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Math question - help please


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Alas, it has been many a decade since old Zorro saw the inside of a school, so please help old Zorro out! Here is my question....


I need some help calculating long term results. If one invests in a company's shares paying a 10% yield, after a 50% drop in share value, and an expected 5% growth in dividends each year how do you calculate results over the long term if:


1. the company pays 10% dividend for 5 years, you reinvest the dividends every quarter

2. After 5 years, stock price doubles in value

3. Each year dividend increase 5%


What I am trying to do is two things: calculate the total return and try and figure out how WEB does this in his head so easily....







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OK, this is not the right way, but I'll try something without paper.


Think of situation as a bond, bought at price $50 on par $100.

There will be capital gain $50 on maturity in 5th year,

which is simple return of $10 per year or 20 pct/yr on $50 cost.

There is also dividend (interest) yield of $5, current yield 10 pct.

Hence bond returns something like 30 pct/year for 5 years,

some of that being taxed as div/int and some as capital gain.


Any decision to re-invest future dividends is a distinct matter.


The investment decision today is whether 30 pct pretax return

is sufficient, given your knowledge of the robustness of "bond",

ie are they backed by a business capable of paying dividends,

will the price return to par (approx value), etc.  The usual

"margin of safety" considerations.


I know that's not exactly the question which you asked,

but believe that approach, separating out the current yield

and the capital gain yield, and interpreting the latter as a

simple return ignoring compounding, may be useful to you.

It can be done while standing in the shower, driving etc.

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ZF - Here's my back of the napkin approach


Stock gain -- A $10 stock doubles to $20 in five years = ~14.4%  (72/5 = 14.4)  I used the rule of 72 -- Divide 72 by the number of years yields approx compound annual growth rate.  (10 yrs ~ 7.2%, 5 yrs 14.4%). It also works backwards, at 10% you'll double your investment in 7.2 years. A handy formula to remember!


Dividend yield -- Initial dividend 10%, approx final dividend 5% (w/o compounding), avg dividend ~ 7.5%


Total compound annual return 14.4% + 7.5% = 21.9%


Using a spreadsheet and CAGR formulas I calculated the ending value of the $10.00 investment as $28.12, a 181% gain, or 23% annually using annual reinvestment of dividends. Thus the dividend re-investment is actually 1.1% more per year than my back of the napkin approach.


The compound annual growth rate formula I used -- CAGR = (1+ total return %) ^ (1/years) -1  or,  CAGR =  (1+ 1.81) ^ (1/5) -1 = 23%      (^ is exponent symbol  4^2=16)


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