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Let's say that I own 1000 shares of a stock at 20$. Every quarter, I get a dividend of 0.20$ which is reinvested (buy more of the same stock). Considering that the stock grows 5% annually, how many stocks will I own in 2, 5, or 10 years?

What's the formula I should use to resolve this problem?

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Your example shows a 4% dividend. If we assume the stock continues to yield 4%, the math drops to something simple. Rule of 72 says your shares will double in 18 years. So in 18 years, 1000 shares will be 2000, at whatever price it's trading. Shares X (1.04)^N years = shares after N years.

This is as good an oversimplification as any.

  • If I read the OP correctly, your answer is ignoring the growth of the stock itself. – Fomite Nov 5 '11 at 6:00
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    My oversimplification is that the company raises its dividend so the 4% is 4% of the stocks price each year. If you allow this assumption, my answer holds. The 1000 shares grows by 4% regardless of the growth in the stock price. After 18 years he has twice the shares at the new price. – JoeTaxpayer Nov 5 '11 at 11:45
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This answer contains three assumptions:

  1. That your 5% annual growth can be equally divided into 1.25% quarterly growth.
  2. Your dividend isn't actually $0.20 but 1% of the share price per quarter.
  3. Everything happens at the end of the quarter

New Share Price: Old Share Price * 1.0125
Quarterly Dividend: (New Share Price*0.01) * # of Shares in Previous Quarter
Number of Shares: Shares from Previous Quarter + Quarterly Dividend/New Share Price

For example, starting from right after Quarter One:
New share price: $20 * 1.0125 = 20.25
1000 shares @ $20.25 a share yields $20.25 * 0.01 * 1000 = $202.5 dividend
New shares: $202.5/20.25 = 10 shares

Quarter Two: New share price: $20.503 1010 shares @ 20.503 yields $20.503*0.01*1010 = $207.082 dividend New shares: $207.082/20.503 = 10.1 shares

Repeat over many cycles:

8 Quarters (2 years): 1061.52 shares @ $21.548 a share 20 Quarters (5 years): 1196.15 shares @ $25.012 a share 40 Quarters (10 years): 1459.53 shares @ $32.066 a share

Graphically this looks like this:

Stock, Dividend and Share Price

It's late enough someone may want to check my math ;). But I'd also assert that a 5% growth rate and a 4% dividend rate is pretty optimistic.

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