Payroll taxes are 15.3% with no deductions. 0-10% on federal sounds about right, but that is not really an accurate picture for what taxes would do to his cashflow.
I agree that it is not morally OK to not report income.
I put in my own numbers for a complicated personal return (business income, capital gains, itemized deductions, etc) and the forecaster agreed with my actual taxes done by a CPA, so it's not making any guesses.
Put in married, $45k in business income, 4 kids. The total federal tax bill comes out to $3700 or 8%. Most of the tax bill was offset by the large EIC for having kids. In reality he'd have many deductions to lower that even further, from business use of a home, to any health insurance he buys, to part of his car expenses and mileage...
If the guy has $45k in business income, then he owes $6885 of payroll taxes (unless he is Amish). I don't care what tool you use, that number is the absolute floor for what he would have to pay out of pocket.
* 61: Add lines 55 through 60. This is your total tax.
* 62-72: Credits and payments, including the Earned Income Credit.
* 76: AMOUNT YOU OWE: Subtract line 72 (total credits) from line 61 (total tax).
That's where his $6.3k SE bill gets nearly wiped out by $5.5k in earned income credit.
Credits, unlike deductions, are subtracted dollar for dollar from total tax owed. If he files jointly with a spouse, it can actually reduce their tax bill to $0 on that income. There's no category of taxes that can't be reduced by EIC, including SE (payroll) tax.
But he gets those credits whether or not he reports his profit. On a cashflow basis, it will cost him 20%. You are right though, his tax bill at the end of the year would be about 8% of $45k.
I agree that it is not morally OK to not report income.