Fri 30 Apr 2004
Back-of-the-Envelope Economics
Posted by Tim Lee under Uncategorized
[28] Comments
Andrew has a post that includes a clever spreadsheet that illustrates the value of revenue-generating assets. A batch of New York city taxi medallions (which provide taxi drivers exclusive rights to operate in the city) were recently auctioned off, and fetched as much as $300,000. Is that a reasonable price for a medallion, he asked? How would we figure out what a taxi medallion is worth?
If you ask an economist, he’ll tell you to calculate the present value of the expected future revenue from a medallion, and compare that to the cost.
So let’s do the math. Given a medallion cost of $300,000, how much does a cabbie have to make to justify buying one? Assuming he’ll use it for 20 years, and assuming a 5 percent discount rate—the forgone return he could’ve earned on a similar investment—he’d need to earn about … $28,300 a year.
That’s not much. So how much do taxi drivers actually earn? According to the New York Times here and here, most drivers pull in about … $30,000 a year.
So it turns out those medallions aren’t so expensive after all, and a little simple economics helps us see that.
Well, not quite. This analysis assumes the opportunity cost of the taxi driver’s labor is zero– that is, if he doesn’t have a medallion, he’d be unemployed for the rest of his life. But that’s clearly not the case. New York’s a pretty expensive place, so let’s imagine (probably conservatively) that your average unskilled worker can make an average of $15,000/year over a 20-year period without a taxi medallion. The medallion is only valuable to the extent that it allows the driver to make more than he would without it. Hence, if his math (and my assumption about wages in New York) are right, the taxi driver would have to pull in $43,000/year to justify purchasing the medallion.
Clearly, taxi drivers are not making that much money. So what’s wrong with Andrew’s model, once you take my revision into account? One factor is alluded to in the New York Times article he links to: the medallion will be his property at the end of the 20 years, and so he’ll be able to sell it and recoup some of the purchase price. A good back-of-the-envelope way to take this into account is to just multiply the purchase price by your discount rate– the result is the revenue you’d need to justify the purchase over an infinite time horizon.
Another possible problem is the discount rate. It’s true that long-term, stocks offer real returns of 7% or more. But stocks don’t give a steady stream of income, which is crucial if your livelihood depends on the medallion. But if you’re looking for an investment that offers the steady income of a medallion, you’re not going to find one that gives 7% long-term returns. Perhaps 5% is more appropriate given the need to avoid volatility.
With those assumptions, the medallion would have to raise a taxi driver’s earning power by $15,000 ($300,000 * 5%) in order to justify the purchase. That means that taxi drivers’ next-best alternatives must pay less than $15,000/year to justify the purchase. That seems at least possible, although it seems like a pretty low estimate for a 20-year career given the cost of living in NYC.
Finally, it’s possible that the individuals bidding for those medallions are over-paying, and will regret their decision. The math involved is complicated enough that many bidders might not be equipped to get it right. Judging from the prices of houses around me and the amount I’m paying in rent, I have a suspicion that most of the homeowners in my neighborhood are making a similar mistake.
