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Yesterday we looked at the simplest dividend valuation model, DVM, one where the future dividends are expected to be constant. In contrast to that assumption, for most companies dividends are expected to grow from one year to the next.
To make DVM analysis manageable simplifying assumptions are usually made about the patterns of growth in dividends. Most managers attempt to make dividends grow more or less in line with the firm’s long-term earnings growth rate. They often bend over backwards to smooth out fluctuations, maintaining a high dividend even in years of poor profits or losses.
In years of very high profits they are often reluctant to increase the dividend by a large percentage for fear that it might have to be cut back in a downturn.
So, given management propensity to make dividend payments grow in an incremental or stepped fashion it seems that a reasonable model could be based on the assumption of a constant growth rate. (Year to year deviations around this expected growth path will not materially alter the analysis.)
Worked example
Progression plc has very recently paid a dividend of 10p, “dividend-zero”, and the next is due in one year, “dividend-one”, which will amount to the same as dividend-zero except increased by a “growth rate”, 4%. This growth rate will apply to all future dividends, thus:
Dividend-one = dividend-zero x 1.04 = 10p x 1.04 = 10.4p
Dividend-two = dividend-zero x 1.04 x 1.04 = 10p x 1.04 x 1.04 = 10.816p
Dividend-three = dividend-zero x 1.04 x 1.04 x 1.04 = 10p x 1.04 x 1.04 x 1.04 = 11.249p
Dividend-four = dividend-zero x 1.04 x 1.04 x 1.04 x 1.04 = 10p x 1.04 x 1.04 x 1.04 x 1.04 = 11.699p
And so on………….
Each of these cash flows to shareholders must be discounted at the required rate of return, say 8% per year.
For dividend-one: 10.4p/1.08 = 9.63
For dividend-two: 10.816p/(1.08)2 = 9.27
For dividend-three: 11.249p/(1.08)3 = 8.93
For dividend-four: 11.699p/(1.08)4 = 8.60
And so on…..
This method could take a long, long time given that you need to discount every future dividend. Fortunately it is mathematically equivalent to the following formula which is much easier to employ:
Price-zero = dividend-one ÷ (discount rate minus growth rate)
Note that, even though the shortened formula only includes next year’s dividend all the future dividends are represented. In using the model you are assuming the inclusion of all dividends stretching to an infinite horizon growing at a constant rate of g.
Value of Progression plc = 10.4p/(0.08 – 0.04) = 260p
Pearson plc
Pearson plc, the publishing, media and education group, has the following dividend history.
| Year | Dividend per share (p) |
| 2001 | 22.3 |
| 2002 | 23.4 |
| 2003 | 24.2 |
| 2004 | 25.4 |
| 2005 | 27.0 |
| 2006 | 29.3 |
| 2007 | 31.6 |
| 2008 | 33.8 |
| 2009 | 35.5 |
| 2010
2011 2012 2013 2014 2015 2016
|
38.7 42.0 45.0 48.0 51.0 52.0 52.0 |
The average annual growth rate, g, over this period has been 5.8%.
If it is assumed that this historic growth rate will continue into the future (a big if) and 10 per cent is taken as the required rate of return, the value of a share can be calculated.
Price = 55p/(0.10 – 0.058) = 1,310p
In the last two years Pearson’s shares ranged from as high as £10 to as low as £5.70. So there were times when investors were a little more pessimistic than we have been in the above analysis, and
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