As I’ve commented previously, on a few posts, ARB is one of my favourite business in my investment portfolio. In fact, I would go as far as saying that it is my favourite. The problem is that the quality of the business is no secret, and is reflected in the share price.
However, businesses like this do not grow on trees, and they tend to keep surprising on the up side. As such, the very notion of selling ARB really goes against the grain, for me.
Nevertheless, in the spirit of “confronting the brutal facts” (to quote Jim Collins), I will run some numbers and I’ll see where they lead.
My analysis is an attempt to answer the question: If I sell ARB, how much value do I gain, versus the value that I sacrifice?
NOTE: Many readers will be very quickly put off by my apparent heavy use of maths, and the sense that I am being overly precise. I can understand how this may appear to be the case, but I don't believe it's correct. In fact, the essence of my method is an acknowledgement that we cannot know the answers we seek with any precision. I really am attempting to be vaguely right here, rather than precisely wrong (to use a well known cliche). Many will be bemused by the apparent detail and even regard this wioth contempt. That' s fine, it's kept me off the streets for a few days.
1. How much intrinsic value is ARB offering?
The concept of “intrinsic value” is one that many value investors like to quote, but few like to back up, publicly, with hard numbers. At footnote * I go into some detail of how I like to guesstimate intrinsic value.
I am here estimating this value by performing a discounted cash flow analysis, and I am assuming a discount rate of 10% (ie, my target return is 10%). Understandably, many value investors, and others, will raise their eye brows at this point. I am aware of the potential pitfalls of DCF analysis, including the fact that it projects a level of precision that is unjustifiable, and that there is a tendency for many practitioners to use it as a method of justifying whatever value they desire.
These are all valid concerns. All I will say in response, is that I don’t believe in tossing out a perfectly sound methodology (perhaps the soundest methodology) because of the shortcomings of many of its practitioners.
I do not use the DCF method to estimate an intrinsic value. I don’t believe in doing this, as this would require me to have a crystal ball. That is, if I don’t have a crystal ball, then I can’t know exactly how the future will play out, and so, in my opinion, I have to allow for a range of possible futures. The way I like to deal with this (for a going-concern that is not likely to be overwhelmingly influenced by singular events), is to estimate a value for a somewhat pessimistic future, and another value for a somewhat optimistic future. I assume there is a 60% probability that the true value sits somewhere in this range (ie, there is a 20% chance of the true value being less than the lower limit, and equally a 20% chance of it being greater than the larger limit).
This is further discussed in footnote *.
Without going into to further details about what assumptions I made in arriving at my value estimates (this would be a major discussion in itself), I here present my estimated value range (drum roll):
Column 1
Column 2
Column 3
1
somewhat pessimistic
somewhat optimistic
2
My estimated value per share:
$12.0
$17.0
Column 1
1
As a side issue: Does this mean that I should buy the business at $12 per share?
Well, that’s a question with no definitive answer. A crucial part of forming an opinion on this, is to think about the odds. Remember, I am saying that there is a 60% probability of the true value sitting within the stated range, with a 40% chance that it will be somewhere outside the range (20% chance of being below, and 20% chance of being above). (See footnote * for a discussion of why I choose these probabilities).
If I buy at $12, then there is a 20% chance that I will achieve a return that is less than my target (receive less value than I pay for), but there is also an 80% chance that I will achieve a return that is greater than my target (achieve more value than I pay for). If we assume, very roughly, that the mid-point of the valuation range is the value that we can expect (the expected value), then we can expect to receive $14.5 of value per share. As such, if we pay $12 per share, we can expect to receive about $1.20 in value, for every dollar we pay. However, there is a substantial risk (20%) that I will receive less value than I pay for.
However, considering the uncertainty inherent not only in my value estimates, and in my estimate of the odds, but also on the suitability of my assumed rates of return (I am basing my valuation on a desired 10% return, however, what I really want is a return that will be, say 7% in excess of future inflation rates). As such, I will normally demand a purchase price that is somewhat below my lower limit. If my expected value is much greater than the value at the lower limit, then I may relax this.
To see how this valuation sits in term of other traditional measures of value, below I quote various metrics that would be implied if the shares were purchased at the limits of my valuation range:
Column 1
Column 2
Column 3
1
If purchased at $12 per share
If purchased at $17 per share
2
grossed up dividend yield(based on my estimate of current “earnings power’’ and prevailing payout rates)
3.1%
2.2%
3
implied long term dividend growth rate(effective growth rate to infinity, on basis of 10% required return in valuation)
6.7%
7.7%
4
Implied dividend growth rate over next 10 years(if we assume growth rate after year 10 settles to 4%)
12%
17%
5
PE ratio(based on my estimate of current “earnings power’’)
23
33
6
EV/EBIT(based on my estimate of current “EBIT earnings power’’)
16
23
7
EV/EBITDA(based on my estimate of current “EBITDA earnings power’’)
11
15
The growth rates, above, may look very demanding. However, I emphasize that this is the growth in the dividend, not in the earnings. What this reflects, is that in my valuation I am assuming that if earnings growth slows in the longer term, ARB with a current payout rate of only 50%, has plenty of room to increase the dividend payout ratio. In fact, whilst I am assuming that returns on capital will be lower, going forward, than what they have been in the last 5 years, they will still be high enough, in the longer term, to allow a large increase in the dividend payout, whilst still funding the more modest longer term growth.
I am happy to assume this for ARB, as it is a business with a strong economic moat (to put it mildly) and a management with a demonstrated focus on sustaining it and using its capital prudently. Hence I am saying that if ARB cannot find sufficient profitable growth, longer term, I trust them to return capital to shareholders (they have already I track record of doing so). On the other hand, if they do find profitable growth longer term, then payout ratio's may not expand (stay closer to current levels), but wealth creation will be greater than what I have assumed. That is, my valuation will turn out to be conservative.
2. If I sell, how much cash am I getting per value forsaken?
At the time of writing, the ARB share price is $15.30. If we divide this by each of the valuation limits, we get:
Column 1
Column 2
Column 3
1
somewhat pessimistic valuation
somewhat optimisticvaluation
2
Cash received per value forsaken at $15.3 per share sale price:
1.28
0.90
So if we ignore taxation implications, we are saying that we can possibly expect to gain an extra 9c of cash for every dollar that we are sacrificing, but there is also a substantial risk (20% based on our methodology) that we will be losing 10c of value for every dollar of sale.
Of course, whether or not the extra 9c of cash received represents 9c of value, is another question. Remember, my valuation has been based on a 10% required rate of return. If I could immediately invest the proceeds into something that offers a high certainty of delivering 10% per annum, or more, then perhaps I might contemplate selling (though for me, the prospect of gaining 9c per dollar of relinquished value, especially at the risk of losing out in the transaction, wouldn’t be enough for me to bother, even if I was talking about a more pedestrian business than ARB).
It will be more useful if we express the above table, in terms of the per share sale price, p, as follows:
Column 1
Column 2
Column 3
Column 4
1
somewhat pessimistic valuation
Mid-point
somewhat optimisticvaluation
2
Cash received per value forsaken at a per share sale price of p ($ per share):
0.083 x p
0.071 x p
0.059 x p
It will be further useful if we express this range as follows: Cash received per value forsaken = 0.071x p+/- 17%
This may look a little scary to some, but it is actually quite simple. All it is saying is that we can expect to receive 0.071x p of cash per value relinquished, for selling out at p dollars per share, but that this may be 17% higher this, and may also be 17% lower (as our valuation sits within a range).
3. But what about taxation?
If you’re anything like me and you’ve held ARB for many years, odds are that the vast majority of the sales proceeds will constitute a capital gain. If this is the case, and you are at the top marginal tax bracket, you can expect a tax bill perhaps approaching 20% of the proceeds. If you’re at a lower tax bracket this will be somewhat lower, nevertheless the tax bill is unlikely to be lower than about 10% of the proceeds.
We can include the influence of tax, as follows:
Cash received per value forsaken = 0.071x px (1-T)+/- 17%
Where p = the sales price in dollars per share T = proportion of proceeds payable as tax
4. What is my opportunity?
If the above numbers indicated that I could receive substantially more cash than my relinquished value, after tax, then I may be willing to suffer the consequences of having cash sitting around earning next to nothing, under certain circumstances. One of those circumstances might be that I want to have some cash in my portfolio, to enable me to take advantage of prospective opportunities. In my case, my portfolio already incorporates substantial cash, and I would need ARB to be very much more overpriced than it currently is, to add to my unproductive cash balance. I would especially need ARB to be heavily overpriced, because, as I say, I would be sacrificing a business that tends to surprise on the upside, and I would also be reducing the level of diversification in my invested portfolio (I hold a fairly concentrated portfolio).
However, I do have the option of immediately investing the proceeds into my existing portfolio. Restricting this to the four highest quality businesses (excluding ARB) of my portfolio, holds some appeal to me. In this case, whilst I would be losing what is potentially the highest quality business in my portfolio, I believe the proceeds would be cycled into something of equal, and in fact better, quality. What I am saying is that I believe that collectively, my next four best holdings represent a higher quality investment than an investment in ARB alone, as they collectively offer better earnings certainty (especially as the four businesses are highly uncorrelated). This may be worth doing, if I believe I am gaining sufficiently more value than what I am sacrificing, to compensate me for the loss of portfolio diversification.
I won’t go into the details of what these four businesses are. Suffice to say that I have valued these, via a similar methodology to what I have discussed for ARB. If I combine the value of these businesses, in equal weightings, I get the following:
Column 1
Column 2
Column 3
Column 4
1
somewhat pessimistic
Mid-point
somewhat optimistic
2
Value of portfolio per dollar of price(for share prices as at the time of writing):
1.3
1.5
1.7
Or expressed in more convenient form: Value of portfolio per dollar of price =1.5 +/- 14% I am treating this as my opportunity
5. How much value will I gain per value forsaken?
I can now combine my value ranges in Item 2 and Item 4 above, to come up with a distribution for the value gained versus the value sacrificed. Here is how:
Ratio of value gained to value forsaken
= (value gained per cash paid) x (cash received per vale forsaken)
= ( 1.5 +/- 14% ) x (0.071x px (1-T)+/- 17% )
I can deal with this by multiplying the mid points and separately determining a new combined range percentage deviation. As the two distributions cover the same confidence range (60%, as previously discussed), the combined deviation can be expected to be the RMS (the square root of the sum of the squares) of 14% and 17%, giving 22%.
As such:
Ratio of value gained to value forsaken = 0.11 x px (1-T) +/- 22%
Remember, as previously discussed, we do not have 100% certainty that the truth sits within this range. There is a fair chance (a 20% chance, if my numbers are right) that reality actually sits somewhere below this range, and equally somewhere above. In other words, this represents a 60% confidence level. Given the various uncertainties with my estimation of the future and the associated odds, I would be far more comfortable dealing with an 80% confidence level. Then the two tails of the distribution would each hold a 10% probability (rather than the current 20%).
For the purpose of estimating the 80% confidence range, I am happy to assume a normal distribution (I would suggest this is likely to be approximately right, especially as this is a distribution which has resulted from the product of two prior distributions). For a normal distribution, an 80% confidence interval will 1.5 times larger than a 60% confidence interval, giving us a new deviation of 1.5 x 22% = 33%.
As such, we can say that to an 80% confidence level:
The ratio of value gained to value forsaken = 0.11 x px (1-T) +/- 33%
At the table below I calculate the resulst of the above equation, for various tax brackets and ARB sale prices:
Column 1
Column 2
Column 3
Column 4
Column 5
1
p (ARB sale price$/share)
T(proportion of sale proceeds payable as tax)
Value gained to value forsaken (80% confidence range)
2
lower estimate
mid point
higher estimate
3
12[/FONT][/CENTER]
0%
0.88
1.32
1.76
4
12[/FONT][/CENTER]
10%
0.79
1.19
1.59
5
12[/FONT][/CENTER]
15%
0.75
1.12
1.50
6
12[/FONT][/CENTER]
20%
0.70
1.06
1.41
7
13[/FONT][/CENTER]
0%
0.95
1.43
1.91
8
13[/FONT][/CENTER]
10%
0.86
1.29
1.72
9
13[/FONT][/CENTER]
15%
0.81
1.22
1.62
10
13[/FONT][/CENTER]
20%
0.76
1.14
1.53
11
14[/FONT][/CENTER]
0%
1.02
1.54
2.06
12
14[/FONT][/CENTER]
10%
0.92
1.39
1.85
13
14[/FONT][/CENTER]
15%
0.87
1.31
1.75
14
14[/FONT][/CENTER]
20%
0.82
1.23
1.64
15
15[/FONT][/CENTER]
0%
1.10
1.65
2.20
16
15[/FONT][/CENTER]
10%
0.99
1.49
1.98
17
15[/FONT][/CENTER]
15%
0.93
1.40
1.87
18
15[/FONT][/CENTER]
20%
0.88
1.32
1.76
19
16[/FONT][/CENTER]
0%
1.17
1.76
2.35
20
16[/FONT][/CENTER]
10%
1.05
1.58
2.11
21
16[/FONT][/CENTER]
15%
0.99
1.50
2.00
22
16[/FONT][/CENTER]
20%
0.94
1.41
1.88
23
18[/FONT][/CENTER]
0%
1.32
1.98
2.64
24
18[/FONT][/CENTER]
10%
1.19
1.78
2.38
25
18[/FONT][/CENTER]
15%
1.12
1.68
2.25
26
18[/FONT][/CENTER]
20%
1.05
1.58
2.11
27
20[/FONT][/CENTER]
0%
1.46
2.20
2.94
28
20[/FONT][/CENTER]
10%
1.32
1.98
2.64
29
20[/FONT][/CENTER]
15%
1.24
1.87
2.50
30
20[/FONT][/CENTER]
20%
1.17
1.76
2.35
6. What is my conclusion (if the above table can be believed)?
Disclaimer: My conclusions are based on the above table, which are based on my estimated opportunity cost. My opportunity cost will be different from yours.
If I had no tax owing on my sale (for some peculiar reason), then I could contemplate selling at current prices (about $15 per share) on the basis that I can expect to receive in the order of 60% more value than I relinquish, with only a small risk (less than 10%) of receiving less value than I relinquish.
If on the other hand, 15% of my proceeds were owed to the tax man, then selling at $15 gives me the prospect of a reward of 40% more value than I relinquish, with a greater then 10% chance of losing out in the transaction. In this tax bracket, I believe a target sell price of $16 would be a more compelling proposition.
At a tax bracket of about 20%, the table indicates, in my opinion, that a sale price closer to $18 would start looking compelling.
There is one last important comment that I should make. There is a good likelihood that further increases in the share price of ARB shares, going forward, will be accompanied with increases in the prices of the other shares in my portfolio. If so, my opportunity will become less attractive, and as such the ratio of value gained to that relinquished, will have to be reassessed.
===========================================================================
Footnote *
Intrinsic value range
Here is how I like to deal with intrinsic value, for a going concern.
I like to dream up two scenarios, one a somewhat pessimistic scenario and another a somewhat optimistic scenario. Obviously the factors feeding into each of these scenarios, and how my opinion is formed with respect to them, are numerous, specific to the opportunity, and perhaps another discussion for another time.
That I assume somewhat pessimistic and somewhat optimistic scenarios to provide my range of possible valuations, is key. I am accepting that I am not anticipating the broadest range of possible futures, from a very pessimistic one, to a very optimistic one. I believe that once we get to extremes, it is very hard to conceptualize the associated odds. For instance, if I assume the lower limit of my valuation is associated with a very pessimistic scenario, then how can I guesstimate the odds that the true value will be lower still? Is it a 10% chance of the true value being lower still, or is it a 5% chance? Is 10% associated with a very pessimistic scenario, and is 5% associated with an extremely pessimistic scenario? In my mind, the limits of the valuation start becoming a little arbitrary.
On the other hand, by assuming that my value bounds are associated with the word somewhat, I am saying that there is a substantial probability that the true value may be lower, or higher, than my bounds. This means I am not needing to dream up outliers in my scenario. I am simply having to think about things that my brain can much more easily get a handle on.
To me a substantial probability means a reasonable chance of. I believe this means a chance greater than 10%, but less than 30% (if the chance was 30%, or greater, then I think we move from a substantial probability to a veryhigh risk of. As such, I am happy to assign a 20% probability that the true value may be lower, or higher, than my estimated range.
In statistical jargon, I am saying that my value range constitutes a 60% confidence interval (20% chance of being below or above each of the limits).
It is important that I state, that I don’t believe I can predict the future. What am trying to do is establish a value range, that I believe gives me a reasonable decision making tool as an investor. This method makes sense to me, as I am not attempting to determine an actual value of the business (which I think is fanciful), and then prescribe an arbitrary “margin of safety” (which seems a little arbitrary to me).
I am simply acknowledging that I expect the true value of the business is likely somewhere within my estimated range, and that if I want to have a high probability of extracting my required return (or exceeding it), then I need to purchase at a price that is below my lower limit. If I purchase at my lower limit, then I am saying that I still have a sizeable risk of not achieving my required return (20%). Of course, my guesstimate of the odds is only that, a guesstimate. So I will probably want to purchase at a price somewhat below my lower limit, to increase my odds of success.
(20min delay)