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Modelling share values

Dividend discount models tell us where share valuations really come from
August 28, 2015

Where does the valuation of a company’s shares really come from? Forget about PE ratios, price-to-book ratios and so on, and focus on the fundamentals of equity valuation. Value can only come from one source – the amount of cash that an investor gets from owning a share. Ultimately, only cash matters, and the only cash that matters to a shareholder is the distributions – mostly dividends – received.

From year to year dividends may arrive as smoothly as drinking chocolate or as lumpily as cold gravy. They may come in strange wrappers. But they are the distributions that a company makes to its shareholders and they are the only factor that drives equity valuation. That must be so; after all, if somehow you know for certain you will never receive a penny in any shape or form from a company as compensation for putting capital into its shares, how much would you pay for them? Nothing. Therefore cash disbursements – dividends – drive value. That being so, it pays to know how to value shares using models based on dividend payments.

Generically, these are dividend-discount models, so-called because they are based on discounted cash flow techniques, and they come in three forms:

■ Zero-growth model

■ Constant-growth model

■ Multiple-growth model

 

The zero-growth model does what its name implies. It assumes that a company’s dividends will stay the same forever, just like the coupon on a fixed-rate bond. Consequently the value of the company’s shares will be the dividend ‘capitalised’ – ie, divided – by an investor’s required rate of return.

Take shares in foods processor Unilever (ULVR), which is an extremely reliable payer of dividends. Now imagine that Unilever’s dividends were never going to grow, but remain at 2014’s 90.2p. What would you pay for the shares? That depends on your required rate of return, but assume it is 8.5 per cent – that is, you want to be better off by 8.5 per cent each year as a reward for tying up your capital. In which case, the fair price would be 1,061p.

Happily, however, Unilever’s dividends will grow; not necessarily smoothly – they may even be cut occasionally – but they will grow. Even so, if we average out that growth over the long term, its pace won’t be very fast. That’s because Unilever is a mature company whose revenues and profits are anchored to expansion in the global economy.

Let’s imagine that Unilever’s dividends can grow at a constant rate of 4 per cent a year. Even that pace puts a whole new complexion on matters. Each year the dividend will rise by 4 per cent – going from 90.2p to 93.8p in 2015, then 97.6p and so on. That proposition makes its shares much more valuable. But how much more? The constant-growth model provides an answer by factoring in that 4 per cent growth rate for ever. It does so by assuming that the investor will be content with a 4.5 per cent income yield in any given year, knowing that his dividend income will rise by 4 per cent each year. In other words, he will still receive his target 8.5 per cent return, but it will comprise a combination of income and capital gain, which can be turned into cash at any point.

In the case of Unilever, we are taking the expected dividend payment of 93.8p and capitalising it at the rate of 4.5 per cent, meaning that its shares – under the circumstances we are assuming – would be worth 2,084p

And if you doubt that we are on the right track – if you question whether this very simple formula can encapsulate the value of all future dividends to be paid – move on a year hence and calculate what the share value would be. By then the dividend will have risen to 97.6p, but the yield must still be 4.5 per cent. So the shares will be worth 2,168p. And by how much will their value have risen? – 4 per cent. Simple and elegant.

However, companies have life cycles. They go from being young start-ups, to vigorous growth companies and on to mature businesses. Or, at least, that’s the ideal. But, if that’s an outline of a company’s development, it can also be used to sketch the dividends it may pay. From that, we can assess the fair value of its shares.

That logic lies behind the multiple-growth-rate dividend discount model. This model assumes that the size and growth rate of a company’s dividends will depend on where it is in its life cycle. For young companies, there may be several years before any dividends will be paid. Then payouts will grow fast from a low base before the pace flattens out with the onset of corporate maturity. Further developed companies may already be in their growth phase. So dividends will be rising fast from year to year, but that won’t last long. The wonder of competitive markets means that soon enough their growth will fade to the average, and their dividend growth will follow suit. Then there are mature companies, whose dividend growth rate will be reliable though comfortably sedate. Putting a value on the shares of all these sorts of companies can be achieved by the multiple-growth-rate model.

At its simplest, this model divides into two phases – the first, where there is period of lively dividend growth; the second, where the assumption is that dividends will grow at the same pace forever. In other words, in the second stage of the model, the constant-growth model, as just explained, applies. However, for the complete works there are two phases of supernormal growth – the first, really fast; the second, a bit less so – before the constant rate sets in.

The company we’re using as a guinea pig is microprocessor designer ARM (ARM), which is clearly at the first stage of supernormal growth – in the past five years its dividend has risen by 24 per cent a year on average.

So let’s assume that ARM packs in another seven years of really fast growth, with dividends rising by 20 per cent a year. Then it follows that with seven years of growth at a fair lick – 15 per cent. And from 2028 – yes, that far ahead – it moves into a mature phase where dividend growth is no better than the nominal pace at which the economies in which it operates expand. Here, we have used 5 per cent.

The question is: in today’s money, what will all of ARM’s future dividends be worth using these assumptions? Spreadsheets can produce an answer instantly. And, indeed, click on this link to go to the calculations used for ARM plus a blank spreadsheet of the multiple-growth rate model. However, spreadsheets can only produce answers that are as good as their inputs. Factors to take seriously are:

■ Be sensible about the supernormal growth rates. Dividend payments are lumpier than most people realise so, even if payments are being averaged over only, say, five years, their growth may well be lower than instinct might suggest.

■ Similarly, be cautious about the required rate of return. This is the rate that will persuade each investor to put his capital into equities. As such, it is also the discount rate that brings future dividend payments back to present value and the higher the required rate, the lower present value will be.

■ Take the answer with lots of salt – and the more that present value derives from the constant-growth phase of the model, the more salt is required. After all, those values are coming from far into the future so they are less certain and more risky than values that should crystallise sooner.

 

How to use the dividend discount model spreadsheet

Before using the dividend-discount model spreadsheet it’s sensible to make a copy of the workbook (see below to find out where you can download the workbook). Then you always have an unspoilt version to go back to, if necessary; meanwhile, you can play around with the copy to familiarise yourself with the changes that you’ll need to make when you apply the model to specific stocks. Next – if you haven’t already done so – read the feature ‘Modelling shares values’. That will give you a reasonable introduction into the logic behind dividend discount models. The zero-growth model, which applied to fixed-coupon securities, is discussed for explanatory purposes. In practice, it is not really relevant to the valuation of equities.

For a useful video demonstration of how to use the dividend discount model, click here.

However, the constant-growth model does have a practical use. It can give a theoretical value based on assumptions for required return and growth rate. Additionally, the constant-growth model is useful for what it tells us about the growth-rate assumptions implicit in a share price.

There is a constant-rate model embedded in the multiple growth-rate spread sheet. To use it, all that’s needed is to input six pieces of data:

i) Company name – cell B1

ii) Recent share price – cell F1

iii) The constant growth rate expected for dividends – B5

iv) A required rate of return – cell B6

v) The forecast dividend for the coming year – cell H10

vi) Adjust the discount factor in cell H12 to “1” – or a value very close to that – since the starting dividend will be the next one paid

Input the data shown for Unilever in the table (above) and the estimate for value, as expected, drops out at 2,084p.

What does it take to make the shares good value at their recent 2,756p? Either expectations of a higher growth rate – maybe 4 per cent is too stingy for long-term nominal rate (ie, before inflation) at which dividends will grow – or willingness to accept a lower rate of return.

Note that the model is sensitive to changes in these assumptions. Imagine that the long-term growth rate in dividends will be 5.5 per cent and theoretical value leaps to 3,127p. Seen from another angle, that’s another way of saying that an investor would be willing to buy the shares up to a price where the dividend yield drops to 3 per cent.

However, for the most part we will be using the model with multiple growth rates in dividends. Even so, the inputs are few, restricted to the blue cells highlighted in the work sheet plus fine tuning to other cells as described below. Start by inputting the following:

i) Company name – cell B1

ii) Recent share price – 1,052p – cell F1

iii) The first phase of supernormal growth – 20 – cell B3

iv) The second phase of supernormal growth – 15 – cell B4

v) The constant growth rate in dividends thereafter – 5 – cell B5

vi) The required rate of return – 8.5 – cell B6

vii) A starting dividend, which will be the most recent full-year payout – in ARM’s case, 7.02p – cell B7.

Now for fine-tuning some other cells in the spreadsheet.

viii) Ensure that the Supernormal phase 1 ends at Year 7; in other words, that no dividends appear after cell B17. Therefore, delete any contents in cells B18-B20.

ix) Hover the cursor over cells B23 and C23 to read the notes contained there. Take your cue from this to adjust the discount factor in cell C23. Sequentially, it must follow on from the last discount factor in Supernormal phase 1. This is “^7” in cell C7, so in cell C23 adjust the discount factor to “^8” and in the cells C24 to C29 adjust the discount factors so that they are sequential – “^9” and so on.

x) Ensure that Supernormal phase 2 also ends after its own Year 7. Therefore delete any contents of cells B30-B32.

xi) Now let’s attend to the Constant growth phase. Ensure that the starting dividend in cell H20 follows on from the previous year’s dividend, which is year 7 of Supernormal phase 2 (cell B29). So adjust the formula in cell H10 to read: “=(B29*(1+$B$5/100))”.

xii) Just as in stages viii and ix, ensure that the discount factor of the Constant growth phase follows on from the previous phase. So, in cell H12, adjust the formula so that the discount factor reads “^15”.