# Living off dividends & the commutative property

In my last post I described the commutative property for dividends, i.e. that a 3% div stock with a 2% growth rate is exactly the same as a 2% div stock with a 3% div growth rate. I showed that the commutative property only holds for investments in non-taxable accounts that are re-investing their dividends. In taxable accounts the property does not hold due to income tax policy and that investors should take this into consideration when choosing dividend investments. Today I want to briefly consider the commutative property for investors, mainly retirees, who are living off their dividends and not reinvesting them and what implications that may have for investors.

First of all, the magic dividend formula does not hold if an investor does not reinvest their dividends. That’s one of the assumptions behind the formula, it calculates compounded returns. The total return for a stock with a 2% dividend and a dividend growth rate of 8% is not 10% without reinvested dividends. Neither is the return of a stock with an 8% dividend and a 2% dividend growth rate equal to 10% without reinvesting. So what are the returns for these two stocks and is one a better investment than the other? In the table below I show the return calculations over 10 years for two stocks a 2% yielder with 8% growth, and an 8% yielder with 2% growth.

As the table shows, the returns for these two stocks are quite different. The lower yielding stock with the higher growth rate has a total return of 9.37% per year over the 10 year period. The higher yielding stock has a return of 7.68% over the same period. Both returns are not equal to the 10% that would be had if dividends were reinvested. Also, note that the lower yielding stock leaves the investor with a higher account balance, \$216K, at the end of the 10 years as compared to the higher yielding stock, \$122K. However, the higher yielding stock provided the retired investor with significant more income over the 10 year period, \$88K in dividends vs \$29K in dividends for the lower yielding stock. Is one investment better than the other? Not at all. It depends on the individual retiree’s situation.

When an investor enters retirement and begins to live off their dividends other factors besides total return come into investment selection. Most retirees require at least some minimum yield from their stock portfolio to live the lifestyle they desire. That lifestyle choice and the allocation percentage to equities most likely drive a minimum dividend yield required by the investor. The dividend growth component threshold of the portfolio should be driven by the investors expectation of inflation in the future. I’ll tackle this topic of portfolio construction for retirees in a later post but the point is that for investors in retirement, living off their dividend income, the level of yield and growth in their stock investments is driven by more personal factors. Thus, one cannot say that in the example above one investment is better than the other for all investors.

There are a couple of other interesting implications of not reinvesting dividends. First, the price of the stock has less of an effect on the investor. As long as the dividend is met and the growth comes in as expected the price of the stock is less important. In the example of the 8% yielding stock with the 2% growth rate, what if the price of the stock in year 10 had been \$100 instead of \$122? The retiree would have received the same amount in dividends but the balance in the account would still be \$100K. The impact has more to do with the wealth you may pass on to your heirs but it does not impact the lifestyle of the retiree. This is one big upside of living off a dividend stream. Secondly, it takes a long time for dividend growth to make an impact on the income stream for a retiree. Again using the example above, how long does it take the dividend stream of the 8% growth stock to overtake the 2% growth stock. It takes a long time, 24 years in this example. Beyond making sure that the income stream keeps up with inflation, dividend growth for retirees has more to do with passing on wealth than improving a retiree’s lifestyle.

In summary, the commutative property of dividends and the magic dividend formula does not hold for retirees living off their dividend stream. The choice between dividend yield and dividend growth for retirees is driven by other factors than just total returns. Beyond the minimum thresholds of providing an income stream that keeps up with inflation, the choice is more driven by lifestyle choices and the desire to continue to build wealth whether it be to pass on to heirs, to leave to charity, etc…

Note: for brevity, I ignored the impact of taxes in this post. The analysis is similar to the one presented in the previous post to calculate after tax returns. It does not change the conclusions in this post.

Full Disclaimer - Nothing on this site should ever be considered advice, research or the invitation to buy or sell securities. These are my personal opinions only.

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### 4 Responses to Living off dividends & the commutative property

1. m.c. taylor says:

thank you, you have cleared up some questions i was pondering. nice, informative, understandable info. thanks, mct

• libertatemamo says:

No problem mct. Happy to help.

2. jim goldstein says:

So why did I not listen and buy Fairfax. Wow. Congratulations on a nice call. You see it today! Jim

• libertatemamo says:

Thanks. Didn’t see it until this morning, Looking forward to their earnings call and their CEO letter. The results weren’t super but I think people were expecting worse because of their huge bond portfolio. I’ll publish my thoughts on the results soon.