How much will the net amount  be?

Trump did away with deducting moving expenses.  You cannot deduct them unless you are active duty military.  

Consequently, the stipend will be treated as ordinary income, subject to fica, medicare and income tax--like a bonus.  The check when you get is likely to withhold at a 22% federal rate which may be too little.

Consult a tax professional. Relocation expenses may be deductible. I haven't checked in a few years, but you used to be able to offset the relocation stipend against actual moving expenses, even if you don't itemize deductions. If that is still true, your net amount could be the full stated amount.

It's "income", just like any other money you get from your employer. Whatever tax bracket you are in - that's what you can figure on deducting.