Archive for the ‘Numbers’ Category

Ode to a billion …

March 1, 2013

A billion is a difficult number to comprehend,

To put a billion in perspective, consider …

A billion seconds ago it was 1981

A billion minutes ago Jesus was alive.

A billion hours ago our ancestors were living in the Stone Age.

A billion days ago no-one walked on the earth on two feet.

A billion dollars ago was only 8 hours and 20 minutes, at the rate our government is spending it.


Think about that the next time a politician casually drops the word “billion”.

Source: viral email

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Want a mortgage? … Then quick, what’s 300 divided by 2 ?

June 18, 2010

Punch line: If you can’t add & subtract, then you probably can’t do a budget … and will eventually end up in financial hot water.

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Excerpted from NY Times: Study Says Math Deficiencies Increase Foreclosure Risk. June 9, 2010

If you can’t divide 300 by 2, should you qualify for a loan?

That is one of the questions raised by a new study led by a Columbia business professor who found that borrowers with poor math skills were three times more likely than others to go into foreclosure.

Survey respondents were asked five questions, with the first requiring borrowers to divide 300 by 2, and the second to calculate 10 percent of 1,000.

About 16 percent of the respondents answered at least one of the first two questions incorrectly. The results were consistent among all levels of education and income.

Over all, 21 percent of the respondents whose math abilities placed them in the bottom quarter of the survey experienced foreclosure, versus 7 percent of those in the top quarter.

Mr. Meier said the study had at least two implications for mortgage lenders.

One alternative would be working to help borrowers improve their financial literacy before they took out the loan.

Another alternative might be to add math tests to the process and screen the math-challenged away.

“People say they’re doctors, so they don’t really need math … So what? We see doctors who took out loans they didn’t understand, and who are in foreclosure now.”

“Many of them don’t understand how to do a budget — which is basic math, I guess,” she said.

Full article:

Hmmm – Inconvenient Facts

July 31, 2008

Excerpted from WSJ “Where’s the Outrage? Really.” Arthur Brooks,  July 31, 2008

According to an emerging journalistic narrative … ordinary Americans are outraged. The anger is simply assumed to exist. Ironically, this assumption is questionable, and is not supported by the data.

In May 2008, the Gallup Organization asked 1,200 American adults how many days in the past week they had felt “outraged.” The average number of angry days was 1.17, and 54% of those surveyed said none. … Despite the litany of horrors presented to us daily by campaigning politicians, most of us appear to be doing really quite well managing our anger.

Indeed, we are less angry today than a decade ago… (in) the glory days of the 1990s, when — according to the media narrative — we enjoyed uninterrupted peace and prosperity. In 1996, the General Social Survey asked exactly the same “outrage” question of 1,500 adults. Then, only 38% had not been outraged at all in the past week. The average number of angry days was 1.5 per week, 29% higher than at present.

Virtually every group in the population is less angry in 2008 than in 1996 … only one major group in the population has gotten angrier: people who call themselves “very liberal.”  …  Today, very liberal people spend more than twice as much time feeling angry as do political moderates. One in seven is outraged seven days a week .

Most Americans recognize that, while gas is expensive and our grocery money doesn’t go as far as it did last year, we are still an enormously prosperous and fortunate nation.

Most …  are reasonable people, and can see the difference between correctable problems within a strong system of democratic capitalism and the kind of catastrophic failure that justifies real outrage.

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Mr. Brooks is a professor at Syracuse University’s Maxwell School of Public Affairs.

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For the full article (worth reading):

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Numbers: Driving Around

July 1, 2008

According to an ABC News Poll:

The average household owns two cars, trucks or sport utility vehicles … and one in four owns three or more … (Big idea to lower gas consumtion:: raise the driving age to 18 — 16 to 18 year olds don’t vote any way)

220 million adults average an hour and a half a day in their cars … 104 minutes for those with kids, 77 without

An average commute by car is 16 miles … and takes around 30 minutes (obviously not DC)

While about half of commuters have some form of public transportation available, only 4% use it to & from work (mostly city dwellers, minorities and lower-income Americans)

84% of driving commuters go solo … 8% regularly carpool … 20 percent of solo drivers say they’d be interested in carpooling  (yeah right — well mabe if gas stays @ $4 / gallon)

65% oppose higher gasoline taxes … even if the money is earmarked for transportation projects

66% approve of roadside cameras to enforce traffic laws (note: they didn’t survey my family)

For the complete report:

Numbers – Oil – The Weak Dollar Effect

June 27, 2008

Note: I credit Martin Evans, Professor of Ecconomics, Georgetown University for remarks that inspired this analysis … of course, I take all blame for any improper analysis or wrong conclusions. 

One of the driving forces behind the recent rise in oil & gas prices has been the weakening foreign exchange value of the US dollar.

Comparing the price of oil — over time — valued in both dollars and another stronger currency helps calibrate the effect of the weakening dollar.  For example, compare the spot price of Brent Sea Crude (a represntative oil price) expressed in $ US and Euros (a relatively strong currency — compared the the US $) :


To visualize the tracking of the curves more easily, shift the Euros curve up a little so that the two curves have the same starting point. In technical terms, this process is “indexing” the two series at a common starting points.

Click chart to make it bigger 

To the extent that the curves follow each other — as they did in 2006 —  the apparent currency effect is minimal.  That is, the oil price changes are due to other factors — say, supply & demand or financial speculation. 

To the extent that the curves diverge — as they start to do in early 2007 — the apparent currency effect is increasingly meaningful.  Note that the separation between the curves increases throughout 2007, and continues in 2008.

In US dollars, the oil price went from $53.68 in January, 2007 to $122.80 in May, 2008 — up $69.12, a 128% increase. 

The oil price went from 41.30 Euros in January, 2007 to 78.93 Euros in May, 2008 — up 37.63 Euros, a 91% increase. 

By inference, if the US $ had held constant relative to the Euro, the oil price in May, 2008 would have been $102.52  ($53.68 plus 91%).  It didn’t, so the $20.28 difference ($122.80 – $102.52 = $20.28) is reasonably attributable to he currency effect of weakened dollar.

Taking some bold statistical liberties, it can be inferred that about 30% of the oil price surge is tied to the weakening dollar ($20.28 / $69.12 = 29.3%) and that about 70% of the increase in oil prices is attributable to non-currency related factors (i.e. fundamentals and speculation).

 Of course, these estimates are quite crude*  … 

* pun intended




Numbers – Price Gouging? Windfall Profits?

June 26, 2008

FYI: (a) I’m not a financial analyst or investment adviser (b) I’m not a big fan of oil companies (c) I do own some shares of Chevron Texaco  and Slumberger — not enough to sway my thinking (d) $4 per gallon for gas gives me pain at the pump, too

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Critics characterize oil companies’ profits as “obscene”, “unconscionable”, and “windfall”.

In a previous post, I compared Exxon Mobil (the poster boy for big oil) to two other mega-corps — Coke & Microsoft.  The data says that Exxon’s profit margins are lower, its effective tax rate is higher, and its ROA (return on assets) is well below Microsoft’s and roughly at par with Coke’s.  Draw your own conclusions.

Drilling deeper on Exxon’s financial performance over the past couple of years (see chart below for details) and putting them in the perspective of standard financial ratios leads me to 5 pivotal conclusions.

1) Exxon is a very, very big company with a market cap over $450 Billion  … so all of its numbers seem supersized

2) From “50,000 feet” , there’s no evidence of price gouging … gross margins have been flat, before and after rhe run-up in crude oil prices

3) Exxon’s already paying a lot of taxes — over 40% of pretax profits, about $90 Billion since Jan. 2005

4) There’s plenty of reinvestment … capital expenditures about 30% of cash flow

5) Almost 70% of cash flow is going directly (and immediately) to shareholders in the form of dividends and stock repurchases

Some Details

1) Size & growth: Revenues have increased by about 9% from 2005 to 2007 (2% in 2006, 7% in 2007) to a whopping $404.5 billion.  Unfortunately, it’s tough to split the increases between volume (more oil sold) and price. Seems reasonable to conclude that a lot of it is price since refinery capacity is relatively fixed.

2) Margins & prices: “Cost of Revenue” has held relatively flat at about 57.5% so, by definition, gross profit margins (the flip side of cost of revenue) have been relatively flat at 42.5%.   Translation: Exxon’s “percentage mark-up” over its costs has stayed flat — if price gouging, would expect margins (i.e. mark-up) to increase.  Of course, as costs go up, the profit margin expressed in dollars (instead of percentages) goes up.  It’s reasonable to infer that Exxon’s profit — in dollars per barrel — is increasing along with crude oil prices, but that’s not evidence of gouging behavior.

3) Taxes: Exxon paid over $90 Billion in taxes from January, 2005 to March, 2008 — an effective tax rate over 40% (46.1% in Q1 of this year)

4) Reinvestment: over the 3 year period, Exxon invested about 30% of its cash flow — almost $50 Billion — in capital expenditures (presumably for drilling rigs, refineries, etc.)

5) Shareholder distributions:in recent years, about 70% of cash flow has been distributed directly to shareholders in dividends ($31.4 Billion in 2007) and stock buybacks (about $85 Billion since Jan. 2005)

So what ?

1) Retail gas prices have gone up proportionately to crude oil prices and gross margins have been flat — where is the evidence of the much touted price gouging?

2) The financial ratios are relatively constant across the years — pre and post the crude oil run up.  Where’s the windfall?

3) An effective tax rate over 40% strikes me as pretty high.  How much higher does it need to be pushed to be a  “fair share”?

4) $50 Billion in capital expenditures — 30% of cash flow — sounds like reinvestment to me.  It’s not in alternative energy sources, but as I like to say “there’s a reason they’re called oil companies”

5) In my opinion, oil company execs have been greedy (and stupid) raking off so much compensation.  But, keep in mind that most of the company’s cash flow is going directly to shareholders, either in dividends or stock buybacks (which prop up the share price for shareholders who sell) .

Note: Exxon has about 5.3 Billion shares outstanding — about 1/2 in the hands of institutions (think mutual funds) and 1/2 held by individuals.  They invested to be owners, and they’re the direct and immediate beneficiaries of Exxon’s financial success.  Said differently, any windfall profits tax would come directly out of their pockets into somebody else’s. Think about it — how fair is that?

Click chart to make it bigger  

Numbers – Obscene Profits ?

June 25, 2008

It’s a popular refrain: oil companies are making too much money and they’re failing to develop alternative energy sources.

McCain says: “I am very angry, frankly, at the oil companies not only because of the obscene profits they’ve made but at their failure to invest in alternate energy to help us eliminate our dependence on foreign oil.”

Memo to Sen. McCain: There’s a reason they’re called “oil companies” — that’s their business — that’s what they do.

Obama says:“I’ll make oil companies like Exxon pay a tax on their windfall profits, and we’ll use the money to help families pay for their skyrocketing energy costs and other bills.”

Memo to Obama: putting more money into the hands of the buyers of relatively scarce commodities will simply bid up prices faster.  It’s  fundamental economics: called the “budget effect”. Any “relief.” is briefly transitional. 

Even O’Reilly piles on, saying that the oil companies are reaping unconscionable profits by price gouging “the folks”. 

What about the obscene,  unconscionable windfall profits?  What do the numbers say?

First, on a comparative basis, it’s tough to make the case (chart below). 

Comparing Exxon Mobil to fan favorites Coke and Microsoft is revealing: 

  • Exxon’s 17.4% EBIT (earnings before interest and taxes — a measure of their profit margins — the difference between their operating costs and the prices they charge) is lower — much lower — than either Microsoft’s (39.3%) and Coke’s (28.9%)
  • Exxon already has a higher effective tax rate (42.4%) than either Microsoft (30%) or Coke (22.7%).
  • So, Exxon’s net income after taxes (10%) is about half of Coke’s (20.7%) and about 1/3 of Micosoft’s (27.5%)

Of course, applying 10% to Exxon’s gigantic revenue base ($404 billion) gives a very big number — $40 billion.  But, it takes a correspondingly enormous level of capital investment (think rigs and refineries) to generate that level of sales.  Exxon has almost $250 billion in assets — one measure of a business’ capital intensity.  Exxon earns a 16.8% return on its assets — 5 percentage points less than Microsoft, and roughly the same as Coke (depending on whether or not Coke’s “intangible assets” are counted).

Bottom line: For sure, Exxon’s profits are high.  But, they’re not “obscene”  or “unconscionable” … unless Coke and Microsoft’s are, too.  

That leaves the question of “windfall” for a follow-up post.                               


Numbers – U.S. Oil Refinery Operations

June 22, 2008

Summary: While the number of refineries has been substantially reduced over the past 25 years (and no new refineries have been built), aggregate refining capacity has increased and refineries have operated practically “full out”.   Source EIA (Energy Information Administration)

In 2008, there are half the number of operating refinerie in the US as there were in the early 1980s … mostly due to the retirement of outdated facilities that couldn’t be economically reengineered to meet increasingly strict environmental regulations.


Refinining capacity has increased from under 16 million barrels per day (mbpd) in the mid-1990s to over 17.5 mbpd in 2008 — an increase of more than 10%.



US oil refineries are consistently operated at utilization levels above 80% of “operable capacity” … which is generally considered to be the practical  “full out”, given normal downtime for repairs and maintenance.