There’s an interesting site that shows the travels and revenue of individual New York City taxis. Go check it out.

Anyway, this is the first time I’ve seen actual revenue figures for individual cabs. Most seem to bring around $600 per day. That’s revenue. It’s not profit, or gross income, or even operating income.

Hmmm. Now, it’s well-known that a taxi medallion goes for about $1,000,000. How do you justify spending that much from $600 of revenue?

There’s actually a pretty simple formula for this that’s taught in the first corporate finance class. The present value of an infinite stream of equal payments is that payment divided by the discount rate.

It’s an approximation, but we could view the profit earned on a cab every day as a constant.

The discount rate takes a little calculation, but some quick work with a spreadsheet shows that a daily rate of 0.01% corresponds to a discount rate of 3.7%. That’s not a bad value for discounting real values when you have a city backing up your license with its enforcement powers.

In that case, $100 per day, discounted at the rate of 0.0001 (so the first number divided by the second) gets you the million dollar price.

The round numbers are convenient: we can quibble about the discount rate, but the round numbers mean that if we double it, we just double the daily profit required to justify the purchase of the taxi medallion.

Now, where does that discount rate mean, and where does it actually come from? The discount rate is the rate people use subjectively, in their own heads, to trade off cash today for cash in the future. No one ever knows exactly what it is, but we can infer from people's actions what they’re thinking. In the business world, managers tend to push for a discount rate that’s consistent with something called WACC — basically, the rate you have to pay to obtain funds (often from borrowing).

I should think, if you could get funds at 0.01% per day, you’re in excellent financial shape. So a really flush investor can justify buying a taxi medallion if they can expect a profit rate of around 16.7% per year (the back-of-the-envelope calculation $100/day profit divided by the $600/day revenue).

But if your WACC is higher, say consistent with 0.02% or 0.03% per day (corresponding to 7.5% or 11.6% annually), then your profit rate would need to be double or triple that.

In the end, all of this makes me think that services like Uber have huge latitude to reduce prices to consumers because, in the conventional business model, consumers are mostly paying for the owner’s medallion.