How the multiple imposes fundamental questions
Some thoughts on multiples, growth, and capital allocation, from an exploratory analysis on BTG Pactual

Recently, I have been trying to become more effective, efficient, and assertive in my research.
In my case, and each person’s situation will be different because of their skill set and processes, the area where I needed the most improvement was focus. Not really focusing more, but rather determining where and how much to focus.
As part of that, I wanted a cascade, or incremental, method of research, under which I would always be able to answer what returns could be expected from a name, and which questions are most valuable to add/reduce confidence in those return expectations.
I also wanted a way to compare returns from different types of companies/stocks. For example, how do we equate PE with growth expectations, or with ROE and quality?
As part of that, I wrote two free-to-read pieces:
Where do stock returns come from, which is my attempt to put all of the factors in a stock into a single “napkin formula”, including growth, capital returns and requirements, PE and PB multiples, and capital allocation decisions (invest vs dividends vs buybacks).
My current screening setup, which condenses that formula into three factors alone: capital returns, multiple, and growth.
So now I can intuitively and quickly compare names in different styles: value versus growth multiples, value versus quality ROEs, or stocks with different distribution policies. Even more important, I can now produce a single number (I called it r-rank) that tells me how much a stock could return, and where the returns have to (emphasis on HAVE TO) come from (distributions, growth, multiple), that works for several kinds of businesses.
In this short article, I want to go through an example using the Brazilian bank BTG Pactual (BPAC3).
The name is interesting because it combines high ROEs and high growth with high multiples (PB and PE), and yet my formula ‘puked’ a 25% r-rank figure, which is fairly high.
It is also interesting because it illustrates how multiples end up determining the potential sources of returns, and more importantly, how multiples therefore determine what type of capital allocation and business developments are needed to materialize the returns. This already directs our attention to key return-driving business questions.
Vamos lá!
Disclaimer: The opinions expressed in the Blog are for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. I may own or later purchase some of the stocks mentioned in this article.
TLDR
A shareholder’s sources of return are dividends, growth, or multiple expansion.
The potential return from dividends or from buyback-driven growth is determined by the company’s earnings yield (extrinsic, market-determined)
The return from growth is eventually capped at the ROE of the business (sustainable growth rate), but is intrinsic, company- and industry-driven.
That means with estimates for growth and reinvestment ROEs, and knowing the multiple, we can estimate returns very well. Conversely, given the business (growth and ROEs), and a desired return, we can determine what price/multiple is good for us.
Because of the multiple, the capital invested in a business can have a hugely different return from the capital invested in the stock of that same business.
Even for companies with the same multiples, ROEs, etc., the stockholder returns depend a lot on capital allocation decisions in the future, primarily: distribute or invest.
When the ROE of a company is higher than its earnings yield on the market, its shareholders will make more money if the company reinvests that money in the business (as long as it can keep returns on capital above the earnings yield).
When a company has a high multiple, it is almost forced to continue growing its capital at consistent or improving returns to realize a good shareholder return.
Company description
BTG Pactual is maybe the most important investment bank in the country, with an expanding commercial lending operation.
Although other banks like BdoB, Bradesco, Itau, or Santander have larger commercial loan portfolios and also participate in investment, BTG is probably the leader in the investment side (investment banking, sales & trading, asset & wealth management, research, etc). The bank doesn’t really participate in retail/consumer, except for investment/wealth products.
Why is it interesting
First off, the bank has fairly high and growing returns on equity, which are naturally above the ROEs of its more pure-bank Brazilian peers (ex: Itau), and closer to pure-financial peers like XP or B3.
At the same time, it has been growing very fast, in both BRL (blue below) and USD (purple).
Finally, despite the ‘improving’ fundamentals in terms of ROE and growth, it trades at multiples close to or below the post-pandemic average (inclusive of the COVID panics).
Of course, none of this means anything by itself! It is only indicative of potential opportunity.
How the multiples ‘corner’ the returns, or why low multiples are so superior
Next, let us see the different ways (and quantities) in which one could theoretically earn a return on BTG, and how they differ.
Dividends could be paid from the earnings. However, because of the multiples (PE or PB), BTG’s high ROEs are cut by 60%+ for stockholders if earnings are paid as dividends. If the ROE is 25% but the P/B is 3.7x, then the dividend yield can only be ~6.5% (assuming no taxes on divs, which eat even more from this).
This is the first insight
Because of the multiple, the capital invested in a business can have a hugely different return from the capital invested in the stock of that same business.
What about buybacks? Same thing. If the P/E multiple is 16x, then in the best scenario the company could repurchase ~6.5% of the stock with the earnings of that year. That increases EPS by ~7%. Unless one assumes a multiple expansion in PE, then the stock price moves up by 7% (same PE, earnings higher by 7%), and the return is 7%.
But hey! It’s not just earnings; the company also has growth! That has to account for something, right? Oh indeed it does. As explained with buybacks, growth in earnings becomes price return unless the multiple falls (which one would not expect in a growing company, barring cyclical or market-driven factors).
The issue is that growth almost certainly requires some capital. The best kind of growth is one that requires very little capital (that’s why software can have so incredible returns sometimes, or why an operationally levered company like a retailer can have volatile ROEs), or one that can be financed with cheap capital (for example, from low rates).
Unfortunately, there is no infinite growth without capital, and no company can leverage its balance sheet forever, meaning that, sooner or later, growth has to consume part of earnings and is capped by the returns on equity.
This is where the famous concept of the Sustainable Growth Rate comes from.
In the long-term (and what long-term means is specific to each stock), the company can only grow at whatever level its own equity can reproduce itself.
Further, as long as a company can grow at constant or improving ROEs, its stockholder returns will be driven by ROE, independently of the multiple.
Take BTG as an example:
For each R$100 of equity, it generates R$25 of net income.
Because each R$100 of equity is valued at R$370 in the market, if the company distributes those R$25, it becomes a 6.5/7% return, as we saw above.
However, if the company invests those R$25 and maintains a 25% return, then it generates R$6.25 in additional earnings, which, if valued at the same multiples (~15x), becomes R$94 of share appreciation, or a return of 25% on the investment.
The same applies to the P/B multiple staying constant and equity growing by R$25.
In fact, we can construct a table showing returns at different levels of growth, based on the current metrics. We can observe that the return to the shareholder is maximized with maximal growth (this is where capital finds its best use).
We can extend the model even more by incorporating lower incremental ROEs. That is, the company can grow, but the new investments are not as good. We observe again that even though returns clearly diminish as incremental ROE diminishes, growth is always higher as long as the ROE is higher than the E/P.
How is the above table calculated? Using the g=15%, ROE=10% example:
The company dedicates 15% of its original ROE to growth (R$15); only 10% (R$10) remain for distribution, which is divided by a 3.7 PB, for a distributable yield of 2.7%
The remaining 15% of ROE is invested, but instead of generating a 25% return, they only generate a 10% return, or 1.5% in additional earnings (R$1.5 per R$100 of original equity). These earnings are paid at the same multiple (~15x) to become R$22.5 in price appreciation, but because our price was R$370 for each R$100 of equity, then our return is ~6.1%, for a total of ~8.8% (the table shows 8.7% because I rounded some figures for simplicity).
This leads to more insights
Second insight
Even for companies with the same multiples, ROEs, etc., the shareholder returns depend a lot on capital allocation decisions in the future, primarily: distribute or invest
Third insight
When the ROE of a company is higher than its earnings yield on the market, its shareholders will make more money if the company reinvests that money in the business (as long as it can keep returns on capital above the earnings yield).
In corporate finance parlance: shareholders make money if the company can invest above its cost of equity.
And the fourth insight
When a company has a high multiple (low earnings yield), it is almost forced to continue growing its capital at consistent or improving returns in order to realize a good shareholder return.
That last insight is maybe the most important. Because the multiples of BTG are somewhat high, I cannot be happy with the business being good and staying the same, because then my returns will be low.
For BTG to make sense, I have to make sure not only that it can keep earning the same ROE, but also that it can reinvest at similar ROEs. That becomes a challenge for a business doubling its equity every three years (1.25 ^ 3 = 1.95).
All of the above is without considering multiple expansion/contraction, especially the latter. An improving business, or more generally, an improving read on the business or the capital market/sector where it participates, can lead to multiple expansion, which is arguably the fastest and most violent way to get returns. Except for very specific cases, I prefer to leave multiple expansion to what Ben Graham would call ‘speculative investment’. If it comes, even better, but I don’t build it into my return models (if for no other reason, because annualizing a multiple return depends entirely on how fast that multiple expansion happens).
However, because of the impositions from the high multiples on growth at high capital returns, when a business cannot grow at reasonable returns, its multiple will probably contract. Therefore, the high-multiple business not only has to grow, ideally at constant returns, but also deal with the eventual loss of multiple when that business cannot grow anymore.
Incorporating a contracting multiple into the calculation is challenging because it would require including a time factor (over which period the multiple contracts). However, we can still think of what kind of multiple would be fair under a slower-growth or slower ROE scenario. The formula is the dividend growth model, with the dividend being whatever is left after growing (the payout ratio). The most important parameter, the required return, can be either set up by us or we can speculate on what the market could pay for it.
The key questions about BTG
At this point, the key questions, those whose answers will have the most impact on future returns for BTG shareholders, should come naturally.
The most important:
Where can the company invest that equity growth (as much as 25% per year), ideally at the same returns?
Derived from this and completing the picture:
Which businesses can consume the most capital, and what are their returns?
Are there businesses that do not consume much capital but that can still grow very fast?
Are there any levers not considered here that can help in the short to mid-term, like operating leverage or financial leverage?
What is a fair multiple at a lower level of sustainable growth? How does that (potentially negative) return impact the rest of the calculation?
I will deal with these in a future article on BTG that will be available only to paid subscribers. In case you haven’t subscribed to Quipus, here is a 20% discount, forever.
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