Hey guys, welcome along.

Thanks for joining. We still got people joining.

My name's Jonathan great to have you on the call.

I've got that open already, so let's jump into that.

When you land on that page, it opens up to that file, it opens up to the welcome sheet.

If you could go to the workout sheet, that'd be brilliant.

So I'm gonna click on the workout sheet, or control and page down if you want the shortcut.

Okay, so we've got an hour together, and, in the hour we're gonna talk about various DCF related topics.

So there are this file contains a number of things that we'll see how we get on, but we'll try and get to, so in the first instance, uh, the first, I think it's three workouts, talk about the terminal value calculation.

And the classic way to calculate that would be to look at a growing perpetuity.

So we would, we would pick up a growth rate, and we're gonna ask some, some pretty serious questions about the growth rate that we're gonna select and whether or not that's supported by the assumptions that might exist in a model.

It's actually a really great set of workouts. We've got several workouts on that.

And then if I scroll down thereafter, we're still on advanced DCF, but it's a different subject.

We're going to look at st stop periods.

So we're gonna build a DCF and say, well, what if you didn't buy the buy a business? Or you don't wanna value the business exactly at that business' year end, which I think is quite a likely thing, but perhaps you want to buy it, acquire it, value it partway through its year.

How would you account for that in the DCF calculation? And at that point we're gonna say, well, in the first year, you're not really gonna grab an entire year's worth of cash flow if you're valuing it partway through the year.

You only look at the cash flows post, post that period.

And I guess that's bad.

But we'll also think about the fact that well, if you buy it partway through the year and the cash flows are received, you know, at certain points in the year, perhaps you don't have to wait quite as long to get the first cash flow.

And that's good. And we'll, we'll try and figure out what impact that makes on the valuation.

We'll, also scrolling down, we're also gonna have a look at WACC.

So weighted average cost of capital is such a massive input into the EV calculation that comes off of the discounted free cash flow.

But it seems worthwhile taking some time to think about maybe some of the nuances therein.

And then if we scroll further down, we've got more, more, more work here more workouts on summer parts valuation.

So we're gonna see how we get on, we'll try and get through as many of these workouts as we can.

We are not gonna get through all of them in an hour, but if we can just get the main themes, that would be, I think that would be great.

So as I've been chatting away a few people have joined.

If you've just joined, welcome along. My name's Jonathan.

You haven't missed anything at all. We haven't really started yet, but it would be fantastic if you've just joined.

If you could jump onto this web address, I'm about to chuck in the chat box.

So if you can go to that web address.

And on the bottom right, there are some files to download.

There's a file called Advanced DCF valuation Workout Empty.

If you can click on that to download it, once that's downloaded, you'll land in a file on a page that looks like this.

If you can go to the workout sheet, and I'm about to kind of crack on with that now, right? So first workout when we think about the terminal value, and I'm gonna grab a highlighter here.

So when we think about the terminal value, there is a traditional formula that we might typically select, which I'm highlighting in blue, which is to say, well, to get the terminal value, we get the free cash flow in the last forecast period, and then we multiply it by one plus the growth rate, and we divide it by WACC minus the growth rate. So we've got a growing perpetuity formula there, and you can see the reference to the growth rate there.

And you might say, where does the growth rate come from? Well, I'm not an economist at all, but I would usually look in, Felix might look in Bloomberg or FactSet or CapIQ, but I'd look in Felix and I'd go and find some sort of long term growth rate that I could apply.

And usually it would be the forecast GDP growth rate.

And you're probably gonna select something like 2% or 3%.

And my issue there is that, how do I sense check that? So, you know, how do I know if I picked say, 3%? How do I know that that's, that's the right number to select? Because it seems like a kind of like a, you know, like a macro kind of thing. And you know, how, how can I, how can I check that? One of the things you can do is you can check it against your, your model.

So I'm gonna, I'm going to show you some numbers to support this because we can do this in maths.

But I wanna explore the idea that the reinvestment in the business must have a relationship with growth.

Now, if you just think about that in a very narrative way, that's not a very profound thing to say.

Is it the reinvestment in a business must impact that business's growth.

I.e. if you have a business and you undertake a very, very small amount of reinvestment, if you hardly invest in the business at all, you couldn't reasonably expect it to grow, could you? Conversely, you might take a business and say, we're gonna perpetually invest very generously in this business.

And if you're gonna invest very generously in that business, you an, you would anticipate a higher long-term growth rate.

So in a narrative way, it feels like there must be a relationship between, between growth and reinvestment.

Let's think about reinvestment in a little bit of detail here. So we, we have got some numbers, which is kind of useful.

Let's just zoom in a little bit.

So we've got a, an imaginary business, it generates some notepad and I'm just gonna show you my formula so you can see what I'm up to here.

Just chuck a few formulas in.

So we're gonna, we're gonna start with notepad.

Let me go and grab that up here of 100.

And then I wanna come down to free cash flow.

I might call that unlevered free cash flow.

It's called free cash flow here.

So I could say, do you know what the free cash flow, the cash flow of the business and the profit, the nopat are the same.

And you might say, really, Jonathan, are they really gonna be the same? And I'd say, well, okay, maybe not, because for one thing, let's look at the change in operating working capital.

If I say equals, we've got here some numbers change in operating working capital minus 20.

So perhaps when you look at profit, what profit doesn't capture is an increase in inventory and an increase in accounts receivable, which sucks cash out the business, right? All other things held equal inventory up, cash down, uh, accounts receivable up, cash down. If you're offering more credit, that's not cash in your, in your pocket.

So that sucks. Cash out the business, perhaps tempered slightly with an increase in accounts payable.

So here we've got minus 20.

So we're saying, you know, in these assumptions we're saying that the business' growth there is apparently we're assuming it's gonna be 3%.

And I'm saying, well, in order to make that growth happen, we need to invest 20 million buying more inventory and offering more credit to our customers.

So that sounds like a, a reasonable thing to say, you wanna agree your business, the business is gonna need more inventory to grow.

You might also say, well, okay, when we're looking at operating working capital, we are dealing with current operating assets and liabilities.

What about the non-current operating part of the business? And I'd say, well, sure, you know, if the business is gonna grow, then you'd probably need to grow your PP&E as well.

So for example, if you're a manufacturer, you'd need to grow your inventory and you'd need to grow your manufacturing equipment, your machinery.

If you're a retailer, you need to grow your inventory and you'd need to grow your property.

because you'd probably have opening be opening new stores.

So the idea of buying more operating, working capital, investing in more owed more PP&E, but they seem quite natural things that a business would do to make growth happen.

Now you could say, great, let's go and grab the CapEx, then X is 60, you could say. So is the PP&E is it growing by 60? Not really.

I mean the 60 million of CapEx part of that is just replacing machinery, PP&E that's already worn out.

So you might call that maintenance CapEx.

And anything over and above the depreciation would be genuine growth.

So let's go and factor in the depreciation.

I guess what we're saying is that we've got a business that generates today nopat of 100 million.

We're expecting going forward, we're expecting it to grow by 3% and to make that growth happen, we're investing 20 million in operating working capital.

And if I grab the net here for the PP&E we're investing 10 million in PP&E.

So we end up with a free cash flow of 70 at the end of it.

You could in fact say, well, let's, let's just look at some, some numbers here.

What sort of reinvestment are you making in the business then? Yeah, sure. I mean, in absolute terms, we reinvesting 30 million into the business and we might say, well, let's look at that as a percentage.

So what's the reinvestment rate? Well, the reinvestment rate would be the sum of that reinvestment.

So, alt and equal, hold down or tap the equals sign to go and grab some function by cursor sitting inside the bracket there. So I'm just gonna press F2 arrow, right F2 again and I'm gonna divide that by nopat.

So I'm interested in looking at the, the reinvestment you make in the business as a rate relative to the profits that have been generated, how much those profits have been reinvested.

I'm gonna show that positively. So I'm gonna multiply it by minus 1.

So we've re really easy numbers.

We've reinvested 30% of our nopat into the business and, and then we're gonna calculate the terminal value.

Now, I reckon there are a couple of ways we can look at terminal value.

I'm just gonna grab my highlighter here in the first instance.

We can, if you refer to the formula above, um, you know, we can calculate terminal value in a very traditional way.

So we can say equals, why don't you take the free cash flow of 70, why don't you multiply it by one plus the growth rate of 3%.

And why don't you divide that by the WACC here is 8%, minus is the growth rate, it's 3%. So there's nothing very controversial about that formula.

That's just a kind of classic terminal value formula. I've got a comment there. Does negative operating working capital mean we get more cash available? So you have to add 20 instead of subtracting it.

I think in this instance, the intention here is I'm going to, it says change in OWC and maybe it's not very clear.

I'm gonna say increase, decrease in OWC.

So we are looking at cash impacts here. If you think about CapEx, CapEx is shown negatively.

So that means PP&E is going up because you're doing CapEx and cash is going down.

If you look at operating working capital, again, we are, we are definitely looking to be consistent at the cash movement here.

So if operating working capital as an asset was becoming bigger, then cash would be going, would be going down.

So I take these, I take the these to be both looking at this in the cash flow perspective to be consistent.

So I would suggest that's an outflow and, and perhaps the word change isn't very clear, so I'll call it increasing bracket slash decrease.

Okay? So we can look at the terminal value formula in that way.

But the thing is you could say, well what if the growth was like, imagine this, what if the growth wasn't 3%? What if it was 5%? And if I hit enter, you could say, well, the terminal value would be worth more.

No, that for me, that doesn't work.

Okay, well, I mean it might be worth more, but, but that you, you, you can't grow for free.

I think I quite like that term of phrase can't grow for free.

So look, if you're say you're gonna grow at 3% and we had free cash flow of 70 million, if you said, oh, no, actually I think we can grow at 5%, I would say, well that's great, you're growing faster and you know, that must make the terminal value worth more from that perspective.

But if you're growing at 5%, how can you expect to have a reinvestment of 30%? Surely if you're growing more aggressively, then you would need to buy more PP and e and you'd need to buy more OWC and see you'd have a lower free cash flow.

I mean they, it feels like those two things must be related.

And I haven't captured that because I've just grabbed that 3%.

Let's maybe we'll just explore that.

I was going to jump down and, and answer row 26 here, but perhaps we just sort of explore that as an idea.

So if I say to other side and you're gonna create some rough workings, if I say, why don't you grab the invested capital 2000 and why don't we grab nopat, which is a hundred.

So if you looked at notepad relative to invested capital, so if I looked at nopat and divided by invested capital, I get return on invested capital.

Return on invested capital, okay?

I'm going to look at nopat and perhaps this will be a little bit circular for me to do this, but if I grab a return on invested capital and I multiply it by the invested capital then I, I I get back to nopat, of course I do, let's just share some formulas here.

And if I go straight to just cut this down, if I go straight down to free cash flow, which from here is 70, then you might refer to this as the reinve reinvestment.

So 70 minus 100 is minus 30.

And then from that, of course you can calculate the reinvestment rate, grab that from down here, which was 30 over 100 by minus 1.

Okay? And I'm interested in, in growth being, I just feel like, and maybe you feel like this as well, looking at this, I just feel like there must be some sort of relationship between return on invested capital and and reinvestment.

I just think if the reinvestment, I think if the reinvestment went up, if a business chose to reinvest more, it should get more growth.

And I feel like if the business had a higher return on invested capital, then uh, it should also, have higher growth.

You know, can you imagine if you had a higher return on invested capital? You've got more notepad, you flow that through, you've got more cash flow, okay? So you could grow more as a consequence of that.

And the growth theory is 3%.

And these numbers, I didn't write these materials, but I like these materials a lot.

If you think these numbers have been designed to be fairly easy for us to deal with, so just look at that, the growth is 3%.

In fact, if we take the return on invested capital and the reinvestment rate, we get to that growth rate.

And actually as we explore this over the next few workouts, you'll see that there is a relationship there.

If a business say, say a business didn't have return on invested capital of 10%, but generated return on invested capital of 15%, then it's got more nopat which it can turn into more unlevered free cash flow and will grow faster, right? You know, it will grow at a faster rate, it grow 8%.

If the reinvestment rate let's just put that back.

So if the reinvestment rate wasn't, if it wasn't minus 30, but if reinvestment was say, minus 50, yeah, we're reinvesting more, then it can grow more.

So a business that can generate higher return on invested capital and reinvests more into itself can generate higher long-term growth.

Now let's just put that back.

What have we got to kind of complete the circle on this? What have we got in this formula? So I'm gonna grab a different highlighter. We're gonna go for green or something maybe.

Yeah, let's go for green. So we've got another formula here.

And it says the terminal values, which noad multiplied by 1 minus 3 investment rate multiplied by one plus G of WACC minus G.

And it occurs to me that notepad multiplied by 1 minus 3 reinvestment rate is the same as three cash flow.

That's the same number.

Nopat of 100 multiplied by one minus the reinvestment rate of 30.

So no pap multiplied by one minus 30%, no pap multiplied by 70% is 70.

And that's free cash flow. So we could we can calculate that here.

And I think when I'm doing the, the calculation for terminal value, I probably prefer to at least think about reinvestment in the formula that this isn't the kind of final iteration of the formula I'd want to use. This is sort of a stepping stone to a slightly more all encompassing formula, which we'll use in the next workout.

So if I say course, I wanna get the terminal value further green highlighted thing here, I'm gonna go and grab a nopat of 100.

I'm gonna multiply it by open bracket, one minus the reinvestment rate of 30% close bracket that gets me unlevered free cash flow.

I'm gonna multiply it by one plus the growth rate of 3% over open bracket, the WACC minus the growth rate.

Okay? And oh, and it would be useful of course if I put the bracket in the right place.

There we go. 1,442. So we get to the same number. You might say which one's better.

I would say the one we've got in green, thinking about reinvestment is probably a, is a good idea, but we're not really done yet with this.

So what I'm gonna do is I'm gonna scoot forward and if we look at workout two, I'm gonna try and keep that on the screen.

If we look at workout two, it says the terminal value formula from the previous workout was written as notepad multiplied by one minus reinvestment rate multiplied by one plus G over WACC minus G.

It was indeed, but it could also be written and we'll need to explore this as notepad multiplied by one minus growth over return on invested capital, multiple one plus G over WACC minus G.

So what we're saying here is that the reinvestment rate, I'm not sure if purple is a good color to use given the highlighting, oh no, it's okay, is equal to growth over a return on invested invested capital.

We've kind of done that above, but let's just do that again.

We're saying that the reinvestment rate is equal to growth over return on invested capital.

That is what that substitution there is saying.

And I think that probably is true.

So if we said, if we said equals and from the previous workout or even this workout because of the same numbers, grab the growth and if we grab the I don't actually don't actually have the return on invested capital, but if I return on invested capital, I can calculate that.

So I'm gonna go and grab the growth turn.

I can go and get the return on invested capital, which is nopat over invested capital or hp.

And if you said, I'd like to calculate the reinvestment rate, share the formulas here, the numbers are the same as in the previous workout and are pretty easy to deal with.

Second, oops, good bunch of workouts here.

So if I said growth per above over return on invested capital, I get to reinvestment there, there's definitely a relationship between the two.

If you are gonna grow the, put it this way, if you were gonna grow not 3%, but you said I'm gonna grow at 5%, you would need to reinvest more in the business to make that happen.

You'd need to buy more inventory, you'd need to buy more PP&E. That's not a very radical thing to say. Is it? If I said, well if I said your returns on invested capital isn't 10%, but it's gonna be 15%, then you don't need to reinvest as much, right? Because if your return on invested capital is higher, that means your nopat is higher.

You still gotta invest the same amount absolute terms to grow the business, but it becomes a lower percentage of your higher nopat number.

So there is a, I think hopefully a fairly logical relationship between those.

So we're going to use this formula next then the one that I've highlighted in pink to really come all the way down to here.

So if I grab my stylus down here, we're gonna try and get to that cell.

Let's put some formulas in down, okay, same numbers as before then.

And let's just put those in bold.

So exactly the same narrative for me as before, hey, we've got no path of 100 and maybe our unlevered free cash flow is also 100.

I don't think that's likely because you're telling me you wanna grow at 3%.

So we're gonna pick up the increase in OWC cash outflow.

We're gonna pick up the CapEx, the increase in PP&E cash outflow.

We're gonna add back the depreciation, which is a non-cash amount to come to 70.

The return on invested capital is nopat over invested capital.

So that is literally the return on that invested capital.

And then we're gonna look at growth over return on invested capital growth 3% turn on invested capital is 10%.

We've got the same numbers as we messing around at the side here.

So if you think about the formula above, the terminal value is equal to notepad.

Now, hang on a minute. The terminal value formula needs unlevered free cash flow.

Yeah, right? So to get to unlevered free cash flow, we need to take the notepad and multiply it, the 1 minus 3 reinvestment rate and instead of the reinvestment rate, what we could do is we could take growth over return on invested capital.

So you could say multiplied by open bracket 1 minus.

So I now want that reinvestment rate, which is growth over return on invested capital.

So I'm gonna go and grab growth of 3% over return on invested capital of 10%.

I guess it could have just grabbed that cell there.

Close bracket, close bracket multiplied by open bracket 1 plus the growth rate of 3%.

So what I've done here in the numerator is if I grab those cells, it even tells you the number there contextually.

Can you see that? It says 70.

When you select cells in Excel under the new version of Excel, it shows you the number, it's 70.

So that is the unlevered free cash flow. That entire formula there is the unlevered free cash flow.

It's the nopat multiplied by one minus reinvestment rate. Well, it's not really, it's the notepad multiplied by 1 minus G over return on invested capital, which is the reinvestment rate, which gets you to unlevered free cash flow, gonna grow it, but multiply it by 1 minus G and I'm gonna divide the whole lot by open bracket, the whack open bracket, the whack minus the gross rate, okay? And I come to the same number.

So those two workouts, one, two were you know, really just dealing with the same stuff.

Let's look at an example where the wheels fall off. Okay? So let's look at an example where things go slightly wrong using those ideas.

If we look at workout three, there's something just inherently wrong about the numbers in workout three.

And if you stare at them, you don't have to stare at them for very long, you'll be able to see that.

So let's just talk through them.

Perhaps I've produced a model for you and in the final year of the model, I'm about to calculate the terminal value.

I'm gonna say I think this business is gonna grow, terminate at 5%.

Now that seems pretty bullish, okay, 5% just in general feels like quite a high number, but you might say, alright, okay, we're gonna grow at 5%.

Well, let's explore that.

We've got WACC of 10%, we've got no pack of 200, and you've got a level free cash flow of 190.

Now we, we will answer this question to the side, but a below, but let's just an, let's just mess around with some numbers to the side.

So you could say, you could say to me, this sounds a bit odd, Jonathan, you could say like, your nopat is 200 and your unlevered free cash flow is 190.

So in absolute terms, the reinvestment, not the reinvestment rate, but the reinvestment in the business is 10.

That doesn't sound like much, right? I mean, what we're really saying in that single line, that minus 10 is we're saying we are modeling that we are not buying much PP&E we are not investing much or maybe reinvesting much in operating working capital.

We're hardly making any investment at all.

In fact, if you wanted that as a percentage, the reinvestment rate, the reinvestment rate, reinvestment rate is, what is it? 10 over 200 multiplied by minus one.

It's only five. It's only 5%.

See, I mean, that doesn't sound like much reinvestment to get what is a fairly bullish growth rate of 5%.

And if we go, just go back up to this example here, we said, I'm gonna copy this and bring this down.

We said, well, we think that reinvestment is growth over return on invested capital.

So I guess we could rearrange that, right? We could say reinvest rate multiplied by growth equals multiplied by, sorry, return on invested capital.

I was thinking equals growth.

So you could, and let's just put that change the sales dollar.

So you could say, let me just check then if you're, if you're reinvesting 5% I guess if we knew the return on invested capital, we could kind of imply the growth rate here.

So do we have the return on invested capital? Yeah, the return on invested capital in here is 10%.

So the, I'm gonna say implied growth, the implied growth rate is 5% multiplied by 10%, which is half a percent.

So you you're kind of saying, look, when we calculate terminal value, there's really like three things in that formula. There's three components to it.

So when, if you go right back up to the top, when you calculate terminal value, you're really looking at the free cash flow.

One, you multiply it by 1 plus the growth rate and you divide it by WACC over the growth rate.

So there's three components, there's free cash flow, growth and wack that help you get to that terminal value number.

Now, if we go back down to the work we've just done here in out three, you're saying of those three components, which I guess I'm just gonna put in bold, we've got here growth rate waxed to the side, you've got growth rate and we've got an number three cash flow.

I do not, you know, I do not believe that you are gonna get a 5%, you're gonna get 5% growth with such an appallingly low reinvestment, okay? In fact, your, your reinvestment is so low in this model that you've built that your unlevered free cash flow is massive, it's much bigger than it should be.

How do you really anticipate getting unlevered free cash flow of 190 of of noad of 200 w which, which seems like a very flattering thing to your valuation to have a really high under free cashflow number.

How do you anticipate being able to do that and at the same time, flattering your valuation with a 5% growth rate? You, I like the turn of phrase that I hear often.

You cannot grow for free, okay? It's not possible.

So you've either in your model, gotta go back to your model and increase your OWC in change your, increase your OWC increase increase your CapEx and accept a lower unlevered free cash flow number.

Or you've gotta use a terminal growth number of half a percent, which seems probably too low, so it's probably appropriate to go back to the model.

I think that number in the model is wrong. Okay? And that's important because what we're trying to do here is sense check a model.

It's a really cool thing to do in a model, to go and check it.

So, we have got some sort of formal workings to do here to properly uh, just tick the boxes and go through those ideas.

So in the first instance the question is what is the terminal values in the traditional perpetuity growth formula? And that traditional formula is equal to, why don't we take the unlevered free cash flow and multiply it by open bracket one plus the growth rate.

I would see these as immediately being incompatible.

Now, unlevered free cash flow is way too high or the growth number is too high.

They can't both be too high.

So immediately I think this is wrong.

You, you're not, I think probably the 190 is just the wrong number to select.

If we divide it by open bracket, the WACC minus the growth rate, we come out with 3,990 as the terminal value.

Now the terminal value is about 80% of your entire valuation.

If you think about that, if you do like a five year forecast, maybe a 10 year forecast, which reduces it a bit.

But if you do a five year forecast, you take this five years and you discount those, you get your terminal value for the remainder and you discount that you get to your ev.

So of your EV about 80% of that comes from your terminal value calculation.

Which means that if you screw up your never free cash flow number in the final year, your whole valuation is totally wrong.

Yeah, totally wrong.

So it's really an important number to be able to sense check.

So I think that that's, that's too high because I see the growth rate and the final year, never free cash flow, not really being consistent with each other.

Let's, let's just try and redo that using the value driver formula, and it's the 190 I've got issue with. Rather than go straight for 190 and grab it, why don't we infer the unlevered free cash flow? So in order to infer it, I'm gonna go back to this formula we used here in pink.

In fact, what was the first color we used Blue? So, that first formula there, let's just grab just so you can sort of see the consistency, let's go and grab that. So that's been calculated using original growth formula and now we're gonna look at the value driver formula.

A superior way of doing it, I would suggest.

So we're gonna say equals, I'm not gonna go straight for your unlevered free cash flow of 190, I'm gonna go for 200 and I'm gonna multiply that by open bracket, one minus the reinvestment rate.

But rather than go straight for the inve reinvestment rate, we're gonna say over here growth over return on invested capital.

So I'm gonna say go and grab the growth rate, which is 5% over the return on invested capital, which is 10% post bracket.

So what I've done with that piece of the formula is I said, this is what I think the unlevered free cash flow should really be given the amount of growth you are looking for and the return on investor capital you think you can generate.

And you might say, but we already know what it is because we've got 190.

No, but I think that number's wrong.

Okay, so I'm, I'm basically putting a line through that and I'm saying take the nopat, consider the reinvestment, consider return on invested capital.

This is really what I think the unlever free cashflow number should be.

Sorry, let me get back into it there. Which is at the moment, which 100 that's quite different, right? What we're really saying is, if you have notepad of 200 and you think you're gonna be able to grow at 5% every year off return on invested capital of 10%, then your leveredfree cash flow is only gonna be 100.

I thought it was gonna be 190. It won't be.

No, you've got no chance. Okay? So if we take that, if we take that revised on lever free cash flow number, which is now consistent with the growth rate, we can multiply it by open bracket 1 plus the growth rate of 5% and we can divide it with by open bracket WACC minus growth.

So what has changed in this formula, if we're being more realistic about the unlevered free cash flow number now, and if we hit enter, we therefore get a more realistic terminal value.

So that is the right number to select. It's just a better way of doing this calculation.

Net reinvestment in the terminal year.

So now we're just gonna summarize some of the things that we've said.

So 200 minus 190 our numbers, assuming that we're only gonna reinvest 10, the invested capital equals.

So I don't know, we've got the nopat number and we've got the return on invested capital.

So if we did notepad divided by return on invested capital, we've got the invested capital.

So if you can imagine the invested capital of the business is 2000 and we think that we're gonna grow it by 10, what does that represent? 10 over 2000 is half a percent. Half a percent.

So, so actually in your model you're saying, I think we're gonna grow up 5% and we're gonna get unlevered free cash flow in the final year of 190.

They don't work either.

You're gonna get unlevered free cash flow of 190 and you're gonna grow at half a percent, or you're gonna get unlevered free cash flow of a hundred and you're gonna grow at 5%.

But both things can't be true.

You can't have growth of 5% and unlevered free cash flow of 190 at the same time.

Okay? So they're really good check to undertake on a model.

The file covers a number of different things.

And so we're gonna have a look at something that's still on DCF, it's still advanced DCF, but it's, it's now a different subject.

If we scroll down, I'm gonna have a look at workout four.

So for workout four it says, an analyst is prepared the following full year forecasts, use the assumptions and data provided below to value the company at the 30th of June.

Assume the end of period discounting assume cashflow falls at the end of each period.

So what we've got is we've got like year one, year two, year three, and year four looks like their year end is the 20, is the 31st of December, 20, 22, 23, 24, and 25.

We're gonna buy it on the 30th to June 22.

So if you think you've got like January sits there, 31st of December sits there and the idea is that we're gonna buy the company or perhaps you're just valuing the company at that date.

So if you're valuing it at that date, there's a few things that we'd need to consider.

One, you're not gonna get that entire cash flow are you, if you, if the business generates 1,056.1 of cash throughout 12 months, if you buy it six months into the year, you're only gonna get the post acquisition cash.

So you're gonna get six months of cash.

So it's about 500 odd of cash.

You're gonna get 500 and whatever, 30 something of cash, just under.

And the other thing is not only are you gonna get all the cash, but when you think about discounting, you don't have to, let's grab a different color.

You're not gonna have to dis you don't wanna discount it by a full year.

You wanna discount it by half a year, one and a half years, two and a half years, three and a half years. And you might say, yeah, of course, because of midyear discounting.

No, it's not because of that, we've not thought about that.

If we go back here, it says assume end of period discounting, assume the cash flows fall at the end of each period.

So the reason we're discounting by say half of year, one and a half year, two and a half years in this instance isn't because of mid-year discounting, but is because you buy the business partway through the year, you've only gotta wait six months to get the first cash flow.

You've gotta wait 15 months to get the 18 months, right, to get the next, next cash flow, et cetera.

So, we've got a few things to do. We're going to need to show some workings here I think to look at this, right? What's the cashflow date? Well, the cashflow date is the 31st of December, 2022. In fact, let's copy that out to the right and show the formula on the extreme right.

And then if I, I'm gonna skip down to, I'm gonna highlight this in maybe yellow or something there.

So in yellow it says FY1 pretty cashflow available.

If I say equals and go and grab 1,056.1, that's wrong, okay? In fact, what I'm gonna do is say equals grab C87 and I wanna multiply it by open bracket C86 minus C82, close bracket over 365.

Let's pause on that for a minute.

So we are saying the cash flow that you would get in year one would be 1,056 multiplied by the 31st of December, minus the 30th of June.

So that's basically six months, or if you, how that 184 days, so it's about half a year.

So you're gonna get, you're gonna get half a year's at the end of the year, minus that point you bought it, you're gonna get 180.

Did it say a 182, 184, sorry, 184 days worth of cash over 365.

I grab those together.

You're basically gonna get like just over 50%, just over 50% of that cash flow.

If I hit enter, I said 530 off the top of my head is that 532.4 million of cash from the first year.

Because you acquire them partway through the year and, and then thereafter your cash flows would just revert to the full year cash flow because you own the business, you, sorry, own the business, it's gonna grab that properly there.

You own the business for the, the entirety of that year and all subsequent years, it's only in the first year that you didn't own the entire, the business for the entire, the entire year.

So we have to just grab the cash cashflow post acquisition.

Now, let's, let's go back a little bit.

So, you could say, well, how many days of discounting are we looking at then? Thinking about what we just calculated down here? And across the entire forecast period, if I said equals, if I grab the end of any given year and I subtract the 30th of June, 2022, and I might press F4 here on this to lock up, okay, 184 days of discounting, yeah going, but my green arrow going back to 184 days.

And if we copy out to the right 549 days, which is that sort of green arrow back to today 915 days, 280 days, et cetera.

So from a a kind of year point of view, how would you view that? Well, at 184 over 365, half a year, one and a half years, two and a half years, three and a half years.

So once your discount factor will equals to one over open bracket, one plus the wac, that's just a class classic formula F4 to lock that close bracket, raise it to the power of the number of years, copy that out to the right.

And then, if we move down, I'm not gonna look at the terminal value just yet, but if we look at the present value of those free cash flows, that is the product of those free cash flow numbers and the discount factor, and then you might say, great, let's calculate the enterprise value.

Well, the enterprise value is gonna be the sum of the present value of those free cash flows and also the terminal value.

We don't have the terminal value yet, so let's work, work that out.

Terminal value formula is really easy.

We're gonna say ecos, let's grab the free cash cashflow available in the final year, which was, it was that cell above.

And we're gonna multiply it by open bracket 1 plus G, which is 3%.

So we're, we're not scrutinizing this in the same way as we did the last example, close bracket over bracket WACC minus G.

So there is always a question about, as we said, that growth rate and if it's consistent with the reinvestment rate, but we're not looking at that here.

So I've got 25,183.5, and if you wanted the present value of the terminal value, it's simply gonna grab nothing unusual going on here, that terminal value and multiply that by the discount rate.

And then our enterprise value will be the sum of those two.

I've got 22,619.

So the idea, and perhaps we, we just got a little time, we we're just gonna have a quick play around with it.

The idea is that if the valuation date wasn't the 30th of June, but perhaps it was the 31st of July, 2022, then I'm not gonna sort of animate my annotation, but this purple arrow will go slightly to the right, yet the purple arrow goes slightly to the right and that means that well it means that you won't have as much cash and that's kind of bad, right? Yeah, if, if that moves slightly to the right, then you won't have as much cash, so that's not as good.

But on the other hand if you move slightly to the right, you don't have to wait as long because you've now got only not six months, but five months.

Don't have to wait as long to get that first cash flow or wait as long to get the second cash flow.

So there's kind of two elements to this. And if we hit enter, let's have a look at the enterprise value and hit enter the enterprise and I can control is a small movement Ctrl Z 22,619.7 Ctrl Y 22,681.

So buying the business at a slightly later date reduces the cash that we're gonna get for that first year, but it brings all the other years closer, including that big terminal value number.

It brings that, it brings that closer to us and it actually changes the valuation.

So the idea of stub periods is be to affect that change.

Question, can you please explain the discount factor a bit? Yeah, absolutely. So, the discount factor formula is, equal to 1 over open bracket, 1 plus the WACC raise the power of the number of years.

So that's the formula of applied. Now I appreciate that. Doesn't really explain it. So let's go and grab a couple of numbers and explain that that's the formula we're after.

So if I go to the site, I could say let's find a bit of space over here.

I could say let's say today pres, let's say today, let's say today I invest, let's just say equal.

Let's say today I invest 1,000 dollars and I multiply that by open bracket one plus some sort of return, a return of 10%, 1 plus 10% for a year, one year.

Okay? So raise the power of one year.

So the question is, I'm choosing some easy numbers here.

What would you end up with if you had a thousand dollars and you invest it at 10% for a year in a year's time, what would you end up with? Well, you dunno it with 1100, right? So 1100 and you could say, well what if we had that 1100 and we invested that for a year, for a year further, okay, another year at 10%.

Well, 10% of 1100 is 110, 110 added to 1100 is 1,210.

So you could say, well, if you had a thousand and you invested it one plus 10% for two years, by the end of the second year, you'd end up with 1,210.

And if we wanted to be a little bit more generic with this, we'd say that the present value is equal to, sorry, we'd say the future value is equal to the present value multiplied by 1 plus r some sort of return required.

Now, the return required by our investors is actually our WACC awaited average cost to capital.

That's the return they require raised to the power of n which should be the number of years.

So the future value, the present value multiplied by one plus WACC raised to the power of n that that would be written generically.

So then you could say, well, could we work backwards if in two years time I knew in two years time that I was gonna receive 1,210, what would that be worth today? And so you could rearrange the formula and say, well I now want to find the the present value, right? So if we take that formula and we say, well, the present value is equal to, so let's take the future value is equal to let's take the future value and divide it by 1.

Plus the WACC raised the power of a number of years, and we can prove that because you could say equals, I know the future value is 1,210.

And if I divide that by one plus the WACC, which is 10%, raise the power of the number of years, which is two years, that should two years rather, that should get us to 1,000, right? Because what we've done is we've discounted.

So what we've done is we've taken that future value of 1,210 and we've discounted it.

Now, another way of writing that, rather than take 1,210 and divide it by 1 plus 10%, raise the power of two.

I could multiply it by 1 over 1 plus 10% of the power of 2, it'll give me the same number of course.

Let's just move that down.

So I could say that the present value is equal to the future value.

The future value multiplied by, I can just put that in, multiplied by one over one plus whack to the parvan.

It's the same. These are the same thing. These, these two lines are the same formula.

Rather than divide by 1 plus WACC to the power of N I've multiplied by 1 over 1 plus WACC to the power of N.

Now, in notation of course, that's the the present value.

This is the future value.

And what name would we ascribe to? That's slightly uncomfortable.

One over one plus wack to the power of N we typically call that the discount factor.

The 10% WACC that lives inside there is the discount rate, but the discount factor is one over 1 plus S WACC raised the power of the number of years.

So you could say, Hey, how do I get to the present value of something? I would say you take the future value and you multiply it by the discount factor.

So if you look at this formula here, you take the future value and you multiply it by the discount factor.

And if you guys look to the left, that's exactly, I'm gonna have to zoom out a little bit.

That's exactly what I've done here.

So to get to the present value, what I've done and maybe we could look at like the, I don't 2024.

So to get to the present value, I take the future value.

So that's the value we're gonna receive in 2024.

And I'm gonna press ft so you can see what I've done.

I've multiplied it by the discount factor.

So it's the product of the two.

So the, the question was, can you explain the discount factor a bit? I hope that, I hope that helps. I hope that makes sense.

Great. Okay, fantastic.

Now we've got just a very little bit of time at the end.

So I think we just squeeze in something in on the WACC because I'd really love to kind of kind of get to that.

So if we look at workout six, so workout six, it says, can you calculate the WACC for the below company? So I'm gonna do this diagrammatically and I'm gonna try and get this done in about four, in about four minutes because I don't wanna hold you guys up. So I'm gonna say asset equals liability plus equity.

And uh, I'm gonna go and grab, I'm gonna color in a box and I'm gonna call this the EV the enterprise values.

That's the operational business.

And I've got a business that's financed with some debt.

I'm gonna put this in blue and I've got a business that's financed with also some equity.

Now, I'm not gonna entirely make these numbers up because we've given some numbers in the question, okay? Yeah. Okay. So if you look at the question, it says, calculate wack for the blue company.

Assuming there are no financial assets in the target capital structure we we're told that we've got a cost of equity and a cost of debt.

We've got return on financial assets, we've got a tax rate. And our heart, this is crucial.

I'm gonna put it in bold debt as a percentage of EV is 40%.

So imagine that the operational business is valued, the asset value is 100.

We know that the debt is 40% of that, so it must be 40 million.

So how much equity must be supporting the business? It has to be 60 million.

Now we know that the cost of debt is 3.5% multiplied by one minus the tax rate because it's tax deductible.

And we know that the cost of equity is 9%.

It should be calculated using the capital asset pricing model, which is beyond the scope of what we're covering here.

That's fine. So you could say, right, the EV is gonna spit out cash flows at the providers of finance.

Yeah. So anyone providing financing to this business, the operational business, the enterprise value is firing out cash flows at them.

What sort of return do they want? Well, we're talking about the weighted average cost to capital.

So the WACC, the debt holders want 2.8% and proportionally 40 over 100, oops, sorry, didn't wanna do that wrong.

Key 2.8% and proportionally 40 over 100 if 40%, debt financed plus the equity holders looking for 9% and it's 60% equity financed.

So the, the average cost of capital is 6.5% on average.

That's what people want.

So you could say, okay, great, let's look at the second example.

It says, what if there were financial assets in the capital structure? My thought here, there won't be, okay, it doesn't make any sense.

We're gonna run the numbers and check this, but assuming there are financial assets, so let me change the diagram a little bit. I'm gonna get rid of these arrows. So let's grab this.

Maybe here, I'm just gonna move, move this up a bit.

So imagine in yellow that we have some cash in the capital structure.

And it says here assume there's 5% cash is 5% of EV.

So imagine it's 5% multiplied by the EV.

And it goes on to say the debt remains at 40% of EV so we've got some cash in the capital structure.

We know that the debt remains the same, so we must have more equity.

I think what's happened here is the business has made profits retained earnings, and so the equity has got bigger and it's held onto that cash.

Now in the long run, the shareholders are gonna say no, like in the very long run they're gonna say like, if you, either you return that as a dividend, you do a share buyback or you reinvest it in the operational business in the EV, you can't just perpetually hold onto cash because it's generating an awful return.

Now let's look at what would happen to the wac.

So I haven't made any changes yet, but that kind of benchmark is the WACC is 6.5%.

If we think about the I'm gonna say return on financial assets, we are told here is 5%.

Now, I guess we could really multiply that by one minus the tax rate.

Because it would likely be tax deductible. Okay? So let's call it 4%, after tax.

So you could say, well, how would the WACC change? I want you to consider that the EV is firing out cash flows to satisfy the requirements of the equity holders and the debt holders. And it's just getting some help now.

So the cash is also gonna fire out returns at 4%.

So what we're gonna do is, there we go. What we're gonna do is we're gonna update our equity number to be a hundred plus five minus 40 makes it 65.

And that pushes up our WACC, right? Which sounds bad, but then we say, no, hang on a minute, the cash is helping you out.

So we're gonna go and deduct from that.

This is a deduction because it's helping the enterprise value out five perc, uh, 4% multiplied by 5 over 100.

We get to 6.8. It's not good enough.

Think about it like without having cash in the capital structure, we had a WACC of 6.5%.

If we decide to hoard cash in the business, the wack goes up to 6.8% because that's gotta be financed somehow.

And in this instance it's financed by equity, which I think is probably fairly likely.

So why would you hold cash in the business, increase the market value of equity, and therefore push up your WACC? It doesn't make any sense. You wouldn't do it. Okay.

So what the workout is trying to say to you is that when you are calculating WACC, really keep it simple.

Keep it simple, okay? Don't, don't try and think about what would happen if they had cash in their capital structure. They wouldn't have cash in their capital structure.

I wanna just show you one thing, but I know we run over slightly, but I wanna show you something in Felix, some real company data, which I think is a really good way of explaining this.

When we do, let's look at, well, let's look at CocaCola. That's fine. When we look at a company, we use the WACC to discount their cash flows.

Terminally. Yeah. In perpetuity. Agreed. Okay.

So we use the weight to average cost after the discount, the cash flows and discount the terminal value, which goes on forever.

Check out Monster. It's the third one down.

Have a look at Monster. Okay, scroll over to the side.

Look at their debt to Capital.

Monster has hardly any debt in their capital structure.

So are you telling me that if you wanted to create, look at the WACC because they've got hardly any debt right now, are you seriously gonna suggest that your pr their WACC is gonna basically be the cost of equity? 'cause they haven't got any debt? That would be wrong.

You know, if you're going to pick up monster's, cash flow stretching out like terminally forever, monster's not gonna have hardly any debt. Terminally, I put it to you that in the long run, look at Coke, look at Pepsi, they've got about 15% debt in that, in that sector.

I would look at the, the large cap, most mature comps in the sector and I would look at their capital structure and I would suggest that that's the target capital structure of the business.

And that target capital structure of the business will never include cash in the long run, not a meaningful amount of cash.

Okay, we've slightly run over there, apologies, but thanks so much for your patience.

I really appreciate you being on the call.

Thanks for the questions on the chat.

I really appreciate that and I look forward to seeing you guys another, another session at some point in the future.

Thanks so much. Take care. Bye now.