Friday, September 11, 2009

"A New Take on Cash for Clunkers"

Please check the math of this chain mail:

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 - so that's 224 million gallons / year. That equates to a bit over 5 million barrels of oil. 5 million barrels of oil is about ¼ of one day's US consumption. And, 5 million barrels of oil costs about \$350 million dollars at \$75/bbl. So, we all contributed to spending \$3 billion to save \$350 million. How good a deal was that ??? They'll probably do a great job with health care though!!

Anonymous said...

3 billion is a fixed cost. 350 million is per year. If the replacement vehicles stay in operation an average of 10 years, assuming those figures are correct, then it actually turns out to be worthwhile, from a simple numbers perspective.

newt0311 said...

You forgot to account for the standard rate of equity return. Namely, 3 billion could have paid interest. After we account for that, assuming a RE of 10% (historical average), we find that annual savings of \$350 million into perpetuity is equal to \$3.8 billion. However, note that CfC does not actually replace the vehicles, just pays for them to be destroyed. Thus the \$3 billion cost noted is a gross underestimation.

Of course, there are a lot of other problems with the analysis. 224 million barrels works out to about 5.3 million barrels which works out to \$400 million at \$75/day. This implies an equivalent figure of \$4.4 billion. Note however again that the cost of getting new cars is completely unaccounted for.

If we take stupidly the assumptions that the \$3 billion captures the entire value of the cars destroyed (valuing the average destroyed car at \$4285.7) and that getting a replacement car will cost the exact same amount (obviously too low, the new car is ... new and has better mpg -- 15 vs. 25), we get a total cost of \$6 billion.

In conclusion, I agree with the sentiment that CfC is a truly stupendous and idiotic waste of money that only a democracy could pull off but with the caveat that that chain mail does not offer a very good proof of this fact.

newt0311 said...

Edit: \$75/barrel.

Also, the analysis simply does not account for the changing price of oil and how that is going to trend. etc...etc...

newt0311 said...

More edits: turns out that there is a minor error in my reasoning (goes to show how annoying econ. can be). The cost of the new car will be only the added price. I.e., total price of new car - price of old car. Note that this will still be something significant and substantial as the new car has demonstrably better features. However, it may not have the same magnitude that I suggested.

Anonymous said...

You could never assume a rate of return like that on such a large amount of money. The long-term bond rate would be a much more useful number.

Brandon Berg said...

"3 billion is a fixed cost. 350 million is per year. If the replacement vehicles stay in operation an average of 10 years, assuming those figures are correct, then it actually turns out to be worthwhile, from a simple numbers perspective."

No, because most of the cars traded in would probably not have been on the road for ten more years anyway. People presumably only traded in cars worth less than the credit, many of them likely nearly worthless. Most likely many (most?) of these people would have bought new cars over the next few years anyway.

newt0311 said...

@Anon 2:49

You are right. The yield for the next 30 yrs on US treasuries is about 4.3% now. However, US treasuries are effectively risk-free. That 3 billion dollar spent is more like a junk bond which have long-term yield of about 20% right now (when appropriately diversified).

10% isn't too bad an estimate. \$400 million perpetually at 15% comes out to a total of \$3.06 billion and at 5%, it works out to \$8.4 billion. Pick whichever figure you want.

Anonymous said...

What is the cost of producing a car measured in gallons of gasoline? Is it worth the savings per year? It seems silly to destroy a pre-built auto in order to save the environment, and then commit 30k worth of environmental damage to replace it.

Anonymous said...

This also assumes people won't drive more with their fuel efficient vehicles.

JGP