I'm going to say hello to everybody again, I'm Chris Cordone.

I'm your host for these 12 sessions. This is number nine on discounted cashflow.

And I've got Yolanda with me as usual, our, our teaching assistant.

So again, uh, for those of you who have been here, you, you know how it goes.

We've got a a, a chat. We've also got a Q&A Some people can't see the chat because of their internal controls.

So if you if you wanna put a question into the Q&A, then certainly everyone will see it. If you want to put it into the chat, because it's easier, that's fine too.

Try to repeat those for everyone.

All questions are good questions.

Don't be ashamed of those.

I always like to say it's generally the questions.

The people that are willing to ask questions are the people that actually feel the most confident in the material.

So I always like to encourage people to do that.

It's not a sign of, am I the only one who doesn't know this so, as I mentioned last week during the discount rate WACC calculation, if I were teaching this in a classroom, I would actually start kind of DCF as an over as an overall topic.

And, and then I would from there, kind of take a pause and do some time on WACC, and then kind of go back to the DCF, and, and that's, that's the way it would work for me in the classroom.

Now we're trying to break these up into segments because it's just everything is about having these, like, bite sized things that we can digest and, and go back to the recording and whatnot and drop in and out of.

So it doesn't, it doesn't quite work like that anymore. It's sort of like an episode versus a series or whatever.

But, I'm gonna back up a little bit first, and I'm gonna talk a little bit more about just kind of this methodology of discounted cash flow.

Now, does anybody recall when I was started to talk about valuation methodologies, we started with the comparables analysis relative comparables analysis one company's trading, performance relative to another.

Does anybody recall how what kind of evaluation method, the DCF is the discounted cash flow? Does anybody recall what that is? Let's see. We still have some people coming in, so I'm gonna share my screen in a second.

All right. Sorry, I'm on a larger second monitor, which is not always better.

Bigger is not always better. Stuff just gets way pushed to the side and such. Lemme get my chat out again. Chat.

Where'd it go? Here we go. Okay.

So if comparables were relative, then the DCF is going to be what we call intrinsic, right? An intrinsic approach.

So, discounted cashflow is an intrinsic valuation method. Now, what do I mean by that? Anybody have a clue about what intrinsic valuation method means? Intrinsic as opposed to relative? No takers. There we go, Max. Thank you.

Max says it's coming from the ability to produce profit or cashflow.

Yeah. That's a good take on of the company.

Yeah. So it's if we think about what the process of the comparables, it was finding how other companies are trading relative to their value driver EBITDA revenues, free cash flow, and then applying that to the target company's value driver and seeing where the EV comes out, or the ev or the equity value.

So we're deriving the EV or the equity value, really from another company's performance.

So I guess I'll just put that in there as a recap.

Relative is deriving the EV or equity value from the performance of other similar companies, Whereas intrinsic, as Max has pointed out to us, intrinsic means that we're no longer really looking at other companies' performance.

We're going to focus on the company itself.

We're just gonna focus on the company itself, and we're gonna look at the value by looking at the earnings or the cash flows that those assets generate, that those that enterprise value generates or that equity value generates. And you can do a DCF a number of different ways, but I'll keep it broad for right now.

So, in theory, we don't need any other companies. We don't know, we don't need to have any knowledge of any other companies to do this.

That's in theory what an intrinsic valuation is.

However, you know, what we'll see very soon is that we're gonna need to peak through the Iron Curtain here, and we're gonna have to look at some other companies at some point.

I mean, we already did sort of with whack, right? I mean, to do a DCF to do a discounted cash flow, you need a discount rate.

I'm gonna go through the kind of steps we're gonna follow in a moment, but obviously we did that for this purpose, and we were looking at other companies left and right. What's the beta, what's the unlevered? What's the levered, what's the target? Capital structure, et cetera, et cetera, right? So we, we know that the ability to look at other companies is, is never gonna be off the table in, in our work, nor should it be really. Because ultimately, if you don't know where the market is, you know, you're probably not serving the client well, right? So this kind of discounted cashflow is the intrinsic approach.

Now, as I said discounted cashflow is actually it, it can be done a number of different ways.

What we're gonna focus on a kind of a traditional DCF and a traditional DCF is what we call an enterprise value, enterprise value technique or an enterprise valuation.

So that means that what we have to do here is we need to make sure we understand when we do a DCF, that we do a DCF to enter to value the enterprise.

And that may or may not be the answer that we're looking for.

We may still ultimately be looking for an equity value, but the, the, this approach is gonna deliver us an enterprise value.

So we're valuing the net operating assets of the company.

And just to rehash the net operating assets of the company are the core assets.

Those are the core operating assets, minus the core operating liabilities.

So enterprise value, remember, left hand side of the balance sheet, these are all of the stakeholders, debt and equity.

So we're not breaking up the assets according to who has a claim on them first or last or whatever. We, we want all of those, all of those assets that are being funded.

And we only at this point in time want the core assets.

We only want the core assets.

Now, why do we only want the core assets? Well, we did talk a bit about this again in an earlier session on M&A. We did some M&A accounting, consolidation accounting.

We did a little bit with trading comparables, where we were really just trying to focus on what are the assets that drive the value of the business.

Now, for the majority of companies, those are the assets that they kind of control, right? So in other words, a company might have a lot of real estate that it's just sitting on that's not being used anymore to run the business.

It's not housing the headquarters or the distribution.

Maybe they lease it out and they generate some revenue from that's great.

But that's not a value driver necessarily for business, because that's a side hustle, right? So we have to kind of figure out the side hustle stuff on its own, and we would, and similarly, if a company, let's say, had an investment in another company, we talked about Coca-Cola owning a stake in Monster.

Well, again, that's valuable.

There's value there, and it may even in fact, move the share price.

But when we're doing an intrinsic enterprise value methodology or even a relative value, we always start with the core assets first.

Because again, this is what we can kind of compare most easily to other to other valuations to see if we're in line.

So we want to start with this, and then we'll, we'll do our adjustments kind of as we, as we need to.

So these are the core assets.

The other important thing to consider here is that these are the assets that are under control.

Meaning that Coca-Cola can't tell Monster what to do.

It can nudge, it can suggest, but it doesn't, it's not running that business.

So it's not really fair to dinging Coca-Cola if monster's running itself into the ground, right? At the same time, what if the invested company like Monster, whatnot, is like blowing up like crazy, like just really going through the roof? Well, now it's kind of the tail wagging the dog, right? So that, that sharp analyst is gonna have to recognize and understand that, that that means that the main company, the core company, might not really be worth a lot because investors are flocking to that equity, to that investment because of that other company that they own a piece of.

There are some, there are some examples of that having happened in real life. There was a a time when Yahoo owned, Alibaba owned a stake in Alibaba, and Yahoo was going way down because Google was going way up and nobody wanted Yahoo, but they, they knew Yahoo had that stake in Alibaba.

So there's the tail wagging the dog, right? So if you wanted to buy Yahoo, Alibaba's gonna be its own company.

So we, at that point, they weren't public.

You wanted to buy Yahoo.

You need to understand what is Yahoo worth, not Alibaba, what's Yahoo worth? What should I pay for this digital, you know, business? And so that's why we wanna make sure that these assets are under control and that they're the kind of the core of the business, right? Okay. So, once we decide that we want that EV once we decide that we want that EV, that that's what we're going after.

Now, the cash flows, the earnings, whatever, just like in the multiples section have to match.

And so the cashflow part of this acronym are the cash flows that are generated by this business, and we'll do some, some work on that.

So they have to be generated by those core operating assets.

So the real estate side hustle, we're not gonna include those.

The pass through earnings from Monster Soda, Monster Beverage not coming through, not gonna count those, right? We're just gonna focus on the cash flows that are generated by the enterprise value.

Anybody done at DCF here? I think I have a fact.

Max, you might have said you did one, one or saw one done, or has anybody done a full DCF? So I was right about max.

Okay, well, I'll, I'll assume the others have not.

So let's talk then about what the steps to doing a DCF are talked about what it is in theory, right? Let's talk about what these steps are to building a DCF.

So the first thing we have to do is we have to calculate those free cash flows.

Where are those gonna come from? Where are we gonna get the free cash flows from? Are they, are they from the past? Are they current? Are they from the future? And then where whatever the answer is, where do we get them after we know, figure out which they are? What cash flows are we talking about here, Max? So it depends on what stage the company is in.

So projected, okay, so do we ever want the past ca Is there a stage of the company max when we want the past cash flows for, for a DCF anyway? Give them a second to type in there.

Not if it's a project where cash not.

So there are situations, obviously, where we have to value companies that are not effectively profitable or not generating cash flows.

And I'll say a little bit more about that later, Max, that's absolutely right. You can't pull them out of thin air.

If a company doesn't have cash flows, then obviously, probably this isn't the right approach.

And I will talk a little bit more about that when I talk about some of the qualifying things here.

But in general, valuation, as we talked about last week, with the exception of the levered valuation, which we're gonna cover next week or the week after the LBO, we're primarily looking at forward earnings because forward earnings or forward value drivers EBITA, ebit, et cetera, revenues, because we're trying to figure out what this company is going to be worth for that next period of ownership.

Now, the past is obviously important, however, we don't, we don't pay to own a stock to reward everybody who owned the stock for the previous period, right? We don't buy a company to reward the owners for their hard work.

I mean that's kind of what they're thinking, but what they're leaving you and what you're buying it for is the future value.

So we need future earnings, we need future cash flows in this and that free cash flows often abbreviated as FCF and FCF is future free cash flows, not future cash flows, but that's actually what we also need.

I guess it's a very flexible here.

So let me just see, we've got Yolanda's just clean it up that Q&A.

So we have to calculate the free cash flows, okay? Now that being said, we want future cash flows. Where do we get future cash flows from? Where can we get this stuff from? How do we find the future cash flows? Well, we did a section on modeling.

It was like the third or fourth session.

And you know, that's one way to do it, is you can actually, you can build a forecast, but you can also find these kind of earnings estimates, cashflow estimates.

Cash flows take a little bit of work, but you can find the components of this calculation really without building a model.

So you don't necessarily need to build an entire model for to do a DCF.

I would say probably over 90% of the ones that I look at emanate from a forecast that forecast may might have come from management.

So you didn't have to do it, but somebody did the forecast here.

So that's the easiest way to start.

But you could also just work off of earnings estimates as well.

There's an exercise in the syllabus that we touched on a little bit last week called the, the, the Felix challenge for DCF.

And that's one where you can actually build a DCF using just like an IBUs earnings estimate, like a street estimate.

And it's a little bit, it's a little bit harder to do, but you can do it that way.

And in that sense, it's I say harder, it's maybe like next level, but it actually requires a lot less time than spreading out an entire three statement model.

So we have to calculate the free cash flows.

I'm gonna, you know, define those cash flows in a moment.

But that's step one.

Now Max said forecast projected, talked about building out a model.

How long do we build a model out for, right? I mean, where, what's the requirement here for, for free cash flows or future cash flows? Now that might, as Max said, that might depend on what stage the company is in. That's a little bit also kind of next levelly stuff I'll try and wrap up with, with some stuff on the, on these top.

If we have time.

What's a typical model forecast? How many years? How many years do you typically build a model for or a financial forecast? What's a reasonable amount of time for us to estimate? Max says 10 years at most.

Anybody seen anything else? I know some of you said you hadn't seen it.

Raphael, welcome to the chat. Five to 10 years.

And that's, that's probably about what you'll see five to 10 years.

Now, why five or 10? Now, that might depend on the kind of company that you're modeling that might depend on that.

It may be the standard internally at your bank, but I'll hold off on the technical aspect of five versus 10 right now, the reality is that it's a little bit arbitrary in a sense, right? That we're just basically kind of picking a number five or 10, whether we have a good reason or not, we're still kind of just picking a number.

Now, the valuation itself is not, or should not be dependent on simply the number of years that we've picked.

In other words, hey, I valued a company, I got five years of cash flows, so my company is worth this.

And someone's like, well, I modeled the company out 10 years, so it's actually worth more.

That's, that's act that's not the way it works, because that would be really kind of silly, right? Just to say, you know, Hey, I'm selling a company, I modeled it five years, this is my price tag.

And then just kind of moving the, the, the data point a little bit down the road and saying, well, you know, if I do it 10 years, I can get a little bit more for it. It's, it's not the way it works.

And a lot of it has to do with the fact that, you know, we're talking about we're talking about a very difficult thing to do, which is to forecast something into the future.

So we calculate the free cash flows for, for the period of time that we think we have the most information for.

And that kind of sets up, you know, sort of the basis of the valuation.

But we also have to remember a couple of things that the company's value does not stop simply when the forecast ends.

What the forecast ends means.

The forecast ending means is that we don't have any more data to meaningfully impact this next five or 10 year period, but this is it.

So I'll put down just, so before I leave this bullet point, usually five to 10 years, and it depends on the data we have and how it impacts the forecast.

So after that, five to 10 years, you know, what do we have? Well, we've got a company that we're either gonna keep because we've bought this company for strategic purposes and we're gonna keep the company.

It's been, it's been, you know, in, in sort of enmeshed in our current operations subsidiary, or however you wanna think of it, or what else could we do with a company? We could sell it, right? And some buyers are strategically buying to create, you know, kind of long-term valuable companies, value added companies, some buyers, they're called financial buyers or, or sponsors.

They buy a company with the idea of running it, improving it, building it up, and then selling it to another buyer, maybe strategic or financial.

So essentially what I'm saying is, is that no matter how you look at a valuation situation, there's always the value after the fact, the value for the next buyer, or the value beyond the forecast.

And that's what we call the terminal value.

So the terminal value, but calculate the terminal value, and that's the value beyond the forecast.

So we can't leave that on the table.

And, you know, again, I'm gonna go through these steps in more detail momentarily, but that's sort of the next thing we need to do.

So we've got the free cash flows, and then we've got the value kind of beyond the free cash flows.

And then what we need to do is figure out what is that value in today's money? Because the minute we move away from today, we start dealing with what's called the time value of money, which is that there are other factors impacting it.

And those factors that are impacting it are what we discussed last week, the cost of inflation, right? Or the risk kind of risk-free rate or cost of inflation, the credit risk, the return expected to own the equity, right? These are the opportunity costs that one investor would give up to invest in something else.

And in this case, what we're trying to do here is we're trying to say, well, how risky are these future cash flows? And if I'm expected to wait 1, 2, 3, 4, 5, 10 years from my return, how should I be compensated for that? Well, from the perspective of the investor, they're compensated at the WACC, they're compensated at the WACC because they're basically saying that the risk of, of holding this investment for these years requires this return.

And so we have to calculate the WACC to determine, based on the riskiness of this investment, what they should be compensated.

And that's the weighting cost, so to speak.

Now, no one's ever called the WACC the waiting cost.

So maybe that's my, my own new, contribution to valuation. Move aside, Mr. Deon, you've got a West coast.

We're gonna do like a, it's gonna be kinda like a west coast Tupac Biggie thing going on.

Deon says one thing, and then I say something else, and then we just have this kind of battle going.

So that's, that's essentially what it is.

it's a cost to wait and what you should be compensated to wait, calculate the WACC, and then we need to, I'm gonna keep this as one step, just so, and then we need to discount, there's the d the cash flows and the terminal value at that cost, cost of capital.

So now effectively what we have is an enterprise value.

Once we discount all these cash flows back today, well, I hate the way, uh, PowerPoint insists on being very boring with, it's like, it goes back to, it doesn't even make it a lowercase one or an a, it just kind of goes back to one, one.

And it's very silly numbering default system here.

The discounted value of the cash flows and terminal value represent that enterprise value that we talked about.

Okay? Now you feel very proud of yourself. You caught, you just did your first DCF, and someone has said to you, Hey, there's,

we're thinking about pitching this to a client, I need a DCF.

You go run off and you do your DCF, and everything works out great.

And, you know, you come back flying into your superior's office and, she says tell me what you got. And you say, I got an enterprise value of this.

And, you know, she says, Hey, that's great, and that's wonderful, except, you know, ultimately what we need here is a share price.

I need to know what, what this company actually is in shares what this value is in shares. Because you're not gonna go to a client most likely and tell them that their company is worth this as an enterprise.

Now, it sounds great, but what they wanna know, because they're sweating the shareholders, they wanna know what does that mean in terms of share price? How, how am I trading in the market relative to this DCF that you're telling me all this wonderful stuff about? So we have to get from the enterprise value to the equity value.

And that's a couple of weeks ago, right? The, the bridge that we talked about.

So we need to walk the equity, the EV, to equity value bridge.

Now, does anybody remember how we get just very generally speaking from enterprise value to equity value? Does anybody remember John, subtract the net debt? Very good. We wanna get those stakeholders out of the way.

Yep. Subtract the net debt.

So we'd be adding the cash, subtracting the debt.

We don't, we don't typically exactly.

Subtract the cash.

Now, John, since I got you on the, on the keyboard here, where do I get the net debt from? So I'm doing a DCF, let's say as of the end of 2023, where we are now, what net debt am I subtracting? Where, where do I get that number from? Anybody else could chime into? Not an easy question.

And I'm thrilled that, that John actually has the bridge working correctly in his head. That's really the toughest part.

So if you recall, oh, here we go.

So another Max Maxwell from the enterprise value, well, the enterprise value Maxwell, we derived, that's the way we did it a couple of weeks ago.

Because we built up the ev that way, equity plus debt.

So that's true. But here we did the enterprise value a different way.

So we value the assets on the left hand side. And the right hand side is just kind of like, we don't know what's on the right hand side. We don't know how it's broken down.

John has come back with a midpoint calculation from year to year.

Raphael has said, money from financing, and these are all very kind of good, interesting, creative answers.

And I think, probably what I want to do at this point is to think about and it's hard to know who's been around, all the weeks that we've done this, but when I started valuation, I said that, that regardless of what methodology you use, the valuation is always a balance sheet exercise.

And it's always valuing a company as of today.

So you do a comps exercise, you look at forward year earnings for second year earnings, whatever you do a DCF, you do a five year, a 10 year a blah, great, all that future stuff is great, but at the end of the day, I've gotta go to the shareholders today with an equity value.

So the equity value that we calculate is always the equity value today.

And therefore, to get from enterprise value to equity value, I need to subtract kind of today's debt net debt.

So we, we generally go back to the most recent balance sheet, which would be a quarterly or an annual, depending on where we are right now, we'd go back to the third quarter, 10q most likely.

And this is the most kind of, I guess, reliable way to do it.

When it comes time to actually start cutting checks to people, like when you're closing the deal and the lawyers are in they're gonna look at your books like as, as the deal is closing and do it. Like, they'll look, they'll doesn't care. They don't care when the quarter was. They're gonna say it's a, it's November 21st.

How much debt do you owe right now? Then that's gonna be right.

But we don't have that when we're, when we're crunching numbers, we never have that.

So we want subtract net debt.

And I'm also gonna add here other stakeholders and other stakeholders because, you know, if there were some preferred shareholders, they've gotta come out. If there were some ncis, they've gotta come out and somebody an anonymous attendee had had hit it some, sometimes my chat goes kind of down below my screen, so that is correct.

The balance sheet, subtract the net debt or the other stakes like preferred NCI pensions and whatnot, those all have to come out.

And here by the way, is actually where we would also begin to think about what other value this company has that has not been factored into the DCF.

And by those I'm talking about monster beverage and real estate that's being rented out.

So we would also here wanna be, be sure to add back any non-core assets.

Now, why, why do we have to do this? Well, think about it.

You're an equity investor.

You've got a share of the net residual assets of pick a company, Coke, apple, whatever.

You don't care what the assets are.

They're all valuable to you.

Core non-core real estate soda pop, you don't care.

All of your funding is going into supporting those, those assets.

So the DCF might be more stable, more reliable if we don't include them.

But when push comes to shove, when you get to get back to my equity value, what I'm worth, I want a piece of those assets because that's what's going to ultimately what, what I'm, what I'm paying for, right? What's gonna flow to me.

So this is where we would value those assets and add them back.

So those are essentially the, you know, the steps to doing a DCF.

Now, what I'd like to do is flip over to the workout, and let's just do, let's just do one just to kind of see the mechanics, you know, flesh out, and then we'll go back over each of these points in a little more detail and hit some of the highlights.

I can't unfortunately spend the time I wanna spend on all these things because we just don't have the time.

But the good thing is, is that the other videos in Felix are there on the full kind of detailed DCF instruction.

So you can do that, and then you can hit me up with questions, you know, on your own.

So I'm gonna go over to the DCF workout empty, and this is from our course syllabus, which is what the lovely lene put in the chat to you earlier.

And if you, if you can't see the chat if you can only see the Q&A this is the, you can see it, but this is that, you know, the online syllabus link go FE training, and our course is 11591, go down to DCF valuation, and we're gonna hit this DCF workout empty file.

So workout number one, everything's been given to us.

It's a lovely day, lovely day.

We've got a discount rate, we've got free cash flows.

They even gave us the terminal value. Amazing.

We have our current balance sheet. You'll notice that my colleague, whoever, whoever it was that set this, um, problem up, did us a huge favor here by reminding us that this is the current or most recent balance sheet.

And then this is the forecast.

These are the forecast periods.

So we're, we're trying to figure out effectively, you know, what the equity is worth for this company today.

And perhaps we, you know, we, we, you know, we, this is a public company, perhaps doesn't have to be.

And we know that this company has, has a current share price in the market of X.

So they hire us, they retain us as investment bankers to say, we think we're undervalued.

Can you help? Bingo, we're on it.

We're gonna do this DCF analysis, and we're gonna see.

Now, I don't have anything to compare to, but this is kind of giving you some context, right? Okay. So the first thing we're gonna do is we're gonna calculate what's called a discount factor.

And the discount factor, what it is, is it's basically just kind of an intermediary step, an intermediate step to show us how time is eroding our investment.

And it just kind of makes the calculation a little bit, a little bit easier, so to speak.

And what, what this comes down to is the, um, the, the, the, use here is basic kind of time value of money bond math kind of stuff.

And that's essentially saying that the present value is equal to one over the, what am I doing here? Future value raised, sorry, hang on a second.

No, sorry. The present value is the future value times one over the discount rate, which I'm gonna call the wack raised to the year that you're in future value times one over the WACC the discount rate raised to the year that you're in.

So the, the discount factor is essentially this component of it right here.

That's the discount factor.

So every cashflow in the future is gonna get multiplied by this factor here.

And so what we're gonna do is we're gonna take one over one over the discount rate.

Wait, is it one plus, Yolanda, am I, am I totally blowing this? Now? I'm trying to think.

Is it one over one plus the discount rate raised to the, yeah, sorry, I'm having, Thanksgiving week mental meltdowns apologies.

One over one plus Six, right? Yeah. One over one plus that rate.

So what we're basically saying is that to wait a year for your investment, you ultimately lose that 7%, right? In other words, to be compensated for that risk, you have to make 7% on that investment.

Now, Raphael has said, do we have a direct Excel formula to do this? Calculate you do. And it's called MPV, and I will show it to you, but, for now, I'm gonna stick with kind of the mechanical way of doing it, because it's actually in most DCF models, it's a little bit easier to kind of show the discount periods this way, the discount factors this way.

So good question, Rafael and I will show you I wasn't making it hard on everyone, including myself for no reason.

So now what I'm gonna do here is I'm just gonna go and anchor my C6 and I'm gonna copy this formula.

And what we can see is just how much time erodes the value of that investment.

So a return earned in year two is only worth 87% in today's dollars, or today's value, 82, 76, 71.

And this goes on and on and on, right? So we can see the farther we get out in time, the less valuable those future cash flows are to us today.

Now, this is actually one of the reasons, one of the reasons why doing a DCF for a longer period of time does not create more value for your company, right? Because those cash flows that are farther out are, are really less valuable.

So we'll see that when we do a terminal value in a moment.

So this is the discount factor.

Now, um, the present value of these cash flows is then gonna be, if I go back to this formula, now that I've corrected it, I'm gonna take my present value and I'm gonna multiply by that formula or that factor, and I'm gonna get what the actual cash flows are worth, again, in the present.

In the present. So it's 93.5 actually today.

Now it's showing in year one.

And that's one of the drawbacks of this kind of approach, is that it's, it's showing you this 96.3 as though it's happening in year five. But what that really means is that in today's value, that's 96.3, 99.2, et cetera, et cetera, et cetera.

Now, the sum of those as of today is what we call the net present value.

I'm gonna put my formula here so you can see it.

Boy, it loves doing this to me, equal form tab, okay? And I'm gonna put this formula here and here, okay? So the, um, the net present value, his name is Raphael, who was asking me, I think, what this is technically.

And in Excel, we have a simple way to do this, and it's called the NPV formula.

So if I do equals NPV open bracket, open parentheses, and then I go up, it's telling me it wants the rate first, that's the discount rate, and then the stream of cash flows, undiscounted cash flows, it's gonna return the same exact value.

So you may say, well, that's a lot easier because if you can get that formula wrong, Chris, I know I can get it wrong.

So why don't I just use the NPV and, and that's fine. But I'll show you maybe an example where this you know, might, it might be better to do it, you know, year by year.

Okay? So those are the five cash flows in today's value.

Now what, I'm just curious, what were the five cash flows just kind of in, in nominal terms, 595.

So we've lost quite a bit of value just waiting for this.

Now, 7% discount rate is not high.

That's a pretty kind of mildly risky company, right? A a mild amount of risk.

Just so we can see what happens here.

When companies are riskier, the discount rate is higher, it reflects the risk.

So the discount rate, let's say if it's 10%, watch what happens to the present value of the NPV. It goes down. So the greater the discount rate, the lower your present value is gonna be, and vice versa.

So now I gotta deal with this terminal value business.

So what is the terminal value? And you know, here again, we're looking at the value of the business at the end of the five years going forward.

So what that means is, again, if I sell the company, when would I sell it at the end of these five years? And if I bought this company to kind of, you know, en mesh it in my own business, how much value is this company gonna contribute for the going concern period? And what they're saying here is that that terminal value is 800.

And what we will, we will calculate this momentarily for in another example, but for now, that's what that is.

So beyond year five is 800.

Now that's kind of interesting because the sum of the cash flows we said was 5 95.

And yet here we are saying that beyond that, where it gets even more kind of murkier and riskier, the business is actually kind of worth more.

So immediately we're, we're opening kind of a window into one of the complexities of the DCF, which is that it's, it's hard enough to figure out the, these values years one to five, one to 10.

But here we're assigning a massive amount of value to the years beyond.

And that's just something to keep in mind.

Now, this 800 is happening as of this, as of this end of, end of year five.

So we have to discount that 800 back to today as well.

And now you can kind of see why it's nice to have the discount factors sort of done for us.

'cause what I can do is I can just take that 800 and multiply it by the 71% and that tells me that my present value of that beyond value is five 70.4.

So my enterprise value, therefore is the combination of the two, the cash flows and the terminal value.

So again, I don't want to go back into my, my superior's office until I've got that equity value because I know what she wants.

And so to get my equity value, I'm gonna take my enterprise value and I'm going to add my cash and subtract my debt.

And that gives me the implied equity value.

And now I want to compare it to where this company is trading in the market.

So I take that and I divide it by the shares outstanding.

And that's gonna give me, and I, you know how I am about not showing shares the right way, and you know how I am, gonna do currency, gonna do two decimals, bang, and then I'm also going to, can I just add that as a style? I think I'm gonna do that. For those of you who ever wanted to add, add your own style, that's how you do it. You create the style, which I just did, which is just a number format.

And then I'm gonna call this shares share value.

I do, I think it has to, I can't have a space in the name if I remember correctly.

So that's gonna be my share value style.

So now the next time I come to a problem, you won't have to hear me complain about it.

I'm just gonna go up there, grab my style, apply it, and I'm done.

Okay, $8 and 3 cents here.

See, the way we were showing it before, we were dipping 3 cents from the value, it was just showing as 8.0.

And if you owned, you know, a million shares, those 3 cents can, can, you know, get you a weekend in Cabo, Cabo, right? So we want, we wanna make sure that those, uh, shares get count, those pennies get counted, okay? Okay. So any questions on that's the overall, okay, uh, we, we always, y and I were just telling, we always have somebody asking about this.

Where do we download the Excel worksheet again? So, Yolanda, can you, can you respond? Yeah, I think the problem is, is that we put it in the chat and not everybody can see the chat because of their internal blocks.

So it's not, it's not the anonymous attendee's fault.

Okay? So this is called the discount factor. Alright, quickly, we gotta hit a couple of points here in, in the last half of class, kind of the more detailed stuff is what we're gonna do in the last half.

Any questions on what I did? Any questions on any of that theory that I gave you? Okay, so free cash flow, let's knock this out pretty quickly here.

It's a term you hear a lot, it's very important.

It also, quite honestly can mean a lot of different things.

And many times Yolanda and I, when we're working with a group that we work with that are already on the job post, you know, kind of post, uh, post training, they're kind of, you know, in the junior banker kind of category we're often seeing lots of different definitions of cashflow because it can be used different ways.

So sometimes you gotta ask, well what, what cashflow metric are you really talking about here? So for the DCF, what we're trying to do is we're trying to match, again, the cashflow to the enterprise value.

So it's gotta be available to all the stakeholders.

Oh, my camera's off. Thank you very much.

I dunno what happened. I might have just jiggled my cord.

Might have hit it. I'm back.

Thank you. Available to all the stakeholders from the core operating assets.

So, kind of once you get, once you get those kind of two principles out of the way, the rest of it I think is so somewhat easy to understand.

Now, there's no need to reinvent the wheel, even though we were using a different term.

Free cash flow is something we haven't seen.

We didn't see it in any of the stuff we've done before.

And we did a whole valuation course, topic on comparables.

So basically what we wanna do is we wanna start with something we have already.

And the easiest place to start for this calculation is with EBIT, because EBIT kind of represents the earnings that are available to all stakeholders and our from the core operating assets, oh, sorry, the most important one must be cash, not accrual, accrual base. So that goes back to class one, which was a bit of a, you know, mess because we had technical difficulties and all kinds of stuff.

But, I talked a lot about the income statement on that day and about how it's really all wrapped up in this accrual stuff. And then, and then we jumped into cash flows a few weeks later and it all kind of came out in the wash, right? So free cashflow, obviously because of the acronym must be cash based.

So, we start with EBIT because EBIT, you know, are these kind of earnings that are from the core operations available to all stakeholders, could do none here.

So that's gonna be EBIT.

Now EBIT kind of fits two of these points, but it does not fit the third.

It actually fits two and a half or kind of one and a half of these points.

It's great because we've already calculated it 995 times out of a hundred.

So it's a good starting place.

But it's really got a lot, has a lot that needs to be adjusted for.

So the first thing we need to do is we need to acknowledge that EBIT is before interest in tax.

And if we're talking about free cash flows, free means that they're available to all the stakeholders, that's what the free means.

It doesn't actually mean that they're literally free.

So because of that, we gotta pay taxes.

So what we're gonna do here is we're going to tax affect our ebit and we're gonna multiply that times one minus.

I'm gonna put marginal tax rate here.

There's a philosophical thing about marginal versus effective.

I don't have time to go into it, but if you're curious, you know, email me or chat or chat me through the FE portal and I'd be happy to explain it. Or perhaps if Yolanda's got a second, now she can explain it too.

Sometimes it's just a matter of what firm, what your firm policy is.

So EBIT times one minus the marginal tax rate, that's gonna give us what's called EBIT EBIT before interest and after taxes, or more commonly known as NOPAT So now we've gotten some of the kind of messy work out of the way we've taken the taxes out.

Okay? So now we're stuck with, you know, kind of another problem, which is that EBIT comes from the income statement.

The income statement is not remotely cash based.

So what we need to do now is we need to start making those adjustments that we made to cash flows to, or in the cash flow statement to get them to become more cash-like on the cash flow from operations.

So the first thing we're gonna do here is we're going to add back the depreciation and amortization.

And that was because DNA was deducted from EBIT or from profit to get to ebit.

Now, question for you all.

If all, all I'm gonna do here is add back the DNA, why don't I start with EBITDA? Is that not a better place to start? Why not just start with EBITDA and go from there? Any thoughts on why? Give it a couple of seconds.

John says the DNA varies based on accounting.

It does, and that is, that is certainly in comparables analysis. Something to consider John.

Because we're comparing maybe different companies that's not as important and intrinsic Because we are, we still have to add the DNA back Because it's still non-cash.

So whether they used some of yours digits or straight line or whatever, we still have to add it back.

You also bring up gap versus IFRS another good point.

But again, since we're doing intrinsic and we're doing cash flows, if depreciation and amortization were deducted from my earnings, which they are always, then I have to add them back to adjust those earnings to get to cash.

So every cashflow statement's gonna have that add back.

So yes, they are non-cash charges and that is why we're adding them back.

The question is why were they in there in the first place? Well, they're in there in the first place because of they're assimilating the use of the assets.

But from a more strategic perspective, they are a tax deductible item.

So we want EBIT because it's got the benefit of the tax shield from the DNA, the lower, lower ebit, lower earnings, lower taxes.

If we taxed EBITDA or tax adjusted EBITDA, let's say with this one times one minus, we would actually be overstating our taxes.

And that's not a good thing for anyone.

Okay, so I'm gonna add, the DNA after this tax adjustment.

And now if we think back to cash flows, the cash flow statement, what else did I have to do? Well, all those kind of kind of weird things that go on with accrual accounting.

Did I make the sale using accounts receivable or did I collect in my accounts receivable? Did I buy the inventory with cash? All that stuff's gotta get adjusted.

So those are gonna be the changes in operating working capital.

Gotta adjust for those too because, you know, a lot of companies spend a lot of money building up their inventory that's part of their business.

A lot of companies, benefit from very, very favorable supplier relations.

So all of these things impact the actual cash flow as we saw weeks ago, right? Okay. Now you might be saying at this point, Chris, that this looks familiar.

We did this in the cashflow statement section.

Why don't we just go to cashflow statement and just take cashflow from operations or whatnot.

Well we could but there's a problem with that because cashflow from operation starts with net income.

As you recall, every cashflow statement on earth starts with net income.

Net income includes interest and its taxes are reflective of the interest and other stuff that's in that bottom line.

We don't want any of that. We want a pure calculation.

This thing that we're doing here only exists for the DCF, doesn't matter.

The tax that we calculate here never gets paid.

Nobody does anything with it.

It's purely academic, purely analytical.

Okay? So while a lot of good stuff is in our forecast cash flow statement, we can go back to it and get all this data from there.

Absolutely. But we, there's no number in our model, our three statement model that exists that can, that, that is the exact number that we need.

We have to calculate this right now.

So adding my DNA adding or subtracting my change in working capital, just like we did weeks ago.

And also because we're dealing with operating assets, we need to check to see what am I investing in these operating assets? What is my CapEx? Very important CapEx or increase in intangible assets such as copyrights, patents, trademarks, right? So that is more or less gonna get us to our free cashflow.

You could also add a few other things in here and I'll maybe do it off to the side.

You could add, any changes in other operating assets and liabilities.

Now what could those be? They could be things like deferred taxes and just a little bit more like next level stuff, other operating assets and liabilities would be the only other things you wanna look at out for any other asset or liability that carries the descriptor.

Operating has gotta get into that free cash flow.

Gotta get in there. Any questions on that? Let's do a quick free cash flow calculation here.

Yeah, just do an easy one just so we can do it.

Okay, so here we have, some metrics.

We've been given EBITDA, DNA tax rate, CapEx, working capital.

Okay, easy enough. So, we weren't given EBIT and I just harped on why we need EBIT.

So we, we could thankfully somebody did us the benefit of giving us the labels here.

But if I said, if there were no labels and there won't be labels in the models you build or there, there might not be because you'll be building it, right?

Don't take the bait and start with ebitda. We gotta get back to EBIT.

So I'm gonna take my EBITDA, I'm gonna take my DNA, which is gonna be the sum of these, and I'm going to net the DNA from the EBITDA to get to my EBIT should always be lower than DNA than EBITDA, right? Always. So be careful of that.

Now I need to calculate this kind of made up tax, which is the 70 times, the 30.

Now I kind of have my own little sort of rules about cashflow statements.

I believe that cashflow statements, unlike income statements, income statements, you can kind of set them up however you want.

But to me, a cashflow statement needs to be positive, negative.

And I believe that because if you were to present an investor with a cashflow statement, that investor needs to know when they look at a number, is it an inflow or an outflow on the income statement? It's not that hard to figure out.

Cost of goods sold is always an expense.

There's not a country on earth or planet in the universe where it's not an expense, right? So that doesn't, that's not gonna trip anybody up. Profit is profit, the income statement is set up to kind of get there.

Cash flow statements. On the other hand, you could be showing really low, really high. It doesn't, we don't know. So I wanna make sure when I'm doing this, I'm always showing my cash flows as positive, negative.

So now my notepad is 49.

The net of those two. And again, this is a completely manufactured number.

We do not have to have anyone from the auditing team come in here and check that number because it's just purely analytical.

Okay? Now I wanna go back and get my DNA added in and then I want to take out my CapEx.

So my CapEx is gonna be the minus 40.

And the working capital, again, that's working capital is a big can of worms, right? It's very challenging topic, I think.

What we're saying here is that the working capital, working capital is a net calculation.

We subtract our assets from our liabilities.

So working capital calculation in this situation is showing it that it is a use of cash.

So that means one of two things that I have an asset balance, meaning I have a lot of, inventory or accounts receivable, or I have perhaps paid off a lot of payables, but whatever, whatever it is it it's showing the cash is going out, right? So that's a negative.

So I'm just gonna link up to this 10 as a negative.

Because it's telling me that it's the increase, decrease, and now my free cash flow is the noad plus the DNA minus, the CapEx minus the OWC.

And there you have it.

Any questions on free cash flow? What should be included? What should not be included? Oh, what I heard about this one time, or what about that, that or how do you know? Anything like that.

Anything like that? No. Okie doke.

So, kind of looking back at our checklist here, the next thing we have to do is move on to our terminal value.

So calculate the terminal value.

All right, well, how on earth are we gonna do this? How are we gonna figure out what this company is worth beyond the ca the forecast period, the cashflow period? How are we gonna figure that out? Well, there's, there's a couple of, couple of ways and they really kind of relate to those two situations that I was talking to you about, which are, hey, we bought a company, we wanted to get into the shoe business.

We bought a shoe company and that shoe company, we expect to generate profits, cash flows, value forever.

I mean, there's no reason to see it not doing that.

Now we know companies don't go on, you know, forever and ever, but the theory of going concern says that, you know, we can expect them to.

Right? So that sounds like we're being greedy.

It's like, Hey, I want to, I wanna buy your company.

How much is it worth? I said, well, you know, here, here are the cash flows I make.

But you know, I expect you to pay me for the cash flows for the end until the end of time too.

You know, that's kind of sounds like you're being greedy, right? So, one suggestion here is that we could treat it as a perpetuity, and that's exactly what it is. What we're saying is that these cash flows are gonna go on forever.

Absolutely. That's called a perpetual cash flow.

Now, a perpetual cash flow.

What that essentially means is that if we think about the, that period, that terminal period, as the years beyond the cash flows, what what's happening here is I'm gonna create years till the end of time, and I'm gonna do that using the power of Excel, which goes on for almost forever.

And if I just copy, these are the periods here, right? Periods in the terminal value. If I just copy these across, oh, I didn't do it right, equals this plus one.

If I just copy that across, we see that Excel gets me the benefit of about 16,372 years.

That's almost till the end of time, but not quite.

Now, if I were to think about these cash flows, the same principles apply, right? Which is to say that to calculate these cash flows as, as my friend has suggested here we have to discount them because the cash flow in year 16,372 is obviously worth less than the cash flow in period one.

And all of these periods, by the way are in the terminal period.

So we're already five or 10 years out, right? This is all terminal value.

So this is the forecast back that way.

The forecast is that way. Okay? So what I'm gonna do here is I'm just gonna we used, I'll just, I'll just put 10% just to make it kind of nice and, what happened to it? It's not showing, put it right here.

There is my discount rate.

So if the WACC, I haven't gotten to the, to the free cash flow yet, my anonymous friend, I haven't gotten there yet.

but I'm gonna, I don't even need to get there because what I just wanna make a point, and the point is that this theory that says the cash flows are gonna go on forever and ever, what it's saying is that if I take, again, that formula of one over one plus my WACC, I'm gonna anchor that and raise it to the number of PE periods in that perpetual terminal period.

Well, what we can see here is if I just copied over 10 years, by year 10, I'm already at 40% in terms of value today, right? Or value at least at the beginning of the terminal period.

And if I go over another 10 years, I'm at 15%.

So any cash flow that's generated 20 years after our forecast period is only worth 15%.

And if I go over even farther, well, Excel can't even really do that math.

But what we can do is take a peak along the way and see that, you know, essentially by year 30, 40, whatever, it's down to a meaningless amount, you know, pennies on the dollar.

And by year 56, it's not really worth anything.

So 56 years is still a long time, but, but we're talking about it being worth pennies even in, you know, 30 years after the fact.

So the formula that this, you know, mathematician came up with effectively says that the free cash flows growing into perpetuity, and we assume that they grow, right? Because they kind of have to grow, even if it's at inflation.

But they have to grow.

I mean, the, the chances of them staying the same are very, you know, doesn't really make much business sense, right? So the free cash flows will grow into perpetuity at a very modest rate.

They can't grow into perpetuity at a very fast rate because they would overtake the economy, right? So we have to assume that they're growing at a very modest rate and that those cash flows can be valued by growing them, as I said, at a, we'll call it a long-term growth rate times one plus.

And I'll put this all over parentheses.

And then to factor in that time value of money, which we just saw, if we take the cost of capital and then subtract that long-term growth rate, that will recreate the cash flows growing forever.

Now, there's a derivation of this formula.

I can't do it and would never pretend to, I couldn't get, you know, the basic one done.

And the last thing I would do is try to do this one.

And it's sometimes called the Gordon Growth Method.

And I don't know if I think, I believe it was a British, I believe it was a British mathematician.

I don't know if his name was Gordon or if he drank a lot of Gordon's.

When I look at the derivation, it makes me wanna drink a lot of Gordon's.

That's kind of what it is.

And so if we take that cashflow that what's called a steady state cashflow, the cashflow that we expect to grow into the future and divide it by WACC minus the LTG will get that value, which in this case was the 800.

Now I don't know what they used in this, um, example.

So we're gonna, we'll go down and look at our own, but what this is called, this free cashflow times one plus LTG, that's called the steady state cashflow.

And that implies that you have a stable cashflow that's growing at a modest rate.

Now, this brings us back to, and we're, we're clearing the chat out just because it gets long, otherwise, but I think it was a couple people, I think maybe it was Rafael, a couple people had questions or comments about five versus 10 years, right? When do you do one or the other? Well, if I need a steady state cash flow to do this, if I need a steady state cash flow to, to do this Gordon growth right? Method, I can't be at a point in time where the cash flows are still growing wildly.

So like, you know, think of a very early, early to middle stage company.

Like one of the tech startup like Uber is still very early stage.

I mean not early stage financing, but their early growth stage, right? Pick one Nvidia, all that stuff, they're growing too fast in five years to be at a steady stage.

So you might have to go out 10 years to get to a place where you're seeing more modest growth, right? One and a half to two and a half percent kind of thing.

Now, of course, they hope they grow 10% every year, but it's probably not gonna happen organically anyway, maybe through M&A.

It's just very rare that a company can sustain that growth.

So the concept of a steady state cashflow is a cashflow that's at that long-term growth rate already.

So let's actually just do a problem and just kind of see all of these components come together.

It's an odd concept, right? It's an odd concept, but it definitely is one that is practiced currently in valuations across around the world.

So let's look at number five.

We do five, right? I actually marked six.

Six is six has just got, let's do five really quick, then we'll just jump in and do six as a recap.

So, question five looks like what we just did above.

Now that's gonna have the other method. All right? Let's just do, why does this one have the EBITDA? I don't want that one. Maybe, maybe we have to do five.

Yeah, let's do six for right now. Let's do six and it'll be kind of a, a recap sort of what we've done and then we'll, we'll be able to to build up to this perpetual cashflow calculation.

Okay? So the first thing we've gotta do here is we've gotta kind of get this calculation into shape.

So I'm gonna go ahead and bring down my year counts from above.

And that's just gonna keep me from having to lock my titles and just, it's a big spreadsheet, so we can't really do that.

So I'm gonna bring my year count down from above and now I've gotta get my free cash flow calculation done.

So quick recap of what we just did.

EBIT is going to be, in this case, equal to my operating profit and it's equal to my operating profit because I don't have any adjustments to deal with like non-recurring and whatnot.

So there's my EBIT.

Now I've gotta go ahead and tax the EBIT.

So I'm gonna take my EBIT times and I want this to be negative.

So I'm taking the opposite of my tax rate of 20% and I'm copying that across, and that's giving me my implied or calculated tax.

So there's my notepad.

Be careful if you use alt equals, don't grab the year count in there.

Now, some of the stuff we talked about, we talked about depreciation, we talked about CapEx, we talked about working capital.

You'll notice that none of that stuff is here.

And that's why I actually had originally thought I would skip this problem.

Because I think it can be a little bit, it can be a little bit confusing. What we're effectively saying here is we're not giving you any detail.

We're just telling you that we've got operating assets and non-operating assets, and we want you to be hyper-focused on, on the operating assets, right? So here we've got change in operating assets are what, what we're calling kind of the working capital here, the working assets.

In fact, the problem I have with this is it's, I find it to be a little bit, the wording to be a little bit, ambiguous.

Like these are operating working liabilities, and then this, these are long-term operating assets as well, right? So we're basically saying is that this is OWC and this is OWC and the change in my long-term assets or my fixed assets, what makes my long-term assets or my fixed assets change? Well go back to modeling based analysis.

Fixed assets go up by CapEx and then they go down by DNA.

So what this problem is being sneaky about is it's kind of hiding where some of these things are.

I don't really see it modeled this way myself in real life.

So, it might be, and theoretically this is correct.

So sometimes you'll pick up an equity research report because you've got a great forecast in there that you want to use and they, they might model this way, and now you're like, what on earth are they talking about? Right? So I'm just kind of breaking this down.

So my changes in my operating assets, I'm gonna take last year minus this year, and that's gonna give me the that, 2.8 negative my assets went up and therefore it reflects cash going out.

Yes. When I say operating working capital, I mean networking capital, I mean networking investment, everyone calls it something different.

I'm sticking with what we kind of call it consistently in our materials.

But yes, absolutely that's what that is.

And that is a good question.

So now my operating liabilities will work the other way.

I'm gonna take this year minus last year to show that an increase in my liabilities is a cash inflow.

And that's why that's positive. Okay? Oh, gimme a break. Now.

My long-term assets are gonna be my PP&E, right? So how much is CapEx? How much is depreciation? I don't know. And honestly, I don't need to know for this.

The net change in my PP&E or the net change in my operating assets, my long-term operating assets is the change that I need.

So if it's going up, it means I spent on CapEx.

If it's going down, it means that I've taken more out of the business than put in.

So I'm gonna do last year minus this year, and that's gonna show me kind of a net CapEx number.

Okay? And now the sum of these up to my notepad is my free cash flow.

Okay? So got my free cash flows, alright, now for terminal value, which is what I wanted to begin with, but can never do enough practice, right? Well the first thing I see when I look at these is that I see that the, these numbers are still a little bit all over the place, right? Because they've got this huge change.

The EBIT is pretty consistent, but there's like a, there's an expectation of a very kind of large CapEx expended. There's a couple of years of very low CapEx and there's a very, then it goes into kind of high gear and that that can actually be very tricky in a DCF.

So if to, pardon, this isn't a great example, that

this would be a challenging example in real life, but we're just looking at it kind of theoretically here.

If I look at my free cash flow, it seems to have kind of stabilized again after it, it was high and then it went low and it seems to be stabilized.

So to my colleagues here who said perhaps 10 years, I really might wanna go out 10 years here to see if I can get to a more stable free cash flow, a steady state free cash flow.

Now, I don't have that ability in this problem.

So I'm just gonna show you mechanically how we capture this terminal value.

Now the formula, once again, I'll just put this in the slides so we have it, the formula once again for the perpetual cashflow or Gordon growth, sometimes abbreviated as Gigi.

Gigi was his, his name when he went out to the clubs, they just called him Gigi.

So that formula again is going to be the steady state the free cash flow times one plus the long-term growth rate.

And that's what we call the steady state cashflow.

And we're going to divide that by WACC minus the LTG.

So doing that here, I'm gonna take the 129.2, multiply it by one plus my LTG and then divide it by my wack minus my LTG.

And that's gonna give me a terminal value.

Okay? So now once again, we can see there's a lot of value there.

Because the sum of the cash flows themselves is what's the sum of these? It was 726.

So it's like over three times, right? Over three times the values and the terminal value.

Now my discount factor is going to be equal to one over one plus my WACC.

This is a great place to name cells by the way.

Raise two the year that I'm in.

I think you took long-term growth.

Yeah, sorry, lemme just do it again.

Because the whole, the whole thing is a mess.

One over one plus this is right in the session where my keyboard, everything starts to slow down because it's zoom is taxing my resources and I'm always off a cell.

Okay? Yeah. And now I copy that over, I didn't lock it that time.

Lemme lock it.

And I copy that over and those are my discount rates.

Okay? So now I can do either the NPV of these cash flows or I can use these discount RA factors, which I just did, right? I can do the NPV formula or I can just do the other one. So I'm gonna just do the other one, which is to apply the cash flow to the discount factor, and that tells me what those are.

And then the sum of these will be equal to just the sum of that array.

And just to check, I'm gonna do the NPV at the WACC of the free cash flows, and that's gonna be the same.

Okay? Now I've got that terminal value sitting way out at the end, which represents everything from the end of year five going forward.

So this what all these cash flows were discounted, but they were discounted back to the beginning of the post forecast period or the end of year five.

So this terminal value has to be discounted back five years.

Now, one mistake that I think I recall being very confused, or I was very confused about this point, and I see this mistake a lot, is people feel that the terminal value is happening after the forecast period.

So it should be discounted back six years.

No. That's not what we're saying.

This is not a new cashflow. It's the value of this company.

At the end of the fifth year, at the end of the 10th year, whatever forecast period we did, we chose.

So this has to be equal to the 2661.9 times the 68%.

And therefore my enterprise value is the sum of those two.

Any questions on that? Oh mercy.

Hmm. Okay, any questions on that? Why it's five years and not six years? Okay, so let's just say now the other thing I don't like about this problem is I can't, I can't do what I want to do in this problem, but that's okay.

I'm gonna pretend to do it anyway.

Let's just say for example, oh, here we go, Rafael, in that case, can you do an NPV in Excel that includes the terminal value? No. Can you do the NPV that includes the terminal value? You can Rafael, but you, what you'd have to, so Rafael is saying is can I still do an NPV that includes the terminal value? But what you'd have to do, Raphael, is you'd have to then, create another kind of label that says, present value of free cash flow and terminal value.

And then you'd have to add the terminal value into that year.

So that Excel is when you do an array in Excel, Excel is counting periods, right? Every cell is a period.

So what I'd have to do here is just to show you what I would do, I would do that, present value of free cash flow and terminal value.

And then here I'm gonna take all of these, sorry, that's not present value and term.

I'm gonna take the sum of well, I'm not totally set up for this, but I'll do it anyway. Just pretend, just pretend that I'm doing this in a real methodical way.

So now the present value, the cash flows, these are the cash flows. Some of this should be some of future cash flows and terminal value.

And now what I could do here is I can do the present value of the free cash flows and terminal value, and that would be equal to the NPV at that rate in this array.

And there it's the same.

So yes, you could do, but you gotta set your model up for the way you want to do it. You don't want to, you don't want it to look clunky, right? Mine looks a little clunky. Okay? So now question is this, your superior comes to you, your md, your vp, your associate, and says, now I'm gonna skip over the equity value part and says, okay, you did your EV calc, nice job on your first DCF, boy, that is a lot of value in that terminal period.

May I ask you, how do you know that your assumptions for the terminal value are correct? And you're like, I don't know. It's what we did on Felix. I mean, we're pulling a lot of numbers out of the air here, right? We're really making a lot of estimates in a DCF, our entire forecast, our estimates now we're throwing more estimates at it.

A whack calculation, a long-term growth rate.

I mean, it's like, how do we really know where we stand with this number? So what we can do is, again, we can kind of peak outside the, the iron, the intrinsic iron curtain here, and we could say, well, let's take a look at what that terminal value represents in terms of a multiple.

So what I could do here is I could say, okay, I'm gonna, Rafael, pardon me, I'm gonna get rid of these other cells because they're just gonna, um, gonna create kind of a problem there.

What I could do here is I could say, okay, here's my terminal value.

What does that mean? How much what is the multiple of that value over a given driver? Now in this case, I don't have EBITDA, I could use EBITDA, I only have EBIT.

So I'm gonna take that 2661.9 and divide it by my EBIT in my last year.

And what that's telling me is that I'm essentially saying that I think I can sell this company in year five for 9.2 times ebit.

Now how do I know if that's right? Well, I hopefully have at this point, or if I don't, I will be told to go create a series of comparables and I will find where all of the competitors are trading on an enterprise value to EBIT basis.

And I will see if 9.2 times is a decent assumption.

If I look at my multiples of the competitor companies and the average EV to EBIT multiple is roughly, you know, nine or 10 times, I feel pretty good that actually my, my assumptions for Gordon growth were pretty accurate.

If I look at my EV to EBIT for my comparable companies and it's 12 or 13, or if it's four or five and I'm sitting there at nine, I'm like that's not good.

Something's gotta be off here.

So this is a sense check, this is a sense check to see where that number comes out.

Now, um, I don't have a lot of time left because as usual talking a lot and covering a lot of material as well.

But what this does is actually opens the door to another methodology.

And the other methodology is, well, yes, you can do that Gordon growth, but you could also, you've got the benefit.

You've already done your comparables.

Let me go into my comp set, figure out what's my, what's the EV to EBIT multiple for this industry, what's my EV to EBITDA multiple and use that to create my terminal value.

I'm kind of doing this in reverse.

So the previous problem is essentially that, wait a minute, I actually just completely skipped.

I I did not see that five was the one that I wanted.

Anyway, okay, so let's go up and take a look at four and four is going to essentially do this.

So we'll do four and five together and that'll be kind of a wrap up.

So five is what we just effectively did, right? It's what we just did in the bigger problem.

Four is saying, okay, we did a comp set and seven is the going rate for buying a company like this seven times EBITDA.

Let's use that to calculate our post forecast amount.

Let's, let's assume that somebody's gonna come along at the end of year three and buy this company for seven times.

So again, go through the ordeal of doing my discount rate,

one over one plus the discount rate.

Yeah, lock that, raise it to the one, copy that across, add the formatting that my colleagues never think I want, but I do.

And apply the free cash flow to that and that gives me my present value of the free cash flows or NPV it as you will.

Okay? Now, value post year three.

So I'm gonna take my EBITDA, which was given to me here, and if you build a model, you'll have it as well.

Now I'm gonna multiply by the multiple and that tells me that I could sell this business for nine 80. That the terminal value of this business, the value post, my ownership is nine 80.

So now I'm going to take the sum of those discounted cash flows and then the present value of my sale price, which is the nine 80 times the 81.6.

And that's gonna give me an enterprise value.

Now, just like, just like we said hey, I made some big assumptions here doing the Gordon growth method.

How do I know that that terminal value is accurate? Well, I did a sense check, right? I checked it based in, I put it in multiple terms.

So down below when I did this problem, I put it into multiple terms and I realized that I was about 9.2 x.

Okay, well, I like the multiple method because I can say that the market backs it up.

I can say that this is where all these companies are trading.

So my seven x multiple has, has weight because of the comp set that I did, but most investment banks and even some equity research and you know, may possibly even private equity uses slightly different methodology are still gonna want to see both methods and they're gonna wanna see both methods in terms of each other.

So what I could do here is I could actually figure out what my implied long-term growth rate is here.

I know the WACC is not gonna change either way, right? But I can, I could look at what my implied long-term growth rate. And the way that I do that is, again, it's a bit of algebra to take that Gordon growth formula and, and solve for the growth rate, which is what we're doing. We're rearranging the Gordon growth formula to solve for the growth rate.

And the, the way this formula works out is you just, you don't have to memorize it, it'll, you just kind of have to have it handy or have it in your model, but it's equal to the WACC times the terminal value, which is that nine 80 minus the free cash flow in the last period.

So I'm gonna put LP the last period there, okay? And then you're gonna take that and you're gonna divide by that same free cash flow in the last period plus the terminal value.

So if I do that, and that's a real hum, dinger of a formula, kind of a good one to kind of end on.

If I take that, I'm basically saying, all right, here's my WACC, which is the 7% times the terminal value, which is nine 80 and now minus the free cash flow in the last period, which is the 60, because that's the one we'd be using to calculate the growth rate, right? To calculate the Gordon growth and then divide all of that by that free cash flow plus the terminal value.

What that's saying here is that my implied, my implied long-term growth rate is 0.8%.

My implied long-term growth rate is 0.8%.

Now, I think that's a little low, personally, I think that's a little low.

So that might tell you that your multiple is too low.

Maybe the multiple should be 10.

That puts it up to 3.7. That's high.

So maybe, you know, maybe it's somewhere in between.

Maybe it's some, I changed the WACC, sorry, I was wondering why that didn't change the, what was it before? It was seven, right? Seven. Yeah. Seven and seven.

So let's just say that should be, let's say we changed this to a 10 x multiple that's gonna pull the long-term growth rate up to two and a half, perhaps two and a half is is right. Two and a half is kind of is an okay long-term growth rate. Again, you don't wanna start getting higher than, you know, historical inflation because then you're starting to basically imply that the company's gonna grow forever at a higher rate than inflation.

It'll overtake the economy some way.

So basically what I was able to get through in these two hours was kind of the, the, the basic kit and caboodle of doing a DCF.

Happy to take any questions.

I would like you if you're curious about this, there is a very good practice file on the system for British Aerospace.

The model's done for you, you just kind of have to pull in, the proper numbers into the DCF like we did and then do these calculations like we did.

I I will reveal the solution for you as well if you want to try it.

If you're really curious, try it without the solution and see how far you get. Message me and, and I'll help you if I can figure out what's not working or you know, what is.

And for those of you who you know, who want the solution, I'll put that there for you as well.

So, once again, I thank you lot of stuff here in a couple of hours and, hopefully it was new stuff for most of you. If you have any kind of more next level questions, again, message me as well.

Message me as well. I'm happy to go over them.

I'll post my notes, put all the solutions up.

I wish you all a happy Thanksgiving and I will see you next Wednesday.

I think we go into what do we go into next Wednesday? We go into LBL. It should be fun, which should be fine.

All right, have a great evening everyone. Thank you Yolanda. Thank you for your help. Keeping me honest here.

Happy Thanksgiving. Everyone doesn't look like there's any questions, so No. Looks like everyone's while down signing It off at, at some, There's always a, There's a couple. Yeah, It sometimes you have to leave it on while you take a call and then, alright, I'll wrap it up.

Thank you Yolanda. I'll see you next week. Yeah, no Problem. Take care everyone. Bye.