Here are two simple formulas to apply that will allow you to prove this out (look up the formulas, they are probably the most commonly used formulas in all of finance)Buying with a mortgage is a more efficient use of your money.

@John Thomas This is a losing formula:  I am looking to invest out-of-state as a long-term, buy and hold investor in the lower cost, higher cash-flowing markets of the midwest and southeastern US.You do not want to focus your investment thesis on cash flow and low barrier of entry markets.

Is there a standard formula that takes into account the fluctuations of interest rates?

Maybe not today with a DSCR formula, but by year 3-5 you likely will be.

Do you have a specific formula?

You are obligated to provide the oldest verifiable operating statement (base year), which is adjusted into today's dollars (Using an LA City formula for inflation) and this is compared to your current year (yes with receipts, cancelled checks, bank statements, k1's etc), which can be significant. 

@Mica MooreBefore you decide to self-manage or hire a property manager, you need to understand what goes into managing rental properties.A novice investor may see a rental property as a simple equation of: rental income - (mortgage + expenses) = profit.While this formula is the basic mantra for an investor, you also need to include your landlord duties and energy into that equation.

For a $450,000 property with a 6.625% interest rate, the principal reduction over 5 years can be calculated using an amortization formula, revealing a significant amount of equity built through loan paydown alone.Take a look at the table below.

Flipping is extraordinary hard right now, I look everyday at deals in 17 counties these range from the nations capital to rural areas with population’s in the hundreds, I also act as my own gc, am a real estate agent and have a relatively cheap line of credit (8.25% no points) and I’ve bought one deal in the last 2.5 years. a flip really is a quite easy formula 1. your purchase price (you make money when you buy)2.

It's not an auction, it's a fixed statutory formula.