"Drawing selectively on existing cost estimates and augmenting them with new calculations, I conclude that the total direct cost of crisis-related bailouts in the U.S. was on order of $500 billion, or 3.5 percent of GDP in 2009. [...] Those conclusions stand in sharp contrast to popular accounts that claim there was no cost because the money was repaid, and with claims of costs in the multiple trillions of dollars."
From 3.1.3. See Wall's analysis of Fannie Mae and Freddie Mac for more detailed discussion of their bailout costs:
"Treasury collected $147 billion from Fannie and $98 billion from Freddie. As explained earlier, interpreting this tally as a cost measure is conceptually flawed for several reasons. Wall (2014) also discusses the shortcomings of this approach, which has been used to argue that the government has been more than fully repaid and that value should be returned to the shareholders."
From the conclusion:
"Nevertheless, the total is large enough to conclude that the bailouts were not a free lunch for policymakers as some have claimed."
What the paper is saying seems pretty clear to me: bailout costs have been inaccurately measured and reported popularly at both ends. It was neither unfathomably expensive, nor profitable to the tax payer.
If you lend me $100 and I pay you back $107 you can declare you profited from the loan if you literally only look at the principal and repayment amount, but finance is not so simple, especially at a national level. Opportunity cost, inflation, depreciation, and numerous other factors exist. The total cost of you lending me $100 could have been significantly more than $107.