Chapter 4: Stock Valuation Models & Dividend Discounting

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Welcome back to The Deep Dive.

We're here to take a stack of dense, complex financial research and sources, distill them down, and give you the fundamental understanding you need, fast.

Today, we are absolutely wrestling with the central question in all of corporate finance.

The billion dollar question.

More like the trillion dollar question.

It represents trillions of dollars of value shifting hands every single day.

That's right.

I mean, if you just look at the sheer scale of the NYSE,

investors are trading over a trillion shares of stock every single day.

It's a massive fluid marketplace.

But what is actually underpinning all that activity?

Why is one share of a major company like Cummins Inc.

worth, say, $154 .46 at a given day, while a share of some startup is worth pennies?

What determines that price?

Exactly.

So our mission today is pretty straightforward.

We're giving you the ultimate shortcut to understanding stock valuation.

This is the art and science of it, right?

It is.

It's about determining a company's intrinsic value.

We want to equip you with the fundamental tools that professional investors and financial analysts use to move beyond just looking up a price online.

Figure out what the price should be.

That's the goal.

And this isn't just an academic exercise for investors either.

No, it's central for the firm itself.

For?

For managers.

Precisely.

The core concept, understanding how value is created and measured, is just critical.

If you're a manager or if you're preparing for a major investment decision, you need to care about this for, well, at least four major reasons.

Okay.

So let's start with the one that feels the most urgent to an active investor.

That would be market imperfection.

The thing is, we live in a world where stock prices are not always right.

We all remember the dot -com bubble in 2000, where some internet stocks were trading at prices that were completely insane based on zero profits.

And the opposite happened in the financial crisis.

Exactly.

During 2007 to 2009, many fundamentally sound companies were trading at rock -bottom prices.

So analysts need these valuation tools to spot when the market has made a mistake.

To find those mispriced stocks.

Right.

Either to take advantage of an opportunity or to avoid a total disaster.

So the market isn't a perfect judge all the time.

You need your own compass.

You do.

And speaking of the market not being there at all, the second reason is private companies.

Right.

Most businesses aren't on the stock exchange.

The vast majority.

So if a successful private family -owned business wants to know what it would be worth if it went public, or maybe sell off a division.

They can't just look up a stock ticker.

There's no ticker to look up.

They have to apply these exact same financial models to figure out that value.

That makes perfect sense.

Okay, let's pivot to the management side of things for public firms.

Well, that leads right to performance assessment.

For a public company, the stock price is basically the ultimate report card from investors.

It's a measure of confidence.

Total confidence.

Or lack thereof.

And importantly, it often directly determines how top management gets paid.

Through stock options, bonuses.

All of it.

If a manager's job is to increase shareholder value, they'd better know what the inputs to that value equation are.

Which flows right into a manager's biggest responsibility,

where to put the company's money.

The fourth reason.

Capital investment decisions.

A firm has to accept investments.

A new factory, a big R &D push, an acquisition that actually increased the value of its shares.

So managers need to know what drives that value to decide what gets funded.

They absolutely have to.

If a project doesn't create value for the shareholder, it's just diluting the wealth of the owners.

It should be rejected no matter how exciting the tech is.

Okay, that really sets the stage.

Let's unpack this whole process now by starting with the very basics, the mechanics of the share itself.

When we talk about owning a stock, we're really talking about these tiny, tiny fractions of a giant company.

Right.

If you look at an industrial giant like Cummins, Inc., our sources say they have about 150 .7 million shares outstanding.

So if you own one share.

You own a truly minuscule piece of the company, and by extension, its profits.

And we have to be really clear about how shares are first issued versus how they're traded later on.

The primary versus secondary market.

Exactly.

When Cummins wants to raise new capital, say, to fund a massive expansion,

they sell brand new shares to investors in what's called the primary market.

And that's the only time the company itself gets cash from the stock seller.

That's it.

The vast majority of the daily action, all those trillions of shares being traded, that happens in the secondary market.

The stock exchanges, we all know.

Yep.

This is where existing shares are just bought and sold between different investors.

So like, Mrs.

Jones sells her Cummins stock to Mr.

Brown.

Perfect example.

She's held it for a decade.

He wants to get into industrials.

The trade happens on the NYSC.

And crucially, Cummins, the corporation,

they're indifferent to this.

They got their money long ago.

Right.

No new capital was raised for them.

They're not involved.

It's just a change of ownership.

And the way those secondary trades happen, it actually differs between the big exchanges.

Oh, they absolutely do.

Historically, the NYSC was famous as a physical auction market.

Right.

With the trading floor and all that.

It's largely computerized now, of course, owned by Intercontinental Exchange Inc.

But the principal is still an auctioneer matching the highest buy bid with the lowest sell offer.

And the other giant, NASDAQ.

NASDAQ is fundamentally different.

It's a dealer market.

Trades happen between investors and professional market makers or dealers.

These dealers stand ready to buy or sell stock right out of their own inventory.

It's a very different structure.

Okay.

Let's move from the mechanics to the metrics.

If we look at a trading summary for Cummins from back in February 2020, we see that closing price of $154 .46.

Let's break down the key stats that price unlocks.

Okay, we have to start with the biggest, most sweeping metric.

Market capitalization or market cap.

Super simple calculation, right?

The simplest.

It's just the market price per share multiplied by the total number of shares outstanding.

So for Cummins, that's $154 .46 times their 150 .7 million shares.

Which gives you a staggering market cap of $23 .211 billion.

That number defines the size of the company in the eyes of the market.

Next up, we look at the company's profit relative to each share of ownership.

That's earnings per share or EPS.

Right.

EPS is the net income, the profit leftover after you pay interest, taxes, all the expenses, and you divide that by the number of shares.

For Cummins trailing 12 months in 2019, this was $14 .48.

And that number, that $14 .48 is the key input for maybe the most famous valuation ratio of all, the price earnings ratio or PE.

If someone asks you to value a company quickly,

PE is almost always the first thing they mention.

It's the standard.

The PE ratio is just the stock price divided by the EPS.

It tells you how many dollars investors are willing to pay today for a single dollar of the company's recent earnings.

So for Cummins, a price of $154 .46 divided by $14 .48 in earnings.

Gives you a trailing PE of 10 .67.

So investors were willing to pay $10 .67 for every $1 of 2019 earnings.

Now, a key distinction here.

We often see a forward PE right next to the trailing one.

And that distinction is vital.

The forward PE is based on analysts'

forecasted future earnings, usually for the next year.

And in Cummins' case, the forward PE was 13 .39, which is actually higher than their trailing PE of 10 .67.

Which is counterintuitive, right?

Yeah, wait a second.

If the forward ratio is higher, that means the denominator, the expected future earnings, must be lower.

Precisely.

It implies that analysts were actually expecting a drop in earnings for 2020.

So investors were willing to pay more $13 .39 for every expected dollar of 2020 earnings than they were for the past dollar of 2019 earnings.

That little jump signals a forecasted decline.

That's interesting.

It is.

Now, for investors who are prioritizing income, they're going to look immediately at the dividend yield.

Which is just the expected forward dividend divided by the stock price.

Yep.

For Cummins, that was 3 .39%.

And finally, you'll see beta, which was 1 .19 for Cummins.

We'll do a much deeper dive on that later.

But it's basically a measure of the stock's risk relative to the whole market.

Okay.

Let's transition now to what is, I think, the core philosophical debate and valuation.

Market price versus book value.

It seems like accountants and investors are looking at two completely different things.

It's a classic conflict.

The book value of equity is the number you find right on the balance sheet.

Total assets minus total liabilities.

Exactly.

It's based on historical costs, depreciation, standard accounting rules.

For Cummins, at the end of 2019, this was $56 .17 per share.

But the stock was trading at $154 .46.

The price to book ratio was 2 .74.

My first reaction is, are investors just being wildly optimistic here?

Not necessarily.

The PB ratio is often much, much greater than one for a successful operating company.

And here's the crucial point.

Accountants calculate book value based on historical costs.

They're looking backwards.

Their job is to report the past, not forecast the future.

Investors, on the other hand, are exclusively focused on future earnings and the potential for growth.

So book value is deficient as a measure of current worth because it's backward looking.

Absolutely.

It ignores inflation.

And crucially, it typically excludes hugely important intangible assets.

Like patents, brand loyalty, that sort of thing.

Exactly.

We saw a tragic example of this with Eastman Kodak.

When they filed for bankruptcy, one of their most valuable assets was their patent portfolio.

It sold for $525 million.

And that value was largely invisible on their balance sheet.

Or minimized because of standard accounting.

And maybe the biggest deficiency is the value that's created just by having all the assets organized into a viable business.

The going concern value.

Right.

Book value just adds up the pieces.

It completely fails to capture the significant extra value you get when those assets are structured, managed, and operating as a healthy profit generating company.

But book value isn't useless.

Oh, not at all.

It provides a really useful benchmark.

It helps you calculate something called market value added.

If Holstein Oil has a market cap of $900 million, but a book value of only $450 million,

its market value added is $450 million.

Management has literally doubled the shareholders' past investment.

And it can also give you a hint about liquidation value, right?

A very good hint.

It can tell investors what they might get back if a company failed and had to sell off all its hard assets.

So if market price can be wrong and book value is backward looking,

analysts need a practical shortcut.

And that leads us to the most common sense approach.

Valuation by comparables.

Or comparable companies analysis.

The idea is so intuitive.

If two things are basically identical, they should sell for the same price.

Exactly.

If two companies have the same risk, the same growth, the same profitability, they should trade at identical valuation ratios like PE or PB.

So we can use the known ratios from public companies to value a private one.

That's the main application.

And you can see this clustering effect really clearly within industries.

Right.

Our sources show that two huge competitors, Coca -Cola and PepsiCo, had almost identical ratios.

A PE of 24 .0 versus 23 .1 and PB of 12 .4 versus 12 .8.

They're practically twins from a valuation perspective.

And if you look at U .S.

railroads, Union Pacific had a PE of 17 .2, almost identical to its peers' average of 17 .1.

So if you're evaluating a new private railroad, you could just apply that 17 .1 PE to its earnings and get a pretty good first estimate.

A fantastic first pass valuation, but the comparables are rarely a perfect fit.

Right.

If you looked at Union Pacific's PB ratio, it was higher than most of its peers, but it was really close to Canadian Pacific's.

This is where the analyst's judgment comes in.

Absolutely.

You can't just blindly use a simple average.

You have to dig into the details and decide which peer is the best match.

Is it geography,

asset age, market share?

So maybe Canadian Pacific is a better match for UNP than the others.

It could be.

And in that case, its PB ratio might be the superior comparable, even if it skews the group average.

And you noted this analysis is most useful when you're valuing those private operations.

Invaluable.

Say a big European bank wants to sell its U .S.

retail division.

That division doesn't have a stock price.

So what do you do?

The analyst would take the division's earnings and its book value and apply the ratios of U .S.

regional banks, like a Capital One, to establish a realistic valuation range.

It provides market evidence where none exists.

Now, before we move on, you mentioned that this approach starts to break down a little because P .E.

is sensitive to how much debt a company uses.

Yes.

That's a key weakness.

It leads us to a more robust concept called enterprise value.

Which is the total market value of the firm.

Right.

The equity market cap plus the market value of its debt.

And when we use enterprise value, we use ratios based on earnings metrics that are calculated before interest in taxes, like EBIT or EBITDA.

And why is that better?

Because P .E.

uses EPS, which is calculated after you deduct interest expense.

So if one firm uses a lot of debt and another uses very little, their EPS figures and P .E.

ratios just aren't comparable.

But EBIT and EBITDA are?

Because they only depend on operating profitability, not financing decisions.

So they're way better for comparing companies with different capital structures.

You find the enterprise value, then subtract the debt to get back to the equity value.

Okay, but valuing a company just by comparing it to others is only half the story.

To find the true intrinsic worth, we have to fall with the cash.

Which takes us back to the foundational logic we use for valuing bonds.

We have to anchor our stock valuation in the same bedrock principle we use everywhere else in finance.

That's right.

I mean, think about it.

A bond's value is just the discounted present value of its future cash flows, the interest payments, and the final principle.

And we apply that same logic directly to stocks.

We do.

The fundamental principle is this.

The stock price equals the present value of all expected future dividends.

And that gives us the core formula for the dividend discount model, or DDM.

It's a summation that goes out forever to infinity.

It has to.

Because unlike a bond, a share of common stock has no maturity date.

The corporation is theoretically immortal, so that potential dividend stream lasts forever.

And the key to this whole formula is the discount rate, which we call $20.

$20 is absolutely central.

We define $20 as the cost of equity.

Conceptually, it's the shareholders'

opportunity cost of capital.

Meaning the return they could get on other investments with the same amount of risk.

Exactly.

If a stock is risky,

$20 has to be high to compensate for that risk.

Now we hit the classic confusion point.

The one that trips up every new investor.

If the rule is, price is the PV of future dividends, why is everyone so obsessed with capital gains?

Right.

And what about companies like Amazon that historically paid zero dividends?

How is their stock worth anything if the sum of all future dividends is zero?

That's the paradox.

And it's the perfect question.

Let's resolve it by looking at an investment over just one year.

Your expected return, $2, comes from two places.

The dividend you get and the capital gain.

The difference between what you sell it for and what you bought it for.

Exactly.

So let's use the establishment electronics example.

Stock sells today for $100.

It's expected to pay a $5 dividend next year and you expect to sell it for $110.

Your expected return, $3, is the sum of that $5 dividend and the $10 capital gain, all divided by the $100 you paid.

That gives you an expected return of 15%.

And this is where market equilibrium kicks in.

This is the mechanism.

If other stocks with the same risk are also offering a 15 % return, then $100 is the only stable price for establishment electronics.

Because if it was higher, say $185, the return would be lower than 15 % so people would sell.

You would sell in a heartbeat, forcing the price down to $100.

And if the price were $95, the return would shoot above 15 % and everyone would rush to buy, forcing the price right back up.

The market polices itself.

Okay, so today's price is fixed by what the next investor is willing to pay tomorrow.

But what determines their price?

It's the same logic.

Just pushed out another year, the price they're willing to pay is based on the dividend they expect to receive, plus the price they expect to sell it for.

We can just keep expanding this horizon out forever.

So today's price is really the discounted stream of dividends up to whatever horizon you choose, plus the discounted price at that horizon.

Yes.

And the math proves this holds true no matter how far out you look.

If we go back to our example, as the horizon gets longer, say from one year to 100 years, two things happen.

The present value of that final terminal price shrinks towards zero because it's being discounted over so many periods.

At the same time, the present value of the cumulative dividend stream gets bigger and bigger.

But the crucial insight, and it's kind of beautiful, is that the total present value, the dividends plus that terminal price, always stays exactly the same.

That's the resolution to the capital gains paradox.

The capital gain you get when you sell your stock is just the present value of the dividend stream the next person expects to receive.

It all comes back to dividends in the end.

Let's clarify a critical mistake here, one that people make all the time.

Trying to value shares based on earnings per share, EPS.

Oh, this is a huge one.

It is absolutely foundational that the value of a share is not the discounted stream of its earnings.

Why not?

EPS is usually a bigger number than dividends.

That's exactly why not.

EPS is bigger because successful firms retain and reinvest some of those earnings.

If you discount that bigger EPS figure.

You're counting the reward,

the higher future dividends from that reinvestment.

But you're completely ignoring the initial sacrifice.

You're ignoring the cash that the company kept, which resulted in a lower dividend for shareholders today.

You have to discount the actual cash you receive, which is the dividend.

So back to the Amazon problem.

If a company pays no dividends because it plows everything back into growth.

The model still holds, theoretically.

Shareholders are happy with zero dividends today because they expect a much, much larger stream of dividends way out in the future or a huge acquisition payout.

What about share repurchases?

Buybacks have become so common.

Repurchases don't invalidate the model either.

They just reduce the number of shares outstanding.

This means the company can pay a higher dividend per remaining share later on.

It doesn't change the value of the whole company.

It just makes forecasting the dividend per share a lot harder.

Which is why analysts sometimes switch to a different model in those cases.

Right.

They'll often switch to a free cash flow approach to value the entire company, not just the individual share.

Okay.

The DDM is a great concept, but summing to infinity is not very practical.

We need a simplification.

And that brings us to the constant growth DCF model, also known as the Gordon growth model.

This is the simplification that makes the math easy.

It is.

It just assumes that dividends grow at a constant perpetual rate, which we call day dollars.

And if that's true, the infinite sum magically simplifies into a very clean formula.

The price today equals next year's dividend divided by the difference between the discount rate, two dollars, and that growth rate, D dollars.

And there's a cardinal rule for this model.

The growth rate, D dollars, must be strictly less than the discount rate, two dollars.

Absolutely.

If D dollars are equal to or greater than two dollars, the formula would sped out an infinite price, which is nonsense.

A company can't grow faster than its cost of capital forever.

It's economically impossible.

Now, the real power of this model is that we can flip it around to estimate the one thing that's really hard to see, the cost of equity.

We just rearranged the terms.

The formula tells us that the expected return, three dollars, is equal to the dividend yield plus the expected rate of growth and dividends,

six dollars.

This is how we estimate the opportunity cost of capital for a stable company.

And the best place to use this is on stable, regulated utilities.

They're the perfect subjects.

In fact, regulators use this exact model to determine the fair rate of return for them.

So let's look at American States Water, AWR.

In 2020, price of seventy six dollars and thirty two cents, expected dividend of one dollar thirty four cents.

That gives a dividend yield of one point eight percent.

Okay, so that's the first part.

Now we need dollars, that perpetual growth estimate.

And analysts have two common ways of doing this.

Method one is just using analyst forecasts.

Right.

If analysts estimate AWR's long term growth at five point six percent, then our cost of equity, three dollars, is one point eight percent plus five point six percent, which is seven point four percent.

Method two is using the company's own financials to find the sustainable growth rate.

And that formula is the plowback ratio times the return on equity, or ROE.

So AWR's payout ratio was about 60 percent, meaning its plowback ratio is 40 percent.

You multiply that by its ROE of about 13 percent.

And you get a jade allotter of five point two percent.

This gives us a second very close estimate for three dollars, Johns.

One point eight percent plus five point two percent equals seven point zero percent.

Both are very reasonable for a low risk utility.

But using this model for anything other than a stable utility is really dangerous.

We saw how the estimates got noisy really fast.

That is the major warning.

Any estimate of three dollars from a single firm's data is inherently noisy.

Good practice is to collect a big sample of similar companies and use the average to balance out the errors.

But the model just completely fails for high growth companies.

It breaks.

We saw two firms, California Water and SJW Group, with implied growth rates of nearly 18 percent and 15 percent.

And when you plug that into the constant growth model, it spits out these crazy high cost of equity estimates like 19 .6 percent and 16 .9 percent.

Those numbers are mathematically correct, but economically worthless.

A company can't grow at 15 percent or 20 percent forever.

The long term growth for the entire U .S.

economy is barely four percent.

The model is just fundamentally wrong for those companies.

Which means we need a model that can handle high growth now, followed by an inevitable slowdown.

This requires DCF models with two or more stages of growth.

This is the practical solution.

We go back to the basic formula.

You forecast dividends individually for a few years up to a horizon or you think the company matures.

I mean, at that point, you use the constant growth model to calculate the terminal value.

Exactly.

You find that terminal price and then you discount everything back to today.

It works perfectly when that near -term growth is unsustainably high.

Let's use the example of GrowthTech Inc.

It's selling for $50 a share.

It's been a high flyer, high ROE of 25 percent.

Plowing back 80 percent of earnings.

Which gives it an unsustainable growth rate of 20 percent.

If an analyst naively used the constant growth model here, they'd get an absurd cost of equity of 21 percent.

But we know that can't last.

Competition will catch up.

Right.

So let's forecast high 25 percent ROE and 20 percent growth for two more years.

But in year three, ROE drops to a more sustainable 16 percent.

At the same time, management sees this and they cut their plow back ratio to 50 percent.

And that shift causes a huge change in the cash flows.

A massive change.

The long -term growth settles at a sustainable 8 percent.

But look what happens to the dividend in year three.

Even though profitability dropped, the dividend actually jumps from $0 .16 to $1 .15.

Why?

Because the payout ratio went from 20 percent to 50 percent.

The firm is sacrificing that crazy high growth for a much bigger immediate cash payout to shareholders.

So we use that settled 8 percent long -term rate to calculate the terminal value at the end of year three.

Exactly.

You calculate P3 using the Gordon growth model with the new sustainable 8 percent rate.

Then you discount the first three dividends and that terminal price all back to today.

And since we know the price today is $50, we can solve for $2.

And when you do the math, you get a much more realistic cost of equity of 9 .9 percent.

Compare that 9 .9 percent to the naive 21 percent estimate.

It just shows you have to use a multi -stage model for these kinds of companies.

You have to.

And high growth doesn't always come from high profitability.

It can come from a company recovering from a downturn like with Phoenix Corp.

Right.

They started with a low ROE and no dividend.

But as they recovered and ROE hit 10 percent in year three, they could start paying and rapidly increasing dividends before settling into a stable 4 percent long -term growth.

The model is flexible enough to handle those cyclical recoveries too.

So the key practical tip is if a business is growing faster than the overall economy, it will inevitably slow down.

You have to use a multi -stage model.

And you have to remember that as the investment required for high growth declines, the cash available for payout increases.

They are two sides of the same coin.

Your dividend forecast has to be consistent with your earnings and investment forecast.

We often categorize companies as either income stocks bought for their dividends or growth stocks bought for capital gains.

And this distinction is where we find the real driver of value.

The present value of growth opportunities.

But let's start with a benchmark first.

The no growth company.

This firm pays out 100 percent of its earnings as dividends.

It has no good place to reinvest the cash.

It's basically a perpetual bond.

In this case, the dividend yield and the earnings price ratio are identical and they both equal three dollars.

So if EPS is $10 and the price is $100,

$20 has to be 10 percent.

It has to be.

Now, what if this company suddenly gets an option to invest $10 per share next year?

It withholds that $10 from the dividend.

And what does that investment earn?

Let's say it earns a 10 percent ROE exactly equal to the cost of capital.

Three dollars.

The net present value or NPV of that investment is exactly zero.

You invested $10 and got a return that just matched what you could have gotten elsewhere.

Right.

And the stock price doesn't move.

The value you lost from the lower dividend is perfectly offset by the value you gain from future dividends.

Growth, in this case, added zero value.

So the magic only happens if that investment has a positive NPV.

If the return is, say, 15 percent.

That is the core insight.

And we can formalize this.

The price today is equal to the value of the firm with no growth plus the present value of growth opportunities or PBGO.

PBGO.

This is what investors are really paying for when they buy a high multiple stock.

Absolutely.

PBGO is the net present value today of all future investments the company is expected to make.

And it's positive only if those investments earn returns higher than the cost of equity.

Let's go back to establishment electronics.

Price was $100, 15 percent.

$2 was 10 percent.

And EPS was $8, 33 cents.

If establishment suddenly adopted a no growth policy, its value would just be its earnings, $8 .33, divided by its cost of capital, 0 .15.

That's $55 .56.

But the actual market price is $100.

So the implied PBGO, what investors are paying for all those future positive investments, is the difference.

$100 minus $55 .56, which is $44 .44.

And we can actually calculate that PBGO directly to check the math.

We can.

We know establishment plows back 40 percent of its earnings and gets a 25 percent ROE.

That first year's investment is $3 .33.

That investment generates a cash flow of $0 .83 starting in year two.

Okay.

The net present value of that first investment is $2 .22.

And since that investment and its NPV are expected to grow at 10 percent forever, we can treat this whole stream of positive NPVs like a growing perpetuity.

That's right.

You value that stream of NPV tickets using the constant growth formula, the NPV of $2 .22 divided by $20 ,000,

and that calculation gets you exactly $44 .44.

The numbers match perfectly.

Which shows us that establishment is a true growth stock because PBGO accounts for a stunning 44 percent of its price.

You're paying for management's ability to find those profitable projects.

And to contrast that, look at Cummins again.

Its zero growth price was about $144, very close to its actual price of $154.

Its PDGO is small.

It's an income stock.

But then a company like Microsoft in early 2020,

its zero growth price was around $65,

but its actual price was $139.

PBGO was more than half its value.

It's the quintessential growth stock because it can reinvest earnings at a rate way higher than its cost of capital year after year.

We need to shift focus now from valuing a single share to valuing the whole business itself.

This is necessary when buybacks are erratic or when you're dealing with a private company.

And this moves us to the free cash flow valuation approach.

The principle is the same.

The total market cap of the equity equals the PV of all expected future free cash flow.

So what is free cash flow or FCF?

Simply put, it's the after -tax cash flow from operations after you subtract all the investment needed for growth.

It's a cash that's truly available for payout to all shareholders, whether it's through dividends or repurchases.

And this method is best for private businesses, divisions of larger companies, or public companies with unpredictable buyback policies.

Exactly.

And the FCF valuation formula is structurally identical to the multistage DDM we just talked about.

Value equals the PV of near -term FCF plus the discounted horizon value.

Let's use the example of Concatenator Inc., a private business being valued by a potential buyer.

We assume a cost of capital of 10 % and a constant ROA of 12%.

The forecast is for high growth, initially 12%, which then slows to a long -term 6 % rate.

Now, if you look at the early years of the forecast, something shocking happens.

The free cash flow is zero.

Or even negative.

That feels wrong.

If the company is profitable, why is the FCF zero?

Because that rapid growth requires massive investment.

All the earnings generated are immediately absorbed by the investment needed to fund the 12 % asset growth.

But that's good news.

It's great news because they're earning 12 % on those investments, which is 2 % more in their cost of capital.

FCF only turns positive when the growth slows down and less cash is needed for investment.

Okay, so we set a valuation horizon at year 6 when growth has settled to 6%.

The PV of the FCF we actually forecast up to that point is only 0 .9 million dollars.

Which means the vast majority of the company's value must be in that horizon value, PVH dollars.

And since that horizon value is so dominant, getting it right is crucial.

Absolutely.

So we use three different methods to cross -check our results.

Method 1, comparables using P -E ratios.

So we assume mature comparable companies traded a P -E of 11.

We estimate the price in year 6 by taking 11 times the projected earnings in year 7.

Discount that back to today and you get a total business value of 14 .4 million dollars.

Method 2, comparables using PV ratios.

Assume comparables traded a price to book of 1 .5.

You apply that to Concatenator's book equity in year 6, discount it back and you get a total value of 15 .0 million dollars.

So these two methods give us a solid market -based reference point.

And method 3, the constant growth DCF.

Here we use the long -run FCF forecast and the 6 % long -run growth rate.

That gives us a horizon value that, when discounted, leads to a total business value of 16 .3 million dollars.

Now that one forecast, the terminal value, accounts for 94 % of the total valuation.

Which highlights how sensitive these models are to long -term assumptions.

And that brings us to the crucial warnings about horizon value.

The first warning is about cause and effect.

Warning 1, growth requires investment.

Higher growth requires more investment, which reduces FCF.

But for Concatenator, if we increase the long -term growth from 6 % to 7%, the total value still goes up.

Why?

Because the firm is earning 12 % on its assets while the capital only costs 10%.

Every dollar invested, even though it reduces FCF today, still generates a positive NPV.

So growth is valuable only when the return is greater than the cost.

Which leads directly to warning 2, about the sustainability of that advantage.

Warning 2, always check for post -horizon PVGO.

Our last calculation assumed Concatenator can earn superior returns forever.

But that's unrealistic.

Competition should eventually eliminate those extra profits.

So we should assume that after the horizon, PVGO is zero.

In many cases, yes.

You assume that competition catches up and the NPV of new investments becomes zero.

And if you do that, the horizon value calculation simplifies dramatically.

It's just next period's earnings divided by the cost of capital.

Four dollars.

And for Concatenator, when you do that calculation, you get a total business value of 13 .2 million dollars.

So depending on our assumption about future competition, the valuation for Concatenator ranges from 13 .2 million dollars all the way up to 16 .3 million dollars.

And that range is the conclusion.

It highlights that your assumptions, specifically about future competitive conditions, drive the entire valuation.

Managers have to understand that value is only truly known when a deal happens.

But these models define the logical range.

This has been a true deep dive into the fundamentals of valuation.

From the mechanics all the way to the core financial theory.

We've really established four essential principles today.

First, the fundamental value of a stock is the present value of all expected future dividends.

That logic always holds.

Second, the cost of equity.

Three dollars is that opportunity cost.

It can be estimated for stable firms, but for high growth firms you absolutely have to use multi -stage models.

Third, the concept of PDGO is the true engine of value.

High growth only leads to a high stock price if the return on that investment is higher than the cost of equity.

And fourth, free cash flow valuation is the best approach for businesses with tricky payout policies or private ownership.

And when you calculate that crucial horizon value, you have to be so careful about assuming perpetual positive PDGO.

That ability to generate superior returns, that positive PDGO year after year, that's the difference between a high growth company and a truly valuable growth company.

So here's our final thought for you to take away.

We learned that the difference between an income stock and a true growth stock isn't just fast growth, but the ability to continually invest earnings at a rate above the cost of capital.

So when you look at your favorite companies, ask yourself,

what intangible asset, organizational advantage, or competitive moat does that company possess that allows it to generate positive PDGO year after year?

That is the ultimate driver of value.

That competitive advantage is what keeps creating wealth for shareholders decade after decade.

Thank you for joining us for the Deep Dive.

We'll see you next time.