by Calculated Risk on 9/01/2009 01:14:00 PM

To calculate the cost of a tax credit per additional unit sold, we need to sum up the total cost of the credit - as an example $2.877 billion for Cash-for-Clunkers according to the Dept. of Transportation - and then divide by the estimated increase in sales because of the credit.

Remember some cars or houses would have been sold anyway (even though they still receive the tax credit), but it is the additional sales that matter. That was the purpose of the tax credit! (update: Shnaps notes that the auto credit had an additional benefit of better mileage)

We have two examples today.

First, for autos, if sales in August had been about the same as June (pre-tax credit), there would have been 850 thousand light vehicles sold (NSA). This is about a 9.7 million SAAR.

Next we add in the tax credit: Although the DOT reported close to 700 thousand car sales associated with the Cash-for-Clunkers program, probably about 550 thousand were in August. If these were all additional sales, then the total sales (NSA) for August would be about 1.4 million, or almost 16 million SAAR.

If Edmonds.com is correct, and total sales were 1.17 million (NSA) in August, then the tax credit only generated about 320 thousand extra sales. Of course some regular car buyers might have put off a purchase to avoid the rush in August, so this isn't perfect, but instead of costing taxpayers $4,170 per car (as announced by DOT), the cost to taxpayers per additional car sold was close to $7,200.

The numbers are much worse for the first-time home buyer tax credit. The NAR reported this morning:

NAR estimates that about 1.8 to 2.0 million first-time buyers will take advantage of the $8,000 tax credit this year, with approximately 350,000 additional sales that would not have taken place without the credit.

I believe the NAR underestimates first-time home buyers, especially considering the definition for the tax credit is anyone who hasn't owned a home in three years - not really a "first-time" buyer. I also think the NAR is overestimating the number of additional buyers.

But using their numbers ...

With 1.9 million first-time buyers, the total cost of the tax credit will be $15.2 billion. Divide $15.2 billion by 350 thousand, and the program cost $43.4 thousand per additional buyer. The actual number could be much higher if there were fewer additional first-time buyers than the NAR's estimate - or if the overall cost is higher (more buyers claiming tax credit).

This is the actual cost per additional home sold. And since buyer interest will fade (like with the Clunkers program), the cost per additional house will increase sharply if the program is extended.