Share valuation using the Discounted Dividend / Gordon Growth model

[TheMotorcycleBoy]

One of the share valuation models that I've recently looked at is called the Discounted Dividend Model, which may well also be known as Gordon's Growth Model. It works by assuming that a share's current worth is that of the sum of all of the discounted dividends received in perpetuity.

I did spend some time subsequently looking the derivation and also at a worked example using Marshalls Plc (MSLH).

That aside, it strikes me as an odd valuation model since it is obviously useless for stocks which don't pay dividends, and at first glance seems odd to suggest the behaviour of the stock is to be modelled forever, i.e. in perpetuity.

The Gordon model, briefly is as follows:

Share price today P = D1 + D2 + ...... + Dn + ....

where Dn is the present value of the dividend received n years after the share's purchase.

The PV of Dn, is best approached by looking at the dividend which will be received after the first year. To establish this figure the model assumes a growth rate to the dividend payouts (this is where I start to struggle with the model, because I can't conceive a company which sustainably pays divs which grow faster than inflation, it seems more realistic to have a model that can end the projection at a point where estimation reliability falls, but I'm content to park those thoughts presently).

So if the last year's div was D0 then the future value of the next year's div (D1) will be:

D1 = D0(1 + g)

hence the model has us assume a rate, 'g' at which the dividends are imagined to grow each year.

However, to make the value of future dividends seem consistent with the current day, they need to be discounted, using a discount rate r.

So the first year's dividend payout is assumed to have a present worth of:

D1 = D0(1 + g)/(1 + r)

If the calculation for the above first year's div is repeated in perpetuity, which is what the wiki derivation does, then we arrive at the formula for the share's estimated value:

P = D0(1 + g)/(r - g)

I'm planning on looking at an example of this model later on using Marshalls as an example. But for now I'm finishing this post with another link, which describes how to assign possible values to discount rate mentioned above.

M&M

[Alaric]

then we arrive at the formula for the share's estimated value:

P = D0(1 + g)/(r - g)

It used to be used by actuaries for the valuation of the assets of defined benefit pension funds. It had the useful attribute that they could make the answer what they wanted it to be by suitable selection of r and g. The natural starting point for value of assets should be market value, but the method was used back in the days when accounting conventions would otherwise state assets at book value.

Another use is to find the values of r and g that equate to the market price. It's quite possible for individual Companies to increase dividend distributions at a faster rate than inflation. Even if there was no inflation, Companies ought to be able to increase their profitability in money terms.

[tjh290633]

There are quite a lot of companies and ITs which have beaten inflation over the years, not necessarily every year but over a long period. Some have had a policy of raising them by more than inflation, others have just had results which achieved that. My own portfolio has given a dividend on the income unit which has grown substantially more than inflation. I don't have the figures to hand, but about three times the rate.

TJH

[SalvorHardin]

I would avoid this model like the plague. It used to be popular when commonly used for actuarial valuations for pension scheme equity portfolios (before the rules changed in the late 1990s to pay more attention to market value). And it worked pretty well.

It is based on very solid grounds; that the mathematically correct price for any investment is the sum of all cash flows (in today's terms) which it will produce for its investors. It's very difficult to argue against this in principle, the problem is that it is impossible to get a "correct" price because there are so many variables.

A big problem is that the model is so sensitive towards changes in D, r and g that small changes in either can produce massive changes in price. But D and g are little more than guesswork when you're looking many years into the future. For a pension fund things which affect D, r and g will produce changes in the value of the assets and liabilities in the same direction (so offsetting each other to some degree). Private investors do not have the same asset-liability profile.

This was why it used to work for pension scheme valuation where you are vastly more interested in the difference between the Assets and Liabilities than each figure indepedently. Also a scheme will have many shareholdings so there will be less volatility in D and g because these will be the weighted average of all of its shareholdings rather than a single holding.

In saying that a share is worth X after you've plugged numbers into an equation, to my mind this produces spurious accuracy. Can you seriously predict dividends in say 20 years time? Or economic growth (which influences dividend growth). Also it cannot cope with companies which do not pay dividends (or suspend them). Unfortunately many people will be highly influenced by a claim that an equation says that the share is worth Y. This is why most economists love to introduce maths into their work wherever possible; doing so makes people think that their predictions are like those in physics rather than educated guesswork.

I used to be an Actuary, have been a private investor for over 35 years and the only time I've ever used this method to value shares was in Actuarial exams.

It's fine for valuing bonds, because their cash flows are much more predictable.

[Gengulphus]

It is IMHO a theoretically-valid but useless-in-practice method of share valuation, provided that it is understood that it's really about any method of paying cash out to shareholders, not just dividends.

It's theoretically valid despite your comment that "it is obviously useless for stocks which don't pay dividends" because it only comes up with a value of zero for a company is zero if it is known that it will never pay cash out to its shareholders in the future. An example of that is Carillion: it still exists as a company (see https://beta.companieshouse.gov.uk/company/03782379 - its "Company status" would be "Dissolved" rather than "Liquidation" if it no longer existed), but there is zero chance of it ever paying anything to its shareholders and its share value is zero (*).

Note that if a company doesn't pay cash out to shareholders, but it's not known that it will never do so in future, the model won't necessarily give a zero valuation. It's perfectly possible that D1, D2, ..., D99 are all zero, but D100 and beyond are large enough to make the valuation very significant (the cash payments would have to be pretty large to overcome the effects of 100 years of the discount rate compounding, of course).

It's useless in practice as a method of share valuation because it relies on forecasts of what will happen in the future - forecasts that may very well turn out to be wrong, especially those for the longer term, and those for the longer term are usually most of the sum. For example, suppose you find a share that costs 100p at present, currently pays a dividend of 4p (and doesn't pay any further cash out to shareholders) and is increasing its dividend at 6% per year, and that you're using a discount rate of 8%. Plugging the corresponding values D0=4p, g=0.06 and r=0.08 into the "in perpetuity" formula P = D0(1 + g)/(r - g) gives P = 4p * 1.06 / 0.02 = 212p, making the shares look quite badly undervalued. But if you add the series up term by term (doable mathematically, but a spreadsheet isn't difficult and lets you see better what is going on, you'll find that it's not until you add in D35 that the total exceeds 100p. Do you really trust the implicit forecast in that model that dividend growth at 6% per year will continue for the next 35 years?

Personally, I would never trust forecasts about companies' futures beyond 5 years, and even that long only for the most reliable companies.

(*) Or being really excessively pedantic, both of those "zero"s should be "virtually zero"s, because it's not absolutely and completely impossible that the liquidators might get hold of enough cash that the company could pay off all its creditors, pay all of the liquidators' fees, and still have some cash left over to distribute to shareholders. Such a thing could happen in principle, but it would require something like a billionaire taking leave of their senses and buying one the company's assets for a few billion (pounds sterling, not lire or yen!). But it's so extremely unlikely that a valuation of 1p for all of its shares combined (i.e. not per share) would be an over-valuation...

Gengulphus

[TheMotorcycleBoy]

I would avoid this model like the plague.
....
....
I used to be an Actuary, have been a private investor for over 35 years and the only time I've ever used this method to value shares was in Actuarial exams.

It's fine for valuing bonds, because their cash flows are much more predictable.

Thank you for this SalvorHardin. This is an excellent answer. I think that over short time frames things like D and g can probably be deduced with some certainty but the value of discount rate I have finally realised is very subjective.

Yes, as you pointed out, it would be nice if you could just rely on maths, with this model it's so easy to form wildly differing estimates by tweaking r slightly.

For instance I did actually look at the Marshall's example, here's some dividend records:

2015	0.07	
2016	0.0965	
2017	0.122	
2018	0.142	
2019	0.15 (estimated by me)

I estimated/guessed a dividend growth rate of 5%.

Being a nervous investor and assuming a discount rate of 12%:

Dividend growth		 0.05
Expected rate of return	 0.12
Estimated share price	 2.14

but were we to settle for a lower rate e.g. 6%:

Dividend growth		 0.05
Expected rate of return	 0.06
Estimated share price	 15.0

Now since the current price is actually 4.40 or thereabouts, and neither of the above are particularly accurate estimates of the real price, this reinforces my earlier opinion, that any methodology based on selective discount rate merely provide investors with indications of possible return of rates based on how much they are prepared to pay, but not indications of the "market price", that being the esoteric notion that it is.

M&M

[TheMotorcycleBoy]

Don't worry Salvor, I'm really not taking this model too seriously, but seeing as it's so easy just to bung another set of numbers in the spreadsheet....

Being much more realistic, I decided that I should fix Marshall's dividend at just over inflation, so say 3%. I'm saying this since, they have always paid a div from 2006

https://www.dividendmax.com/united-king ... /dividends

(a big cut, and stagnation is evident after the CC is apparent between 2009-2013, but there is still a div, then a period of recovery). So I actually see a fraction over current inflation rate is probably a good conservative guess.

Then choosing a discount rate of 6%, i.e. about 4.5% above the risk free rate - a fairly conservative rate. Lobbing these figures into my spreadsheet gives a surprising result:

Dividend growth	         0.03
Expected rate of return  0.06
Estimated share price	 5.00

I say surprising, because it gives a result incredibly close to the target price from the 4-traders site:
https://www.marketscreener.com/MARSHALL ... consensus/

Anyway, I'm thinking of taking a look at the "Cash profits" valuation methodology next.

M&M

[TheMotorcycleBoy]

Anyway, I'm thinking of taking a look at the "Cash profits" valuation methodology next.

I briefly looked at my "How to pick quality shares" books (Phil Oakley) and could find little to convince me that the "quantity" of "cash profit" was much different than that of free cash flow. Actually I wasn't particularly convinced by his explanation of the model at all, so I'm leaving it there for now. There's an open invitation for anyone to differ with what I've said above, mind you! Since I'm not exactly a world authority....
Matt

[flopski2]

One of the ways of trying to get more "accuracy" in this type of model is by using 2 or 3 stage approach to the cash flow. Given the current dividend and next couple of years are more "forecastable" (you can use some of the city forecasts), you can plug those into a discount model and then use different assumptions about growth to perpetuity (2 stage) or a step down period if near term growth is expected to remain very high and then steady growth to perpetuity. I agree with the earlier poster that models of this type can bring spurious accuracy but they are probably good at examining your assumptions about how the company will grow cash flow in the future to continue paying dividends. Your confidence can be expressed via the discount rate but it is sometimes good to keep the discount rate the same and see what dividend growth assumptions put you close to the current share price. It is good to test this approach relative to other approaches such as relative valuation. This model falls down on not looking at the value to another player - M&A can drive out additional value that this model wouldn't capture.

[TheMotorcycleBoy]

One of the ways of trying to get more "accuracy" in this type of model is by using 2 or 3 stage approach to the cash flow. Given the current dividend and next couple of years are more "forecastable" (you can use some of the city forecasts), you can plug those into a discount model and then use different assumptions about growth to perpetuity (2 stage) or a step down period if near term growth is expected to remain very high and then steady growth to perpetuity. I agree with the earlier poster that models of this type can bring spurious accuracy but they are probably good at examining your assumptions about how the company will grow cash flow in the future to continue paying dividends. Your confidence can be expressed via the discount rate but it is sometimes good to keep the discount rate the same and see what dividend growth assumptions put you close to the current share price...

Thanks for this flopski,

I use a similar approach when using the Discounted Cash Flow method, that is use a forecast-type (or one based on the past few years) rate for the initial 2-5 years, and just assume a conservative growth (e.g. something close to current inflation) to go till perpetuity. I prefer the DCF technique over and above the DDM valuation, mainly because the former technique is relevant for firms regardless of their dividend policy.

...It is good to test this approach relative to other approaches...

Yes, definitely. I currently try to apply the DCF and EPV models to a valuation - and play around with some of the assumptions - but make sure that I compare like-for-like regarding the discount rate.

..such as relative valuation.

I've not heard of that method as yet, Flopski, but would like to learn more about all such methods. Sounds like a good idea for another thread.

thanks Matt

[flopski2]

Relative valuation is just a simple comparison between simple measures such as PE, Price/Sale and EV/EBITDA for similar businesses/sectors. You can use prices and ratios paid in M&A deals to gauge what metrics trade buyers use to value businesses. For example ex-growth, low margin businesses are generally bought at 0.8-1x sales, higher growth/margin businesses can be 4-6x sales. These types of techniques can be used in a sum-of-the parts approach to more complex businesses with more diverse business lines.