Here's how this deal looks. You buy at $400,000, put about $73,700 into the rehab, and carry it for 5 months. All in, the property costs you $507,333 before furniture.
If the appraisal lands at $560,000, you created $52,667 of equity through the work.
The refinance at 75% of ARV is a $420,000 loan. After paying off the purchase loan and closing costs, $67,400 comes back to you.
Short-term rental: $78,074 gross, $44,672 NOI, $858/month after the mortgage, with $124,533 left in the deal and 8.3% cash-on-cash. DSCR 1.30.
Medium-term rental: $36,720 gross, $16,546 NOI, -$1,486/month after the mortgage, with $123,333 left in the deal and -14.5% cash-on-cash. DSCR 0.48.
Long-term rental: $30,780 gross, $17,540 NOI, -$1,404/month after the mortgage, with $100,533 left in the deal and -16.8% cash-on-cash. DSCR 0.51.
On cash flow, short-term rental wins in this scenario.
The short-term rental breaks even at 51% occupancy. Below that, it costs you money every month.