I got that number by subtracting market rents-expenses= 1471Is this right?

Wait till the current lease it terminated and then have the place professionally cleaned, subtract that from the security deposit.

Subtract all expenses from $78,750.

After doing my math and subtracting 70% the MAO was about $117k.

Equity is what you have left after you take your property value and subtract any liens (mortgages) you have on the property. 

To analyze a purchase, you take the annual rental income, subtract all the expected operating expenses (taxes, HOA fees, maintenance, utilities, etc.) and divide by the purchase price.

Next take your sale price and subtract a profit margin of 25%, subtract sales commissions, carrying costs, construction cost, land improvements.

The total cost is 40k.However, because the property has appreciated to 150k and I can get 70% of the ARV on a refinance, I am able to pull 105k. 105K subtracted by the 80k initially owed is 25k. 

Just subtract that $200k from the $563k = $363k?

I've heard take annualized rent, subtract 50% for expenses and vacancy, and then divide by going cap rate.