Reinvesting stock dividends can make a huge impact on your wealth over the long term. To illustrate this, we first consider how a total returns index is calculated by assuming dividends are reinvested. Thanks to Prof. Robert Schiller for making monthly S & P 500 data available from 1871 for calculating the Schiller PE with the trailing 12-month dividend yield.

Thanks also to *DQYDJ (Don’t Quit Your Day Job)* for making a fantastic online calculator based on the above data. Without this, I could not have constructed the S& P 500 total returns index from the price index from Jan 1900 (the earliest date that Excel will allow). Without this, I would have thought there is a mistake in the total returns index calculation and given up!

## How to calculate the total returns index

The best way to understand the magic of reinvested dividends is to understand how the total returns index is calculated.

A stock or mutual dividend is **not **

*a return.*It is merely corporate action where a small chunk of the stock’s (or fund’s) value is given to holders in the form of cash or units. Then the price (or NAV) drops to the extent of the dividend. For calculating investment returns, one must always assume that dividend is reinvested. That is we find out the price or NAV by assuming no dividends were declared. Detailed descriptions of how this is done are given below.

For the purpose of this discussion, let us consider the S & P 500 as a single stock as assume we held on such stock in 1899. In Jan 1900, suppose a dividend of 0.018 $ per share was issued and price after the issue is 6.1 $.

We now assume the 0.018$ is used to buy more shares of the S&P 500 at a price of 6.1 $. Fractional shares are typically not issued, but we will have to assume that they are.

So we can by 0.018/6.1 = 0.00297 shares!! Taking our grand tally to 1.003 shares. If this looks insignificant, hang on. The total returns index now has a value of 6.1 x 1.003 = 6.118.

The next month, in Feb 1900, the approximate dividend issued per share is again 0.018 $. However, we now hold 1.00297 shares. So the total dividend is 1.003 x 0.018 = 0.019 $. This is reinvested at the current price of 6.21$ per share. Then the no of shares held becomes 1.006.

The total returns index now is 6.21 x 1.006 = 6.24.

The real-world total returns index calculation will require us to factor in corporate action like stock splits and bonuses. Those interested in the exact formula may consult this resource.

Suppose we keep doing this right up to Sep. 2016, the one stock held in 1899 will become 10 stocks by 1940 and 100 stocks by 2000.

Thus the magic of reinvested dividends is due to the additional shares obtained. This translates to more returns and a higher corpus due to the productivity growth of the country.

This graph is log scale. The growth from 1 to 10 is the same as the growth from 10 to 100. Notice that the rate of growth has slowed down – probably because of development and recession.

## S & P 500 Total Returns Index

Here is the S & P TRI plotted along with the price index.

If plotted in a normal scale, the price index is flat compared to the TRI!! Which is why we need log plots.See of instance: Are you ready to climb the Sensex Staircase?!

## Extra returns from reinvested dividends

This is extra return obtained year after year due to the reinvested dividends.

The dip in dividends received is more apparent here.

Naturally, it is impractical for a single person to have enjoyed these riches. So let us not push this illustration too far.

## Related Posts on Dividends

How to calculate returns from Stocks including dividends

When do mutual funds declare dividends

How to calculate returns from Dividend Mutual Funds

Growth vs. Dividend Reinvestment Mutual Funds: Which Should I choose?

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Very approximately, compounding at ~ 12% over ~100 years yields a sum roughly an order of magnitude more than ~ 10% compounding over ~100 years. Power of compounding – Eighth wonder of the world.