than global GDP. Doesn’t make sense. You can’t set your terminal growth rate faster than 3 percent, pick your number, 3.5. If you’re just valuing a slow-growing domestic US company, you may want to set the terminal grade to 2, 2.5 percent. These are low growth rate fools. You can’t have your Year 10 growth rate in the last year of your model 50 percent. Then all of a sudden year 11, it’s two percent, doesn’t work. It’ll fade your growth rate down. For the terminal value, you have to pick your terminal growth rate. Then you take the free cash flow the last year of your projection period, that’s your 10. You multiply it by one plus your terminal growth rate, that’s your numerator. You divide that by r minus g, by your cost of capital, that’s r, minus your terminal growth rate.

Once again, the formula for the terminal value for the perpetuity, you take the free cash flow in Year 10 for your numerator. Your numerator’s free cash flow Year 10, multiplied by one plus your terminal growth rate, let’s say it’s 2 percent, divide that and your denominator is your cost of capital, which we said was 8 percent, minus your terminal growth rate, which we said was 2 percent. That gives you your terminal value. But that also has to be discounted back to the present. How do you do that? The same exact way we discount our free cash flows. You take that terminal value number, you divide by one plus the growth, your terminal growth rate, which is 2 percent raised to the power of 10, raised to the number of years you have in your projection period. Now we have summed up, we’ve added up the present values of free cash flow in Year 1 through Year 10. We have that sum. To that we add the present value of the terminal value. You get enterprise value. You now have a present value of the estimated enterprise value of that business. Enterprise value means the value of the firm. We calculated the free cash flow that we calculated fools, which we just said was no path in this model, minus reinvestment. That is something called free cash flow to the firm, FCFF. That’s free cash flow available to debt and equity holders. We have just estimated a firm value, and enterprise value. But what are we trying to do?

We’re trying to value the equity and the stock, not the firm, but we’ve just calculated the firm value. What do we do? We subtract debt. We have to pay back all of the debt holders. Subtract debt. Any cash that is leftover because we’ve just paid back debt-holders. Any cash that is left over after we pay back our debt, now belongs to the equity holders. We add back cash. We have this present value of the terminal value, this firmwide value. We subtract debt, and we cash. Now we have equity value, the value of the equity in that business. But we don’t have the value of the stock yet. To do that, you just take the value of the equity that you just estimated, divide by the number of shares outstanding, the number of fully diluted shares outstanding. You have now calculated an estimated value per share. You take that estimated value per share, and you compare it to the current stock price. If the estimated value per share is higher than the stock price, then maybe you found yourself a bargain. If you think the company is worth a 100, that your estimated value per share and the stock’s only trading at 50, then maybe you found yourself a bargain. Maybe you found yourself a company whose stock is selling at a discount to its intrinsic value. Maybe you have found yourself a stock that offers you a margin of safety. Now, your value that you just estimated is going to be wrong because you can’t be precise. You can’t be precise. It’s going to be wrong. Buying is going to be wrong. Everyone is going to be wrong. Next step, we do some scenario analysis, so that we can come up with a range of estimated fair values. Just coming up with one precise to the decimal point estimated fair value, that’s not going help us much. We’re going to come up with now a range of estimated fair value. This a model. Everything is connected. All the sales are connected. So you can just go in, change some growth rate assumptions, change some margin assumptions, change the discount rate, hit enter and the intrinsic value estimate will change instantaneously.

How do you come up with a range of estimated fair values? One way is to do a bear case, a base case, and a bull case. Your base case is the medium case. It’s the case that you think is most likely. The case that you have the highest conviction in. It’s the medium case. You come up with that estimate fair value. Then if you are a bear case. A bear case means you think growth will be slower than in your base case. You think margins will be lower than in your base case and that gives you a lower estimate of intrinsic value. Then you come up with your bull case. Your bear case was what you go wrong. Now you’re coming up with your bull case. What could go right? This one has slightly higher growth assumptions than your base case, slightly higher margin assumptions than your base case and this gives you a higher estimated intrinsic value. Now Fools, you’ve come up with an estimated range of intrinsic values per share. For companies that are more predictable, like Pepsi, like a utility, like **Coca-Cola**, your range of estimated fair values is going to be more narrow. We’re valuing a crazy start off that’s growing a 100 growing a year, has not achieved scale yet, has not proven it can do so. It’s much harder to value that company. It’s much less predictable.

Companies go to a 100 percent a year, literally in year 10, you don’t know if it’s going to be growing 30 percent or 10 percent. But PepsiCo growing four percent next year, come on, you can feel pretty confident that 10 years from now it’s going to be growing two or three percent. But a company growing 100 percent, you don’t have a clue. No one does. No one. Your range of estimated fair values has to be much wider. For a company that’s not generating profit margins, it’s not generating profits and it’s burning through cash, you don’t know what its profit margins are going to be in 10 years. You don’t really even know if it’s going to be profitable in10 years. That’s why you do the work. That’s why you do the research. That’s why you do the due diligence. Your model hopefully will model out and show you possible paths to profitability. That’s a beautiful model. You hear investors all the time saying, “It was not profitable, but I see a path to profitability.” Show me the path. Show me the model. That’s what the model let you do. It lets you see at least potential paths to profitability and self-funding and free cash flow generation. But for these businesses earlier in their life-cycle, they’re not yet mature. Lots of competition.

You’re going to come up with a wider range of estimated bear values. Last thing I’ll say. What is fair value? We already defined intrinsic value or fundamental value as the present value of future free cash flows. I’m going to give you the exact same definition just another way. What is fair value? Fair value is the price that you can pay for a stock and earn your discount rate and earn your required rate of return if your model is somewhat correct. That’s what fair value is. If you pay fair value for a business, if you think the stock is worth a 100, that’s your estimate of fair value. That’s your base case. You think the stock’s worth a 100 and the stock is currently trading at a 100, that’s OK. You can still buy that stock. That just means it doesn’t mean you’re never going to make a penny. Because, why? Because intrinsic values grow overtime. If it’s a great profitable growth business with an enduring competitive advantage, intrinsic values grow overtime. If you pay $100 for a stock that you think is fairly valued at 100, if you pay fair value, that means you should expect to generate an annualized return roughly equal to your discount rate, which we said was eight percent. That’s a point that gets overlooked all the time. If you’re paying fair value, that means you should generate an annualized return overtime on average of roughly your discount rates, which we said was eight percent. Now what if you set your discount rate at five percent and you pay $100 for a stock that you think is fairly valued at a 100? Well, then if your model is roughly right and if you buy the stock at a 100, you should only expect to earn a rough annualized return of now five percent, [MUSIC] because now we set the discount rate at five percent. Fools, this was discounted cash flow modeling. I am John Rotonti. Thank you so much. Fool on. [MUSIC].

**Dylan Lewis:** As always people on the program may have interests in the stocks they talk about and The Motley Fool may have formal recommendations for or against stocks mentioned, so don’t buy or sell anything based solely on what you hear. We’re off tomorrow for the Easter holiday, but we’ll be back on Monday. I’m Dylan Lewis, thanks for listening. We’ll see you soon.

*Dylan Lewis has no position in any of the stocks mentioned. John Rotonti has no position in any of the stocks mentioned. The Motley Fool owns and recommends NextEra Energy. The Motley Fool has a disclosure policy.*