# Warren Buffett's Math Lesson

Last Updated Oct 19, 2011 10:32 AM EDT

It's safe to say that most people would call Warren Buffett the greatest investor of our generation. And I personally have the greatest respect for him, citing his advice to investors many times. Yet, it seems Mr. Buffett needs a lesson in basic math.

I'm referring to his comments that the rich should pay higher taxes -- he should pay a higher tax rate than his secretary. The fact is that he already does, as you'll see. It's only a matter of having the proper perspective.

Let's consider two key areas of the tax code, where "first-stage thinking" allows Buffett to conclude that he's paying a lower tax rate than his secretary. Once we view the picture from the proper perspective and engage in "second-stage thinking," you'll see that Buffett's effective tax rate is much higher than it seems.

The first example looks at the tax on dividends and capital gains, which are both currently taxed at lower rates than wages or ordinary income, which in turn leads Buffett to draw his conclusion. However, he fails to consider that the dividend and capital gains distributions have already been taxed at the corporate tax rate of 35 percent. The following example should help illustrate this. Consider two organizations identical in all ways except that one is formed as a partnership and the other as a corporation. Earnings of the corporation are taxed at the corporate level of 35 percent. Earnings of a partnership are proportionally allocated to the owners and taxed at the individual rate.

So let's consider the cases of Company ABC and Partnership XYZ. Both are owned by a high-net-worth individual whose marginal tax rate is 35 percent. Let's assume that both firms are capitalized with \$1,000 and valued at their book value, currently \$1,000. Both entities earn \$100 in year one. Now let's see how the tax system works.

Company A Company A pays \$35 in taxes on the \$100 it earned and is left with \$65 in after-tax income. It pays that out in the form of a dividend, taxed at the preferential rate of 15 percent. The owner of the company thus earns net income of \$55.25, and his company is still worth \$1,000. The owner would only report taxes of \$9.75, or 15 percent of his taxable income of \$65. Yet, the effective tax rate is clearly 44.75 percent, not the 15 percent rate Buffett is focusing on.

The same thing would be true if no dividends were paid out, but instead the owner sold the company one day later to receive long-term capital gains treatment. The company would have a book value of \$1,065, and he would pay \$9.75 cents in capital gains taxes. Total taxes paid are the same \$44.75. So once again we see that the tax rate was not 15 percent, but 44.75 percent.

Even worse would be the case if the proposed "millionaire's tax" was imposed -- a surcharge of perhaps 5 percent on incomes above \$1 million. Now consider the following. Let's assume an entrepreneur starts a company, runs it for 40 years, sells it for a gain of \$1,000,001, and that gain is his sole income for the year. The tax rate would then be at the 5 percent higher rate than the regular long-term gains rate. Yet, the right way to think about it is that the income was earned over 40 years, or just \$25,000 a year. Clearly, a tax designed this way would cause all sorts of irrational, uneconomic behavior to avoid it. For example, companies or shares would be sold before the gain got so large that the incremental tax would be imposed. Or since income can fluctuate highly, people will behave in ways to try and smooth income out. Thus, the expected realization of tax revenue will never be realized to the degree expected.

Now let's look at the other entity, Partnership A.

Partnership A As a partnership, the \$100 of earnings is taxed at the owner's 35 percent tax rate. Thus, \$35 in taxes is paid, and there are no further taxes. So let's assume that the owner withdraws the \$35 to pay his tax and also withdraws the \$65 of earned income. The total tax rate is 35 percent. And if he sold the company, he would get \$1,000 (which was his basis), producing no capital gain.

Both cases are identical in terms of how much was earned. Yet in the case of Company A, Buffett would say the tax rate of 15 percent was less that that of his secretary. Yet, we see that he actually paid a much higher effective rate. 44.75 percent. Our tax system creates what we might call a framing problem, causing Buffett to make the claim that his tax rate is lower than it really is.

While I can't know for sure (since Buffett is obviously a very smart man), my own view is that he certainly knows the math, but he has a political agenda that is motivating his statements.

Let's now turn to a second example, another framing problem.

Municipal Bonds Municipal bonds currently receive preferential tax treatment at the Federal level. The interest income isn't generally taxed (except if the bonds are considered private activity bonds or are bought at a significant discount -- if the discount isn't considered "de minimis," the discount must be amortized and counted as income). Note that in return, Treasury debt also receives preferential treatment at the state level. Interest income on Treasury bonds isn't taxed at the state or local level.

Because of the preferential tax treatment, municipal bonds have typically traded at rates well below those of similar term Treasury bonds. For example, a AAA-rated one-year municipal bond might trade at 65 percent of the one-year Treasury yield, and a AAA-rated 10-year municipal might trade at 80 percent of the 10-year Treasury. So for example, if a 10-year Treasury yielded 4 percent, a AAA-rated municipal bond might yield just 3.2 percent. How does this affect Buffett and his thinking?

All of the income from municipal bonds could be taxed at a zero rate. That could result in his ability to claim that he paid a lower tax rate than his secretary. However, that's the wrong way to look at the picture. First, Buffett has effectively paid a tax of 20 percent, because he gave up the opportunity to earn 4 percent if he had instead bought a 10-year Treasury. So right away we see that there's a framing problem. But the story is actually much worse.

Treasuries are much more liquid than municipal bonds. Thus, municipal bonds should carry a liquidity premium for that extra risk. And even AAA-rated municipal bonds have more credit risk than Treasuries. Thus, they should carry a credit risk premium as well. In addition, most longer-term municipal bonds have call features, allowing issuers to call the bond prior to maturity, which they'll do if rates fall. Thus, investors should again receive a risk premium to compensate them. Thus, to make the two investments comparable on a risk adjusted basis, the yield on the municipal bond should be considerably lower. Thus, the true effective tax rate is higher than even the 20 percent indicated difference in yields in this example.

The bottom line is that the effective tax rate on municipal bonds is much higher than 0.

I would note that while municipal bonds have generally had lower yields than comparable term Treasuries, this hasn't always been the case (and isn't today). Whenever there are crises which result in flights to quality, the spread between Treasuries and municipals narrows, which can even result in municipal rates being higher. The other time when this can happen is when there appears to be a threat to the preferential tax treatment municipals receive. Since we have both of those currently occurring, it shouldn't be a surprise that even AAA-rated municipals are currently yielding more than Treasuries. For example, as I write this the 10-year Treasury was yielding 2.08 percent, and 10-year AAA-rated municipals were yielding about 2.52 percent, or 121 percent of Treasuries (making them an apparent bargain).

Before concluding I would like to make a few other points, the first of which relates to the just mentioned comments. If the federal government eliminated or reduced the tax preference on municipal bonds, investors would react by requiring higher rates, rates sufficiently higher to make their risk-adjusted yields comparable to that of Treasuries. Thus, municipalities would have higher costs, imposing a further burden on them. In other words, all that would be accomplished is that there would be a shift in income from the states and municipalities to the Federal government. Investors would end up with the same risk-adjusted returns. But that's stage-one thinking. We need to do stage-two thinking.

It seems likely to me that if the Federal government were to tax municipal bond income in any way, causing the states to pay higher interest rates, the states would react by taxing Treasury debt to offset their extra expenses. That might result in the Treasury having to pay a bit higher rate on its debt, but certainly would result in lower Federal taxes collected as individuals would report higher taxable income on their state tax returns, paying higher state income taxes, and the result would be larger itemized deductions, and lower Federal taxes collected (perhaps exactly offsetting the gains from taxing municipal bond income). Of course no politician proposing to eliminate or reduce the tax preference on municipal bonds will discuss stage-two thinking with anyone, at least not in public. They want you to focus on the "get the rich to pay more taxes" message. That sounds much better.

Finally, I want to make it clear that I'm not arguing one way or another about whether the tax rates should be raised on higher income earners or that the wealthy should pay more taxes. That's an entirely different discussion. But as the above examples show, the higher income earners are already paying much higher effective rates than Buffett claims they pay. While they want you to be fooled by the "illusion," you shouldn't allow yourself to be "framed."

Photo courtesy of Ethan Bloch on Flickr.
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