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This tutorial written and reproduced with permission from Peter Ponzo

Okay, here’s the story:

In 1944 Anne Scheiber, a lifelong federal employee whose income never surpassed \$3,150 a year, invested \$5,000 in blue-chip stocks. When she died in 1995 her stocks were worth \$22 million and she was receiving an annual income of over \$1 million in dividends from them. The book by RoxAnn Klugman (a tax-law attorney and retirement and estate planner), Dividend Growth Investment Strategy, tells how she did it.

#### Sounds too good to be true, eh?

The title of the book noted above says:

“How to Keep Your Retirement Income Doubling Every Five Years”

So I figured we should investigate:

You buy K shares of some blue chip stock for \$P(0) per share. Your original portfolio is then worth K P(0) dollars.

The stock pays an annual dividend of 3% of the market value of the stock.

If the dividends are reinvested in the stock, then after one year, you’d get 0.03K new shares.
(That’s 3% of K shares.)

In another year you’d get another 0.03K shares, etc. etc.

After n years you’d now have the original K shares plus 0.03Kn new shares
(from the reinvested dividends).

That makes a total of K + 0.03Kn
= (1+0.03n)K shares.

If, after n years, the stock is worth \$P(n), then your portfolio is worth (1+0.03n )KP(n).

The n-year gain factor is [final portfolio] / [initial portfolio]
= [(1+0.03n)KP(n)] / [K P(0)] = (1+0.03n) P(n)/P(0).

But P(n)/P(0) is the gain for the stock price itself.

That extra factor, namely (1+3n/100), is due to the reinvested dividends!

#### And that increases your gain, right?

Yes, so if we’re talking n = 5 years, then (1+3n/100) = 1+15/100 = 1.15 is the dividend factor. If the market price of the stock increases over 5 years by 50%, then the gain factor for the stock itself is 1.50. Reinvesting the dividends will increase your portfolio gain factor to (1.15)(1.50) = 1.725 and that’s a 72.5% return.

#### That’s significant!

Yes, but note that it’s about what you’d get if you just added the 3% to the annualized stock price return. That is, if your stock increased by 50% in 5 years, that’s an annualized return of 1.51/5 – 1 = 0.84 or 8.4% for the stock price. Now add 3% to this for the reinvested dividends, and you’d get a portfolio return of about 8.4% + 3% = 11.4%. Over 5 years your portfolio would then grow approximately by a factor of 1.1145 = 1.72 or 72%.

#### But are dividends a fixed percentage of the stock price, like 3%?

Not necessarily, but suppose:

You invested in a stock whose P/E Ratio stayed constant at, say, 20.

If the stock price were \$100, then earnings per share would be 100/20 = \$5 per share.

Suppose, further, that the company paid dividends which were 10% of earnings per share. (That’s the Payout Ratio.) That’s 10% of \$5 or \$0.50 per share.

(As a percentage of a \$100 investment, that’s only 0.5%. Chicken feed, eh?)

If the stock price increased at 8% per year, earnings would increase at 8% per year (since Price/Earnings is fixed at 20).

Hence your dividends (as a percentage of earnings) would increase at 8% per year and, as a percentage of stock price, that’d be fixed at 0.5%.

After n years, if the gain factor for the stock were P(n)/P(0), then the gain factor for your portfolio would be greater than this by a factor (1+0.5n/100).

#### That looks just like (1+3n/100)?

Yes, but now dividends aren’t 3% of the stock price, but just 0.5%. In general, if dividend yield is x% (example: x = 3% or x = 0.5%), then your n-year portfolio would be greater than the increase in stock price by a factor: (1 + x n / 100). After 5 years, for example, we’d have: 1 + x 5 / 100 = 1 + x / 20. If the stock grew by a gain factor G after 5 years, then your portfolio would grow by a factor (1+x/20)G.

If we expected our portfolio to “double” in 5 years, then we’d need (1+x/20)G = 2. Of course, a stock growth of G in 5 years means an annualized stock return of r where G = (1+r)5. That leaves us with a magic equation relating x, the dividend yield (as a percentage of the stock price), and r, the annualized stock return, namely:   (1+x/20)(1+r)5 = 2

That relationship is shown in Figure 1. The graph is (very nearly) x + y = 14.9 (since a 14.9% annual increase will double an investment in 5 years).

#### Uh … it looks like, for an 8% stock return I’d need about … looks like 7% dividend yield.

It’s 7.2%, actually.

#### That’s a pretty big dividend, eh?

Yes, but we needn’t ask to have our portfolio double … that’s a 100% gain. Maybe we’d like a gain of, say 80% or 90% or … Figure 1

The chart below would suggest a dividend yield of about 4.5%. #### That’s the magenta dot, but what’s the red dot?

Don’t you recognize her? That’s the dot in Figure 1.

#### But can’t the dividend increase, as a percentage of the stock price?

Sure. For example, although the AFL stock price increased by some 60% over the past 5 years, the dividend increased by about 160%.

See Figure 2?

As a percentage of stock price, the annual dividend went from about 0.5% of the stock price to about 1% of the stock price. For example, if the dividend yield started at x and added y each year, then it’d be x+jy after j years. Note: Here we use x as a fraction, so a yield of x = 0.0123 means 1.23%. If you started with K shares, you’d get xK new shares (via reinvestment of the dividend), in the first year. You’d get (x+y)K in year 2, (x+2y)K in year 3, etc. After n years you’d have your original K shares plus all the shares due to reinvestment of the dividends, namely:

K + (x+y)K + (x+2y)K + … + (x+(n-1)y)K = [ 1 + nx+(n-1)ny/2 ] K.

Your portfolio would be worth [ 1 + nx+(n-1)ny/2 ] K P(n). Your n-year gain factor would then be (dividing by your original portfolio: K P(0)):

[ 1 + nx+(n-1)ny/2 ] G

where, as before, G is the n-year stock gain. Figure 2

For the AFL example, the 5-year stock gain is about 60% so G = 1.60. The dividend starts at 0.5% so x = 0.005 and increases to about 1% in 5 years, so the increment is 0.1% per year, so y = 0.001. The dividend factor is then [ 1 + nx+(n-1)ny/2 ] = 1 + 5(0.005)+4(5)(0.001)/2 = 1.04. So the 1.6 stock gain is amplified by 1.04 to give a portfolio gain of (1.6)(1.04) = 1.7 or 70%.

#### Okay, so what about that error that peter noted, on the Webring Forum?

The expression above for the number of shares after n years was: (1+0.03n)K. But (as peter pointed out), the new shares you get via reinvested dividends also get dividends. That means there’s compounding goin’ on. That will change the number of shares (after n years) to: (1+0.03)n K. In our 3% example, after 5 years, that’d change (1+0.03(5)) = 1.150   to   1.035 = 1.159.

Note that (1+x)n is approximately (1+nx) if nx is small. But since we’re talking about this “doubling every five years” stuff, so n = 5 and the dividend yield is maybe 0.03 or thereabouts, then nx = (5)(0.03) = 0.15 is small so then I’ll just leave it as is because …

#### Because you’re too lazy to change it!

Do you have anything useful to say?

#### Yeah! Do you have an example where your portfolio doubles in 5 years?

Well, I don’t really understand this DGIS, but I maybe they’re talkin’ about dividends doubling in five years. Now that I can believe. Of course, if you wanted an income of, say \$40K (from dividends) and the dividend yield were, say 2%, you’d need a portfolio of about 40K/0.02 = \$2M. However, maybe they’re talking about investment returns doubling every five years. Now that ain’t easy.

#### So buy the book!

If I bought a book every time I wrote a tutorial I’d be a pauper.

#### Not if your income doubled every five years!

Ps (1)

Today I got e-mail from somebuddy who has the problem of managing about \$2M. His job is to see that it’s invested appropriately (meaning VERY safe), so that it’ll provide scholarships for the next umpteen years.

#### And he’s asking you for advice? That’s a laugh!

Thanks! Anyway, I suggested (among other things) that he consider investing in GE stock. General Electric has paid quarterly dividends for over 100 years and the dividend has increased every year for the past 30 years. The current dividend is about 2.8% of the current stock price.  That’d provide about \$58K each year for scholarships.  Not only that, but GE stock has had an annualized return over 12% (including reinvested dividends) for the past 40 years. Not only that, but …

Exactly!

#### Maybe that’s what’s meant by DGIS?

Probably …

Ps (2)

There’s a spreadsheet that looks like this: Click on the picture to download and/or run the spreadsheet

It’s meant to give y’all just some idea of this CGIS stuff. You download ten years of stock data … pray that Yahoo has the data. Then you …

#### Wait! The picture doesn’t allow you to specify your stock, does it?

You download ten years worth of quarterly dividends … pray that Yahoo has the data. Then you stare in awe at the charts

#### And the spreadsheet actually works?

Uh … you gotta pray for that, too.