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, McGraw-Hill 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
Cash-on-Cash Return
Cash-on-Cash 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
Re-characterize 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
Break-Even Ratio
Break-Even 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)
Loan-to-Value 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
Principal Balance/Balloon Payment
This is iterative. Will be discussed later on.
Principal and Interest per Period
See Principal Balance
  • Interest portion of a payment = Outstanding Principal Balance x Periodic Rate
  • Principal Portion of a payment = Payment amount less Interest portion
Maximum Loan Amount
Maximum Loan Amount = NOI / Minimum Debt Coverage Ratio / Mortgage Constant (annual)
Property Taxes
Property Taxes = Assessed Value x Tax Rate
Appraised Value
Appraised Value = Assessed Value / Assessment Ratio
Adjusted Basis
  • Original Basis (Purchase Price)
  • plus Capital Additions
  • plus Costs of Sale
  • less Cumulative Depreciation, Real Estate
  • less Cumulative Depreciation, Capital Additions
  • = Adjusted Basis
Depreciation
Depreciation Allowance (annual) = Depreciable Basis / Useful Life
Gain on Sale
  • Selling Price
  • less Adjusted Basis
  • = Gain on Sale
Acres to Square Feet
Acres x 43,560
Square Feet to Acres
Square feet x 0.000023 (or divide by 43,560)
Acres to Square Meters
Acres x 4046.86
Square Meters to Acres
Square Meters x 0.000247
Acres to Square Miles
Acres x 0.0015625
Square Miles to Acres
Square Miles x 640
Square Meters to Square Feet
Square Meters x 10.76391
Square Feet to Square Meters
Square Feet x 0.092903
Meters to Feet
Meters x 3.2808399
Feet to Meters
Feet x 0.3048
Gross Building Area (GBA)
Total area of all floors, including basement
Usable Square Footage (Occupied Space aka USF)
GBA - Common Area
Rentable Square Feet
USF + portion of Common Area