The, uh, the session is gonna cover a variety of topics on DCF.

So the kind of things that you would, um, you would maybe look at in the larger model and it be difficult perhaps to see, um, to, to see that, the sort of detail of how these things work. So we're gonna look at 'em as a, a series of shorter workouts.

Okay? Right. So the file we're looking at is advanced DCF valuation, workout empty.

If you can click on that to download it, that would be fantastic.

I have that open already and I'm gonna jump into that imminently, right? So I'm gonna jump into, I'm gonna jump into the file.

So you should land on a sheet that looks like this.

Let me grab my stylus. It'll open up on the welcome sheet.

And what we wanna do is go to the workout sheet.

So it'd be great if you could either click on the workout sheet or if you could hold down control and tap page down a couple of times to get you to the workout sheet.

We've got, uh, a series of workouts covering some topics.

They're all really important points to make on DCF.

So broadly, we're gonna think about growth rate, long-term growth rate, and terminal value.

Really important terminal value, what, 80% maybe of the enterprise valuation.

So a lot rests on that terminal year, and a lot rests on the growth rate.

So we're gonna think about the growth rate.

We're also going to think about sub periods.

So if you are building a DCF, and perhaps the first cashflow wasn't gonna land exactly in 12 months time, but the valuation date was nearer to that cashflow, how would we deal with that? How could we build a model that was sensitized around that? So we we're gonna talk about that, and we're also gonna talk about whack weighted average cost to capital.

So some of the nuances of WAC we've got just under an hour, and it's a reasonably ambitious amount of content to cover, but I know that we will get through it.

So let's look at workout one, workout one, workout two, and workout three all cover the same sort of topic.

And that's the growth rate.

Now, if we just read the first part of the question, and then I'm gonna go to the side and have a think about a few things, um, in addition to the question.

So it says, the traditional terminal value formula is free cash flow multiplied by one plus growth rate over wack minus G.

And I agree with that.

You know, when I build, uh, A DCF, I might build out, say, a five or a 10 year forecast, and thereafter the end of the forecast, because a businesses a going concern, what we need to do is capture the value beyond that forecast period.

And we call that the, the terminal value.

And the typical formula is to take the unlevered free cash flow in that final year of the forecast, multiply it by one plus the growth rate, and divide it by WAC minus G.

Where do you get that growth rate from? Because it has a profound impact on not just the terminal value, but the, but the EV that we're, we're ultimately arriving at.

So where does it come from? Well, you could go and look at a data provider like Felix, for example, and go and grab the unlevered free cash flow from there.

But what I want you to consider, I guess what I want you to consider is there must be a relationship between that growth rate we're talking about and the reinvestment in the business, and also maybe the return on invested capital that the business generates.

So we're gonna try and consider that as, um, as an idea.

And I look the, the, I just think the, the phrase that's in my head is, you cannot grow for free.

You don't get something for nothing. Okay? So what I mean to say is that in the final year of your model, if you think about your DCF, you're gonna have your, your notepad number.

So EBIT, EBIT multiplied by one minus the effective tax rate.

So you, you, you're gonna have your, your notepad number, and then you would, what would you do? Add back DNA, subtract CapEx and adjust for changes in o WC to come to unlevered free cash flow.

So if you think about, let's go to the side. If we think about just drawing something out, if I said asset equals liability plus equity, I'm just gonna make something up.

It will actually, we'll loosely relate to the question, but I'm, I'm making some numbers up, really.

So imagine, let's go further down.

So imagine that we have a business that has shareholders equity.

So these are balance sheet numbers, not, no, not market values, but shareholders equity of 600.

And maybe we've also got debt.

So we've got debt of perhaps 500.

And that means that we've got total, the total capital in the business is 1100, and that capital needs to go somewhere.

It needs to be invested somewhere, or you might say employed somewhere.

Now, maybe some of the capital that we've raised, maybe it isn't doing very much at all.

So what if 100 million of that capital is just kicking around as cash? It'll probably generate a return, but, you know, cash is not gonna generate a very exciting return for us.

However, the remainder of the capital has been invested, I'm gonna call it invested capital, and that would be 600 plus 500, excuse me, uh, minus 100.

So there's your 1100.

So when you think about invested capital, like what is in there? What is, if you peel the, the skin away from it, what's inside invested capital? What are we investing in? Well, we're investing in things like property, plant and equipment, and also operating working capital.

So when we talk about invested capital, we've bought retail stores, we've bought factories, we've bought machinery, we've bought inventory, we've offered credit to our customers.

When I say we've bought inventory, we might not have bought the inventory and financed it through debt and shareholder equity.

'cause some of it might be financed through accounts payable.

So we've, we, we've got, uh, we've got PP and E and we've got the kind of networking capital position of the business living inside there.

Now, um, when we talk about growth, and, and I'm gonna jump in and out on the numbers in the question.

This says here, growth of 3%. Like, what does that mean? Like, what do you mean growth of 3%? Well, if we're talking about long-term growth, what we're talking about is growth in PP and e.

If PP and E is growing by 3%, that must mean that CapEx is greater than depreciation.

It has to mean that because the PP and E is growing.

If OWC is growing by 3%, that must mean that we're increasing the size of our inventories, that we're increasing our accounts receivable and maybe our accounts payable is increasing, uh, alongside that.

Now, you might say, but I don't know, Jonathan, is that sales growth or is that growth in the, in the balance sheet numbers? But it would be both. If we're talking about the, the, the, the terminal state that the business is in, then they would both be the same.

Now, if we go backwards a bit, if you've got an early stage business, a startup business, then actually your invested capital might be growing ahead of your sales.

So you would tend to, you know, build up more capacity and then your sales would follow.

But as the business becomes mature, the growth in the invested capital and the growth in the sales and the, and the, the operating profit and the notepad need to be the same.

If they weren't, if terminally the invested capital was, say, growing faster than sales stroke notepad, or if notepad was growing faster than invested capital, then the return on invested capital would be changing.

But, but actually we are assuming the return on invested capital in the terminal state is stable.

So that has to mean, it just has to mean that that growth rates to revenues, it relates to earnings, it relates to invested capital.

Everything's growing.

We call it the steady state, at the steady state.

So we're gonna grow, grow that by 3%.

I mean, I'm not even answering the question at the moment, I'm just chucking numbers around to see if I understand them.

But when we say it's growing by 3%, that invested capital number is a thousand.

And if it's growing by 3%, then it's growing by 30.

And if it's growing by 30, that means that the pp e need pp, e and o WC together need to go up by 30.

Now, I'm just gonna mess around with a few numbers, but if I, if I say equals, look, look to the side here.

Can you see that we've got CapEx of 60.

So you could say, well, PP E is going up by 60. Not really.

I mean, the CapEx is replenishing pp e that's just worn out.

And maybe if CapEx is greater than depreciation, ignoring inflation, um, then we're actually growing it.

In fact, you could say if you take the, the CapEx and you net off the depreciation, you could argue that the PP e is growing by 10.

And you could say, but above you said we need that 3% was a 30, uh, growth of 30 million.

We've captured 10 for PP and E. Well, that's true.

Um, but we've also got growth in OWC.

Now that's a negative number.

And I think what, uh, I didn't write these materials. My colleague, one of my colleagues wrote these, and I think what she was trying to suggest here is that if operating working capital goes up, then cash goes down.

So this is the cash impact of the change in OWC.

So there's your 30.

So actually this, I would suggest to you as a casual observation that the increase in PP and e and the increase in OWC is consistent with a 3% growth rate when viewed relative to a thousand of invested capital.

So I think these numbers are actually gonna stack up really nicely.

Now, let me get a little bit more formal about what we're doing here.

I'm gonna, um, I'm gonna, I'm gonna answer the question.

So let's, let's chuck some numbers, proper numbers down here.

Okay. Um, so these are really easy.

From above, we've got notepad of 100.

So the notepad is our operating profit, but it's been tax adjusted at the ETR, we're gonna add back the depreciation and subtract the CapEx.

So that gives us some reinvestment.

Yeah, we've got reinvestment of 10 so far, and we've got the change in OWC, which is 20.

So now we've got reinvestment of 30.

If we thought that the long-term growth rate was gonna be 3%, and if the invested capital is a thousand, that means we'd need to invest 30 million increasing the OWC increasingly invested capital.

And that seems consistent with the increase in PP and e and the increase in o wc.

So these numbers actually work really nicely.

Uh, that means that our free cash flow would be 70 if you want to grow by 3%, then you will end up with an unlevered free cash flow of 70.

So there's nothing fundamentally wrong with these numbers, but it will be a little bit further forward.

So what I'm gonna do is I'm gonna calculate the terminal value.

I'll ignore this line on reinvestment rate at the moment because I'm gonna use the formula above.

So the traditional kind of terminal, terminal value formula is the free cash flow of 70, multiplied by open bracket, one plus the growth rate of 3% closed bracket divided by open bracket WAC of 8% minus the gross rate of 3%.

Okay, so I've got 1, 4, 4 2.

So traditionally that's how I'd calculate, uh, the, the terminal value.

But let's just cast your eye at some other information we're given here.

So let's grab a stylus, grab a different stylus here, and, uh, we have another formula below, which is, I'm gonna put a ring around in green.

Now, it, it's actually the same formula, but rather if I highlight in yellow rather than the free cash flow, the suggestion is that you could use notepad multiplied by one minus the reinvestment rate because they're the same number.

Now, the, the, the numbers we are given here in this example are really easy.

So hopefully that's quite obvious.

But look, the free cash flow is 70 here.

And rather than just go and grab that 70, what you could do is you could take the notepad of 100 and you could multiply it by one minus the reinvestment rate.

Well, what's the reinvestment rate? Well, the reinvestment rate, and I'm gonna go below now and fill this out.

The reinvestment rate is the sum of the reinvestment in absolute terms in the business, in the business, sorry, let me do this properly.

So the sum of that reinvestment in the business divided by the notepad.

So the reinvestment rate is saying how much notepad is getting sucked away to reinvest in the business before we get to un levered free cash flow? The higher the reinvestment rate, probably the more growth.

I mean, it, it feels like that's a natural thing for me to say. If you reinvest more, you probably grow faster.

Doesn't seem very controversial, but if you've got a high investment rate, you've also got less unlevered free cash flow. So there are some pros and cons there.

You know, high growth is good.

Lower unlevered free cash flow is bad. Okay? So I've got a reinvestment rate of 30%.

I actually think I'd quite like to show that positively.

So the suggestion is here, if you look at the ring, I put around this formula in green that rather than pick up the unlevered free cash flow of 70, I could delete that and I could grab the notepad and I could multiply it by, multiply it by open bracket one minus the reinvestment rate.

So a hundred multiplied by one minus 30% is 70.

So we should get exactly the same answer. Okay? So there's no difference here.

I'm gonna say that the reason we get the same answer is 'cause the person that the analyst that has built these numbers has picked a growth rate that is consistent with the amount of reinvestment.

And that's quite an interesting thing for me to say.

So if I scroll down, I feel just to expand, this is the same question, it's using the same numbers, but just to expand my understanding a little bit of what we're trying to show, I think that there is a connection between return on invested capital, reinvestment and growth.

And we don't have to do any maths on this to get our head around this.

So just linguistically, if you think about what I'm saying, if you have a business and I have a business and our businesses are almost identical, but if your business generates higher returns than my business and it chooses to reinvest more than my business, then it seems likely all other things held equal that it would grow faster.

It seems that you would grow faster than me if you generate more returns.

'cause that means you've got more surplus if you generate more returns.

And if you actively choose to reinvest more of those returns back into your business, you would stimulate higher growth.

So I just wanna formalize that bit.

I'm gonna say return on invested capital multiplied by reinvestment rate equals growth.

Now, I think these are brilliant numbers, uh, because the, the numbers will come together very nicely here. They're not my numbers. Uh, I, I would quite like to just before we sort of move further forward, no, may maybe, maybe we don't need to do that.

Maybe, maybe I'm gonna muck around with something here.

Look, do we know what the return on invested capital is? If you cast your eyes down this data, I'm not directly given return on invested capital, but if we go back up to my diagram that I drew earlier, if the invested capital is the PP and e and the OWC, the invested capital is the operating business.

So you might look at that and say, I'd, I'd love to calculate the return on invested capital, and it feels like the return on invested capital would be equal to profit.

I'm being very generic there divided by invested capital.

Let me just grab a stylist just to divide one by the other.

So you'd say, I think it's probably profit divided by invested capital.

The question would be, well, like what kind of profit would it be? I tell you what, it wouldn't be, it wouldn't be net income.

It really wouldn't because we are looking at the operational business.

So we need to pick up, we need to pick up an operational profit number.

Net income is affected by interest, income and interest expense. They relate to cash and debt respectively.

You can see on the diagram, they fall outside of that box.

So we want an operational earnings number and you know, um, operating profit could work quite nicely.

You could use that, but it's a dirty number.

And by that I mean that it'll have non-recurring items in it.

Uh, you could pick up EBIT and I think EBIT would be, would be okay.

I mean, it would be unusual, but you could use ebitda.

What would be most typical would be to used in notepad.

So typically when we look at return on invested capital, we take NOPAT over invested capital.

And if we, uh, scroll down, uh, to my, my thoughts.

So do we know the return on invested capital? I think my answer to that question is no.

But what I do have is notepad divided by invested capital.

Okay? So it's 10%. Um, and do we have the reinvestment? Do we have the reinvestment rate? Well, I can't really see the reinvestment rate here in the question, but these numbers are exactly the same as the previous question.

And in the previous question, we looked at the reinvestment in the business relative to the notepad, we came out with 30%.

Now check out these numbers.

I'm saying above return on invested capital multiplied by reinvestment rate gives you the growth rate.

Now look at the growth rate here, it's 3%.

What would happen if you took a reinvestment rate of 30% and you multiplied it by 10%? Well, let's see, growth.

So these numbers are, you know, are really straight, straightforward numbers.

So we get to 3%.

And what my colleague is trying to do is to say there is a consistency in these numbers.

The next workout, we're gonna break that, but there's a consistency here.

The analyst who built this, but this business has a return on invested capital of 10%.

They, they have invested capital of a thousand.

They have, uh, they have for the forecast suggests that they're gonna reinvest, uh, they're gonna reinvest, um, uh, 30 relative to noad of a hundred.

And so what that means is that we're gonna have, uh, um, uh, we're gonna have a growth rate if you multiply the return on investing capital by the reinvestment rate of 3%. And it just all works really nicely. I've got a question.

I'm gonna just, uh, I'm gonna read it as you know, I'm gonna say it as I read it.

Uh, how do you think about reinvestment rate for heavy, uh, infra businesses like regulated elect electrical industries? It's a good question where CapEx, DNA notepad is often near 200%.

Yeah, I mean, so, um, it, it is a, it is a problem.

Um, uh, yeah, it, I mean it is gonna be an issue.

Um, I think it becomes, um, a more difficult metric to use for businesses like that.

And so I think we're looking at kind of, um, you know, like, I don't know, regular kind of like manufacturing businesses or retailers or things like that.

So it does have its limitations. I'll concede that. Okay.

Right. Let's get, uh, let's get some numbers in here then.

So I don't think I'm gonna do anything very controversial.

I'm, I'm just gonna re-engineer some of the stuff that we've already talked about.

So, uh, let's do the numbers.

So, uh, everyone's gonna be happy, I think, to grab notepad of a hundred from above to grab depreciation of 50 in CapEx of 60, representing an investment of 10 million.

Everyone's gonna be happy with grabbing 20 as a, as an investment in OWC, and that definitely means that the unlevered free cash flow is 70.

I don't think anyone's gonna gonna blink at that.

The terminal value here, if I do it, just do it the very traditional way.

If I say equals, if I take the unlevered free cash flow, if I multiply it by one plus the growth rate of 3%, and I divide it by WAC minus GI can't remember what it was like 1, 4, 4 2 or something like that.

I think maybe, uh, it was, it was 1 4, 4 2 was the terminal value number.

So what we're gonna do is we're just gonna re-engineer that a little bit.

I'm not happy from the model, just grabbing the unlevered free cash flow.

I'd actually like to infer the unlevered free cash flow.

So I know the model gives it to me, but let's, let's not look at that.

Let's infer the unlevered free cash flow number.

So do I know the return on invested capital? Um, yet we've talked about that above.

So I've got NOPAT of a hundred and I've got invested capital of a thousand.

So it's 10%. And can we calculate growth over return on invested capital? Well, hang on a minute. Why would I do that? Because if you cast your eye to the side here, return on invested capital multiplied by the reinvestment rate is equal to growth, which we've proven below.

So I could rearrange that, right? I mean, I could move the, uh, I could move the return on invested capital to the other side.

So I'd have reinvest rate would be equal to growth over return on invested capital.

And actually that's what we're trying to show down here.

So my colleague says, Hey, why don't you go and grab the growth rate of 3% and divide it by the return on invested capital of 10%.

That gives you the reinvestment rate.

So I know it's not labeled as such, but that is the reinvestment rate.

So that is the required reinvestment.

Now, rather than in the formula, grab the unlevered free cash flow from the model.

Why don't we infer it? So you say you wanna grow at 3%? Yeah, well, we're gonna stick with that. We're gonna use 3% and we're gonna figure out how much you'd need to pump into the invested capital to hit, you know, hit your, your growth rate and therefore we're gonna figure out what your, um, your endeavor free cash flow would be.

And you could say, you know what it is, it's there, it's 70.

Yeah, but is that the right number? I mean, and we'll explore that in the next workout.

So I'm gonna, um, I'm gonna go back up to, well, let's escape.

I'm gonna go back up above and I'm just gonna grab my highlighter.

Um, here, I'm gonna grab my highlighter.

And we before said we'd not take unlevered free cash flow, but in the last, in the last up we said NOPAT multiplied by one minus reinvestment rate was a kind of an equivalent is equal to the unle free cash flow than, rather than grab the reinvestment rate, rather than grab the investment rate, reinvestment rate in, in place of that, we're gonna go grab growth over, return on investor capital.

They are just the same number.

Uh, what I'm gonna do is lemme just grab, lemme, lemme just screen grab that formula, it be useful just to maybe chuck that down here, paste that down here.

We don't need it to be quite that big. Okay? So that's the formula we're we're gonna use now.

So rather than the unlevered free cash flow number directly from the model, I'm gonna delete that and I'm gonna go and grab the notepad and I'm gonna multiply that by open bracket one minus three investment rate.

Well, I'm gonna multiply it by one minus growth over return on invested capital, which is given, um, which is given above, sorry, let me correct that.

So I'm gonna grab the, uh, notepad multiplied by one minus that reinvestment rate, close bracket, um, multiplied by now if I hit entry, come to the same number.

And that is because in this example, if I select those references, can you see contextually that comes to 70? So that is 70.

So we're, the model spits out 70 million and our, our analysis says that actually is gonna be 70 million.

So this all works. And now at this point you'd say, what is Jonathan really trying to prove here? Well, if we go onto the next workout, which is a similar idea, but they're different numbers, this is what I often see.

So if I'm reviewing some work that someone's done, you've built a DCF, you've done five-year DCF, and you've, you've attached the terminal value to that.

If you've got a five-year DCF and you've got the terminal value thereafter, when you look at the enterprise value, the, the, the, the, the terminal value component will probably be about 7% of your EV.

So if you screw the terminal value up, you'll profoundly impact your EV and your MO and your enterprise multiples off the back of that. So we really wanna get this correct.

Now, what I see people do, uh, very common to do this would be to build a model.

And in the model you're making assumptions on the growth in, uh, uh, in the amount of CapEx you need. You're making depreciation assumptions, you're making change in OWC assumptions.

So they come out with a certain cash flow and then arbitrarily totally disconnected from the model.

They'll go and grab a growth rate maybe from Felix and say, do you know what? I reckon that, um, I think business is gonna grow at like 3%. That sounds like a reasonable number, maybe 4% or 5%.

They'll go and grab that number and and apply that.

But I'm like, I'm thinking you can't just say that because that needs to in some way have a relationship with you unlevered for each cash flow, that growth rate you need. You know, if you grab a growth rate, then the model needs to, the reinvestment in the model needs to support that.

And, and it very, very often doesn't do that.

So let's have a, let's have a look here at some numbers.

Now we don't need to answer this question to know that something is wrong, okay? So just stare at the numbers with me and something is, looks very, very wrong here.

Now, the long-term growth rate is relatively high. That must be at the upper bound.

I mean, it's not crazy, but it's 5%.

Now I, I'm saying in my head, if you wanted to grow at 5%, I mean you, you'd need to, you'd need to have quite a lot of reinvestment, right? I mean, if you wanted to grow at 5%, that's quite aggressive.

So I think you'd need quite a lot of CapEx over and above depreciation.

You'd need quite a big increase in o wc.

So as long as we've got that in the model, then maybe 5% growth rate is achievable.

But let's cast our eye further down.

Now I've got NOPAT of two nine of 200 and I've got unlevered free cash flow of 190.

So in absolute terms, the reinvestment has to be to, I'll do it positively, has to be 10.

Yeah, because if you take a walk from notepad to unlevered free cash flow, the bit in the middle is your CapEx over and above your depreciation. You changing o wc. So they've got a reinvestment of 10.

Now it doesn't sound very much, but let's try and put that into some context.

Do we know what the invested capital is? It's a bit disappointing actually because I don't have at my fingertips the invested capital number here, but I do have return on invested capital and I do have notepad.

So if you think about it, if return on invested capital is notepad over invested capital, if you wanted to rearrange that, you could do so. Let's just write that out below. So return on invested capital, capital is invested capital over NOPAT.

Um, return on invested capital is NOPAT over invested capital.

Let's just show that there. Okay? So, uh, I know what return invested capital is, is, is 10% and I know what the notepad is, it's uh, it's 200.

So I can just flip this around to solve for invested capital.

So if I say equals, if I take the notepad and I divide it by the long-term return on invested capital, it's 2000.

Okay? So suddenly you're thinking, hang on a minute, if we were thinking about growth, you, you are gonna reinvest in absolute terms, 10 million into two, into 2 billion of invested capital.

I mean, it's a very small number that represents like represent half a percent.

So you're only gonna grow up by half a percent.

And we were saying here, you're gonna grow, grow by 5%.

And so something's not quite stacking up here. It doesn't really work. Let's try and formalize this a little bit. We'll try and get, get some numbers together. Okay? So, um, it says terminal values in the traditional growing perpetuity formula.

I think that's a good point of reference.

So let's say I've built the model and in building the model, I have really flattered the unlevered free cash flow by modeling in an unbelievably anemic amount of investment in cap in, in pp e and an unbelievably small amount of investment in o wc.

So the model maps artificially shows a really, really solid unlevered free cash flow number.

Um, so that's really great, but at the same time I'm saying, oh, and we're gonna get incredible growth.

I cannot, in my mind, reconcile those two things.

You can't get something for nothing.

You can't have 5% growth and make hardly any reinvestment.

Something's gotta break.

Either your growth rate has to come down or your reinvestment has to come up.

But they, you, you, you, you can't have, you can't have the best of both worlds.

So, um, using the, but we're gonna roll with what we've got now. If I built this model, you are gonna take the unlevered free cash flow in the final year. You're gonna multiply it by one plus growth rate.

So you, you've got what I think is an incredibly generous unlevered free cashflow number and you're multiplying it by an incredibly generous growth rate number.

And we're gonna divide it by WAC minus the growth rate.

Uh, Matt? Yeah, minus the growth rate.

I, I was thinking really it's a big number now I've got 3, 9, 9 0.

I don't like that. Okay? Uh, if I'm gonna highlight that in red, I, I don't like that number.

Uh, but traditionally that is exactly how I would calculate that.

And, and someone, if you were reviewing work, your own work or someone else's, you should look at the reinvestment.

It's really easy to do it.

And you should look at the growth rate and it should just tell you these numbers don't work together.

Now, what we're gonna do, it's my, when we look at that formula, I am, all right, I'm gonna roll with a growth rate of 5%.

I'm gonna go with that. Let's assume that that's okay.

What I'm gonna con what I'm gonna, uh, uh, uh, question is that unle free cash flow number, I I don't think it's gonna be like, uh, 190, you know, I think it's gonna be lower.

I mean if it was like, maybe let's just mess around with it. If it was 150 for example, then the terminal value would come down and that would represent growth rate of 2.5%.

And we're not there yet, are we? Like if it came, comes down to a hundred, I'm just playing around with it, it comes down to a hundred and then we've got five, we've got, uh, uh, we ultimately have 5% growth rate. And I guess what I'm saying is that you really need, you know, you really gotta be realistic. If you're gonna grow at 5%, which is what we're gonna go with, then you have to, you have to accept that you're just not gonna get the cash outta the business that you've modeled at the moment.

Let's go backwards a little bit. Let's just put that back.

So what I'd, uh, what I'd like to do is do the terminal value using the value driver formula.

So I'm gonna say cause and we're gonna use, can I just grab that from down here? Just move that down a bit. It'd be nice to see it on the screen.

I mean we don't have to, but just so you can see what we're doing.

Okay, there we go. So we're gonna use that formula that we've, we've, we've kind of derived, so if I say equals, I'm gonna get the notepad of 200, then I'm gonna multiply it by open bracket, one minus the, and I'm gonna have to open a bracket again, the growth of 5% over the return on invested capital.

So that, and I'm gonna close the bracket again.

So that basically says you've got NOPAT of 200, but we're gonna multiply it by one minus the, the, the growth over the return on invested capital.

Uh, and and is that number gonna be 190? No, no, it's not, it's not gonna be 190.

And that's the point. So if I then multiply that by open bracket one plus the growth rate, so I'm basically gonna roll with a 5% growth rate and divide it by wack minus the growth rate.

The problem is I come out with a very, very different terminal value and that's gonna profoundly impact the EV and the multiples overall.

'cause it's maybe about like 80% of the total valuation.

Now I'm gonna green light that because I would say that is the right nu check for you to perform.

You should do that in any DCF that you, you you create and uh, and you just play around with some numbers.

I've done some messing around at the side here to kind of like solve for the growth from the reinvestment, uh, that, that has been planned in the model.

We can do that below as well.

So, uh, I could uh, you know, go and grab for example, go and grab the net reinvestment, which is ridiculously low.

I think we're just covering stuff we've already talked about, which is 10.

I can go and get the invested capital in the terminal year, which is the notepad over the return on invested capital.

And then I can get the implied growth rate. So 10 over 2000.

So it's half a percent. Okay.

Um, got a, just another question.

How should you think about the increase in deferred tax liability from perhaps, uh, bonus depreciation when, uh, comparing the notepad free cash flow in out three? Uh, so how should I think about the increase in deferred tax liability from bonus depreciation? I'm not, uh, I'd probably need you to clarify that 'cause I'm not quite sure what you mean.

So we'll definitely have like a DTL impact for, uh, depreciation.

Do you mean like when tax depreciation? I think you mean like when tax depreciation, uh, is different from accounting depreciation? I think that's what you mean. Um, actually I, I think I get that.

Um, so we are, what we are doing here is we're, we're taking a fairly broad approach.

We are assuming that the depreciation, which if I go backwards, the depreciation, uh, that is baked into the numbers, work out one and work out two, we are assuming that those are the cashflow numbers as well, like the, the add backs.

So we're assuming that, uh, the depreciation expense from an accounting point of view, um, is gonna get added back to get to those cashflow numbers.

And there they can be variations obviously if you've got deferred tax.

But, uh, that is not gonna make a big, I mean it's not gonna be hugely material.

Um, for, for our purposes in our, in our DCF and it's a little outside of the scope, I don't have any particular materials on that right here, but there is some great stuff on uh, DTL, um, in, in Felix.

So I shall leave you to have a look at that.

Okay, we've got about 20 minutes left and there's a couple of other things that I wanted to grab a look at.

So, uh, I'm gonna go down to the next workout workout for, we won't get all the workouts done, uh, in this, but I really wanted to look at workout four.

It's a totally different topic, okay, but it still relates to DCF.

So one of the things that maybe makes a DCF model more complex for me when I'm looking at maybe a model on the desk is dealing with stub periods.

And so we've got a valuation date and we've got the, the cashflow date.

And typically what a model will do is it will, uh, it will be built in such a way that we could change the valuation date one way or the other.

And the, um, the discounting would change around that.

And it could be quite complicated to see the detail of really what's happening there.

And so rather than look at a big model, what we've done is we've distilled that idea down into a workout.

So it says an analyst has prepared the following full year forecast, use the assumptions and data provided below, devalue the company at the 30th of June.

Assume that the end, end of period discounting is being used and assume cash flows fall at the end of each period.

So it looks like, from the numbers we've been given, it looks like the valuation date here is the 30th of June.

It's 2022, actually 30th of June, 2022.

And it looks like the first cash flow is going to occur on the 31st of December, 2022.

So that's, that's like six months, right? To get back to the valuation date, we've got another cash flow on the 31st of December, 2023.

That's about 18 months.

And we've got the next cash flow at the end of 24 and the next cash flow at the end of 25.

So what I'd quite like to do is build a model that is not using mid-year discounting.

We, we've not made it that complicated, uh, but what the model does is it takes the cash flows at the end of the period and it discounts them back to the valuation date.

I'd also like to build a model whereby I can change that valuation date to say 31st of July or the 30th of November.

And the, the discounting will work appropriately.

So let's try and build something out. We've got some cashflow numbers here, uh, that occur at the end of each year.

And so, um, we're gonna think about the cashflow dates.

So in this example, the cashflow date is just the same.

And I'm gonna show some formulas here.

The cashflow date is just the same as the dates we've got above, uh, the free cashflow forecast dates, we're gonna drop those down.

Now, in terms of days of discounting, it doesn't look like we have to wait a full year for that first end of year cashflow.

It looks like we have to wait for about half a year.

So what I'd like to do is I'd like to figure that out.

If I say equals, I'm going to go and grab the end of the period when the cashflow occurs, which is in C 89 30 1st of December, 2022.

And I'm gonna subtract from that the 30th of June, 2022.

I'm gonna press F four to lock that because we're gonna copy this out to the right and I always want it to make reference to our valuation date.

So we've got 184 days, apparently that red line, that red arc I've drawn is 184 days.

What about the next arc I've drawn? Well that would be five, five hundred and forty nine days.

And then if we copy that out to the right 915 and 1,280.

So that tells us how many days we've got away, not because we're using midyear discounting at all because we're not, but because that is when the cash flows come in relative to the valuation date, it might be quite nice to have a year count.

So I'm gonna grab that number and divide it by 365 and I'll copy that out to the right.

You can see the formula on the right hand side.

So we are not using midyear discounting, but we've only gotta wait half a year until the end of the year.

So what's the discount factor? Well equals one over open bracket one plus the wack.

Let's press F four to lock that close bracket raise to the power of the appropriate year count.

Okay? Now it sounds a bit like if we buy the business later in the year, it's a good thing because the, the first cash flow is received nearer to us it sounds like that's good.

So we should buy it later in the year, but there has to be some negative there.

Now if we assume that the cash flow is, uh, if we assume that the business is accruing, you know, cash throughout the year, and if we buy it halfway through the year, we are only gonna get the earnings post acquisition, which if you work that through your model, we're only gonna get the cash post acquisition.

So what we wanna do is, and I'm gonna color this in, I dunno, maybe yellow or something.

Um, and I'm gonna, I'm gonna put a formula here next to this so you can see what I'm doing.

So what we wanna do is we wanna think about how much cash are we gonna get if we buy on the 30th of June, 2022.

If I cast my eye up to 1050 6.1, that's a good starting point, but that's not the cash we're gonna get 'cause we're only gonna get cash post acquisition.

So I'm going to take that number and I'm gonna multiply it by 184 days and I'm gonna divide that by 365.

So that means that we'll get 532.4. We'll get basically half right of the, of the cash. That's the back end of the year post acquisition.

If you buy the business on the 31st of July, you'll get a bit less.

If you buy the business on the 30th of November, you'll get much less cash.

So there are some pros and cons here.

If you buy the business on the 30th of November, then the first cash flow is gonna be received quite close to the valuation date.

On the other hand, you'll only get a couple of, uh, you only get one month, one 12th of the full cash flow for the business post acquisition.

Uh, right. So let's skip over the terminal value. We can come back to the terminal value in a minute.

And let's, let's go down to the present value of the free cash flow.

Well, in the first year, we've got the five through 2.4 every subsequent year.

We of course have the full year of cashflow.

So it doesn't matter when in 2022 you bought this business in 2023, you'll have owned the business for the full year and you'll get the full cashflow.

And that'll also be true of 2024 and 2025.

So to calculate the present value of the unle free cash flow, I'm gonna take the discount factor and I'm gonna multiply it by the, um, appropriate cash flow.

So in year one, that's in C 93, but in every subsequent year I'm gonna take the discount factor and I'm gonna multiply it by the numbers in row 87, 'cause we're talking about full year.

Okay, we probably should do the terminal value.

And we had a really good discussion on terminal value in the last exercises that we looked at, and that's still completely relevant, but it's for simplicity, we're just gonna ignore that.

We'll assume that in this model, the reinvestment rate, the return on invested capital and the growth are all consistent.

So we are absolutely good using a traditional approach here to calculating the terminal value.

I'm gonna say equals I'm gonna grab the unlevered free cash flow in the final year.

I'm gonna multiply it by one plus the growth rate.

We are given 3% close bracket and I can divide it by the whack minus the growth rate.

And so just very much a standard approach, I've got, uh, 25183.5.

So if we bring, uh, maybe bring that to the present value, I've got the terminal value hanging out in that final year, I'm gonna multiply it by the discount factor and then the enterprise value would be the sum of these numbers.

Let's show the formulas here so we can see what we're doing.

And that's a ultimate answer.

So if we changed our valuation date from say, the 30th of June to the 31st of July, 2022, and I haven't hit enter yet, but when I do hit enter, you are gonna see, I mean, I guess you won't see it, but you can imagine this red arrow is gonna move slightly closer to those Xs. So there'll be less days of discounting and that's gonna be a really good thing for the valuation.

On the other hand, you'll see the 5 3, 2 0.4, which is the cash we receive post acquisition.

You'll see that number come down a little bit because we're gonna buy the business a bit further forward through the year.

Okay, so what, ultimately, what impact will that have on the, on the enterprise value if we hit enter here, you can see that the un unlimited free cash flow has come, uh, has come down a bit in year one.

You can see the discount factors are less aggressive because we're, you know, we're nearer to, they're nearer to the valuation date.

And if I control Zed and control why that, that's had a small impact on the model.

But the point is that we've built a model where we can sensitize the valuation date and the model will work around that.

That's a very typical thing to do.

But I think when you're looking at a more comprehensive model on the desk, it's more difficult to see how that's really functioning.

I'm gonna change the valuation date to the 30th of November, 2022, just to see that a little bit more profound.

So the, if I hit enter here, the unlevered free cash flow is gonna come down, but these discount rates are gonna, these discount factors are gonna be less aggressive.

Let's hit enter. So actually they've got very little cash coming in in the final year, now only one 12.

Um, but their discount is less punishing.

So these numbers tend towards a hundred.

And if you look at the enterprise value control Z, control Z, control y, control y, you can see that being animated.

Okay, we don't have a huge amount of time left, but we've got at most 10 minutes and there's another exercise I'd quite like to have a look at.

So if we scroll forward to workout six, I'd really like to have a look at workout six in closing.

And we're gonna look at WAC here.

Now, I think it's really important to say that when you have A-A-D-C-F, you'll have a forecast. Let's assume it's a five-year forecast, and then you'll have, uh, beyond that you'll have the terminal value and you're gonna use the WAC to discount all of those cash flows.

So it seems to me logical that the weighted average cost of capital you apply should be representative of the long run cash flows, the target, uh, capital structure of the business, um, because you might have a situation where the business has a peculiar amount of debt or a peculiar amount of equity right now.

And I don't think that that would be the right way to think about discounting those forward cash flows if the current capital structure is an anomaly.

Let me show you something real on this.

So I think we've got time to do this and I, I think this would be a nice thing to look at.

So if I jump into Felix, and I'm gonna look at the beverages industry, so we'll just have a quick look at Coca-Cola.

I'm gonna go to the valuation sheet and if we scroll down and look at the comps here, we've got Coca-Cola, PepsiCo, monster Beverage, et cetera.

Now look at Monster Beverage.

If you look at the debt to capital, it is zero.

So if you are gonna build a DCF, what are you going to use for the DCF is your, because they've got no debt, is your wac, is your WAC gonna be what? Just their cost of equity? Are you seriously gonna discount their cash flows in one year's time, two years time, three years time, and terminally thereafter, uh, at uh, at the cost of equity? I mean that would, you could do that, but you would have to be supremely confident that in the long run, and I mean over like a thousand years and beyond that monster will always be only equity finance.

I don't think that's true. You could say, well, well what do you think the capital structure would look like? I don't know what it might look like, but I could take a guess.

If you look at the most mature businesses in the sector, which is Coca-Cola and Pepsi, Coca-Cola's got about 12% debt to capital and Pepsi's got about about 18%.

So somewhere between 12 and 18% would be a decent assumption as to where the long run capital structure would be.

So I would use the target capital structure when I'm doing discounting, when I'm, when I'm arriving at the wac.

Now that's an idea and it really kind of informs some of the thinking around this question.

So, um, it says, can you calculate the whack for the below company, assuming there are no financial assets in the target capital structure.

And assuming f financial assets are fi uh, are 5% of EV in the target capital structure and debt remains at 40% of EV Let's, let's make this more obvious.

Let's say asset equals liability plus equity.

And I'm gonna have some market value numbers, I'm gonna draw some boxes.

They might not, they won't be quite to scale, but they'll just, just a diagram.

So lemme just draw a few boxes here and we're gonna put a box in for cash, although I'm gonna have it as zero.

Um, but I hope that won't be misleading.

Uh, so let's just chuck a few boxes in. There we go.

Let me label them up. So I'm gonna have debt, I'm gonna have equity.

This is market cap, these are market values.

I'm gonna have cash, I'm gonna have EV and we're gonna add this together.

Now in the question, we're not given a number for EV and it doesn't really matter.

I'm just going to put an easy number in.

So just imagine that the EV is a thousand.

I'm being told in the question that the debt is 40% of the EV and I'm being told that the cash, what does it say? Assume there are no financial assets in the target, capital structure is zero.

And so that must mean that the equity is the enterprise value plus the cash minus the debt, but the equity is 600, okay? And there are costs associated with these. So there's a cost of debt, I'm gonna say post-tax.

So post-tax, the cost of debt is 3.5% multiplied by one minus the marginal tax rate.

So that's, I'm gonna zoom out slightly just so we can see everything on the screen. That's 2.8% and there'll be a cost of equity.

And the cost of equity appears to be 9%.

And there's a, I'm going to do this above. So there's return on financial assets, which if we do it post tax is actually quite high.

Uh, so right now it's 6% and that's maybe quite attractive. There's an argument you should borrow money and be investing it if your borrowing is cheaper than the investment, but that can't be sustainable in the long run, right? That just doesn't make sense economically.

But let's roll with that. So I'm gonna multiply that by one minus the tax by open bracket, one minus the tax rate as well, which is 21%.

Okay? So, um, that's 4.7%.

Okay? And then we've got our EV I don't know what the return on invested return on invested capital would be.

It, it doesn't really matter. Um, I dunno. Let, let's say it was like 12%, I guess let's make something up.

So let's say it's 12%.

So, um, at the moment in this example, we don't have, I know I've got it in the diagram, but we don't have any cash.

So can we calculate the WAC in the target capital structure? The WAC calculation should be pretty easy.

So I could say equals I can get 9% and I can multiply it by open bracket one minus 40%.

So if you look at my diagram, that's 9% cost of equity multiplied by 600 over a thousand.

Okay? So it's 60%.

And I'm gonna add to that the cost of debt, which I should tax adjust.

So multiplied by open bracket, one minus the tax rate of 21% multiplied by 40%.

So we've got a whack as a sort of benchmark of 6.5%.

And then the question is, we are thinking about the long-term target capital structure.

Is it reasonable in the long term that the business would hold cash? And you could say, well, there's a benefit there, there is a benefit there.

If they hold cash, they're gonna get 4.7% return on it. That's good. Okay? But do they really wanna do that in the long term? Because if they had load of cash, wouldn't they be better off investing it in the operating business to generate 12% in the long run? Or if they couldn't do that, wouldn't they be better off using that cash to pay down? Maybe not debt, but pay down equity, okay? Pay down equity, which is more expensive.

And that's the kind of idea we're gonna think about.

Now in the diagram, uh, it says here, imagine the company has 5% cash relative to its EV.

So if I take that 5% and I multiply it by the EV, um, we know that the debt remains at 40%.

So the the, the question is, should they hold cash, which returns 4.7% and finance equity, which would, which which costs them 9%? The obvious answer is no, but let's just prove that.

So if we go into the EV calculation, I shall redo it.

So I'm gonna go and grab the, um, cost of equity, uh, which is 9% and I'm gonna multiply it by open bracket.

Now, let me get this right, I'm gonna multiply it by um, uh, one minus 40% plus 5%.

So that should be what, 65%, which is what we're seeing here, 650.

I'm going add to that the cost of debt, which I'm gonna multiply by one minus the marginal tax rate. And I'm gonna multiply that by 40%.

And now it's probably true that the, uh, the EV doesn't have to do all the heavy lifting here because what we do have is we have cash, which is providing us a return.

So it's gonna take a bit of, bit of slack away from the whack.

So if I say minus, and I'm gonna go and grab the 6%.

So I've subtracted this 'cause this is taking some of the weight off of the, off of the wac, uh, multiplied by one minus the tax rate.

And I'm gonna multiply that by, and I'm gonna multiply that by the 5%, now it comes out at 6.7%.

And what this, and I've got a minute left and what this is trying to say, it doesn't make sense in the long run for a company to hold a meaningful amount of cash, it might hold a very immaterial amount of cash to absorb fluctuations in networking, capital, operating working capital, but a meaningful amount of cash, it doesn't make sense.

And we could say, well, what if you say hold like 20%? If you hold 20% financial assets, your WAC goes up.

And so when you think about the wac, think about the target capital structure and keep it simple.

They're gonna hold some debt, they're gonna hold some equity, and they're probably not gonna hold anything else in the long run.

Okay. And that absolutely, as I look down the, the clock has struck the hour, so that's the end of the session.

But guys, thanks so much. We had massive numbers on this. This is probably one of the best, biggest Turnouts we've had, I think, on anything I've run on these sessions.

So thanks so much for everyone that dialed in. It's been really, really good. Um, and uh, I look forward to seeing you in other sessions.

Have a fantastic Friday. Cheers guys.