Image: An SAT exam © The Christian Science Monitor Archive

What is a big SAT score improvement worth? A whole lot -- sometimes.

Picture a high school student from New York state. His grades are excellent; his transcript is a sea of A's. He has taken challenging courses and held leadership positions in a few clubs, as most admissions counselors advise. He volunteers at the local hospital on weekends. He's sure to impress with his application essays.

Further, his parents are successful, so unless he receives merit aid, his family will probably pay full tuition -- and room and board -- at whatever institution he attends. Of course, if he attends a school in New York that offers in-state tuition rates, his family will pay those instead.

Picture, in other words, a fictional student for whom SAT scores will make all the difference. Here lies the value of good SAT prep to him and his family.

PayScale has compiled median starting salary data, and, more interestingly, median "midcareer" salary data for bachelors' degree graduates of most colleges and universities in the United States. The Chronicle of Higher Education has a searchable tuition database. And many schools provide the 25th and 75th percentiles (usually called the "middle 50%") of their students' SAT scores.

From this I made some sweeping assumptions and crunched some numbers. First, I assumed that historical data for salary rates for graduates of different schools is a decent predictor of the future, at least for rough predictions of which graduates will make more and which will make less. Then I looked at net present values of 20 years of cash flows -- four years of full tuition (or full in-state tuition for New York schools), followed by 16 years of salary based on PayScale's numbers. NPV differences are biggest at low interest rates, and they grow more muted at higher ones. Rather than make a prediction for interest rates for the next 20 years, I looked at differences for a range of possible interest rates.

Under the right conditions, even pricier SAT prep options can be a heckuva deal. Say, for example, that our student's SAT scores are 1700. That puts him in a good position for admission to Adelphi University (middle 50%: 1480-1780) but makes admission to Stony Brook University (middle 50%: 1660-1970) a stretch. Assuming he'd rather attend Stony Brook if he can get in, what might be the value, in today's dollars, of a score increase that would seal the deal? Turns out, it would be more than $100,000 in future earnings, at any reasonable discount rate.

But before you drop everything to start calling tutors, consider another example. Let's say our student is instead scoring around 1900 on practice tests, and that he'd happily attend Fairfield University (middle 50%: 1710-1910). However, in his heart of hearts, he'd really rather attend New York University (middle 50%: 1940-2230) if he had the scores to get in. The pursuit of dreams is a perfectly good reason to spend some money, but his parents should do so with eyes wide open. PayScale's numbers say that the present value of attending NYU is $50,000 less over the next 20 years than that of attending Fairfield.

Of course, these are cherry-picked examples, and admissions offices are cagey about exactly how much SAT scores matter. But the numbers make a good point. It's important to think through the goals of test prep, beyond the immediate desire for higher scores. For almost everyone except test prep professionals, actual scores won't be worth a hill of beans once acceptance letters are sent out. But where those acceptance letters come from might or might not be worth a great deal.

Want to play with my numbers, or try different school matchups? Here's the spreadsheet I used. You can save a copy for yourself and edit it however you like.

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