Share valuation using the Discounted Free Cash flows

[TheMotorcycleBoy]

So as a few of you here know Mel and I being new to share purchasing, and knowing we might be at the top of the market, have found the dilemma of buying at the right price a little fraught. (Though, of course, market prediction is foolish, we could be anyway in the cycle, whatever.) But regardless, after our first few purchases, this year, some being blessed by luck, others not so, we've been looking at, aside from the brokers' consensus, at trying to have a crack at valuing share market prices ourselves.

I did look at the discounted dividend method of valuation last week, and I think that the conclusion there was the model could be way off target, firstly due to forecasting errors and secondly due to the subjectivity of one's estimate/specification of the discount rate. This model is bound to fall victim to the same shortcomings. However, seeing as I've looked at DDM already, and that FCF may be higher in the food chain than Divs, I thought I'd look at this one. Again with Marshalls MSLH (which we hold) using https://www.marshalls.co.uk/investor/investor-centre as my example.

To find out how to do this calculation, I looked at How to Pick Quality Shares by Phil Oakley. He does a reasonable study of this, using the book's reference company of Dominos (DOM). Alas, this is the odd typo, or perhaps it's just that he makes one or two leap in the description process, which meant I took a while to quite understand what was happening.

However, after reviewing and after familiarising myself with other models (DDM), I realised that the method (as a described by Phil), is basically

1. Get the last reporting periods "Free cash flow per share", i.e. FCFps
2. Select a discount rate that you expect of the investment
3. (This is the bit I don't like much) Assume a growth rate to the FCFps, e.g. 10% for the next 5 years, then 6% for the next 5 years. And for each flow you discount it back to the present.
4. You then need to a "terminal value". This is basically because after 10 years you assume that the growth rate in the CFs is constant. And to derive this terminal value you basically use a similar formula to the DDM approach i.e.

Terminal Value  = CF(1 + g)/(r - g)

where CF is the last flow you've estimated, i.e. the one at year 10, g is the CF's growth rate, and r is the discount rate.

5. Finally you sum together all of those cash flows you got from step 3. along with the terminal value you arrived at with step. 4. However, there is a twist to the final value of the terminal value, and that is this: basically although the application of the discounting formula is already applied (i.e. CF(1 + g)/(r - g)) it's worth bearing in mind that this value is currently discounting all the future flows from 10 years to perpetuity just back to year 10, and obviously must now be discounted back to the present value. So it must be divided by (1 + r)^10.

And it is this result, i.e. the sum of the DCFs from 3. and the fully discounted Terminal value from 4. that result in the final "valuation" for the share price.

I found Phil's method a little confusing and for a reasonably well established firm like DOM or MSLH probably too optimistic. So I established a simpler approach in application of this method, using MSLH as an example, which I will post later on.

Matt

[Dod101]

A comment unearthed by Nick Train 'The terminal value that underpins the much worshipped DCF calculation is little more than a rough guess multiplied by a wild estimate.' From Jonathan Knee in Class Clowns. Might be worth taking a look at.

Dod

[SalvorHardin]

A comment unearthed by Nick Train 'The terminal value that underpins the much worshipped DCF calculation is little more than a rough guess multiplied by a wild estimate.' From Jonathan Knee in Class Clowns. Might be worth taking a look at.

Indeed. DCF looks respectable because there is some maths underpinning the method, but the flaws that the dividend discount model has are replicated with discounted cashflow (these have been discussed on another thread on TLF).

Some people decided several decades ago that because DCF works for bonds it works for equities. Similar to how EBITDA is useful for bonds, but I reckon that for equity investors both are to be avoided.

It's often said that Warren Buffett's secret is using DCF calculations. Yet Charlie Munger said that he'd never seen him doing one. DCF became popular after Robert Hagstrom's book "The Warren Buffett Way" was published; I remember the UK and US Fools running portfolios using DCF which did quite badly.

[Alaric]

Some people decided several decades ago that because DCF works for bonds it works for equities.

At a pinch if you were comparing the equity of a Company with its Corporate Bonds, discounting the cash flows of both might give you an insight.

It's an observation on high yield strategies. If you never see the return of capital because the Company goes out of business once it has self destructed by paying all its wealth as dividends then you should value it as a short term guaranteed annuity for the lifetime that it survive.

Indeed in more general terms, if part of the dividend is effectively a return of capital, you could value it as such and not double count by assuming the share has either a decent residual value at the end of a control period, or that the dividend stream can stretch to infinity.

[Dod101]

SH I think you said you were an actuary so I would not attempt to say any more than that I assume DCF works reasonably well with bonds because they usually have a fixed term to maturity and the coupon is fixed. Neither of these applies to equities.

Actually I am rather sceptical of most investment theories and have done perfectly well without even understanding what alpha and beta means in the investment world.

Dod

[SalvorHardin]

SH I think you said you were an actuary so I would not attempt to say any more than that I assume DCF works reasonably well with bonds because they usually have a fixed term to maturity and the coupon is fixed. Neither of these applies to equities.

Actually I am rather sceptical of most investment theories and have done perfectly well without even understanding what alpha and beta means in the investment world.

Yes, I used to be a Pensions Actuary for my sins (mostly mis-selling calculations and investigations). Really glamorous stuff

DCF works with bonds because their cashflows are highly predictable as you've said (pre-determined amounts and dates of payment). Equity cashflows are much less predictable so valuing a share using DCF introduces a lot of spurious accuracy.

DCF worked when doing pension scheme equity valuations and asset-liability modelling, but that's because the calculations did not attempt to claim whether equities were cheap or expensive; just how they compared to the liabilities which were valued using the same method.

I too have ignored alpha and beta, asides from when needed for exams! The capital asset pricing model, which they come from, is somewhat flawed.

That said Seeking Alpha is a good website for investors in North American shares.

[dspp]

M&M,

The discount rate is composed of two parts: the risk free rate + the risk premium.

If buying lots of assets (shares, bonds, or perhaps a company with lots of projects), to be held for long periods of time, then using the concept of a discount rate is reasonable, provided you are using asset-specific risk premiums (or provided that all the assets share the same risk premium). Because any errors in ascribing the risk premium on any one asset will likely be balanced out by an opposing error on another asset. Provided there are enough assets and provided there are no systemic errors in your assessing the risk !

However if just valuing one share, for a relatively short period of time (several years), then the risk premium is no longer an aggregate. There is a very real risk that your asset may come across a very specific issue that causes it to be impaired or extinguished (being a pessimist), or strike gold or somesuch (being an optimist). So it is useful, as a thought exercise, to sketch the probability chain for several years and think of the outcome.

Another way of thinking is as follows. If the risk premium was (say) 7%, plus a risk free rate of (say) 2%, total discount rate = 9%; then what the 7% is saying is that on average this company will go bust in 10years time. Gulp. ie, after setting aside the risk free amount (2%), that leaves 7%. Compound 7% for 10 years and you double your money. 50/50 outcome of bankruptcy is therefore back to where you started, i.e. your initial stake. BUT on individual companies that bankruptcy risk could occur in year 1 or in year 19 (average is 10 years ..) or any of the other years from 0 to 20.

Think BP Macondo for a specific example. Or Bhopal. Or Barings. Or check survivor bias in aerospace companies over last 100 years (that's a biggy ! across a whole industry).

You may say that what I am describing is a bit pessimistic, but it is quite common to hear people bandying around a 10% discount rate without really thinking about the implications. At the moment it is unusual to get a risk free rate of 2%, so 10% discount is implying 8% risk rate, i.e. more than 50/50 of going bust at 10 years. Strewth.

Can you correctly price risk premium for an individual company ? I know I can't.

But it is still an interesting approach and I use it myself for project analysis. Less so for company analysis.

regards, dspp

(ps. It is a lazy Sunday morning in USA where I am travelling for work, hence having a tadge of time off)

[Gengulphus]

It's an observation on high yield strategies. If you never see the return of capital because the Company goes out of business once it has self destructed by paying all its wealth as dividends then you should value it as a short term guaranteed annuity for the lifetime that it survive.

I think it's very easy to value such companies than that - the answer has a single digit and every remotely sensible investor agrees about it! ;-)

The valuation problem is for companies that might go on to do that in the future - as for anything else involving what companies do in the future, it involves forecasting what they will do in the future, and all forecasts are unreliable to a greater or lesser degree.

And the same problem without specifying exactly how the company pays out all its wealth exists for any type of strategy. For instance, huge numbers of start-ups have self-destructed by paying out all their wealth on developing products that they then fail to sell...

In short, no, it's not an observation on high yield strategies, it's one on valuation methods.

Gengulphus

[TheMotorcycleBoy]

Ok, here's what I did with MSLH. Basically I came the conclusion that the reason why Phils description is so confused/confusing is that he tries to illustrate that you can assume staggered growth rates - i.e. growth gradually falls over time. Personally I find this approach a bit farcical, especially with more mature firms like DOM and MSLH. And furthermore it is the insistence of having the different phases of company growth that result in the need for the separate stand-alone TV, that's all; as it's just the equity prediction from a point in the future then onto perpetuity.

What I did with MSLH was simpler. Firstly I grabbed a few ARs and focussed on the "Consolidated Cash Flow statements" for 2013-17. (You need to search for diluted as well to get the number of shares in issue). So I then just grabbed the figures which I think best document the main FCF movements. You have to make some assumptions, and I was intentionally harsh, so any monies from resaling spent production equipment I've not included.

So below, the first 6 rows are in 1000s of GBP, the number of shares is in millions, and FCFps (free cash flow per share) is in GBP. I soon realised that the FCF looks reasonably steady for the last 3 years. But as I had got the figures down already I whacked them in.....and you can see the actual cash flow for earlier 2013-2014 period (recovery? genuine organic growth?) is quite sporadic, which rendered growth rate estimation so choppy that to be honest it's worthless in my opinion. Kind of what I expected!

Year	                        2013	2014	2015	2016	2017		
Net cash from operations        27124	29117	49685	49393	57305		
Tangible capex	                -5462  -11269	-14016	-12939	-18895		
Intangible capex	         -596	-741	-909	-934	-1750		
							
							
FCFF	                       21066	17107	34760	35520	36660		
Some financing costs	         -95	  269	-166	-40	-3407		
							
							
FCFE	                       20971	17376	34594	35480	33253		
Diluted shares(M)	         195 	196	199	200	199		

FCFps (in GBP)	               0.107	0.088	0.173	0.176	0.167
						
Diff		                        -0.0185	0.0846	0.0035	-0.0096		
Growth rate of FCF	                -0.173	0.955	0.0204	-0.05434

The average growth of FCF = 75%

So what I did then was what I'd assumed all along would be the best approach. Basically as MSLH is reasonable mature, but construction is probably a bit cyclical, so I thought the best thing to do is just to assume the free cash flow ps is fairly steady these days at 17p, and it will grow at the current rate of inflation or thereabouts. So seeing as the BoE in absense of Corbyn, I guess, is aiming for 2% and we seem to jumping between there and 2.7% ish, I just decided that the growth rate into perpetuity should be about 2.5%. I then assumed a modest discount rate of 6%, since that's about 4.5% above a 10yr gilt and (coincidentally) about the YTM of a fairly junk bond (e.g. PMO1). Then I just lobbed these figure into the DDM model:

Valuation = FCF(1 + g)/(r - g)

where r=discount rate, g=growth of FCF, and FCF is the last FCF that I was happy about[/pre]

Last CF	                0.17
Growth rate of FCF     0.025
Discount rate	        0.06
Estimated value GBP	4.98

Which bizarrely is very close to both [url=https://www.lemonfool.co.uk/viewtopic.php?p=168406#p168406]my final post on the DDM thread[/pre] and also to that target price on the "4-traders" site.

[Charlottesquare]

I am not totally convinced discounting earnings or dividends ought to be totally ignored, merely that they are both very crude (and riddled with assumptions) re measuring actual current value, and the discounted value to infinity does bother me so I prefered, when playing with such calculations, to consider over shorter periods

Where they to me appear slightly more useful is when comparing two or more shares competing for my money.

Say A with a lower starting dividend/earnings but expected say 5 years of growth at x then five years at x/2 , B at a starting dividend/earnings but growth for say 10 years expected at x/2, which do I buy?

If a shorter timeframe there does need to be implicitly some valuation of share price at say year 10, possibly based on forecast dividend/earnings at year 10 with an assumed P/E ,discounted back to today. At least when using to compare, if similar discount rates re current PV applied to both, the error re this is to a degree matched on both sides of the scales.

Whilst I have always been hard pressed to get these sorts of calculations anywhere near the current share price, a comparison of CalcA/Current Price against CalcB/Current Price of B may elicit some assistance re relative value as to whether I want to invest my limited capital in A or B. In effect it is considering bird in the hand and the bush re two or more shares, ideally in similar sector.

It is a fair few years since I tried number crunching shares by this quasi, Heath Robinson,approach, and I have no data to suggest it was successful, these days I more buy ITs by my crude, subjective, beliefs in macroeconomics (choose geographies over companies) and leave my share selection choices to the IT managers.

[TheMotorcycleBoy]

M&M,
The discount rate is composed of two parts: the risk free rate + the risk premium.

Many thanks for this one, DSPP. I actually have deliberated over the meaning of discount rate quite recently, i.e. just here and for me the penny regarding the risk premium dropped big time here. i.e. in a tie-up of the firms cost of equity capital along with the investor expected rate of return.

Another way of thinking is as follows. If the risk premium was (say) 7%, plus a risk free rate of (say) 2%, total discount rate = 9%; then what the 7% is saying is that on average this company will go bust in 10years time. Gulp. ie, after setting aside the risk free amount (2%), that leaves 7%. Compound 7% for 10 years and you double your money. 50/50 outcome of bankruptcy is therefore back to where you started, i.e. your initial stake. BUT on individual companies that bankruptcy risk could occur in year 1 or in year 19 (average is 10 years ..) or any of the other years from 0 to 20.

I'm all for merely viewing this as just a way of interpreting statistics, but if you want to talk more on it, please do in that other thread that I referred to, since it's definitely an area I'd like to chat about some more? Not wishing to sound bossy though!

Can you correctly price risk premium for an individual company ? I know I can't.

Oh crikey no. But I think I only see the Disc rate as being the type rate of return I expect from the firm, and so of course this "guess" merely effects the valuation estimation one way or the other.

(ps. It is a lazy Sunday morning in USA where I am travelling for work, hence having a tadge of time off)

Well, don't work too hard!

[Pastcaring]

I would be sticking to crystal balls and tea leaves,they'' ll be just as accurate as centuries of weird theories and thinking that somehow a mathematical equation must predict the future.

[Gengulphus]

However if just valuing one share, for a relatively short period of time (several years), then the risk premium is no longer an aggregate. There is a very real risk that your asset may come across a very specific issue that causes it to be impaired or extinguished (being a pessimist), or strike gold or somesuch (being an optimist). So it is useful, as a thought exercise, to sketch the probability chain for several years and think of the outcome.

Another way of thinking is as follows. If the risk premium was (say) 7%, plus a risk free rate of (say) 2%, total discount rate = 9%; then what the 7% is saying is that on average this company will go bust in 10years time. Gulp. ie, after setting aside the risk free amount (2%), that leaves 7%. Compound 7% for 10 years and you double your money. 50/50 outcome of bankruptcy is therefore back to where you started, i.e. your initial stake. BUT on individual companies that bankruptcy risk could occur in year 1 or in year 19 (average is 10 years ..) or any of the other years from 0 to 20.

So there's no hope of it surviving 21 years or more? Or less obliquely, that appears to me to be based on far too unrealistic a model of how long a company is going to survive.

But more important, I think discount rates and risk premiums are basically measures of investors, not of individual investments or portfolios of them: the discount rate is the rate of return the investor thinks they can realistically get, the risk premium is that minus the risk-free rate (though an investor might either choose them that way or by deciding first on the risk premium they think they can realistically get over the risk-free rate and then adding the risk-free rate to get the discount rate).

If one wants, one can then define the discount rate of a particular share (or other investment/portfolio) in relation to its current value and a discounted valuation method to be the discount rate a shareholder would have to use to reckon it was fairly valued at that value, or its risk premium to be that minus the risk-free rate. But that's a secondary definition, in that it's dependent on the primary definition of an investor's discount rate / risk premium.

Gengulphus

[Alaric]

I think it's very easy to value such companies than that - the answer has a single digit and every remotely sensible investor agrees about it! ;-)

Some of the shares that have come up as recommendations for HYP purchases at various times seem to not attempt a filter that the dividend is partly a return of capital, or even worse a distribution of the Company's borrowings. The mantra that you ignore future prices encourages this.

My personal filter is to look at the share price history. If a share has a 5% running dividend yield because five years ago it had a 1% yield and the price is now 20% of what it was then, that's the warning signal.

Moderator Message:
Discussion of the validity of the HYP Strategy is best carried out on the High Yield Share & Strategies - general board. Thanks - Chris

[dspp]

So there's no hope of it surviving 21 years or more? Or less obliquely, that appears to me to be based on far too unrealistic a model of how long a company is going to survive.
Gengulphus

Geng,

There is of course a probability of it surviving more than 20 years, just I was giving a simplified explanation in a way a simpleton like me can understand. However for most companies the probability x the time-value-of-money = very little present value, looking at everything 20+ years out. Certainly approaching negligible value in PV/share terms for most steady-state companies.

DCF is a tool in the box. It has limitations, but is a tool to be used. Actually I think it is both helpful in the steady state case, and in the growth case, but as with all models one must be wise to its limitations.

I came across a study about 20 years ago that assessed aerospace valuations. They had gone back about 95 years and assessed the value created in every company that they could find that had ever existed in the aerospace industry. It turned out that only half a dozen companies had ever created shareholder value over their lives, all the others were net negative. And went out of business, leaving only the likes of Aerospace, Boeing, UTC (P&W, HS, Sik), RR, CFM. In fact I think they calculated that once you added up all the + and all the -, then the residual value was just Boeing and Airbus. So 1) there is an enormous survivor bias in the market ; and 2) a lot of bad things terminate asset value, and 3) picking the winners is important.

regards, dspp

[TheMotorcycleBoy]

I am not totally convinced discounting earnings or dividends ought to be totally ignored, merely that they are both very crude (and riddled with assumptions) re measuring actual current value, and the discounted value to infinity does bother me so I prefered, when playing with such calculations, to consider over shorter periods
....

I agree. My preference (from our very limited, time frame of 8 months!) is that discounted free cash flow is a more accurate method than using discounted dividends, since:

1. some firms don't pay divis
2. and firms as Alaric says can use either borrowings or capital value neglect to bankroll divis.

I was also very judicious in my calculations for the FCFs, just taking Net cash from operations then subtracting what look like ongoing "stay in business" expeditures.

I guess a reasonable check, (which I have heard won't apply to some business sectors), is to also ensure that capex(s) exceed depreciation and amortisations by a slight margin too?

[Charlottesquare]

I guess a reasonable check, (which I have heard won't apply to some business sectors), is to also ensure that capex(s) exceed depreciation and amortisations by a slight margin too?

For any company not fully distributing its earnings I suspect you first look at its FCF from operations less loan amortisation less its dividends and then would in the round expect (maybe not year on year but averaged over a few years) its capex to be close to the resultant remainder. (Apart from deducting debt, paying dividends and investing the remainder why is it retaining my share of its earnings springs to mind)

So your check really also needs to factor in an expectation of capex (inc re goodwill) much higher than depreciation/amortisation where the company is retaining your money to reinvest, implicit in such an earnings retention is that it is going to deploy the funds to earn you even more in the future.

(Though beware those whose sole means of growth is by acquisition, buying the opposition is usually fine until you start going too far, a which point overpaying can be an issue, symptoms sometimes being when goodwill starts ballooning- catch is it can be tricky to spot without hindsight)

[Charlottesquare]

Ok, here's what I did with MSLH. Basically I came the conclusion that the reason why Phils description is so confused/confusing is that he tries to illustrate that you can assume staggered growth rates - i.e. growth gradually falls over time. Personally I find this approach a bit farcical, especially with more mature firms like DOM and MSLH. And furthermore it is the insistence of having the different phases of company growth that result in the need for the separate stand-alone TV, that's all; as it's just the equity prediction from a point in the future then onto perpetuity.

What I did with MSLH was simpler. Firstly I grabbed a few ARs and focussed on the "Consolidated Cash Flow statements" for 2013-17. (You need to search for diluted as well to get the number of shares in issue). So I then just grabbed the figures which I think best document the main FCF movements. You have to make some assumptions, and I was intentionally harsh, so any monies from resaling spent production equipment I've not included.

So below, the first 6 rows are in 1000s of GBP, the number of shares is in millions, and FCFps (free cash flow per share) is in GBP. I soon realised that the FCF looks reasonably steady for the last 3 years. But as I had got the figures down already I whacked them in.....and you can see the actual cash flow for earlier 2013-2014 period (recovery? genuine organic growth?) is quite sporadic, which rendered growth rate estimation so choppy that to be honest it's worthless in my opinion. Kind of what I expected!

Year	                        2013	2014	2015	2016	2017		
Net cash from operations        27124	29117	49685	49393	57305		
Tangible capex	                -5462  -11269	-14016	-12939	-18895		
Intangible capex	         -596	-741	-909	-934	-1750		
							
							
FCFF	                       21066	17107	34760	35520	36660		
Some financing costs	         -95	  269	-166	-40	-3407		
							
							
FCFE	                       20971	17376	34594	35480	33253		
Diluted shares(M)	         195 	196	199	200	199		

FCFps (in GBP)	               0.107	0.088	0.173	0.176	0.167
						
Diff		                        -0.0185	0.0846	0.0035	-0.0096		
Growth rate of FCF	                -0.173	0.955	0.0204	-0.05434

The average growth of FCF = 75%

So what I did then was what I'd assumed all along would be the best approach. Basically as MSLH is reasonable mature, but construction is probably a bit cyclical, so I thought the best thing to do is just to assume the free cash flow ps is fairly steady these days at 17p, and it will grow at the current rate of inflation or thereabouts. So seeing as the BoE in absense of Corbyn, I guess, is aiming for 2% and we seem to jumping between there and 2.7% ish, I just decided that the growth rate into perpetuity should be about 2.5%. I then assumed a modest discount rate of 6%, since that's about 4.5% above a 10yr gilt and (coincidentally) about the YTM of a fairly junk bond (e.g. PMO1). Then I just lobbed these figure into the DDM model:

Valuation = FCF(1 + g)/(r - g)

where r=discount rate, g=growth of FCF, and FCF is the last FCF that I was happy about[/pre]

Last CF	                0.17
Growth rate of FCF     0.025
Discount rate	        0.06
Estimated value GBP	4.98

Which bizarrely is very close to both [url=https://www.lemonfool.co.uk/viewtopic.php?p=168406#p168406]my final post on the DDM thread[/pre] and also to that target price on the "4-traders" site.

If you have a look at note 22 re the acquisition in the year (2017) it suggests that the new sub would in a full year increase profits before tax by circa £4.204mto £56.255m rather than £52.051, circa 8% increase. Accordingly when forecasting ongoing cashflows you possibly want to forecast using a higher starting figure than the 2017 figure of 17p (assuming said profits will lead to improved cashflow)

You also may want to consider that the loan increased by circa £28m re the acquisition, at average interest in the notes of 1.97% this will possibly reduce this £4.204m by possibly £500k re extra interest, but even then earnings growth ignoring inflation on existing 2017 earnings, ought to be circa £3.7m, circa 7%, and one would hope that they think they can actually do better than that with synergies and given the cashflow return they make re existing assets.

Given the acquisition of the business is reasonably significant re their size (B sheet net assets £237m) and they generated op cashflow of £57m on same (some 24% op cashflow on net assets employed) I suspect (albeit they may have restructuring to allow for though I expect that will have already been provided) that your starting 17p per share possibly needs increased to allow for this acquisition and what it possibly will do re increased cashflow per share,accordingly 18p per share might be a better reflection (16.7 x1.07 rounded up for synergies)


https://www.fundslibrary.co.uk/FundsLib ... _documents

Note, I have not fully read the accounts, I merely glanced at them to see where you got your numbers from and spotted the note 22 reference in the cashflow.

[TheMotorcycleBoy]

If you have a look at note 22 re the acquisition in the year (2017) it suggests that the new sub would in a full year increase profits before tax by circa £4.204mto £56.255m rather than £52.051, circa 8% increase. Accordingly when forecasting ongoing cashflows you possibly want to forecast using a higher starting figure than the 2017 figure of 17p (assuming said profits will lead to improved cashflow)

You also may want to consider that the loan increased by circa £28m re the acquisition, at average interest in the notes of 1.97% this will possibly reduce this £4.204m by possibly £500k re extra interest, but even then earnings growth ignoring inflation on existing 2017 earnings, ought to be circa £3.7m, circa 7%, and one would hope that they think they can actually do better than that with synergies and given the cashflow return they make re existing assets.

Given the acquisition of the business is reasonably significant re their size (B sheet net assets £237m) and they generated op cashflow of £57m on same (some 24% op cashflow on net assets employed) I suspect (albeit they may have restructuring to allow for though I expect that will have already been provided) that your starting 17p per share possibly needs increased to allow for this acquisition and what it possibly will do re increased cashflow per share,accordingly 18p per share might be a better reflection (16.7 x1.07 rounded up for synergies)

https://www.fundslibrary.co.uk/FundsLib ... _documents

Note, I have not fully read the accounts, I merely glanced at them to see where you got your numbers from and spotted the note 22 reference in the cashflow.

Many thanks for doing this CS. I didn't make a full study of your post, but will do so over the next few days...and probably get back with a few more questions knowing me!

thanks again,
Matt

[Gengulphus]

Year	                        2013	2014	2015	2016	2017		
...
FCFps (in GBP)	               0.107	0.088	0.173	0.176	0.167
						
Diff		                        -0.0185	0.0846	0.0035	-0.0096		
Growth rate of FCF	                -0.173	0.955	0.0204	-0.05434

The average growth of FCF = 75%

I'm not quite certain what you did there to produce that figure of 75%, but it's definitely wrong. My best guess is that it's the sum of the "Growth rate of FCF" row, interpreted as a rounded-to-whole-number percentage. But that's wrong in two respects: it's a sum rather than an average, and the appropriate type of average for growth rates over consecutive years is not the normal average (which would differ by a division by 4 and so be 19%) but their CAGR. In this case, it comes out as FourthRoot(0.167/0.107) - 1 = 0.12 rounded to two decimal places, or 12% in percentage terms. So really a lot smaller than 75%!

To see why the normal average is not appropriate, imagine that the FCFps values for 11 consecutive years were 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1. The corresponding yearly growth rates are 100%, -50%, 100%, -50%, 100%, -50%, 100%, -50%, 100%, -50% and their normal average is 25%, while their CAGR is 0%. The latter much better reflects the fact that it's basically just fluctuating from year to year, not growing. And especially when compared with what the FCFps sequence would be if it really were growing at 25% each year: 1, 1.25, 1.56, 1.95, 2.44, 3.05, 3.81, 4.77, 5.96, 7.45, 9.31 - IMHO clearly far better than 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1!

Gengulphus