Where do stock returns come from? A napkin framework.

Distilling down a DCF to its simplest components

Table abacus - Author and time unknown, probably XVIth Century, Strasbourg

The investment universe is huge. Hundreds of names, even in a single industry or country. Furthermore, this universe is in constant flux, as events happen and prices move.

In such an environment, having some form consistent yardstick is crucial for reviewing different companies and stocks. Otherwise, how can we know whether A or B is the best decision?

The problem is that stocks and companies are not unidimensional. They score better in some measurements and worse in others: A has a lower earnings multiple, but B grows faster. B requires more capital to grow, and therefore A pays more dividends. A is in a riskier market than B.

How do we aggregate all of this information? Is there a way to make it comparable? For example, is there a way to equate growth and multiples, i.e, that a 10x P/E at 2% growth becomes equivalent to a 12x P/E at 5% growth?

Investment theory’s answer to this problem is the DCF valuation. This type of calculation incorporates all of the nuances above into a unidimensional outcome, a fair value price.

However, traditional three-statement DCF models have a big disadvantage: in their extension and complexity, they hide the assumptions that end up driving the majority of the returns (or lack thereof). They suffer from overfitting.

This article tries to offer a simplified, napkin-style DFC model, derived from the original equations, that still forces us to think through the key assumptions, but that is easier to create, communicate, and think about.

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.

Inverting the discount rate

A DCF valuation basically says that the value of a stock today is equivalent to all the cash flows it will generate in the future, discounted to the present by a specific rate. It only has two components: a series of cash flows and the discount rate.

The discount rate is probably the more theoretically complex part of the equation. Its role in the DCF equation is to make two cash flows at different times equivalent. For example, if I believe the discount rate is 10%, then $100 today is equal to $110 in one year, or to $121 in two years.

The problem is that the discount rate is not something we can observe. It isn’t quoted on any exchange, and there’s a lot of discussion around how to determine it. There’s even discussion about what it represents in real life (the opportunity cost of money, the return required for taking a specific risk, the return that the investor expects, etc.).

In the majority of models, the discount rate is derived from the market via a series of statistical equations. It is supposed to represent the cost of opportunity of investing the money in another asset of similar risk. That is, if the aggregate of stocks that are similar to A generate a yearly return of 10%, then the cost of investing in A is the return missed from using the money on A and not in the other names. This is called the cost of equity. I don’t like this approach for many reasons: it is unnecessarily complex, it removes attention from what’s important, it has an incorrect definition of risk, and it obtains important assumptions from the market instead of from the head and work of the investor. I analyzed these problems in more detail in previous posts (The epistemology of value investing and Stock markets are the enemy of investors).

In my opinion, it is much more useful to determine the discount rate yourself.

One way to do this is to think of your desired return (your own cost of equity, let’s call it). For example, whereas the market cost of equity might be 10% for a stock, you might only be happy with a 15% return. This will mean that, even when sharing the market consensus expectations about future cash flows, you will require a lower price for the same stock.

The second method, and the one I prefer the most, is to invert the equation above. Mr. Market already tells us what he believes the result of the equation is. We can replace DCF with P (the current price). Then, the result of the equation (explained variable) becomes the discount rate.

This simple change completely modifies the use and value of the DCF formula. Now, the model tells you, given some expectations about cash flows, what the expected annualized return is if you buy the stock at price P. When the Price goes down, the expected return goes up.

In this way, we have also saved a lot of brain power. Instead of wasting it in endless debates about the nature and best way to estimate the discount rate, we can concentrate on what’s most important, the cash flows.

Incrementally dissecting the cash flows

The return has become the final explained variable. It is the result of cash flow expectations and a market price. We already know the market price, it’s as easy as asking Google. Therefore, we can concentrate our effort on understanding, modelling, and forecasting cash flows, and wait for the market to offer a price for those cash flows that provides us with an adequate return.

There are only two types of cash flows we can receive from a company: dividends or the price from selling the stock. All other variables, such as earnings multiples, buybacks, operating margins, and leverage, must affect one of these two cash flows in order to generate an effective, i.e., pocketed, return.

In the following section, we will start with the most basic type of DCF and slowly add complexity with more and more components.

The simplest case: no dividend, no growth stock, only multiple expansion return

Let’s begin with a very simple, yet sometimes misunderstood case, that value investors usually encounter. It is a company that does not grow earnings (or we do not expect it to), but that trades at a low multiple of earnings. We expect that the multiple will correct upwards, and at that point we can (ideally) sell it, to pocket a return. This case looks like the equations below.

This is the basic DCF equation from the section above, before modifications. The price today (earnings today by the current earnings multiple) is equal to the price in the future (same earnings but a different earnings multiple), discounted to the present.

First, we need to rearrange this to put the discount rate (i.e., the return) at the center.

The above basically says that the aggregate return (left-hand side of the equation) is equal to the change in the multiple from the beginning (P/E0) to the end (P/En). This is very intuitive: if we buy at 10x and sell at 12x, and earnings have not changed, then the total return is 20%.

But we can simplify the equation even more by expressing the change in the earnings multiple as (1+m).

The result, super simple, says that the yearly return is equal to the expansion in multiple, divided by the number of years it took. Again, this is super intuitive. If the multiple changed from 10x to 12x in one year, then the yearly return is 20%; however, if it took 5 years, the yearly return is only 4%.

The above equation has an approximation (symbolized by the ~). The correct annualized return is (1+m)^(1/n), or the nth root of the multiple expansion. This is called the compound rate of return. However, this can be approximated to m/n, called the arithmetic rate of return. The arithmetic rate approximates the compound rate fairly well, as long as both ‘n’ and ‘m’ are relatively small. Below is the difference between the two up to 10 years, for a total return of 20%.

Takeaway: If a company does not grow its earnings and does not pay back shareholders in the form of dividends or buybacks, then all returns must come from multiple expansion.

The problem is that this is the ‘worst’ type of return, because it relies exclusively on sentiment changes. We are effectively trying to predict that others will pay more for the same earnings in the future. Sometimes this is a reasonable speculation (say a company trades at 5x earnings versus the whole market at 15x), but sometimes it is not (12x to 15x). Further, the returns from multiple expansion need to be relatively fast or relatively violent (say from 5x to 10x) to represent a significant annualized return.

Although the above sounds somewhat obvious, I have seen (and made) many value pitches where the main thesis is that a stock without much growth or capital returns trades at 7/8x earnings but should trade at 10/12x. This type of thesis basically assumes a quick revaluation to generate a large return, but this is really hard to predict.

Adding growth

Let’s make the original example a little more complex by adding growth. For example, we might have reasons to believe the company can grow revenues, expand margins, or pay down debt, leading to higher earnings over time.

The question we are trying to answer is how much growth and for how long. We expect the company to grow at a rate of ‘g’ for a number of years ‘n’.

Although that sounds simple, this is the most complex part of the DCF. Markets eventually saturate, margins cannot expand forever, debt has limits, etc. Forecasting growth requires company and industry-specific considerations. This is not the focus of the article, but its importance should not be understated.

Let’s assume we think a company can expand its earnings 20% over 5 years. That is a compound rate of 3.7% (1.2^(⅕)), or approximately 4% from the simplification above (20%/5years).

How does growth affect returns in a discounted cash flow model? Again, assuming no dividend payments or buybacks, we only need to add an earnings growth component to the original equation from the previous section. That component is (1+g)^n if using a compound rate, or (1+g)*n on an arithmetic rate. It affects the original earnings, which grow by ‘g’ for ‘n’ years.

After some simplification, we get the equations below.

We have added another layer of approximation, which is that [(1+m)^(1/n)](1+g) is approximately equal to m/n + g. We had already dealt with the first term (m/n), but we are adding another approximation because (1+x)(1+y) is not exactly 1 + (x+y), but is close enough. The difference is the term 2gm, which should be small enough.

Takeaways: Growth in earnings is a direct source of returns that we can approximately add up to (or subtract from) the move in the multiple. This makes intuitive sense: if a stock generates 20% more earnings, and it maintains the multiple constant, then the price will go up by 20%.

Further, we can start thinking about the interactions. In value or deep value names, sometimes growth goes hand in hand with multiple expansion, especially if there is a cyclical turnaround or business model inflection point. That is a double engine of returns. However, the opposite can also happen. For example, a cyclical name can grow, while its earnings multiple decreases, so that the return is low. Or also very common is the situation where a growth name trades at a super high multiple, and ends up growing a lot during an extended period of time, but the return is low because the multiple also contracts a lot. In a previous article about growth stocks, I showed the example of Amazon. EBITDA doubled, but the multiple halved, so that the stock price (i.e., the source of returns) barely moved at all.

Adding capital returns and capital allocation

So far, we haven’t dealt with the earnings that are generated while we own a stock. The models above dealt only with purchase price, sale price, and earnings growth, but not with the ‘stock’ of earnings that builds up.

When a company makes money, its capital (equity) grows. This capital can be put to different uses, some of which are positive for stockholder returns, while others are not. Therefore, we need to distinguish the company’s capital allocation policies to understand how earnings become (or don’t become) returns. One of the biggest mistakes induced by talking of earning multiples or yields in abstract (and I have made this mistake a lot in the past) is that earnings do not automatically become shareholder returns. They need to be ‘allocated’ to some profitable use to become returns.

We can consider five potential uses of capital: holding cash, debt repayment, growth (either capital expenditures, working capital, or acquisitions), dividends, and buybacks. We will go one by one on each, and the effects they have on returns.

Let’s start with holding cash. This is mostly an intermediary state. Eventually, cash has to be put to one of the other four uses, so the question of returns remains ‘what will the company do with this cash and when’. There is one special case, and that is the use of cash as part of working capital (especially on a seasonal basis), but this should not be a large component in almost any company.

Growth investment becomes ‘g’ only if used correctly

The next possibility is growth. Most companies need capital to grow. This is a requirement, not a desire.

For example, retailers need to invest in store fixtures (CAPEX) and also hold more inventory (working capital). Manufacturers need to build more factories and hold more receivables and raw materials. Banks need to own capital in order to grow their balance sheets while maintaining healthy leverage ratios.

Therefore, when we think of the ‘g’ of growth above, we must also think about what capital requirements are needed for that growth. That capital will not be part of our returns and therefore does not enter into the equations above (it is money we do not receive directly). Rather, that capital is the cost of ‘g’.

Coming back to examples, if a retailer has a net working capital turnover of 2 (that is, in order to sell $1 billion in one year, it must hold net working capital of $500 million), has a net margin of 10%, and we expect it to grow revenues by 5%, then it has to dedicate 25% of its capital to working capital. If its D&A is $100 million, but it consistently spends $125 million in CAPEX because it is building stores, then the remaining $25 million is also a growth requirement. In this case, talking of a 10x earnings multiple or a 10% earnings yield in abstract makes no sense, because the company needs to plug 50% of earnings back into the business in order to grow.

This is why good capital allocation and working capital management are important. In the example above, the company is investing $50 million in order to generate a potential earnings growth of $5 million per year. This is a 10% return on the capital invested per year. Is it good enough for us? Or we could potentially do better if the company did not grow, but paid those $50 million in dividends to us?

The exact same reasoning goes to acquisitions, only that instead of being a more predictable ‘flow’ of capital use, acquisitions are bumpy. Companies can eat all of their cash reserves and then go into debt in one and a half years during an acquisition spree. The task at hand is to understand how those acquisitions will become ‘g’ above. If the company invested $100 million in an acquisition, will it add $10 million in earnings or not?

Finally, debt repayment is also a form of earnings growth and capital allocation. When the company pays down debt, it pays less interest, therefore letting more operating income flow to equity. The question is again one of allocation. If the debt has an interest rate of 14%, then for each $100 the company pays, it saves $14 on interest. That is a good use of capital. If the debt has an interest rate of 2%, then repaying it before it matures might not be very useful. The same can be applied to taking on debt. If a company takes on debt for $100 at 5% ($5 per year) but those $100 invested can generate $10 in earnings sustainably, then the debt was a good capital allocation decision, with an enormous return on equity (the $10 in additional earnings cost no equity).

A great example of how capital allocation is ignored is the case of software and tech companies. One usual argument among value investors is that tech and software stocks tend to irrationally trade at higher multiples than other low-tech, ‘boring’ companies. Value investors argue that less intelligent players get attracted by fantastical growth stories and overpay for promises. However, this argument usually ignores a fundamental advantage of software companies in capital allocation: they don’t need much capital to grow. A software company’s cost to sell to 1,000 or 2,000 clients is very similar. It doesn’t need more inventories or factories. Compare that to a brick-and-mortar retail company, which would need to double its capital investment to double the number of clients it serves. Therefore, software companies can generate higher shareholder returns despite a lower earnings yield (higher earnings multiple).

Takeaways: Growth has a capital cost. This cost is paid with current earnings, past earnings (cash holdings), and future earnings (debt). We need to evaluate where the company is allocating those earnings, and what return it generates on them. Sometimes it doesn’t make sense, from a shareholder perspective, that the company continues to grow. The shareholder would be better off receiving that capital via buybacks or dividends, and putting it to work somewhere else.

Again, the specifics of capital allocation evaluation should be discussed in another article, because there are hundreds of particular cases: different industries, situations, positions in the cycle, etc. However, it is something we should never leave out of our evaluation.

Buybacks become ‘g’ adjusted for repurchase timing

Instead of (or in addition to) growing in size, companies can also buy back their shares. This is a very effective way to grow earnings per share, because the same amount of profits is divided among fewer shares.

Therefore, buybacks have an effect that is equivalent to ‘g’ above, and can enter our equation.

What is the correct value of ‘b’, in this case? It depends on the assumptions we make about the earnings yield (the inverse of the earnings multiple) at the time of the buybacks, and what portion of net income is used for buybacks.

For example, if the company trades at a P/E of 10x (earnings yield of 10%) and uses all of its net income for buybacks, then ‘b’ is 10%. Think about it: each year it buys back 10% of its stock, and therefore earnings per share grow by 10%. If it uses half of its net income (because the other half goes to growth), then ‘b’ will be 5%. However, if the name trades at a P/E of 20x, then under the same assumptions, ‘b’ will be one half less, or 5% and 2.5% respectively.

The problem is that the earnings yield moves over time, and companies might not have a fixed buyback policy (say ‘buy back 50% of net income every year’). We need to make a forecast, and there are lots of cases to consider. For example, the company can hold cash reserves, and then only buy back shares when it is very attractive to do so, during a market downturn. In this case, it increases ‘b’ because the repurchases are done at low P/Es. It can also spend a fixed percentage of its net income on buybacks independently of price. Sometimes, in the worst case, the company will get hyped up during a bull run and buy shares at unsustainable all-time highs.

We need to look back at the previous history of the company, management team, and Board, and see what they did in the past. During earnings calls management can also comment on their capital allocation policy.

My own simplification in this case is that (barring evidence of the contrary) the company will spend a fixed percentage of earnings on buybacks, and that those buybacks will happen at a normalized P/E (for example, the P/E we use for the sale of the stock, P/En).

Coming back to the examples above, if I believe the normal P/E for a company is 10x, and that it will spend 50% of its net income in buybacks over time, then ‘b’ is 5%. If the company buys back shares consistently, then it will sometimes buy above, sometimes below, and the net effect will be approximately the same.

If we want to go deeper into the bushes, then we need to consider what happens with stock-based compensation, too. One very simple way to deal with it is simply to use the net income above, which already removes an estimation of SBC from earnings. Another estimation is to look at how diluted shares move over time. If the company buys back stock, but the diluted share count goes up, then the company is diluting more than buying back, and ‘b’ should actually be a negative figure on returns. The more correct way is to add back that estimate to earnings, and then actually forecast how many shares will be issued. For that, we need to separate between actual shares issued (RSU), performance shares (PSU, only issued if the company reaches certain goals), and stock options (only become shares if the share price reaches a certain value). For example, if a company today trades at $10 and issues options that have a strike of $20, it will expense those options as SBC today, but those options might never become shares, because the stock price might not reach $20 before expiration. Forecasting this obviously requires a lot of estimates, and sometimes it is simply not worth the hassle because of the uncertainty around all of the estimates.

Takeaway: Buybacks are direct earnings per share growth and are therefore a direct source of returns. They are also a clear yardstick against which to measure capital investments: if the stock trades at 10x earnings, then there’s a simple way to generate $1 in earnings for each $10 invested, which is buying back stock; that means any capital investment should return significantly more than $1 for each $10 invested, because it carries much higher risk.

Beautiful dividends

Dividends are considered boring and old-school by many people. They seem antiquated and unsophisticated, and they generally receive a relatively negative tax treatment versus buybacks or growth investments in most countries.

However, dividends are the most direct, real, and unambiguous form of shareholder return. All of the previous sources of return require us to work with assumptions: that the multiple will be stable or move favorably, that growth will materialize, that buybacks will be done at correct prices, etc. All of the above sources of return depend on the final sale price, but dividends do not. Dividends are hard cash, received periodically. Further, dividends remove capital from the company that could easily be squandered in bad capital allocation decisions. I have rarely seen a large dividend-paying company have a low return on equity, even in the worst industries.

Therefore, don’t underestimate the value of a good dividend payout ratio (the ratio of net income paid as dividends).

In our equations above, dividends represent an additional complexity because each dividend should be discounted at a different compound rate. Whereas all of the sources above become a single cash flow at the end (all discounted at (1+r)^n), each dividend is discounted on the year it is received, meaning (1+r)^1, (1+r)^2, etc. Further, dividends also grow with earnings.

There is a correct closed-form formula to represent the present value of a dividend stream alone, the ‘growing annuity formula’ below (second term of the right-hand), where D0 is the first annual dividend.

My mathematical abilities (or O3’s for the matter) cannot obtain a simplified form for (1+r) from the above formula. However, approximation comes to help again.

One simplified alternative is to think that the dividend yield (dividend per share over the stock price) is equivalent to the return generated by dividends. This is intuitive in the first few years. For example, if I buy a stock at $10 and the first year it pays a dividend of $0.5, the yearly return is 5%. This simplification becomes more complicated when we add growth, because the return of the second year might be $0.53, and the third year $0.57, etc.. However, unless growth is very high or the period evaluated is very long, growth should not add a lot in terms of return, and our estimation would actually underestimate the effective return (which is generally better because we want to be conservative with estimations).

If we wanted a more mathematically accurate approximation, we could use the ‘g’ we obtained and apply it for ‘n’ years to the dividend. Then, we take the average of the current dividend and the final dividend as the dividend yield. For example, if the stock pays $0.5 today but we expect it to grow 5% for 5 years, then we can expect the final dividend to be $0.63. In this case, a better approximation of the dividend return is $0.56 (average of $0.5 and $0.63), instead of $0.5. Again, considering a current stock price of $10, the difference is an expected return of 5% versus 5.6%.

Therefore, we can simply add a ‘d’ to our return equation, where ‘d’ is the dividend yield at initiation, or the better approximation from averaging start and finish dividends.

Takeaways: Dividends are probably the most underappreciated source of return. Many people consider dividends a simple result of earnings. However, the difference in return between a dividend-paying stock and a non-dividend-paying stock can be substantial.

A beautiful example of this is The Buckle (BKE), a small denim brick-and-mortar retailer, without the brand power of the large apparel companies, and with much lower growth investments. Its stock price has barely moved in the past 15 years, and yet its total returns (green line below) match the returns of the S&P500 (SPY ETF) during one of the most impressive bullruns in the American stock market.

Conclusions

The ‘value’ of the equation above is that it strikes a balance between the oversimplification of earning multiples and the complexity of most DCF models. It puts very clearly that returns come only from capital returns (buybacks or dividends), growth, or multiple expansion. It forces us to think a little more clearly about each of the components, instead of relying on a single multiple-figure.

Earning ratios alone can work for names that are super-undervalued or that have a clear growth inflection. These cases can be considered one instance of the formula above, in which the m/n factor is the main driver of returns. Because m is the only figure divided by n, these cases need to work fast in order to generate good annualized returns.

When thinking about longer periods or names where the earnings ratio is not super low, then breaking down the assumptions is important. It can help weed out value traps, names with low growth and low capital returns, that only offer the uncertain expectation of a multiple correction.

Further, this formula is very useful to distinguish between names with similar multiples, because it puts emphasis on differences in growth and capital returns. Two names in the same industry and with similar multiples can have very different return profiles if one returns capital and the other does not, for example.

This approach obviously needs some additional modeling and thinking that we have skimmed over in this article. This is especially true for the capital returns and growth portion. This forces us to think about the important long-term drivers: market share, margins, capital structure, investment requirements, management quality, etc. Hopefully, however, this modelling does not turn into a dozen Excel sheets, but rather a handful of key assumptions that can be more clearly communicated and questioned.

Although simple, thinking through the equations above and incorporating them into my analysis has made me evaluate names more thoroughly. I hope it helps you too.