Overpaying defined as what? PAying more than the market value? Paying more than the Asking Price? Paying more than what your analysis tells you is the maximum offer you should make based on your own criteria for a good deal?
The best way to answer this question is to define what the definition of "cost" is. There are two definitions:
1 - Total Cost of the property includes things like Purchase Price, loan interest, utilities, insurance, taxes, rehab, repairs, closing costs, etc... In short, everything it takes to buy the property plus everything it takes to own the property.
2 - Investor cost includes all the cash that comes out of the REI's pocket. Period. This includes the DP, negative CF, REI's contribution to pay down the mortgage principle,...anything that the REI pays for in cash
What makes a deal, is also two things:
1 - The cost (Cash out of pocket...see above) to the REI
2 - The terms where the rest of the Total Cost is paid for by someone/something else.
Profit is simple: Profit starts when the REI recovers all of their cost from the income in the property (cash flow). So, the lower the cost, the quicker the cost is recovered and profits are generated.
Back to the beginning, and my questions regarding the definition of overpaying. Taking in consideration the definitions of Cost and what makes a deal, the answer to the original question of, "is it OK to overpay", comes down to how that potential overpayment impacts how fast the REI's costs are recovered.
You can pay more than the AP, or the MArket Value, and still have a great deal, depending on the cost to the REI and the terms for the rest.