# Cash for Clunkers: the Math

I saw this on the internet and although I can’t source it, the numbers make sense in a black humor sort of way…(oops–can I say that?)

A vehicle at 15 mpg and 12,000 miles per year uses 800 gallons a year of gasoline.

A vehicle at 25 mpg and 12,000 miles per year uses 480 gallons a year.

So, the average clunker transaction will reduce US gasoline consumption by 320 gallons per year.

They claim 700,000 vehicles were traded in the clunker program – so that’s 224 million gallons per year saved.

That equates to a bit over 5 million barrels of oil.

5 million barrels of oil is a little over ¼ of one day’s US consumption.

5 million barrels of oil costs about $350 million dollars at $75/bbl. (Today the price is only $70…)

So-o-o-o, we all contributed $3 billion of our hard-earned tax dollars to save $350 million.

How good a deal was that?

AND…there are very likely 700,000 ‘really legitimate air-polluting clunkers’ still on the road being driven by folks who could not afford to take on the debt of trading it in for a new government-subsidized car–even with a $4,500 rebate. The so-called clunkers that were destroyed could have been given to these needy families, real clunkers would have been gotten off the roads, and we would all be breathing cleaner air.

We still have all the pollution. We taxpayers are out $3 billion and the car dealers who signed up for this have yet to receive their payments.

It took me less than a half hour to check the math on a cheap 4-function calculator I got for free *and* do the fact-checking on the Internet *from government sources*. Did no one in Congress do this?

And we are being asked to trust them on a nationalized healthcare plan! The cost/benefit calculation there is orders of magnitude more complex. Why, they might even have to use a spreadsheet or two.

Kids: *do *try this at home.

Math Teachers: this is a great practical math exercise. The numbers are big enough that you could introduce the notion of scientific notation.

Science Teachers: You could create a spreadsheet to show how changing the assumptions changes the results.

Social studies Teachers: This exercise could include how to do research on the Internet, the relative merits of different kinds of oil and where it comes from. Also, one could probably prove that reduced demand for oil resulting from unemployment had a greater effect on consumption than cash-for-clunkers did.

NEA Teachers: While your propagandizing our kids about Saving the Planet, you can show how bad public policy simply wastes resources while doing nothing to Save the Whales or the Polar Bears.

A note on methodology.

I’ve added a couple of references in the hyperlinks that validate the assumptions. The numbers above are round: In almost every case, if you substitute the exact numbers the result is worse. For example, the number of gallons of gas in a barrel of oil is assumed to be the standard definition of a barrel, e.g., 42 gallons. There’s a great discussion at the DOE link above, whose bottom line is that a barrel of oil does indeed yield 42 gallons of petroleum products–but it might not be all gasolene and some crude oil yields more gas than others. Petroleum engineers (God bless ’em!) have figured out ways to increase the gasolene yield, but with fewer gallons of gas per barrel, the result of the calculation is even worse.

The above information should be enough to create a lesson plan. If you’ve created one around this, please send it to me and I’ll link it to the post.

I’ve had a few people email your example above.

While I’m with you 100% on limited government, fiscal responsibility and free markets and I am very conservative, I’m also a CFA and an actuary (Fellow of the Society of Actuaries) so I tried reproducing your numbers. Perhaps I am making a mistake of some sort, but here is what I got, using your references:

224 mm gal of gas saved – so far so good.

224 mm gal gas = 5 mm barrels of oil – I don’t see that.

When I go to your source, there seems to be agreement on 42 gal = 1 barrel.

When I go to your source, I see only 2 numbers regarding oil/gas conversion. One says 30% of a barrel turns into gas, and one says 19.5 gal gas / barrel of oil, or about 45%.

Let’s split the difference and use a conversion of 37.5% gas per unit of oil.

That means to get 224mm gal of gas, we need 224/.375 = about 600mm gal of oil. 600mm gal / 42 gal/bbl = about 14mm bbl of oil. So I get an amount of “saved” oil that’s higher than yours by a factor of about three (obviously I’m rounding here & there).

14mm bbl oil x $75 = about $1bil, again about 3 times your number.

That’s Part 1 of my critique.

Part 2 has to do with financial equivalents, or present values. In pricing financial instruments, one can roughly equate a stream of income to a lump sum present value, assuming the amount of payment, period of payments, and the discount rate. For example, a 10 year stream of annual payments of $100 using a discount rate of 5% yields a present value of about $772. So assuming that the old cars would have lasted 10 years and that the new cars would last 10 years, when we apply the factor of 7.72 times my annual savings of $1bil per year, the present value is $7.72 billion. This obviously exceeds the “investment” of $3 billion. Even if we used your savings number of $350 million, when you take the present value of a 10 years stream of $350mm at 5% you get $2.7 billion – not much different than the $3 billion “investment”.

I certainly do not approve of the massive govt intervention we are seeing today, including cash for clunkers. However, that doesn’t mean that I turn off my critical thinking skills just because I see something that supports my position.

Finally – the more fundamental questions of this situation revolve around economics – such as govt spending vs private investment, the “crowding out” of private capital, the fundamental economic idea that “could that $3bil have been better spent and invested by individuals in a free market economy rather than having been collected by the government (not including the costs of collection, etc. which means that to get $3bil of money for the govt to spend actually requires a much higher amount of money to be taken away from individuals in order to result in a net collected amount of $3bil), etc. This is a far more complicated subject, but this is where the fallacy of stimulative fiscal policy truly shows through when held up to the light of critical thinking.

If I have missed something, please feel free to let me know, as I don’t pretend that I’m never wrong and I am open to constructive criticism, as that keeps us all more informed.

Keep fighting the good fight.

Whew! A lot of good info in your reply. Let me make a few observations:

Part I

There were a number of comments at the first DOE site regarding the gals of gas recoverable from a barrel of oil. Texas & Arabian yield 28, Venezuelan only 5. But that’s just the easy stuff: with further processing almost the whole 42 gal is convertible to gas. So that’s why I stayed with the 42 gal number.

If we say worst case the savings is $1b–is it still worth spending $3b to get it?

Part II

This one has me scratching my head. I understand PV/FV but the $350 million is a one-year savings compared to a one-year outlay. Consumption, BTW, was for 2008 and the price of oil is a bit high. If they inflate the currency the way I expect they will, how does that affect your PV calculation?

Are you saying that the return is better calculated over ten years rather than one? Could be a better approach–but $2.7b is still less than $3b. It also complicates the assumptions about price, consumption and alternatives. Another way to ask that question would be: over what period of time would we recover the cost of the clunker program? When we find the answer, would we still do it?

Part III

You ask really good questions: I wish Congress had asked themselves some of those!

To beat the same drum you did, in an open society this is the kind of discussion that results from free and reasoned debate. The strength of Hoover’s progressive approach in the 1920s, I think, is the belief that if we can reduce a public policy issue to an engineering problem, we can come up with the best solution. But the 111th Congress isn’t interested in debate. They’re pushing a socialist agenda heedless of cost.

Thanks again for your comments. Guess we could use this example in econ class, too!