RE Math Cheat Sheet
I have cited the book that has helped tremendously in understanding Real Estate mathematics. This cheat sheet references the formulas directly from the book cited
"What Every Real Estate Investor Needs To Know About Cash Flow" by Frank Gallinelli, McGrawHill Education, Copyright 2016 Order of Operations Refresher
 (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally
 Parenthesis
 Exponent
 Multiply
 Divide
 Add
 Subtract
 Simple Interest

Interest = Principal x Rate x Time
Amount = Principal x [1 + (Rate x Time)]
 Compound Interest
 Amount = Principal x (1 + Periodic Rate) ^ Number of years
 Rule of 72's (approximately when a property will double in value)
 Result = 72/Rate of Growth
 Present Value of a Future Cash Flow
 Present Value = Future Value / [(1 + interest) ^ years]
 Gross Rent Multiplier (GRM)
 GRM = Market Value / Annual Gross Scheduled Income (GSI)
 Market Value
 Market Value = GRM x GSI
 GSI (Potential Gross Income)
 GSI (for the target year) = Total Occupied Rent Payable + Total Vacant Potential Rent (at market rates)
 Vacancy and Credit Loss
 Vacancy and Credit Loss = GSI x Estimated % Vacancy and Credit Loss
 Gross Operating Income (GOI)
 Gross Operating Income = GSI  Vacancy and Credit Loss
 Net Operating Income (NOI)
 NOI = GSI  Vacancy and Credit Loss = GOI  Operating Expenses
 Capitalization Rate (Cap Rate)
 Cap Rate = NOI / Value
Where the above Value = NOI/ Cap Rate
Where the above NOI = Value x Cap Rate  Net Income Multiplier (NIM)
 NIM = 1 / Cap Rate
This give you the reciprocal of a Cap Rate so you can get an approximate property value as follows:
Present Value = NIM X NOI  Taxable Income

 NOI
 less Mortgage Interest
 less Depreciation, Real Property
 less Depreciation, Capital Additions
 less Amortization, Points and Closing Costs
 plus Interest Earned
 = Taxable Income
 Cash Flow (Before Taxes)

 NOI
 less Debt Service
 less Capital Additions
 plus Loan Proceeds
 plus Interest Earned
 = Cash Flow Before Taxes
 Cash Flow (After Taxes)

 Cash Flow Before Taxes
 less Income Tax Liability
 = Cash Flow After Taxes
 CashonCash Return
 CashonCash Return = Annual Cash Flow / Cash Invested
 Sale Proceeds

 Selling Price
 less Costs of Sale
 less Mortgage Payoff
 = Sale Proceeds Before Taxes
 less Tax on Sale
 = Sale Proceeds After Taxes
 Discounted Cash Flow
 Add PV's of each year till your target year.
 Net Present Value (NPV)

 NPV = PV of all future cash flows
 less Initial Cash Investment
 Profitability Index
 PV of all Future Cash Flows / Initial Cash Investment
 Internal Rate of Return
 Recharacterize the present value (PV) as your known present cost (i.e., the amount of cash you have to invest in order to make this purchase) and treat the discount rate (the rate of return) as your unknown.
Now forecast the future cash flows and the PV of your actual cash investment, you can calculate the discount rate, which you call the internal rate of return.  Price, Income, and Expenses per Unit

 Price per unit = price / number of rental units
 Income per unit = GSI / number of rental units
 Expenses per unit = Operating Expenses / number of rental units
 Prince, Income, and Expenses per Square Foot

 Price per square foot = Price / Gross Building Area or Net Rentable Area
 Income per sq ft = GSI / Gross Building Area or Net Rentable Area
 Expenses per square foot = Operating Expenses / Gross Building Area or Net Rentable Area
 Operating Expenses Ratio
 Operating Expense Ratio = Operating Expense / GOI
 Debt Coverage Ratio
 Debt Coverage Ratio = Annual Net Operating Income / Annual Debt Service
 BreakEven Ratio
 BreakEven Ratio = (Debt Service + Operating Expenses) / Gross Operating Income
 Return on Equity (ROE)
 Method One: ROE = Cash Flow after Taxes / Initial Cash Investment
Method Two: ROE = Cash Flow after Taxes / (Resale Value less Mortgage Balance)  LoantoValue Ratio (LTV)
 LTV = Loan Amount / Lesser of Property's Appraised Value or Actual Selling Price
 Points
 Points are fees paid to the mortgage lender as a premium for making the loan. It is basically prepaid interest on the load. One point equals 1%. The formula is as follows:
1 Point = Mortgage Loan Amount / 100
Dollar Amount of Points Paid = Mortgage Loan Amount x No. Points / 100  Mortgage Payment/Mortgage Constant
 The actual formula is a bit complicated but I will list it for reference:
Payment = (PV x I)  (1  [1 + I] ^  N)
where I = Interest, N = number of periods.  Mortgage Constant
 This is iterative in nature and will be covered in later on, but you think of it as the Monthly Mortgage Payment per $1
 Mortgage Payment (Preferred Method)
 Use Excel or my favorite Google Sheets and inside one of the spread sheets cells enter the PMT function as follow:
=PMT(Periodic Rate, Number of Periods, Present Value)
Replace the above words within the formula with actual numbers
 Interest portion of a payment = Outstanding Principal Balance x Periodic Rate
 Principal Portion of a payment = Payment amount less Interest portion
 Original Basis (Purchase Price)
 plus Capital Additions
 plus Costs of Sale
 less Cumulative Depreciation, Real Estate
 less Cumulative Depreciation, Capital Additions
 = Adjusted Basis
 Selling Price
 less Adjusted Basis
 = Gain on Sale