The current payment and the new payment are each a standard monthly principal-and-interest calculation on the balance, rate, and term you enter. The monthly savings are the old payment minus the new payment. Break-even months are the closing costs you enter divided by that monthly savings, when the new payment is lower.
A lower rate on the same balance reduces the payment. If closing costs are $6,000 and the payment falls by $200 a month, the costs are covered in 30 months. After that, the lower payment is the gain. If the new payment is higher, there is no break-even from payment savings.
The result is not a lender quote. Cash-out, points bought with a higher fee, mortgage insurance, and prepayment penalties are only present if you have already put them into the balance or the closing-cost field.