How to value shares with a Dividend Discount Model

As a value investor, I’ve spent most of the last ten years valuing companies using valuation ratios such as dividend yield and the cyclically adjusted price-to-earnings ratio (CAPE or PE10).

However, I now think such backward-looking ratios are inferior to the more theoretically correct Dividend Discount Model (DDM), which values companies based on an estimate of their future dividends.

So in the rest of this blog post, I’ll explain what the Dividend Discount Model is and how you can use it to guide your buy, sell and position sizing decisions, especially if you’re interested in dividend growth stocks.

Warning: This is a long blog post so you may want to get a cup of tea and a slice of cake before you settle in for a long read. Or, bookmark this page and come back to it when you have a spare moment or three.

Table of Contents

• Why focus on dividends?
• What does it mean to discount dividends?
• Valuing a company which will pay a single future dividend
• Valuing a stream of dividends with no growth
• Valuing a stream of dividends with constant growth
• Using the Gordon Growth Model to value Admiral
• Valuing a stream of dividends with multiple growth rates
  • Stage one: Valuing dividends over the next ten years
  • State two: Valuing dividends after the next ten years
• Valuing Admiral using a two-stage dividend discount model
• Key factors influencing future dividends
  • The quality of the business
  • The defensiveness of the business
  • Market growth and market share growth
  • Return on capital employed and dividend cover
  • Estimating Unilever’s dividends using capital employed and dividend cover
• Calculating a Buy Price and Sell Price
• Calculating and adjusting position sizes

If you’re allergic to maths then don’t panic; Dividend Discount Models require very little in the way of maths and what they do need you can easily get a spreadsheet to do the work for you (feel free to use my investment spreadsheet, although it’s probably best to read this post first).

I’ll start at the beginning with a simple question:

Why focus on dividends?

“A cow for her milk, A hen for her eggs, And a stock, by heck, For her dividends. An orchard for fruit, Bees for their honey, And stocks, besides, For their dividends.”

John Burr Williams (inventor of discounted cash flow analysis)

“All investing is laying out cash now to get some more back in the future.”

Warren Buffett (billionaire value investor)

At its most basic, investing is about putting money at risk with the expectation (the rational expectation) of getting more back at some point in the future.

Exactly how much risk you’re willing to take and how much you expect back in return (and when) are up to you. But at the end of the day, that’s what investing is all about.

So how do we get money back from investing in shares?

Actually, that’s the wrong question. When you invest in stocks and shares you’re actually investing in businesses, so the correct question is:

How do shareholders get money back from the companies they own?

From this business owner’s perspective, there are two main ways to get a return from a company: (1) dividends and (2) selling company assets (factories, computers, subsidiaries and so on) and returning some or all of the proceeds to shareholders.

Since almost nobody invests in shares with the intention of forcing a company to liquidate some of its assets, I think most investors should focus on dividends as the primary source of future returns.

But what about Amazon, I hear you ask. It doesn’t pay a dividend and it’s been an incredible investment over the last 20 years or so.

Indeed it has, but that doesn’t change the fundamental point that the only return Amazon as a company is likely to give its shareholders is (a) dividends and (b) cash from the sale of assets.

While Amazon doesn’t pay a dividend now, investors explicitly or implicitly expect it to pay dividends at some point in the future. And as those expected dividends grow and come closer to being paid, that is reflected in its growing share price.

So regardless of whether a company currently pays a dividend or not, the true value of that company is based solely on its expected future dividends and other cash returns.

As investors then, one of our primary jobs is to estimate future dividends.

But estimating future dividends alone is not enough. We have to turn those estimates into something useful, such as a target buy or sell price. And to do that, we need to discount the future.

What does it mean to discount dividends?

“I have no confidence and have not had any for over 20 years in price-to-book, price-to-earnings, price-to-cash flow, price-to-sales, even, as a measure of true value. A measure of true value is the long-term discounted value of a future stream of dividends.”

Jeremy Grantham (billionaire value investor)

“The value of any stock, bond or business today is determined by the cash inflows and outflows – discounted at an appropriate interest rate – that can be expected to occur during the remaining life of the asset.”

Warren Buffett (billionaire value investor)

Here’s an easy question:

Which would you prefer? £100 today or £100 a year from now?

Most people would prefer £100 today because (a) they want to spend it right away or (b) they can invest that £100 today and get back more than £100 in a year.

The fact that £100 today is preferable to £100 in one year means that £100 today is more valuable than £100 a year from now or, alternatively, that £100 a year from now is less valuable than £100 today.

In other words, we intuitively discount (reduce in value) the future relative to today.

Let’s say I repeat the above proposal and you choose to take the £100 today.

You then invest that £100 into a sure-fire investment guaranteed to provide a 100% gain over the next year.

How much would I have to pay you a year from now for you to not choose the £100 today?

Since you have a guaranteed way to gain 100% on the £100 over the next year, I would almost certainly have to pay you more than £200 a year from now to lure you away from taking the £100 today.

And if I offered to pay you £200 in a year you would probably have no preference, because that offer would be equivalent to taking the £100 today and putting it into your sure-fire investment. Either way, you’d have £200 a year from now.

So £100 today and £200 a year from now have the same economic value to you, which means the present value of that £200 a year from now is £100 today (in this case a bird in the hand really is worth two in the bush).

We can also say that your discount rate in this example is 100%. In other words, if we delay your £100 payment by one year, you need that £100 to grow by 100% before you’d prefer it over having £100 today.

You can also think of the discount rate as your required rate of return if that makes more sense to you.

Let’s use a bit of maths to see how this works.

If:

• v = present value of a future cash payment
• d = the future cash payment (£200 in this case)
• r = your discount rate or required rate of return as a decimal (100% or 1.00 in this case)

We can then calculate the present value of that £200 payment with this dividend discount formula:

• v = d / (1 + r)

Filling in the number:

• v = £200 / (1 + 1.00)
• = £200 / 2
• = £100

So the present value of £200 a year from now at a 100% discount rate is £100, as expected.

Here’s another question:

How much would I need to offer you in two years to lure you away from taking £100 today and investing it in your sure-fire 100% per year investment?

We know that if you took the £100 today you could turn it into £200 in a year. Then in year two, you could double that again to £400.

So I would have to offer you more than £400 in two years for that offer to be more valuable than taking the £100 today. In other words, the present value of £400 in two years is £100 today, at least with a discount rate of 100%.

We can tweak our dividend discount formula to work out the discount over two years like this:

If:

• v = present value
• d = future “dividend” in two years (£400)
• r1 = discount rate in year one (100% or 1.00)
• r2 = discount rate in year two (100% or 1.00)

Then:

• v = d / (1 + r1) / (1 + r2)

All we’re doing here is taking the original formula and discounting (dividing) it again by the discount rate for the second year.

Plugging in the numbers gives:

• v = £400 / (1 + 1.00) / (1 + 1.00)
• = £400 / 2 / 2
• = £100

And so we get the expected result, that £400 in two years has a present value of £100 if we use a discount rate of 100% per year.

But what if we wanted to calculate the present value of a future dividend paid ten years from now? We would end up with a horribly long formula with “/ (1 + r)” repeated many times.

That would be a terrible idea, so instead we can generalise the previous formula so that it will discount a future dividend paid any number of years in the future.

We can do this because x divided by y twice (x / y / y) is the same as saying x divided by y raised to the power 2 (also called y squared or y²). In other words, we can use powers or exponents to generalise the equation.

Let’s add the number of years to this list:

• v = present value
• d = future dividend
• r = discount rate
• n = number of years before the dividend is paid
• ^ means raised to the power

The generalised formula is:

• v = d / (1 + r) ^ n

So working through the previous example again we have:

• v = £400 / (1 + 1.00) ^ 2
• = £400 / 2 ^ 2
• = £400 / 4
• = £100

This will work no matter how far in the future the dividend may be, so it’s a very handy formula.

Now that we know how to discount a single dividend, let’s get on with the more interesting task of using this knowledge to value companies.

The first example looks at a company which will pay just a single dividend.

Valuing a company which will pay a single future dividend

Let’s say we have a company which is in serious trouble. It doesn’t pay a dividend and if its assets were sold off in an orderly manner, they would fetch the equivalent of 400p per share, after all the company’s debts had been paid off.

The company’s shares are currently trading at 100p each.

You think it would be possible to buy up enough shares to get a place on the board of directors and then force the company to sell everything and return the net proceeds (that 400p per share) to shareholders.

You think this might take a couple of years to pull off.

Because this involves quite a bit of work, you would like a 100% annualised rate of return.

Here are the inputs for the dividend discount formula:

• d = dividend (asset sale proceeds of 400p)
• r = discount rate (required rate of return of 100% or 1.00)
• n = number of years to wait (2)

Plugging those into the formula gives:

• v = 400p / (1 + 1.00) ^ 2
• = 400p / 2 ^ 2
• = 400p / 4
• = 100p

The formula tells us that the present value of that future 400p “dividend” is 100p.

This happens to be the current share price, so assuming your analysis is sound, this “deep value” (asset-sale-based) investment meets your criteria.

Deep-value investments like this made up a significant part of Warren Buffett’s early investment career, and it shows that the dividend discount model works just as well with non-dividend-paying companies on the brink of bankruptcy as it does with high-quality dividend growth superstars.

So now we know how to discount a single dividend. Next, we’ll look at an easy way to discount an endless stream of identical dividends with an even simpler formula.

Valuing a stream of dividends with no growth

Let’s start with something simple: A company that pays exactly the same dividend every year for the rest of its life.

Since the only return shareholders can get from a company is the cash it pays out (either as dividends or as the proceeds from asset sales), the value of a company (its intrinsic value, not its price) is the present value of all those future “dividends”.

We already know how to value a given year’s dividend with the dividend discount formula:

• v = d / (1 + r) ^ n

All we need to do is calculate the present value of every dividend a company will ever pay during the rest of its lifetime, and add them up.

The problem, of course, is that companies can be around for decades or even centuries, and estimating and discounting hundreds of individual dividends is not my idea of fun.

Fortunately for us, there’s a handy mathematical shortcut which makes all that hard work disappear.

The shortcut is based on the fact that the further out into the future you go, the bigger the discount will be. So if the future value of those dividends is constant, their discounted present value will gradually shrink towards zero.

So even if a stream of constant dividends were infinite, its present value would be finite, and the formula for calculating this finite number is very simple.

We have:

• v = present value of an infinite dividend stream
• d = fixed value of each dividend
• r = discount rate

And here’s the formula for calculating the present value of a perpetual stream of zero-growth dividends:

• v = d / r

It’s an incredibly simple formula, so let’s flesh it out with an example.

Let’s say we have a company paying a 100p dividend which you think will continue to be paid essentially forever but will never grow. You require a 10% return from an investment otherwise it isn’t worth your time.

So:

• d = 100p
• r = 10% or 0.10

Plugging those into the constant dividend formula gives:

• v = 100p / 0.10
• = 1,000p

This intuitively makes sense. If you can buy the shares for 1,000p and the dividend is 100p, the dividend yield is 10%. There is no growth so the only return you’ll get is from that yield, which is why the dividend yield equals your required rate of return (your discount rate).

Let’s move on to the slightly more realistic situation where a company pays a regular dividend which is growing at a constant rate.

Valuing a stream of dividends with constant growth

Let’s say the company from the previous example starts to grow its 100p dividend by 4% every year, and you expect that growth rate to remain constant essentially “forever”.

The formula for calculating the present value of a stream of constantly growing dividends is basically the same as the one we used for a stream of constant zero-growth dividends.

The only difference is that we have to take into account the dividend growth rate.

As you might reasonably suspect, dividend growth works in the opposite direction to the dividend discount. Growth makes their present value larger while discounting makes it smaller.

The opposing nature of growth and discounts is reflected in the constant growth DDM, otherwise known as the Gordon Growth Model, named after economist Myron J. Gordon.

Here are the variables:

• v = present value
• d = The next dividend to be paid
• g = constant growth rate
• r = discount rate

And here is the Gordon Growth Model:

• v = d / (r – g)

The only difference between this and the constant dividend DDM formula is that we subtract the growth rate from the discount rate. This effectively reduces the discount and therefore increases the present value (the higher the growth rate, the higher the present value).

One thing to remember is that the growth rate cannot be greater than the discount rate, otherwise, we’ll end up with a nonsensical answer (in practice the present value would be infinite).

This is why the Gordon Growth Model isn’t very good at valuing high-growth companies. For that, we’ll need a multi-stage DDM, but let’s leave that to one side for now.

The Gordon Growth Model is very simple and very useful in the real world, so let’s have a look at a real company where it’s reasonable to assume a constantly growing dividend “forever”.

Using the Gordon Growth Model to value Admiral

Admiral Group has a long history of near-constant dividend growth and that’s one reason why it’s been in my portfolio since 2013.

Admiral has grown its dividend by more than 10% per year, on average, since it became a public company in 2004.

In 2019 it paid a dividend, including its regular special dividend, of 140p and its share price as I type is 2,960p.

My required rate of return from an investment is 10%, so that’s my discount rate.

All we need now is an estimate of Admiral’s future dividend growth rate.

Although Admiral’s historic dividend growth rate is more than 10% since 2004, I want my estimate of future dividends to be both realistic and conservative. That way I’m more likely to be pleasantly surprised than unpleasantly disappointed.

To start with I’ll assume Admiral will increase its next dividend (2020) by 10% to 154p because the interim dividend went up slightly more than that. I’ll also assume that beyond 2020 Admiral will grow its dividend by 5% “forever”. I think that’s realistically conservative given its budding international and home insurance businesses.

Here are our variables then:

• v = present value of Admiral under these assumptions
• d = an estimate of next year’s dividend (154p)
• g = constant growth rate (5% or 0.05)
• r = discount rate (10% or 0.10)

Plugging those into the Gordon Growth Model gives:

• v = 154p / (0.10 – 0.05)
• = 3,080p

The current share price of 2,960p is slightly lower than my estimate of Admiral’s present value, so from a valuation-only point of view (ignoring all manner of other important considerations) Admiral seems to be good value today.

As you can see, the Gordon Growth Model is a very simple way to value companies and it works best with very mature businesses operating in very mature markets.

Its biggest drawback is that it doesn’t work for companies that (a) don’t pay dividends today or (b) are expected to have more than one growth rate in the future (typically high growth when the company is relatively young and slower growth as it matures).

To deal with zero dividends and varying dividend growth rates we’ll need to use a multi-stage dividend discount model.

Valuing a stream of dividends with multiple growth rates

Multi-stage dividend growth models cope with unusual dividends and varying growth rates by breaking down the estimate of future dividends into two or more stages.

Let’s keep things simple by focusing on a DDM with just two stages.

The first stage typically covers the next five or ten years. It estimates each individual dividend over that period, and that allows us to factor in zero dividends, special dividends and other oddities so we can come up with a better estimate of dividends in the near (and therefore hopefully more predictable) future.

The second stage covers the period after five or ten years. Here we use the Gordon Growth Model to estimate the value of all dividends after that initial five or ten-year period.

Let’s start with the stage one.

Stage one: Valuing dividends over the next ten years

The first stage is based on our trusty dividend discount formula:

• v = present value
• d = future dividend
• r = discount rate
• n = number of years until the dividend is paid

• v = d / (1 + r) ^ n

Just plug the formula into an investment spreadsheet and you can calculate the discounted present value of each estimated dividend for the next ten years.

The tricky bit is coming up with an estimate for those dividends in the first place.

In some cases, like Admiral, you could just use a constant growth rate to estimate the nominal value of those dividends, and then discount them back to today.

Here’s an example of what that might look like for Admiral (taken from my investment spreadsheet and using slightly different values than the example above):

Note that the “discount factor” in that table is the cumulative discount, shown so that you get an idea of how much those future dividends are discounted by. The “buy price” is another name for present value when the discount rate is the target rate of return. I’ll explain more about buy and sell prices later on.

Okay, back to the topic of estimating future dividends.

If you have a company where the dividend is currently suspended, you can just enter a zero divided for the next year or three, based on your judgement, and then estimate future dividends beyond that.

Alternatively, if you have a high-growth company then feel free to increase the dividends by 20% or 50% per year. For stage one it doesn’t matter if the growth rate is higher than your discount, so this method is very suitable for young high-growth companies.

If the growth rate is expected to be high for a long time you can just stretch out stage one to twenty, thirty or however many years you like, but beware of drifting into fantasy land to justify a lofty share price.

For this to be anything more than just a guessing game you need to have done your due diligence first by analysing the company in depth.

In my case, that means looking at the company from a quality defensive point of view and then conservatively but realistically estimating future dividends based on that analysis. I’ll cover that in a bit more detail later on.

State two: Valuing dividends after the next ten years

Eventually, all sufficiently long-lived companies see their growth rate slow to a crawl. If they didn’t they’d end up larger than the entire global economy, which is obviously impossible (for now let’s leave aside the possibility of intergalactic expansion).

This means all companies will eventually end up with a long-term growth rate of 5% per year or less, although it may take them many decades to get there (and most companies die long before they reach their maximum potential size anyway).

We can use this handy fact to simplify the task of estimating dividends over the next ten, twenty or fifty years.

How? We just assume the company eventually settles into slow, constant long-run dividend growth and use the Gordon Growth Model to calculate the present value of that dividend stream.

In this case, I assume Admiral can grow by 5% per year over the longer-term as it has operations in multiple countries and the potential to move into multiple adjacent markets (it already has a toe in the house insurance and personal loan markets).

Here are the numbers from that Admiral table above:

• d = dividend paid in 2029 (275.4p)
• g = long-term growth rate (5% or 0.05)
• r = discount rate (10% or 0.10)

That gives:

• v = 275.4p / (0.10 – 0.05)
• = 5,508p

That’s the “present value” of all Admiral’s dividends from 2029 to infinity, but “present” in this case means the year 2029. We have one last job to do, and that’s to discount the 2029 “present value” back to the present value as at today.

This is actually quite simple. All we need to do is treat that 5,508p as a single very large dividend which will be paid in 2029. We can then discount it to get today’s present value using the usual dividend discount formula:

• d = 5,508p
• r = 10% or 0.10
• n = 10

Which gives:

• v = 5,508p / (1 + 0.10) ^ 10
• = 5,508p / 1.1 ^ 10
• = 5,508p / 2.59
• = 2,124p

So the present value today, of all Admiral’s estimated future dividends beyond 2029 (using these specific inputs) is 2,124p.

Now all we have to do is calculate the present value of all Admiral’s future dividends, which is simply the sum of stage one and stage two.

Valuing Admiral using a two-stage dividend discount model

Here’s that table of Admiral’s discounted future dividends again for reference:

The present value of all the individual stage one discounted dividends is 1,100p.

The present value of Admiral’s long-term constant growth dividends from 2029 and beyond is 2,124p.

Adding those together gives us the present value of all of Admiral’s estimated future dividends, which is therefore the estimated present value of the entire company.

That present value (under the assumptions of 7% growth over ten years, 5% growth after that and a required rate of return of 10%) is 3,224p.

The actual share price is slightly below that level, so if those assumptions are reasonable and conservative then there’s a reasonable chance (but no guarantee) that Admiral will produce annualised returns of 10% per year or more over the long term.

This is all very mathematically precise, but in the real world, the future is full of uncertainty so what really matters is the quality of your inputs (remember: garbage in = garbage out). In this case, that means the quality of your dividend estimates.

If they’re conservative and realistic then on average you should get more than your required rate of return if you can buy companies for less than their estimated present value.

In the Admiral example above I used an estimate of 7% growth over ten years and 5% growth after that. These estimates weren’t pulled out of a hat; they were based on a combination of Admiral’s past results, its competitive strengths, its growth prospects across its various businesses, the long-term growth potential of its markets and other relevant factors.

So just plugging in dividend growth rates without sufficient thought is potentially dangerous. To help reduce that danger we’ll look at some of the main factors you should take into account when estimating future dividends.

Key factors influencing future dividends

The first thing to remember when you’re estimating future dividends is that your investment returns will largely depend on them, so your estimate should be conservative and realistic. I’ll say that again because it’s important:

• Your estimate of future dividends should be conservative and realistic

It’s important to be conservative because if you’re not, the actual dividends paid are likely to be less than you expected. If the gap between your estimates and reality is wide enough you could end up consistently overpaying for companies, and that is not a good way to invest.

It’s also important to be realistic. I could be conservative and say that Admiral is only going to pay a dividend of 50p from now on (about a third of its 2019 dividend). That’s very conservative, but it’s unrealistic and the share price is unlikely to ever get low enough to justify a purchase based on such a ridiculously conservative estimate.

So if you’re unrealistically conservative, you’ll probably end up missing out on many great investment opportunities.

As for exactly what you need to look at to estimate future dividends, that depends very much on the individual situation.

Since this blog is about investing in steady dividend growth stocks, I’ll focus on those, but it’s important to remember that DDM is as applicable to Tesla as it is to Tesco.

With all that in mind, here are some of the main factors I look at, in order of importance (in my opinion):

1. The quality of the business

A quality company is one with durable competitive advantages. Enduring competitiveness is very important if you’re looking for steady dividend growth because without it, companies can be battered by all manner of existing and new competitors.

Think of a company’s ability to pay dividends as a goose which lays golden eggs. Everyone wants the eggs so to protect the goose you’ll need a strong castle with a wide and deep moat. That’s the sort of protection that enduring competitive advantages provide, and without them, somebody is bound to turn up and steal the company’s goose.

Or less poetically, without enduring competitive advantages it’s hard to say what will happen to a company, so it’s hard to estimate its future dividends over the next ten years and beyond.

2. The defensiveness of the business

“Your goal as an investor should simply be to purchase, at a rational price, a part interest in [a] business whose earnings are virtually certain to be materially higher five, 10 and 20 years from now”

Warren Buffett (billionaire value investor)

Companies don’t have to be traditionally “defensive” for you to be able to estimate their future dividends, but (a) it helps and (b) the company’s cyclicality is definitely worth thinking about.

Let’s say you’re looking at a UK housebuilder and its dividend has grown 20% per year over the last decade.

Is it conservative and realistic to estimate dividend growth at 18% over the next ten years followed by say 5% as the long-run growth rate?

Perhaps, but probably not.

Housebuilders are notoriously cyclical and the UK has been through a government-sponsored house price boom over the last ten years. It’s very likely that at some point we’ll have a housing downturn, regardless of how much the government tries to artificially boost prices. And when that downturn comes, it’s likely that housebuilder dividends will be cut or suspended, just as they were in the global financial crisis of 2007-2009.

So with a cyclical business, you may want to estimate a level of dividends which you think the company could pay through boom or bust (although perhaps ignoring exceptional situations such as a global pandemic).

That will seem to be overly conservative during a boom, but it may save you from investing in cyclical companies that appear cheap but only because their short-term growth has been boosted temporarily by a cyclical boom.

If you want to know how I assess a company’s quality and defensiveness, have a look at my investment checklist.

3. Market growth and market share growth

A company with a 1% market share can easily double in size and nobody would notice. But if a company has a 40% market share then doubling in size by taking further market share is, in almost all cases, pure fantasy.

So market share is an important limiting factor for future growth. Companies can get around this limitation by (a) operating in growing markets so that even a stable market share provides ample growth opportunities and (b) expanding into additional markets.

Let’s say we’re looking at Marks & Spencer. Traditionally it was known for having a store (or two) on every high street in the UK. That’s great, but it doesn’t allow much room for further growth.

If M&S opens a third or fourth store in a given area it probably isn’t going to add additional revenues. Instead, it will just take sales away from existing stores so the same amount of sales will be generated by a larger and more expensive cost base. And static sales and higher costs are not a recipe for higher profits and larger dividends.

So when you’re estimating future dividends, think about:

• how much room the company has to grow in its existing markets over the next ten years
• how much market share it could take
• how many more outlets it can have before they have a negative impact
• what other markets it has already entered and how they’re progressing
• what untapped markets could be potential avenues for future growth

Again, be realistically conservative. Don’t be too negative and don’t think that every possible growth avenue will work out perfectly because they won’t.

One last point about market growth is to think about potential market disruption and decline over say the next ten or twenty years. Obvious candidates are oil & gas, petrol and diesel cars, tobacco and anything standing in the way of the internet.

Investing in companies operating in declining markets isn’t necessarily a bad idea, but you should think about using a negative growth rate in stage two of your model.

4. Return on capital employed and dividend cover

Another important factor that can limit a company’s growth is the rate of return it gets on capital employed within the business.

Let’s start with an analogy. You put £100 into a savings account which pays interest at 10% per year. At the end of year one you receive £10 in interest. You withdraw £6 to spend and retain the other £4 in the account, which leaves you with £104 of capital in the account.

If the account continues to earn 10% on its capital, and if you continue withdrawing 6% and retaining 4%, the capital in the account and therefore the earnings (interest) it generates will grow by 4% each year.

Another way to put this is to say that under those conditions, 4% is the maximum self-fundable growth rate this savings account can achieve.

The account cannot grow faster than 4% unless (a) its interest rate increases or (b) you retain a larger portfolio of that interest within the account or (c) you take additional external capital (e.g. borrow money from your parents or kids) and put that into the account.

This is relevant to us because exactly the same concept applies to companies.

If a company has £100m of capital employed, earns a net return on capital employed (net ROCE) of 10%, pays out 6% as a dividend and retains 4% to fund investment in growth assets, the maximum self-fundable growth rate for that company is 4%.

The only way to get that company to grow faster than 4% is to add in additional capital from an outside source such as borrowings or leased assets (e.g. shops or factories).

What does this have to do with estimating future dividends?

The answer is quite a lot, at least in most cases.

Instead of just coming up with an estimate for short and long-term dividend growth rates, I prefer to think about how quickly the company could grow its capital employed and how that growing capital base could drive earnings and dividend growth.

To make this more concrete, here’s an example using one of my current holdings.

Estimating Unilever’s dividends using capital employed and dividend cover

In 2020, Unilever‘s capital employed amounted to 1,619 Euro cents per share (Unilever’s results are reported in Euros). Over the last ten years, its average net return on capital employed was 16% and it paid out 65% of that return as dividends (giving an average dividend cover of 1.55).

Note: I use SharePad and ShareScope as an easy way to download ten years of financial data.

We can use that information to produce an estimate of Unilever’s maximum self-fundable growth rate. This usually gives a conservative estimate of potential future growth because it assumes the company won’t take on any additional debt or leases to drive faster growth.

I’ll conservatively but realistically assume a net return on capital going forwards of 15%, slightly below the historic average.

If Unilever’s capital employed in 2020 was 1,619 cents and its ROCE is 15%, that will give estimated earnings in 2021 of 243 cents.

The 2020 dividend came to 165.8 cents, so if we assume a 2021 dividend cover of 1.45 we end up with an estimated 2021 dividend of 167.5 cents.

This seems conservative and realistic to me as it estimates dividend growth next year of just 1%, far below Unilever’s historic 7%-plus dividend growth rate.

With earnings of 243 cents and a dividend of 167.5 cents, that leaves 75.5 cents retained within the company to grow its capital employed.

Those retained earnings increase capital employed by 4.7%, taking them to 1,694 cents by the end of 2021.

A similar process can then be repeated over and over to come up with an estimate of Unilever’s capital employed, earnings and dividends for the next ten years (stage one). For stage two we can use the Gordon Growth Model to give an estimate of the value of dividends beyond ten years.

Here’s a snapshot of what that looks like using my investment spreadsheet, although don’t expect to be able to read this on anything other than a large screen:

And here’s a visual representation of those dividends and discounted dividends, showing how discounting gradually reduces the value of far distant dividends towards zero:

Remember, this approach only gives you an estimate of the company’s maximum self-fundable growth rate. This may be the most important growth-limiting factor, but the company may be more limited by market share, market growth or other factors.

If external factors such as market growth are more important, you can take that into account too. If a company cannot grow quickly because of external factors then this will show up as either:

• (a) falling returns on capital, as newly retained and deployed earnings won’t be able to generate historic levels of profit, or
• (b) less retained earnings as management realise they won’t produce attractive rates of return so they pay earnings out as dividends instead.

This gives us two levers to adjust to make a more realistic and conservative forecast.

Let’s say we think Unilever can only grow at 2% per year because its markets are growing slowly and it has maxed out its market share.

In that case, we might gradually reduce its ROCE over the ten-year period and/or increase its dividend payout by reducing dividend cover.

We can tweak these in our spreadsheet until we get a DDM that (a) gives us our expected dividend growth rate of 2% and (b) is realistic and conservative.

Ultimately this comes down to a combination of experience, judgement and learning from the accuracy (or not) of past estimates.

Okay, so now we’ve looked at all the major aspects of the dividend discount model. The only thing left to do is use it to help us make investment decisions.

Calculating a Buy Price and Sell Price

The obvious way DDM can help us make investment decisions is that it gives us a share price which should (on average and only if our DDMs are conservative) produce at least our target rate of return.

When I use my target rate of return as the discount rate, I call the present value my Buy Price. If the share price is below the Buy Price then as long as I’m happy with the quality and defensiveness of the company then I’ll invest.

Looking at the Admiral example from above again:

The Buy Price for Admiral is 3,224p and the current share price is 2,960p, so I would be willing to buy more of Admiral shares at that price if I had cash available and if its existing position size wasn’t already maxed out (I’ll cover position sizing in a moment).

As for Unilever, here’s the DDM again:

Unilever’s Buy Price in pence is 2,509p whereas the share price today is 3,890p. So Unilever’s share price is comfortably higher than its Buy Price so at least for me it isn’t a screaming bargain at the moment.

However, I do own Unilever, so if it’s priced above my Buy Price, why haven’t I sold it?

The answer is that at its current price, the estimated rate of return is still around 8%. That’s below my target return of 10%, but it’s better than the expected long-term return from the overall UK stock market (around 7%).

On top of that, Unilever is a very steady dividend growth stock. Steady dividend growth is something I want from my portfolio, so I’m happy to hold it even if the expected returns aren’t spectacular.

But that doesn’t mean I would hold onto Unilever at any price. At some point, the expected return would be below the expected return from the overall market, and at that point, I’d be better off selling and reinvesting the cash elsewhere.

A reasonable Sell Price then is one that would produce a return at or below the long-term expected return of the relevant market. In my case, that’s the FTSE All-Share where the long-term return is about 7% annualised.

You can work out the Sell Price by simply changing the dividend discount rate to 7% (or whatever your minimum acceptable rate of return is) and hey presto: the calculated present value now represents your Sell Price.

• For Admiral, the Sell Price is 5,725p
• For Unilever, the Sell Price is 5,074p

Of course, DDM valuations aren’t set in stone and they don’t last forever. They need updating at least every year and they should be reviewed whenever a company publishes any material news.

So that’s an overview of how DDMs can be used to help investors with their buying and selling decisions. The next thing we need to think about is position sizing because discounted dividend models can help us there too.

Calculating and adjusting position sizes

Somewhat obviously, the more attractive an investment the more you should invest in it, as long as you stay within your risk tolerance.

For me, attractiveness is the combination of a company’s quality, defensiveness and value.

In summary, high-quality defensive companies priced below my target Buy Price should have the largest positions, while low-quality cyclical companies priced above my target Sell Price should either be sold or shouldn’t be in the portfolio in the first place.

There are a million ways to make position size decisions, so I’ll just briefly explain how I’ve decided to manage position sizing in a relatively concentrated portfolio of quality dividend stocks.

The first thing I do is calculate a default position size. This will be the target position size when a holding’s valuation is good. Not awesome, not terrible, but good enough for it to deserve a reasonably sized place in my portfolio.

Default position sizes will mostly depend on how many stocks you expect to hold. In my case, I’m currently targeting 25 holdings, so my default position size should be something close to 1/25th (4%) of the portfolio.

In practice I use two default sizes; one for Quality Defensives and one for Quality Cyclicals:

• Default position size for Quality Defensives= 4%
• Default position size for Quality Cyclicals = 3%

This captures the fact that all else being equal, I’d rather have more invested in defensive companies than cyclicals.

As I’ve already mentioned, the target position size should increase as a company becomes more attractively valued and shrink as it becomes less attractively valued.

I measure this attractiveness with something called the Margin of Safety.

My definition of Margin of Safety is based on the discount between the current share price and the stock’s Sell Price. For example:

• If the share price equals the Sell Price then:
  • Margin of Safety = 0%
• If the share price is halfway between the Buy and Sell Price then:
  • Margin of Safety = 50%
• If the share price equals the Buy Price then:
  • Margin of Safety = 100%

This Margin of Safety is a continuum which extends from above the Sell Price (where Margin of Safety is negative) to below the Buy Price (where it’s above 100%), and is easy to calculate using my investment spreadsheet.

It’s useful because it can be used to adjust position sizes as share prices move up and down. For example:

• If Margin of Safety = 0% (price = Sell Price)
  • Target size = 1/2 default size
• If Margin of Safety = 50% (price halfway between Buy and Sell Price)
  • Target size = default size
• If Margin of Safety = 100% (price = Buy Price)
  • Target size = 1.5-times default size

Here’s a more concrete example:

Imagine a Quality Defensive holding with a Margin of Safety of 50% (the share price is halfway between the Buy and Sell Price). This gives it a target size of 4%. Let’s say its actual size is also 4%.

If that company’s share price fell until it equalled the Buy Price then its Margin of Safety would increase to 100%. In turn, this would increase the target size to 6%, assuming the dividend model remained unchanged.

However, because the share price has fallen the actual position size is now probably below 3%, which is nowhere near the target size of 6%.

At this point, it might make sense to reduce a less attractively valued holding (preferably one which is overweight) and top up this attractively priced but now underweight holding until it’s somewhere close to 6% of the portfolio.

Now imagine that the company’s share price shoots up a few weeks later following some good news. The share price doubles and eventually reaches the Sell Price (again, assuming nothing changed in the dividend model).

At this point, its actual position size may have also doubled to 12%, which is a lot. However, the Margin of Safety is now zero so the target size has fallen to 2% (half the default size for a Quality Defensive holding).

This could be a good time to trim back that holding, take some profits and risk off the table and reinvest the proceeds into a more attractively valued (and preferably underweight) holding.

One thing to keep in mind if you’re going to carry out this sort of rebalancing adjustment is to make sure you (a) don’t do it too often and (b) don’t make small adjustments, otherwise your returns will be eaten up with fees and taxes.

Frequent small adjustments may not be worth the effort anyway, so I try not to make more than one or two adjustments per month and only when broker fees will be less than 1% of the transaction.

Putting discounted dividend models to work

To draw this long article to a close I just want to emphasise that your dividend models will never be 100% accurate and that’s not even the point.

Instead, they’re a very useful tool which forces you to think about the future prospects of any company you’re thinking of investing in, and they can form a central part of a sensible investment process:

1. Pick a company you’d like to review
2. Estimate its future dividends (which requires a thorough analysis of the company and its markets, perhaps using an investment checklist and spreadsheet)
3. Discount those dividends by your target rate of return
4. Use the resulting dividend discount model to guide your buy, sell and position sizing decisions