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It must have been frustrating for officials at the Congressional Budget Office to read Sen. Lamar Alexander’s in Sunday’s Washington Post. In the column, the Republican Senator from Tennessee mistakenly cites work done by the CBO to argue that Congress is currently considering to eliminate the Federal Family Education Loan (FFEL) program in favor of direct lending would “overcharge” students for their federal loans.

At issue is a that CBO sent to Sen. Judd Gregg (R-NH) showing that the pending legislation would save the government $47 billion over ten years using private market estimates. As Senator Alexander correctly points out, that figure is considerably less than the $87 billion in savings under official accounting rules, and it does indeed more accurately reflect the bill’s true savings. But here’s where he gets into trouble. Somehow the Senator came to believe that the $47 billion in savings is the result of the government earning money off direct loans by “overcharging” students.

“The Education Department will borrow money at 2.8 percent from the Treasury, lend it to you at 6.8 percent and spend the difference on new programs,” Senator Alexander writes.

“… if there really is $47 billion in savings to be found, Congress should return it to students as lower interest rates, not trick students by overcharging them…”

The CBO letter, however, shows that all of the $47 billion in savings comes from eliminating subsidies to private lenders in the FFEL program. Yes, every last penny. That’s because the estimate Senator Alexander touts actually assumes the government will not make money off of direct loans.

In other words, Senator Alexander got it backwards.

In fact, CBO’s market cost estimates show that students with direct loans get a subsidy on their loans from the federal government, . That means under 100 percent direct lending the government won’t be “overcharging borrowers,” nor will the loans make money for the government. Rather, students will get loans at terms more generous than those offered in the private market, which results in a cost to the government. Thus the $47 billion is purely and simply the private market value of the offered to private lenders under the FFEL program. A switch to direct loans eliminates those subsidies.

It’s all the more surprising Senator Alexander didn’t see that $47 billion as subsidies for lenders given that he proudly tells readers, “Nonprofit lenders such as Edsouth use the revenue generated under the [federal] student-loan system to operate and provide these valuable benefits [college-admissions assistance, etc.].”

Revenue, huh. Generated under the federal student-loan system, you say. Senator, I think we found the $47 billion you want to give back to students.

Disclosure: The author worked as a staff member for the U.S. Senate Budget Committee and Senator Judd Gregg.