You Don't Understand Share Buybacks

Disclaimer: this is not investment advice, it is not a recommendation to buy or sell, and I own shares in Evolution.

In a previous post, we talked about the theory of buybacks: what they are, when they create value, when they destroy value, and why looking only at EPS does not tell you much.

Recently, Evolution Gaming ($EVO) announced a pretty juicy buyback program. And that made me realize something important:

And I do not mean that as an insult. It is normal. Buybacks look intuitive until you try to put numbers on them. In the previous post, we saw the conceptual side: if a company repurchases shares below intrinsic value, with sensible financing, and without sacrificing better reinvestment opportunities, the buyback creates value. So far, so good.

But then comes the real mess: how much value does it create exactly?

If a company repurchases 10% of its shares, has it created 10% of value for shareholders? 15%? 5%? Does it depend on the discount? Does it depend on how much cash it uses? Does it depend on how many shares remain afterward?

When Evolution announced the buyback, many people reacted more or less like this:

“If they buy back 17% of the company, I gain 17% more value.”

But that is not how it works. And it may surprise you.

Things you have not considered

To start with, there is a small mathematical trap that many people miss: if a company cancels 17% of its shares, your ownership of the remaining business does not increase by 17%, but by more.

The math is:

1 / (1 − 0.17) − 1 = 20.5%

In other words, if you previously owned 1 out of every 100 shares and the company eliminates 17, you still own 1 share, but over a much smaller share base. Your slice of the pie does not increase by 17%. It increases by roughly 20.5%.

If earnings remain constant, EPS also rises by around 20.5%. Seen this way, it looks like an absurd value-creation machine. The company presses a button, shares disappear, and you are richer.

Fantastic, right?

Not so fast.

As always, there are a couple of traps. Those of you who read the previous post already know some of them, but I do not think you know all of them.

The first trap

As we already know, the company had to spend cash to do it. And this is where many investors confuse EPS accretion with intrinsic value per share accretion.

A buyback does not create value just because it happens. A buyback only increases the intrinsic value per share of the shareholders who do not sell when the shares are repurchased below intrinsic value.

If the opposite happens, if the company repurchases shares above intrinsic value, the effect reverses: the shareholders who sell win, and the shareholders who stay pay the bill.

So a buyback does not create value ex nihilo. It redistributes value between two groups:

• the shareholders who sell;
• the shareholders who remain.

Let's use an example:

Evolution recently announced a €2 billion share buyback program.

There are many nuances, but let's simplify: if the program is fully executed at current prices and the shares are cancelled, the buyback represents around 17% of the company.

What does that mean for the shareholder who does not sell?

At first glance, EPS rises by 20.5%. This part is mathematical, but only under one important condition: that net income stays constant.

Of course, this is obvious. But in real life, several things need to be considered. Let's start with the most obvious ones:

• The business can improve or deteriorate.
• There may be taxes.
• There may be opportunity cost.

But then there is the part many people do not see:

• The cash used in the buyback no longer earns interest.
• If the buyback is financed with debt, there will be interest expense.

That is why a buyback that reduces the share count by 17% does not guarantee a real EPS increase of 20.5%.

In reality, it will be lower because the cash stops earning interest, or, if debt is used, because of the cost of that debt.

The mechanical effect does say that: fewer shares, same profit, higher EPS. But the real world adds an annoying footnote: that profit may no longer be exactly the same, because the cash that used to earn interest is gone, or because the debt used to buy back shares now requires interest payments.

And, above all, even if EPS rises by 20.5%, that does not mean intrinsic value per share has risen by 20.5%.

Because the company did not find money under the couch.

It spent cash. Or it took on debt.

The second trap

Everything above assumed the company repurchases at fair value. In other words, that it pays exactly what the share is worth.

But we already know that a good buyback is not simply about buying back your own shares. It is about buying them below intrinsic value.

So we return to the original question:

How much value does a 17% buyback create?

17%? 20.5%? Something less?

It depends on two things:

1. What percentage of the shares is cancelled.
2. What discount exists versus intrinsic value.

We already have the first point: let's assume Evolution cancels 17% of its shares.

The second is more subjective. Nobody knows the exact intrinsic value of a company, although some people talk as if they received it engraved on a stone tablet. But let's assume, for simplicity, that the stock trades at a 30% discount to intrinsic value.

The simplified formula is:

(c × d) / (1 − c)

Where

c = shares cancelled

percentage of shares the company repurchases and retires

d = discount to intrinsic value

difference between the estimated value of the share and the price paid

Applied to the case:

(0.17 × 0.30) / (1 − 0.17) = 6.1%

In other words, if a company cancels 17% of its shares at a 30% discount to intrinsic value, the intrinsic value per share of the remaining shareholders rises by roughly 6.1%.

Not 17%. Not 20.5%.

Only 6.1%.

Why so little?

Because the 30% discount does not apply to the whole company. It only applies to the part the company repurchases. The company is not buying 100% of the business at a 30% discount. It is using a specific amount of cash to buy a specific portion of the shares at a discount.

That 6.1% is the added value from buying back shares cheaply versus buying them back at fair value.

And careful, because this does not mean that as a shareholder you “only receive” 6.1%. You receive more things. Your ownership of the business increases, mechanical EPS rises, and cash leaves the company to concentrate value into fewer shares.

But the part that is truly created, the part that was not there before, is that 6.1%.

The rest is redistribution.

It is similar to a dividend. When a company pays a dividend, the shareholder receives cash, but the company is worth less because that cash is no longer inside the business. No new wealth has appeared. Value has simply moved from one pocket to another: from the corporate pocket to the shareholder's pocket.

Something similar happens with a buyback. If it is done at fair value, it does not create value. It only changes how value is distributed: less cash inside the company, fewer shares outstanding.

If it is done cheaply, then yes, an additional gain appears for the shareholders who remain. But that gain is not the 17% repurchased, nor the 20.5% proportional increase.

It is the arbitrage between the price paid and intrinsic value.

In this example: 6.1%.

This seems to confuse many people because it mixes two different things that look similar, but are not the same:

• the mechanical increase in ownership per share;
• the new value created by buying below intrinsic value.

And if you do not separate those two layers, you end up thinking that any large buyback is automatically a money-printing machine.

It is not.

The machine only prints money when it buys cheaply.

Why a 30% discount only creates a 6% increase per share

Suppose the intrinsic value of the company is €100.

The stock trades at a 30% discount, so the market values the company at €70.

If the company repurchases 17% of itself:

Concept	Value
Intrinsic value of the company	€100
Discount to intrinsic value	30%
Market value	€70
Percentage repurchased	17%
Cash spent	€11.9
Intrinsic value of the shares retired	€17.0
Difference captured	€5.1

The company pays €11.9 of cash to retire shares that are intrinsically worth €17.0.

The difference is:

17.0 − 11.9 = 5.1

That €5.1 is the economic value captured by the shareholders who remain.

But now there are fewer shares outstanding. Only 83% of the original shares remain. So that additional value is spread over fewer people:

5.1 / 83 = 6.1%

Or, equivalently:

(0.17 × 0.30) / (1 − 0.17) = 6.1%

Here is something interesting: the return on the cash used is enormous.

17.0 / 11.9 − 1 = 42.9%

In other words, each euro used in the buyback buys roughly €1.43 of intrinsic value.

But that 42.9% return does not apply to the whole company. It only applies to the portion of capital used to buy back shares.

After the buyback, the situation would look something like this:

Concept	Value
Intrinsic value before the buyback	€100.0
Cash spent	-€11.9
Intrinsic value after the buyback	€88.1
Shares remaining	83%
Intrinsic value per remaining share	€106.1

So intrinsic value per share goes from €100 to €106.1.

That is the true value increase for the shareholder who does not sell: 6.1%.

And here is the important nuance:

The shareholder who remains does not receive the €11.9 of cash. That cash goes to the shareholders who sell their shares to the company.

What the remaining shareholder receives is something else: a larger ownership stake in a company that managed to retire shares below their real value.

Redistribution versus added value

I think this is where people get most confused, because mentally we mix up “the company has distributed a lot of value” with “the company has created a lot of value.”

They are not the same thing.

But out of that €17.0:

Component	Value	% of value retired
Cash paid to sellers	€11.9	70%
Value captured by buying cheaply	€5.1	30%
Total intrinsic value retired	€17.0	100%

In other words:

• 70% is simply cash handed to the shareholders who sell;
• the remaining 30% is the additional value captured by buying cheaply.

That 30% is the only part that is really “created” for the shareholders who remain.

Everything else is redistribution.

It is similar to a dividend. When a company pays a dividend, the shareholder receives cash, but the company is worth less because that cash is no longer inside the business. No new wealth has appeared. Value has simply moved from one pocket to another.

Something similar happens with a buyback.

If the buyback is done at fair value, no value is created. The structure simply changes: less cash inside the company and fewer shares outside it.

The magic only appears when the company repurchases below intrinsic value.

Then there is a real economic arbitrage.

And in this example, that arbitrage is worth roughly 6.1% for the shareholder who remains.

What if the stock trades 50% below intrinsic value?

Here the math starts to get much more aggressive.

If the company cancels 17% of its shares at a 50% discount to intrinsic value:

(0.17 × 0.50) / (1 − 0.17) = 10.2%

Intrinsic value per share would rise by roughly 10.2%.

Concept	Value
Price before the buyback	€100
Intrinsic value before the buyback	€200
Shares cancelled	17%
Increase in intrinsic value from buyback	+10.2%
New intrinsic value per share	€220.5

If the market continues to value the stock at the same 50% discount, the price would move from roughly €100 to €110.2.

And here there is another important distinction.

The buyback has only created the 10.2% increase in intrinsic value per share.

The rest of the potential upside would come from something different: the market stopping applying that discount and rerating the multiple.

They are two different engines:

• the buyback increases intrinsic value per share;
• the market decides how much it is willing to pay for that value.

Mixing both things usually leads to fairly unrealistic expectations about what a buyback can do by itself.

The implicit return of a buyback

A buyback is not ROIC in the normal operating sense.

The company is not building a factory, launching a product, developing software, or buying another business. It is not expanding capacity, entering a new market, or creating a new revenue line.

It is not an operating investment. It is a capital allocation decision.

And, like every capital allocation decision, the question is not only “does this increase EPS?”, but:

what return does the company get by using the money this way instead of using it for something else?

A useful way to think about it is this:

The expected return of a buyback depends on the expected return of the business and the price paid versus its intrinsic value.

Mauboussin formulates it quite elegantly:

r / (P / V)

Where

r = cost of equity

return required by shareholders to invest in the company

P = price paid

price at which the company repurchases its own shares

V = intrinsic value

estimated economic value of those same shares

In other words, if a company's cost of equity is 8% and the stock trades at two-thirds of intrinsic value, more or less a 33% discount, the implicit return would be:

8% / (2 / 3) ≈ 12%

The intuition is simple. If you buy an asset that, at fair value, should give you 8% a year, but you buy it at a discount, your expected return rises. Not because the business magically became better overnight, but because you are paying less for the same future cash flow.

It is the same logic as always, but applied inward: instead of buying another cheap company, the company buys a cheap piece of itself.

That is why, in a stable company, the earnings yield or free cash flow yield at the repurchase price can serve as a shortcut. In other words, as a quick approximation so you do not need to build a DCF every time someone announces a buyback.

But it is only that: a proxy.

You have to keep in mind that this proxy only works reasonably well if current earnings or free cash flow are a good approximation of normalized cash flow. I leave the numerical work on Evolution in the appendix, because if I put it here, we would drift too far away from the main idea.

In Evolution's case, if a €2 billion buyback ends up representing around 17% of the company, Evolution would be buying a very meaningful portion of its own future earnings. That can be very attractive if the stock is below intrinsic value. But it is not automatic.

A large buyback is not necessarily a good buyback. A large buyback is only good if the price paid makes sense.

A good mental model

A buyback has two components:

1. The first is the part that does not create value, but can be useful as a way to return capital to shareholders. In this sense, it is quite similar to a dividend: cash leaves the company and that cash ends up, directly or indirectly, in the hands of shareholders.

2. The second is the truly interesting part: the difference between the price paid and the intrinsic value of the shares repurchased.

That is where value is created or destroyed.

If the company repurchases below intrinsic value, the shareholders who stay capture value.

If it repurchases above intrinsic value, the shareholders who sell capture value at the expense of those who remain.

That is why a large buyback does not create value by itself, not even if it represents 17% of the company. It may simply be a way to move value from one place to another. A financial sleight of hand: less cash inside the company, fewer shares outstanding, and the appearance of higher EPS.

The interesting thing is not that the buyback is large. The interesting thing is that it is good.

Conclusion

If a company repurchases 17% of its shares:

• Your proportional ownership of the remaining business rises by roughly 20.5%.
• EPS can rise by roughly 20.5%, before financing costs, lost interest on cash, and changes in earnings. In practice, it will probably be somewhat less.
• Intrinsic value per share only rises if the stock was undervalued.
• At a 30% discount to intrinsic value, the increase in intrinsic value per share is roughly 6.1%.
• At a 50% discount, the increase is roughly 10.2%.

And with that, I hope it is clearer how much value a buyback GENERATES, so you can apply it to your investments with concrete numbers and do not have to rely on vague notions of “it is cheap.”

To be honest, it is a bit disappointing. At first, you would expect more value to be created by buying something at a 50% discount. But of course, you are only committing a relatively small portion of the capital. And if you stop to think about it, it is logical: if you repurchased 100% of the shares at a 50% discount, the increase would indeed be 50%.

The positive note is that this added value compounds over time and, in a way, is “free.” Not because it does not cost cash, but because it does not require inventing a new product, making a brilliant acquisition, or opening a new market. It only requires money, discipline, and a stock that is cheap enough.

And a management team capable of doing that boldly and opportunistically is probably the kind of people you want running your companies.

Appendix: quick valuation of Evolution

The earnings yield or FCF yield proxy only resembles the previous formula if we assume the company does not grow or shrink too much. In other words, if current earnings or free cash flow are a reasonable approximation of what the business can generate on a normalized basis.

If the company grows, the current earnings yield or FCF yield probably underestimates the expected return, because you are only looking at today's cash flow and not the higher future cash flow.

If the company declines, the opposite happens: the proxy can overestimate the return, because current cash flow looks cheap, but perhaps it is not sustainable.

The intuition can be written like this:

y ≈ r / (P / V)

Where

y = FCF yield

free cash flow divided by market capitalization

r = cost of equity

return required by shareholders

P = price paid

price at which the company repurchases its shares

V = intrinsic value

estimated economic value of those shares

First, we solve for how much the market is paying relative to intrinsic value:

P / V ≈ r / y

And from there, the implied discount is simply the part of intrinsic value you are not paying for:

discount ≈ 1 − (P / V) ≈ 1 − (r / y)

Now let's apply this to Evolution with approximate numbers. At the time of writing, Evolution trades at an earnings yield close to 9.6% and an FCF yield close to 10.8%. In addition, the official buyback program announced by the company is for up to €2 billion.

If we use the FCF yield as a proxy and assume the business is stable, the implicit return from repurchasing shares would be roughly that 10-11%.

Does that match the 12% from the previous formula?

Quite closely, but not exactly. To get to 12%, we assumed an 8% cost of equity and that the stock traded at two-thirds of intrinsic value. With an FCF yield of 10.8%, the implied discount depends hugely on the cost of equity you use:

1 − (8% / 10.8%) ≈ 26%

1 − (9% / 10.8%) ≈ 17%

1 − (10% / 10.8%) ≈ 7%

So, using only current FCF and without assuming growth, Evolution seems closer to a 20-30% discount than a 50% discount. To justify a 50% discount with a 10.8% FCF yield, you would have to use a cost of equity of barely 5.4%, which seems too low to me for a stock like Evolution.

We can also flip it around and ask: what growth does the market seem to be pricing in?

In a very simplified version, if we treat free cash flow as a perpetuity that grows at a constant rate, the relationship would be:

g ≈ r − y

Where

g = implied growth

approximate annual growth of free cash flow that the market would be pricing in

r = cost of equity

return required by shareholders

y = FCF yield

free cash flow divided by market capitalization

With a 10.8% FCF yield, this gives us something interesting:

g ≈ 8% − 10.8% = -2.8%

g ≈ 10% − 10.8% = -0.8%

g ≈ 12% − 10.8% = 1.2%

In other words, if you require an 8-10% return, the current price appears to be discounting something close to stagnation or a slight decline in normalized FCF. If you require 12%, then the market would be discounting barely 1% annual growth.

We can also do the exercise the other way around: if you believe Evolution can grow FCF at a specific rate, what valuation would that imply?

Here, we have to be very precise with the language. In this formula, FCF growth is not simply “growth over the next two or three years.” It works as a normalized long-term growth rate, almost a terminal rate. That is why it has to be used very carefully.

The simple version would be:

V ≈ F / (r − g)

Where

V = intrinsic value

estimated economic value of the company

F = normalized FCF

annual free cash flow we use as the starting point

r = cost of equity

return required by shareholders

g = perpetual FCF growth

normalized long-term annual growth of free cash flow

Another way to read the same formula is this:

y ≈ r − g

In other words, the fair FCF yield is the return you require minus the perpetual growth you expect. If you require 10% and believe FCF can grow 4% sustainably, then buying the business at a 6% FCF yield would be enough.

y ≈ 10% − 4% = 6%

And the implied value comes from dividing FCF by that fair yield:

V ≈ F / y

If we use LTM FCF of approximately €1.19 billion as a starting point and a 10% cost of equity, the sensitivity would be:

Perpetual FCF growth	Fair FCF yield (r − g)	Implied value	Discount to current market capitalization
2%	8%	€14.9bn	26%
4%	6%	€19.8bn	44%
6%	4%	€29.8bn	63%

This shows why you have to be very careful with this kind of formula. Going from 2% to 6% growth does not add a little value. It practically doubles it. This happens because the denominator, r − g, becomes very small.

That is why even 6% perpetual growth is already a demanding assumption. It can make sense as growth for a few years, but not as an eternal rate unless you have a lot of confidence in the duration of the moat, regulation, the end market, and the ability to keep reinvesting or buying back shares well.

This should not be taken literally. We are using LTM FCF, not ten-year normalized FCF, and we are ignoring future buybacks, margin changes, taxes, reinvestment, regulation, and terminal value. But as an order of magnitude, it is useful: Evolution's price does not seem to require a spectacular growth story to make sense. It seems to require that FCF does not deteriorate too much.

That said, this changes if you believe FCF will grow. In that case, the current FCF yield falls short, because it only captures today's cash flow. If you believe the business can grow sustainably, the real discount could be larger than this quick calculation suggests. If you believe the business is in structural decline, the real discount would be smaller.