For the first time in more than 150 years, freshmen at Cooper Union will face a tuition bill this fall. For a college that has historically been free to undergraduates, the policy change is huge and controversial.

But they've found the rosiest possible spin. Cooper Union says on its website that it's actually being very generous: All new students are getting a $20,000 scholarship to offset part of a $39,600 tuition bill!

It's as if Starbucks announced that lattes would cost $10 from now on, but every customer will get a $5 coupon when they walk in the store. In fact, as Cooper Union tells it, it was actually already charging tuition this academic year and giving every student an even better discount:

The Cooper Union tuition charge for undergraduate students for 2013-2014 is $39,600 per year ($19,800 per semester). Each registered undergraduate student receives a tuition scholarship worth $39,600 per year ($19,800 per semester).

This sounds insane. ("I'm not giving you a free lunch. I'm charging $100 and giving you a $100 discount for being such a great customer.") But it's just an extreme example of a confusing fact about college costs: What colleges say they charge in tuition and fees often doesn't line up with what most students actually pay.

That's partly because of federal grants to help low-income students. But it's also because colleges, particularly private colleges, hand out a lot of discounts to students regardless of income.

According to the National Association of College and University Business Officers, colleges knocked off about 45 percent of their stated tuition price for freshmen, on average, through scholarships in 2012. That doesn't mean that every student got a 45 percent discount, but it means that a majority of them weren't ever charged what the college says it charges.

This makes it very difficult to talk about how much college really costs. It's why higher education experts distinguish between "sticker price" (Harvard said it costs almost $58,000 in the 2012 academic year) and "net price" (75 percent of students at Harvard get financial aid, and they ended up paying an average of $16,445).

some people worry the high price tag discourages low-income students from applying

Why do colleges do this? In theory, the practice allows them to make tuition pricing more progressive by charging lower prices to needier students. But middle-class and rich students get discounts too, and some people worry the high price tag discourages low-income students from applying.

The federal government now requires college websites to include a calculator to give students a better idea of what they might actually have to pay to attend. But why don't colleges just make their pricing more transparent in the first place: charge less, hand out fewer discounts, and make scholarships more meaningful?

Some colleges are trying that. But the rampant confusion about what colleges charge versus what students pay allow them to frame more realistic pricing as a huge discount. Converse College cut its tuition from $29,000 to around $16,500 — when the average student was paying around $17,000 even before the change.

What Cooper Union is doing is just a more brazen version of that.

(Hat tip to the New America Foundation's Kevin Carey for pointing out the Cooper Union announcement on Twitter.)

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