• “The return that investors expect from stocks must be equal to the dividend yield plus the growth of dividends.” p.304 Valuing Wall Street by Smithers and Wright.

I'm not the only one who believes in adding yield and dividend growth to obtain the expected return…who believes “the way to value a stock is by the cash it puts in your pocket over time”. © Connolly Report 2010

(My sister, who teaches at Ryerson University, travels around the country and to Australia and other places presenting papers. My brother-in-law, who teaches Corporate Finance at Ryerson, presents papers too. I no longer teach Business. I write. This is my 'paper' on adding yield and dividend growth to quickly estimate the return on a common stock. This contention has not been confirmed by empirical tests. It has not been peer reviewed. You might persuade yourself, however, after reading this paper, that the concept is reasonable. If not, that's fine. Go about estimating your return in some other way.

• “Simply put, your expected return is equal to your dividend yield, plus any dividend growth, plus any change in valuation that occurs.” James Montier, Behavioural Investing, page 563
• John M. Keynes talked about focusing on “the prospective yield of an investment over a long term of years” in Chapter 12 of his 1936 General Theory, page 155. What is 'the prospective yield' but the initial yield and any increases in it over the years.
• “One simple way to gauge equity returns is to take yield and add expected growth.” Rob Arnott, Report on Business, March 1 2010

• “From 1900 through 2007, the calculated annual total return on stocks averaged 9.5 per cent composed entirely of investment return, roughly 4.5 per cent from the average dividend yield and five per cent from earnings growth” John Bogle in Enough.

Is Mr Bogle saying that your return, in the long run, is the yield and dividend growth? I think so. You do not see the two concepts connected very often. Average dividend growth of the stocks in my list, so far in 2009, is 5%. So, if you buy a stock with a 6% yield and obtain 5% dividend growth, your return will be 11%, eventually,…right? Next year it will only be 6.3% (6 * 1.05)…but eventually.

• “A rough calculation for the forward-looking risk premium would be to add the dividend yield of 3% to the expected long-term nominal dividend growth (in line with GDP) of 5% and then subtract the ten year bond yield of 2.7%. The result is a risk premium of 5.3%” The Economist 2009. (equity risk premium is the extra return investors should demand for holding shares)

AN EXAMPLE: As I write this in August 2009, BCE's yield is 6.3%. On April 15 2009, BCE increased its dividend by 5.5% from .365 to .385 cents per share, per quarter. Hence, if you buy BCE at $25 or so, and if BCE's dividend growth continues at the same rate, your return will be 6.3 + 5.5 = 11.8%. This will not happen next year, or any time soon, but eventually your return must be your yield and any dividend growth you receive. You are going to get 12% on your money. It's hard to believe, eh. And that's not all: as the dividend rises, the stock price will, in all likelyhood, go up too…eventually. Why? If it didn't the yield would become extraordinarily out of line. James Montier is so very correct when he says “Simply put, your expected return is equal to your dividend yield, plus and dividend growth, plus any change in valuation that occurs.”

• “The textbooks tell us that the value of a stock is dictated by the present value of the stream of future dividends, discounted by a risk-adjusted rate.” CIBC World Markets, November 26 2009, 'Divvying Up the Rewards'

Adding yield and dividend growth is an important topic. It's hard to understand/believe. In a way it is simple. Some say though, that you should multiply, not add. That's true. But, in the long run, you add. You must agree that if the dividend is growing, the return, if the yield starts at 6.3%, must eventually be more than 6.3%, right? All we are discussing is how much more and by when. How much more is tied into the dividend growth. As the dividend rises, so does your return. You end up receiving much more than your original yield…eventually. And your capital tends to grow as dividend grows (This is another interesting concept with dividend growth investing. Arnold Bernhard illustrates the effect of dividend growth on price of stocks from 1946 to 1958 in his 1959 book Evaluation of Common Stocks with 12 pairs of charts. One stock in each pair had dividend growth, the other did not. The stock price differences between dividend growing commons and the stocks which did not grow their dividends were astounding).

• John Burr Williams, in Chapter V of his 1938 book, The Theory of Investment Value, on page 57, addresses the objection that future earnings should be in this calculation and not future dividends. “But should not earnings and dividends both give the same answer under the implicit assumptions of our critics. If earnings not paid out in dividends are all sucessessfully reinvested at compound interest for the benefit of the stockholder, as the critics imply, then these earnings should produce dividends later; if not then the money is lost.” TC: This gives one something to ponder.

• “The key equation is this:

Cash return = cash yield + g

where g is the growth rate of the cash flow from the stock. Since a bond's cash flow stays the same each year, g = 0 for bonds.” Dow 36,000 by Glassman & Hassett

• from Buttonwood Blog in The Economist May 8 2009 “In theory, the value of a stock is equal to the future cashflows received by investors, discounted at the appropriate rate. The curse of investing is we know neither what those cashflows will be, nor the right discount rate to use. But because we have data going back many decades, we do know what cashflows investors actually received from individual stocks. As to the discount rate, we can use either the return from the overall market or that return suitably adjusted for a stock's volatility (its beta).”

TC: In my view, dividend growth is one way of estimating future cash flow. As a result, and realizing that future stock prices are uncertain, but that dividends are more reliable, I have no trouble adding yield and dividend growth. My brother-in-law who teaches Corporate Finance at Ryerson University, does not either: he teaches the dividend discount model. If you have trouble adding yield and dividend growth, that's fine. Estimate you return another way: there are a lot of methods of determining financial value. In the end, as Emanual Derman¹ says on page 268 of My Life as a Quant, “it's the unpredictable I's - people like you and me - who determine financial value.” I do not expect you to believe, straight away, that you can add yield and dividend growth to estimate your expected return. For, as Fischer Black said, expected return is unobservable. My studies and experience, however, have persuaded me that adding yield and dividend growth provides a rough estimate of expected returns from dividend growth stocks. You can put it to the test. Buy a dividend growth stock. Make a note of the initial yield and your estimate of the common stocks's dividend growth (preferreds do not grow their dividends). Wait a decade or so, and then compute your return. After some thirty years of following dividend growth common stock, I've had it happen: our return, on most of the stocks in our portfolio, certainly not all of them, is roughly, the initial yield and the dividend growth which generates share price appreciation.

• John Burr Williams - Reading John Burr Williams' 1938 book The Theory of Investment Value could convince you that dividends are connected to investment value. In fact, on page 4, John Burr Williams defines an investor “as a buyer interested in dividends.”

¹ Emanuel Derman is a professor of Financial Engineering at Columbia and Head of Risk at Prisma Capital Partners. He began working on Wall Street in 1985. His Black-Derman-Toy interest rate model, and other models to determine the value of securities, are widely used (but certainly not by me…I just add yield and dividend growth). Fischer Black defined expected return as “the amount by which people expect to profit when buying a security”. Emanual Derman, on page 171 of My Life as a Quant said, “Our estimates of expected return are so poor that they are almost laughable.” TC: Some people scoff, also, when I add yield and dividend growth too. Even in troubled year like 2009, our dividends, in the main, grew. I smile at the arguments non-believers while we enjoy the growing income. After 30 years, and at age 70, we are going to add running water and a bathroom to our 1880s hewn-timber cottage in 2010. I'll miss the outhouse: Louise won't, especially in May with the bugs and in November with the cold rain!

My Life as a Quant is not my favourite book and I do not plan to finish it. I had to read too much to discover the gems of wisdom, I like. However, Emanual Derman's chart of the distribution of possible future stock prices over 30 years on page 151 was worth the $19 price of this paperback, especially when you flip the page and look the the 30 year distribution of possible future bond prices. It's worth a walk into a book stock to see. While you are there, glance at pages 171 ('uobservables'), 261 and 268 also. Derman's prologue, an interesting read, explains what/who a quant is.