Share valuation using the Discounted Free Cash flows

[TheMotorcycleBoy]

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

Hi Geng, I can't spend too long on this post, as I've just started the day job, and have vowed to really get my head down this week.

Essentially I extracted the FCFps for 5 years, i.e. 0.107,0.088,0.173,0.176,0.167. I then formed 4 sets of adjacent pairs from the 5 datas, in the form of (FCFn+1,FCFn), where n is the year number reference. So then I arranged into difference terms i.e.

diffn = (FCFn+1) - (FCFn)

and in doing so I arrived that:

0.088 - -  0.107 = -0.019
0.173 - 0.088 = 	0.085
0.176 - 0.173 = 0.003
0.167 - 0.176 = -0.009

Then armed with the diffs above, I divided each by the FCFn value i.e. the earlier year's value, so:

-0.019 / 0.107 = -0.1776
0.085 / 0.088 = 0.956
0.003 / 0.173 =  0.017
-0.009 / 0.176 = -0.051

Now what we have is 4 discrete growth rates for periods 2013-14, 2014-15, 2015-2016, 2016-2017.

Which summarise to 0.745. And then.......dammit!!......you're dead right.....I forgot to divide by 4 to form an average!! (Very embarrassing )

if I had remembered I would then I have divided by 4, and arrived at 0.19 or 19%.

Yup. Silly me. That's the problem with multitasking all my weekend chores and responsibilities with looking at figures I suppose....

But regardless, what I did it the end, was to ignore the forecast of FCFps growth rate and just use current inflation rate (2.5%) which probably give rise to a more conservative valuation.

Thanks for spotting this Geng, I'll read yours and other posts tonight. And apologies for scrappy notes above! I've gotta dash.

Matt

[TheMotorcycleBoy]

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

Thanks again, Geng

I followed that link on CAGR. I'd seen this acronym previously before, but being the silly muppet that I am had not bothered studying it any further. But, yeah, the geometric technique is the natural way to view this trend, i.e. it's akin to "compound interest", so it has been duly noted by myself. In fact the main reason why thought, "I know I'll just use an arithmetic average" was basically because in this book it is what the author uses to deduce an equity (NAV) growth rate.

I imagine the author just uses the simple i.e. commonplace technique to derive the average, since as it's an introductory book, he perhaps does not wish to overwhelm the reader with too much detail. He may be well refer to CAGR at some stage to be honest, it's a while since I read it.

So perhaps a better way of doing DFCF valuation for MSLH would be

1. assume 12% growth for next 5 years
2. use 2.5 growth thereafter for the terminal value

but as alluded to by others, the "devil" is in the choice of rates, and perhaps my earlier approach, i.e. just approximate using the current/forecast inflation rate is preferable, unless one is looking at real rocketship of startup/tech/growth company etc.

Matt

[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)

A ha. That acquisition. I'd deliberately ignored that. Being a cynical employee often in the midst of acquisitions, I'm often a little circumspect, of how quickly their +ve impact (on the earnings) occurs. Probably because I work on software R&D type stuff, so of course the benefits of my kind of enterprise often take 2-3 years before reaching fruition, and acquisitions (changed internal processes) usually throws a big spanner of the works.

However, as MSLH are involved in construction materials, and the sub. is "CPM Group Limited, a precast concrete manufacturer", it is probably much more straightforward for the earnings to be redirected and continued in this scenario.

In other words, this assumption of additional of profit/FCF seems to be likely.

Indeed, silly me, I know recollect that I tried to do a forecast earnings, P/E estimate for MSLH and the earnings boost as reported in an interim note, which I have since forgotten about was published. And is this announcement it states the first 6 months of 2018 resulted in £32.5m PBT.

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)

I'm struggling a tiny bit on this one. I can see as much as that I *think* you are assuming proportionality between NAV and op cashflow. (I think).

But where does the 1.07 come from? Is that a 7% I'm seeing? Regard NAV, the Marshalls B sheet says £237m and the acquisition on note 22 says £26m. Hmm... I'm puzzled, since 26 is probably >10% of 237. Help!

Anyway, it's all good stuff, so if you have time to shed any more light that would be appreciated.

thanks,
Matt

PS What does "Monies paid into escrow" mean in the note 22?

[Charlottesquare]

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)

A ha. That acquisition. I'd deliberately ignored that. Being a cynical employee often in the midst of acquisitions, I'm often a little circumspect, of how quickly their +ve impact (on the earnings) occurs. Probably because I work on software R&D type stuff, so of course the benefits of my kind of enterprise often take 2-3 years before reaching fruition, and acquisitions (changed internal processes) usually throws a big spanner of the works.

However, as MSLH are involved in construction materials, and the sub. is "CPM Group Limited, a precast concrete manufacturer", it is probably much more straightforward for the earnings to be redirected and continued in this scenario.

In other words, this assumption of additional of profit/FCF seems to be likely.

Indeed, silly me, I know recollect that I tried to do a forecast earnings, P/E estimate for MSLH and the earnings boost as reported in an interim note, which I have since forgotten about was published. And is this announcement it states the first 6 months of 2018 resulted in £32.5m PBT.

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)

I'm struggling a tiny bit on this one. I can see as much as that I *think* you are assuming proportionality between NAV and op cashflow. (I think).

But where does the 1.07 come from? Is that a 7% I'm seeing? Regard NAV, the Marshalls B sheet says £237m and the acquisition on note 22 says £26m. Hmm... I'm puzzled, since 26 is probably >10% of 237. Help!

Anyway, it's all good stuff, so if you have time to shed any more light that would be appreciated.

thanks,
Matt

PS What does "Monies paid into escrow" mean in the note 22?

Contingent sums on a contract will often go into an Escrow account, in effect a bank account where the monies are locked until both sides agree their release, I would need to read the accounts fully but I would suspect the sellers get it if certain things happen/seller assurances etc borne out. In effect they get £26m now and £12m if they have not sold Marshalls a pig in a poke- the terms re handing it to the seller etc will be in the small print of the contracts. Total purchase is however £38m not £26m.

I was in effect saying the 16.7p M & M were using I thought needed increased re the acquisition, I calculated that note 22 suggested the £4.2m was a 8% augment re the full year but was not sure if this allowed for the finance cost of the deal which given extra debt I calculated at £500k, hence net increase 7% (unless finance cost already included in note 22 full year impact statement figures)

My point re cashflow to net assets was more an indicative point, a sort of cashflow equivalent of ROCE, I am always cautious re ROCE and add ons as the current relationship could be based on already heavily amortised goodwill/written down net assets, or a business grown organically so no goodwill, however if they paid out £38m to get £4.2 extra profits I expect they think they can do better than this so I would hope at least for a little synergy, however my suggested 18p allowed very little for this. In effect 16.7p per M & M. 7% add on 1.16 , 0.14 re synergies/ sweating the assets gets 18p- I expect the 18p is actually conservative.

[TheMotorcycleBoy]

Contingent sums on a contract will often go into an Escrow account, in effect a bank account where the monies are locked until both sides agree their release, I would need to read the accounts fully but I would suspect the sellers get it if certain things happen/seller assurances etc borne out. In effect they get £26m now and £12m if they have not sold Marshalls a pig in a poke- the terms re handing it to the seller etc will be in the small print of the contracts. Total purchase is however £38m not £26m.

A ha. That makes good business sense.

I was in effect saying the 16.7p M & M were using I thought needed increased re the acquisition, I calculated that note 22 suggested the £4.2m was a 8% augment re the full year but was not sure if this allowed for the finance cost of the deal which given extra debt I calculated at £500k, hence net increase 7% (unless finance cost already included in note 22 full year impact statement figures)

Yes, I see. The assumed profit boost is approximately 8% of MSLH's prior reported. Yes that makes sense.

And FWIW TheMotorcycleBoy is now my new handle. See this thread for the explanation.

My point re cashflow to net assets was more an indicative point, a sort of cashflow equivalent of ROCE, I am always cautious re ROCE and add ons as the current relationship could be based on already heavily amortised goodwill/written down net assets, or a business grown organically so no goodwill, however if they paid out £38m to get £4.2 extra profits I expect they think they can do better than this so I would hope at least for a little synergy, however my suggested 18p allowed very little for this. In effect 16.7p per M & M. 7% add on 1.16 , 0.14 re synergies/ sweating the assets gets 18p- I expect the 18p is actually conservative.

Ok, I understand.

Matt (from M&M)

[TheMotorcycleBoy]

I want to finish my research into share valuation using Discounted FCFs. Firstly I'm using the "last calculated" FCFps value of 18p after Charlottesquare tweaked my original estimate of 17p.

By playing with various discount rates we can see the following estimates for stock prices with the actual price and the broker (from 4-traders) consensus falling in between the values obtained using rates of 6-7%.

Using Charlottesquare's 18p for last FCFps and various discount rates of 6-9%:

Last CF	                0.18			
Growth rate of FCF	0.025			
Discount rate	        0.06	0.07	0.08	0.09
Estimated value GBP	5.27	4.10	3.35	2.84

Now I'm going to attempt a valuation again using DCF but this time looking more like Phil Oakley's example in "How to pick Quality Shares" where we assume an initial "over inflation" growth the FCF for the first 5 years, and then calculate a terminal value (using FCF growing with inflation), and adding the two.

To start with for the first 3 years, I'll use 12% as the growth rate after Gengulphus shared with me the true path of using the CAGR to calculate the rate in this event using previous actual FCFs, then for the next 2 years 5% is used, before dropping it to 2.5% to calculate the Terminal value to perpetuity.

I used 6.5% as my discount rate at first, since that rate yielded the "most likely value" of the estimate (i.e. closest match to broker consensus target price) in the earlier simple model where I just used the expected inflation rate (2.5%) as the growth of FCF from now to perpetuity.

Of course, since in this valuation the initial (i.e. first 5 years) rate of growth is assumed as being a lot greater than 2.5%, it came as no surprise that initially the estimated valuation using the 2-stage approach was much greater, at £11.30 per share:

Moderator Message:
RS: Matt wrote the next part of the post incorrectly and would any interested parties proceed to next post but one for the corrected version."

[TheMotorcycleBoy]

A ha.....

I just double checked my working out

Made a bad spread sheet error

FCF	Growth  Year	DFCF	
0.18	0.12	0		
0.20	0.12	1	0.19	
0.23	0.12	2	0.20	
0.25	0.50	3	0.21	
0.38	0.50 4	0.29

Hmm.... that will have ruined things. Will redo model later.

[TheMotorcycleBoy]

Ok

This is my corrected version, of a discounted FCF valuation of MSLH using 18p as the FCFps on year zero, growing at 12% for the first 3 years, then 5% for the next 2 years and then 2.5% until perpetuity.

The valuation due to the

FCF	Growth	Year	DFCF	
0.18	0.12	0		
0.20	0.12	1.00	0.19	
0.23	0.12	2.00	0.19	
0.25	0.05	3.00	0.20	
0.27	0.05	4.00	0.20	
0.28		5.00	0.19	

Sum of first 5 DFCFs=	0.97	

Using 0.025 as growth rate to perpetuity gives=5.20				
Discounted the TV back to present value (i.e. back 6 years)=3.27	
					
So this gives an estimate with 8% discount rate
Sum of first 5 DFCFs+TV=4.24

Other valuations

Discount rate%    Value £
6%                      6.78
7%                      5.23

Sorry about the earlier mess, it's what happens when I try to rush things out before tea. Now time to put m' feet up!