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When I divide 33.6 by 4.78 I get an effective tax rate 14% not 27%
The figures for 2015 and 2014 14.6% and 13% this gives us a much average of 13.7%. Which makes more sense to me as I think I remember Buffett answering a question at an annual meeting to the effect that Berkshire effective rate was around 13%.

First, let me recount the figures (for my sake) for 2016:

Pre-tax income: \$33.6B
Income tax expense: \$9.2B

Of this \$9.2B, about \$6.5B is recorded as current.

Cash taxes paid during the period (the year 2016): \$4.7B

The effective rate is \$9.2B divided by \$33.6B, i.e., 27%, not 14%.

The cash taxes paid number of \$4.7B (which is what you want to use in the numerator to get the 14%) is the cash
outflow that occurred in 2016 for income tax payments. It has less to do with taxes on taxable
income in 2016 and more to do with taxable income in 2015 (but even that is not the full story; see below).

Now maybe what you are confused about is that the taxes paid in 2016 (\$4.7B) should roughly be equal
to the current portion of taxes in the year end 2015 financial statements. This latter number is
\$5.4B. This discrepancy is probably due to minor differences of when the cash actually left

For instance, you might expect the total cash payments in 2016 and 2015 for income taxes to not
have much of a discrepancy between the current portion of tax expense recorded year end 2015 and
2014.

The former (cash taxes paid) is: \$4.5B + \$4.0B = \$8.5B
The latter (current portion of income tax expense) is: \$5.4B + \$3.3B = \$8.7B

However, this is not the full story. If you looked at very long periods in time, the cash taxes
paid number will (or would in the future) start exceeding the total current portion of income tax expense
(because the deferred amounts would eventually have to be paid).

The point is the same as before: the aggregate cash taxes paid will match the aggregate income tax
expense recorded in financial statements. It is just a matter of how long a period it takes for the
timing differences to manifest.

You are confusing effective tax rate (what Berkshire owes the government as a percentage of its
income, regardless of when the cash outflow occurs), with actual cash outflows occurring in any given period.

Think about it this way. Look at an "inverted" situation. Should unrealized capital gains not be
counted as increases in book value just because the cash inflow hasn't occurred (oh but maybe it
will occur relatively soon... really... look at the KO holding =D).

Is there any way estimating how much of the difference between the statutory rate and the effective rate is deductions and how much is tax credits?

Yes. I have to give a snarky response here: are you actually reading p.95 of the 10-K?
Because it is right there in the only table on the page, kinda hard to miss.