I'm from MA and I graduated from Stonehill College with a BS in Biology. I took a class at Stonehill titled, "The Impact of News of Financial Markets," in which I presented a class project titled, "Analysis of Financial Contagion in South America Following Argentinian... More

Note: The dividend drill model produces a conservative dividend growth estimate, so any points to the left of the diagonal line represent years in which the dividend growth rate was below a conservative growth estimate.

By using the "Rule of 72," one can easily estimate the amount of time an investment yielding X% would take to double in value. For example, according to this rule, an investment yielding 3% per annum would take about 24 years to double in value (72/3 = 24). This is very close to the actual doubling time of 23.45 years. These answers can be confirmed by using the future value equation:

While certainly useful, neither the rule of 72 nor the future value equation is able to model the complexity of dividend growth stocks in which there is capital appreciation/depreciation and dividend growth. I attempted recently to quantitatively describe the growth of a DG growth stock investment, and came up with an equation,

(click to enlarge)

in which,

(click to enlarge)

The on the right side of the equation, the right chunk is the stock price after Q quarters, and the left chunk attempts to capture the number of shares owned after Q quarters, i.e. (Future Value_{Q}= (Stock Price_{Q} * Shares Owned_{Q}). The Shares Owned_{Q} chunk introduces inaccuracy by "smoothening" dividend growth; it should instead include some kind of step function, as the dividend increases abruptly every four quarters. Because the shares owned chunk does not accurately capture the actual number of Shares Owned_{Q}, the equation underestimates the Future Value_{Q}. However, within a particular range of inputs, the equation does give an accurate Future Value_{Q}.

Since the inaccuracy increases with Q, the equation's utility is limited to Q <= 40, or 10 years, unless a correction is made to Future Value_{Q}, or a large margin of error is acceptable. I attempted to quantify the equation's inaccuracy across a range of inputs. To do this, I compared the equation's Future Value_{Q} after 10 years to the results of an algorithm with calculates the exact Future Value_{Q} given the same inputs. The result of this test is below:

(click to enlarge)

This 4D graph illustrates how the equation's underestimation of Future Value_{Q} after 10 years changes depending on the values of the various inputs (DGR, Cap. Appreciation, Initial Yield). The coloring corresponds to the magnitude of underestimation for each combination of inputs, ranging from 0% (blue) to 7.2% (red). By using this graph, one can see the inputs that are accurate with the equation and use it for only those values, or one can find the percentage underestimation to recalculate a closer Future Value_{Q}. This graph represents data in which Q = 40 (10 years). With increasing Q values, the percentage by which the equation underestimates increases.

A notable limitation of using this equation for analysis, is, of course, that a constant DGR and capital appreciation rate are assumed. Despite this shortcoming, however, I think it is still useful to be able to take the growth and capital appreciation of a DG stock into account to calculate a Future Value_{Q}.

I hope to get feedback on this project. In particular, do you have any suggestions regarding how the Shares Owned_{Q} term might be changed to accurately describe how many shares are owned after Q quarters?

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## RE: Microsoft Or Disney - Which To Buy

(click to enlarge)(click to enlarge)Note: The dividend drill model produces a conservative dividend growth estimate, so any points to the left of the diagonal line represent years in which the dividend growth rate was below a conservative growth estimate.

Disclosure:I am long MSFT.Additional disclosure:Data retrieved from Morningstar## Calculating The Future Value Of An Investment Taking Into Consideration Dividend Growth And Capital Appreciation

By using the "Rule of 72," one can easily estimate the amount of time an investment yielding X% would take to double in value. For example, according to this rule, an investment yielding 3% per annum would take about 24 years to double in value (72/3 = 24). This is very close to the actual doubling time of 23.45 years. These answers can be confirmed by using the future value equation:

While certainly useful, neither the rule of 72 nor the future value equation is able to model the complexity of dividend growth stocks in which there is capital appreciation/depreciation and dividend growth. I attempted recently to quantitatively describe the growth of a DG growth stock investment, and came up with an equation,

(click to enlarge)in which,

(click to enlarge)The on the right side of the equation, the right chunk is the stock price after Q quarters, and the left chunk attempts to capture the number of shares owned after Q quarters, i.e. (Future Value

_{Q}= (Stock Price_{Q}* Shares Owned_{Q}). The Shares Owned_{Q}chunk introduces inaccuracy by "smoothening" dividend growth; it should instead include some kind of step function, as the dividend increases abruptly every four quarters. Because the shares owned chunk does not accurately capture the actual number of Shares Owned_{Q}, the equation underestimates the Future Value_{Q}. However, within a particular range of inputs, the equation does give an accurate Future Value_{Q}.Since the inaccuracy increases with Q, the equation's utility is limited to Q <= 40, or 10 years, unless a correction is made to Future Value

_{Q}, or a large margin of error is acceptable. I attempted to quantify the equation's inaccuracy across a range of inputs. To do this, I compared the equation's Future Value_{Q}after 10 years to the results of an algorithm with calculates the exact Future Value_{Q}given the same inputs. The result of this test is below:(click to enlarge)This 4D graph illustrates how the equation's underestimation of Future Value

_{Q}after 10 years changes depending on the values of the various inputs (DGR, Cap. Appreciation, Initial Yield). The coloring corresponds to the magnitude of underestimation for each combination of inputs, ranging from 0% (blue) to 7.2% (red). By using this graph, one can see the inputs that are accurate with the equation and use it for only those values, or one can find the percentage underestimation to recalculate a closer Future Value_{Q}. This graph represents data in which Q = 40 (10 years). With increasing Q values, the percentage by which the equation underestimates increases.A notable limitation of using this equation for analysis, is, of course, that a constant DGR and capital appreciation rate are assumed. Despite this shortcoming, however, I think it is still useful to be able to take the growth and capital appreciation of a DG stock into account to calculate a Future Value

_{Q}.I hope to get feedback on this project. In particular, do you have any suggestions regarding how the Shares Owned

_{Q}term might be changed to accurately describe how many shares are owned after Q quarters?