Using only dividend data to calculate estimated returns. Right or Wrong?

I’ve been involved in a back and forth in the comments section of this article on Seeking Alpha.

It is my contention that in the real world you cannot estimate a return by adding dividend yield to dividend growth. In the comments to the article, in response to a comment in which a formula was produced, I explained that the formula doesn’t work in the real world. More details of the formula can be found here. Mathematically the infinite series can be re-written as:

r is the real rate of return, and g is the real dividend growth rate. The assumptions are that r > g , that r and g are both constant, and that g is less than economic growth. If you’re wondering about the second assumption it is there because if you have a perpetuity growth number that exceeds economic growth you are saying that the asset being valued will eventually become the entire economy. The value that the series converges to (right hand side of the arrow), can be used to derive this formula:

D is the dividend, P is the price, r is the real rate of return.

The thing is that this series converges very slowly for typical values of r and g. The smaller the difference between r and g, i.e. the smaller the dividend yield, the slower the convergence. What this means is that for typical investment horizons the formula that is derived by summing all terms to infinity is nothing like what you get in practice — and after all it is the real world that we live in — i.e. it doesn’t even constitute a good approximation.

Here is a plot to show you what I mean. A 3D plot of real rate of return vs number of years. The orange surface is what you get using the simplified textbook formula and the green surface shows the real world. We can see that in the real world the surfaces are not very close to each other (understatement) due to the infinite series converging very slowly. The calculations where made using a real dividend growth of 1.3% which is the number cited by one of the adherents to this model in the comment stream. This actually seems high for perpetual growth. I note that no error estimate accompanied this number.

Here is a video to get a better idea of the gap between real world and textbook:

www.screencast.com/t/MWZlM2U0YzQt

As a result of the textbook situation bearing no resemblance to the real world, I maintain that the use of the formula to calculate a rate of return is a crock, useless, a waste of time, and so on.

As a postscript, for those interested, for an expansion over a finite number of years ( y years) the formula is:

which means that the theoretical relationship between rate of return, dividend yield, and dividend growth, is actually:

discounted cash flows · dividend growth · dividend yield · Gordon model · perpetuity

In March blogger Matt Trivisonno wrote an article titled “Payroll Withholding Taxes Surge in March“, which was published at The Big Picture. Somewhat strangely the figure that accompanied the blog actually showed continued decline in tax revenues. Sure there was a rise in the line on the chart but the rise indicated that revenues were less negative, it didn’t indicate positive year-on-year (YOY) growth. Those sort of charts represent a continued source of irritation for me as described here:

• Debunking ‘Some Good News on Jobs: Tax Withholding Improving
• Interpreting Economic Data

So while there has been a YOY increase in withholding taxes in March (see below) the chart accompanying the article showed the opposite.

Zero Hedge ran an article on April 7 titles “Now, About This Alleged Increase In Tax Withholdings By The Government…” which began

“We are a little confused by all the recent hype in the media about a surge in individual tax withholdings by the US Treasury. Our confusion is predicated primarily by the fact that this is patently not true.” (their emphasis)

There was no indication in the Zero Hedge article that they were taking a shot at anyone in particular. And there have been several “taxes are rising” type stories recently.

Whether Zero Hedge had Trivisonno in its cross hairs who knows, but Trivisonno decided to rebut the Zero Hedge article, with a rebuttal titled “Zero Edge– Rebutting Faulty Tax Analysis“, which led Zero Hedge to respond with “Some Afternoon Confusion“. Both Zero Hedge and Matt Trivisonno claim to get their numbers from the daily US Treasury statements which are available here. So are taxes rising or falling YOY?

Trivisonno says in his rebuttal that

“The purpose of looking at the withholding data is to try and get an idea of how many paychecks are being cut, not to make an accounting of the federal government’s cash flow.”

So presumably a study of the daily receipts could be used as a proxy to forecast employment changes ahead of the monthly BLS official figures (or other releases such as ADP).

Since the debate seems to be about Q1 receipts in 2010 versus 2009 I’ve taken the monthly Treasury data, specifically data from Table 4 of the monthly Treasury statements (for anyone interested in reproducing this). The first chart shows federal income tax withheld — this is the first line item in Table 4 of the monthly release.

Clearly there is a rise in income tax receipts. The next chart shows total tax withheld, i.e. income taxes plus social security and Medicare taxes. Note that this next chart excludes the 3rd “Individual Income Taxes” line item called “other.” March 2010 receipts exceed March 2009.

When you add the “other” item the story is much the same:

A criticism Trivisonno had of the Zero Hedge analysis was that new tax changes took effect in April 2009:

“And since Zero Hedge did not take into consideration the tax-credit that began in April 2009, their unadjusted numbers understate withholdings for the first three months of this year by a substantial amount.”

On that basis Trivisonno believes that adjustments are necessary to the 2010 numbers. The problem I have with that is that the shortfall in the total Q1 receipts is due to a decline in social security and Medicare withholding, and the tax rates for these items has not changed. Since these taxes are a flat tax shouldn’t they provide a much better indication of how many pay checks are being cut than income taxes which vary depending on the distribution of tax rates among the population? What do readers think?

Social security and Medicare tax receipts are falling. This surely tells us much more about paychecks and employment than some of the other data being reported?

But back to the question: Are Federal Withholding Taxes Rising or Falling YOY? In March total tax withholdings were rising.

federal taxes · Matt Trivisonno · zero hedge

March retail sales and the CPI were both released today. Retail sales data in nominal dollars in the table below:

We see a huge surge in nominal dollar sales Year-on-year. After seasonal adjustments the numbers look like this:

Even with inflation is running at 2.3% the March number is pretty good. Interestingly when you look at the breakdown of the sales most of the increases came from higher gasoline and motor vehicle spending. The next table shows where we are in real dollars relative to before the crash:

This months data confirms that a recovery is occurring but remains very shallow.

retail sales