**Series Part 4: Back to the future.**

In parts 1-3 of this series I established some of the key principals to my analysis:

- Comparing dividend growth stocks of different yields and growth rates is non-obvious
- Solution: Compare dividend growth stocks to bonds
- Separate risk analysis and cash-flow analysis into two separate steps. This article focuses on the second

The final element before we look at real data is the topic of future dividend yield. Since dividend yield is defined as the ratio of the dividend to the price of a stock, any future assumption of the dividend yield means an assumption of the future price of the stock.

When comparing any two assets, the one with the lower starting yield must eventually grow its dividend to surpass the higher yielding one, or it can never provide more total cash return, as discussed in Zeno's paradox in part 2. As previously pointed out, when comparing two assets you must re-invest the excess yield of the one with higher cash flow in a given year to be fair. When re-investing dividend yields the amount of new stock that can be purchased depends on the yield at the time the future growing dividend is paid.

After analyzing various scenarios using real historical data as well as different idealized scenarios, I have come to the firm conclusion one should not use the future stock price in any calculation. It distorts the result to the point of not being useful. Using a pure analysis also leads to better investment decisions.

I will summarize the reasons why I reject any use of future stock price (and therefore future dividend yield) in any financial cash-flow valuation analysis for DG stocks:

- It is circular reasoning
- Historical data shows large fluctuations in dividend yield independent of growth rate
- Dividend yields of all stocks are often re-priced as a group
- Back testing shows this model produces better returns with lower volatility

Instead, the only future values I use are the interest rates on bonds. There are a number of reasons for this choice, but the main one is that it is better that bond interest rates are a better choice than future stock prices and yields, for the reasons outlined above. I should point out that no attempt at models for valuation of growing dividend yields has been proposed that does not use some type of future interest or discount rate. The reason for that is self-evident: Long interest rates are non-zero (for now) and inflation is non-zero, and a growing dividend necessarily derives much of its value in the future. A dollar today is not worth the same as a dollar in the future. If you need a certain amount of income and are not concerned about interest rates, you can instead substitute your estimate for the rate of inflation. Any interest rate, inflation rate, or discount rate will do.

You are probably wondering what I think I have solved, substituting one hard problem (valuing future growing dividends) with another (forecasting interest rates). My solution is deceptively simple: Use the currently available long-term bond rate. Since equity has infinite term, the longer the better. At least 20 years, but 30 or even 40 may be better. There are several reasons for my choice, but chief among them is that it is an "available rate". When valuing a DG stock, look at it as a real practical choice: At this point in time (today), get a quote on the stock and a quote on a suitable bond. Make your projection and judgment on the growth rate for the stock, and the credit quality of the bond. Then calculate based on "assume everything goes as planned" - i.e. the stock and bond perform exactly as projected. This is the concept of "separate risk and valuation" explained in part 3. You can build in provisions for bond defaults and dividend cuts to your portfolio after the calculation is complete.

So far I have assumed a constant interest rate in my work. The main reason is that it is available: You can in practice buy a zero coupon long bond that will have a constant compounded rate to maturity. Floating rate or inflation-indexed bonds often carry such a low current yield that most often the DG stock has a higher start yield and is very unlikely to underperform such a bond. I also ran calculations on different interest rate changing scenarios and the answers I get depend more on the starting interest rate at the time of the choice and the rate in the next few years, rather than the rate in year 10 or 20. Thus a constant rate is a reasonable assumption. This makes sense since future dollars are worth less than current dollars. I also notice that bond rates do not fluctuate as much as dividend yields in the 1-5 year period after the choice. There are some other technical reasons as well why the answer does not vary much with constant rate or changing rate due to the re-investment.

In summary, the fourth principal is that future stock prices and yields should not enter into the calculation at all. The only inputs I use are:

- Currently available long bond rate ask quote (20-40yr)
- Currently available stock yield ask quote (dividend/price)
- Projected compound annual dividend growth rate (method up to the investor)

Thus you can view the metric as a practical choice: Do you buy a certain long bond, or the dividend growth stock in question? If you are comparing two stocks to a bond, I have found that at some points in time you will buy either the first stock, or the second stock, or the bond. As all three assets re-price daily, that answer will change over time. More on how to use that information will be explained in a later section.