**Series Part 2: Oranges and Orangutans**

This is the second in my series on dividend growth stock [DGI] pricing. In my first Instablog I introduced the question of how to price DG stocks.

I will now complicate things further. If you need to compare apples to oranges and you are having difficulty, the solution is often to compare them both to something else, say orangutans. Let us introduce C:

A) 2% yield, 15% dividend growth rate

B) 3% yield, 10% dividend growth rate

C) 4% yield bond, 4% coupon, 30 year maturity

Well that did not seem to help. The bond has no income growth rate, or so it appears at first. C has twice the start yield rate compared to A and even at 15% growth rate it will take a while for A to catch up with C. Or will it ever catch up? Let us explore this question.

A key concept is that if you are comparing two different securities, you must re-invest the excess yield of the higher yielding security by subtracting the at least the lower yield. In the above A vs. C example, you can debate about whether you should spend 100% of the dividend, or 100% reinvest it, or keep it in the bank at zero interest, or somewhere in the middle. But you cannot argue that the excess 2% yield (4% - 2%) of the bond must be re-invested.

Think of it another way: If you are willing and able to accept the lower rate of A and if you are making a choice between the two, then you have to also be willing to accept the same 2% rate from C. In practice you can game-play different scenarios such as re-investing all of A and C's yield, or none of A and the difference A-C, or some in-between amounts, or raise the amount not reinvested by inflation, and many other variants.

The key constant, which will later prove to be very important, is that you must re-invest *at least* A-C yield (4% - 2% = 2%) on the higher yielding security in the first year.

Now let us say we spend all of the dividend from the stock in year one, and the same portion from the bond's interest to keep things fair, and reinvest the excess interest from the bond into more bonds. It will take a number of years for the 2% yield of A to grow to 4%. However, the excess interest re-invested in more bonds will increase the total income of the bonds beyond 4%. It will take some more time for the stock to catch up, and again the bond will have increased. You might wonder: Will the stock income ever catch up?

This problem is analogous to a famous mathematical paradox known as "Zeno's paradox of Achilles and the tortoise". Sometimes also called the "tortoise and the hare". The paradox is explained like this: Give the tortoise a 100 ft. head start in a footrace, and let us say it runs half the speed of Achilles (similar to our bond and stock above). By the time Achilles runs 100 ft., the tortoise has run (or crawled?) another 50 ft. By the time Achilles gets to 150ft, the tortoise is now at 175 ft., and so on. Zeno hypothesized the tortoise will never be caught.

Of course we know from every day experience that in practice Achilles blows by leaving our intrepid tortoise in the dust. I will leave the mathematics aside, but it was later irrefutably proven mathematically that we can calculate precisely the distance at which Achilles will reach the tortoise, and there is a simple formula for that. Similarly, we can calculate at what point in time the dividend yield will pass the compounding bond precisely.

Note: Zeno is a little simpler than our example since there is no re-investment to consider in the footrace. In our case each year the amount of excess bond income reinvested will decline as the stock yield rises exponentially. This complicates Zeno's formula. But with the power of computers it can still be solved in a straightforward way.

As a side note, I will mention a little known fact that is most often overlooked in discussions of Dividend Growth Incoming investing. For purists that care only about the future dividend stream the future price of the stock is not relevant. (This is often termed Yield Over Cost or YOC). These investors are called "income-only" investors compared to "total return" investors who care about both income and future stock price. If there is enough of a gap between the start yield of a stock and bond, and if the dividend growth rate is low enough compared to the re-investment rate of the bond, the stock dividend income never catches up. If you are an "income-only" investor the bond will always be superior. This little detail is often overlooked, but once you know it you can see why it is important to gain a more accurate understanding of how to value these securities.

From this section you should now be able to see that valuing these various securities in purely financial terms is not as easy as it first appears. Particularly when the yields and growth rates are fairly close, it is not that easy to know by gut instinct which will have a higher income in the future. In fact our instincts might sometimes mislead us. Even a mathematical approach at first seems straightforward but it gets surprisingly complicated.

One of the chief advantages of bonds is that they are easier to compare to one another than growing dividend streams. This is due to the intentional design of the instrument. There are hundreds of books on valuing bonds compared to one another, and I will not reiterate those details. Suffice to say it is relatively easy to sort through thousands of bonds and pick the ones that have the best relative price on a given day. This is the reason why I picked bonds as my orangutan. All we need to do is come up with a method to rank two DG stocks compared to a given bond, and then we can also know which DG stock is better, and by how much. Bonds also have another advantage in that like orangutans they are real, if not easier to catch. It may turn out the bond is better than both stocks by some metric at a particular price point. In that case you can simply purchase the bond.

In the next part of the series I will explore risk and reward, followed by narrowing down some key concepts and assumptions.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.