Analyzing Deal Skills – Math Skills
📊 Analyze Deal Skills — Math Skills
The Numbers That Drive Every Profitable Real Estate Deal
Real estate finance, by its very nature, requires mathematical calculations. The numbers most often manipulated in this field are dollar amounts of principal, interest, payments, property taxes, income taxes, insurance premiums, assessment charges, depreciation, discounts, returns on and of investments, and other indicators of the advisability, stability, and profitability of investments.
When purchasing a home, most buyers are initially concerned with the amount of cash down payment required. Next, they look at the amount of monthly payments, including costs of utilities, as an indication of their ability to afford the property. Commercial property purchasers have additional concerns, including cash flow and breakeven analyses used to estimate the returns on and of their investments.
This guide covers the methods of computing various forms of interest, the time value of money, alternative loan repayment schedules, measurements of profitability, and discounting of mortgages and trust deeds.
📑 Table of Contents
Chapter 1: Introduction — Why Real Estate Math Matters
Real estate finance requires mathematical calculations. The numbers most often manipulated include principal, interest, payments, property taxes, income taxes, insurance premiums, assessment charges, depreciation, discounts, and returns on investments.
Tools of the Trade
- Basic calculator: A nonprogrammable calculator is sufficient for most problems.
- Financial calculator: Preprogrammed with formulas for amortization schedules — invaluable for complex analysis.
- Interest factor tables: Provided throughout this guide for quick reference.
Chapter 2: Basic Math Review
Percentages
A percentage must be converted to a decimal before any mathematical computations can be completed. Move the decimal point two spaces to the left.
| Percentage | Decimal |
|---|---|
| 50% | 0.5 |
| 3% | 0.03 |
| 115% | 1.15 |
To convert a decimal to a percentage, move the decimal point two spaces to the right:
- 1.43 = 143%
- 0.03 = 3%
Fractions
A fraction is composed of a numerator (top) and a denominator (bottom). To convert a fraction to a decimal, divide the numerator by the denominator.
| Fraction | Decimal |
|---|---|
| 4/5 | 0.8 |
| 1/2 | 0.5 |
| 3/4 | 0.75 |
Chapter 3: Area and Land Measurements
Basic Units of Land Measurement
| Unit | Equivalent |
|---|---|
| Township | 36 square miles (36 sections) |
| Section | 640 acres or 1 square mile |
| Half Section | 320 acres |
| Quarter Section | 160 acres |
| Quarter of a Quarter | 40 acres |
| Acre | 43,560 sq. ft. |
| Mile | 5,280 ft. |
| Square Mile | 27,878,400 sq. ft. or 640 acres |
Area Formulas
- Rectangle or Square: Area = Length × Width
- Triangle: Area = (Base × Height) ÷ 2
Sample Problems
Problem 1: A rectangular lot is 1,230 ft by 2,340 ft. What is the area in acres?
Solution: Area = 1,230 × 2,340 = 2,878,200 sq. ft.
2,878,200 ÷ 43,560 = 66 acres
Problem 2: A rectangular lot is 10 acres. Length is 500 ft. What is the width?
Solution: 10 acres = 435,600 sq. ft.
435,600 ÷ 500 = 871.2 ft.
Problem 3: A triangular lot has a 200 ft base and 150 ft height.
Solution: Area = (200 × 150) ÷ 2 = 15,000 sq. ft.
Irregular Lots
Divide the irregular lot into squares, rectangles, and triangles. Compute each area and add them.
Example: A lot composed of a 50×50 square, a 30×25 rectangle, and a 40×30 triangle:
- Square: 2,500 sq. ft.
- Rectangle: 750 sq. ft.
- Triangle: 600 sq. ft.
- Total: 3,850 sq. ft.
Chapter 4: The Percentage Formula in Real Estate
The Three-Way Formula System
When using this system, one item equals the other two. Place one item in the top half of the circle, and the other two in adjacent quarters of the bottom half.
| Formula | Equation |
|---|---|
| Interest | Rate × Principal |
| Income | Rate × Value |
| Area | Width × Length |
| Commission | Rate × Sales Price |
| Net Operating Income | Capitalization Rate × Value |
Commission Calculations
Problem 1: A broker earns a 3% fee on a $100,000 home.
Solution: Fee = 0.03 × $100,000 = $3,000
Problem 2: An agent shares 40% of a 3% fee on a $245,000 sale.
Solution: Broker’s fee = 0.03 × $245,000 = $7,350
Agent’s share = 0.40 × $7,350 = $2,940
Problem 3: A 6% fee is split 50-50. You receive 70% of your broker’s share on a $149,500 sale.
Solution: Total fee = 0.06 × $149,500 = $8,970
Seller’s broker fee = 0.50 × $8,970 = $4,485
Your share = 0.70 × $4,485 = $3,139.50
Selling Price and Cost Rules
Selling Price Rule: Subtract the percentage of profit desired from 100%, then divide the cost by the remainder.
Example: Joe wants 10% profit on a lot costing $60,000 plus $460 closing costs.
100% – 10% = 90%
$60,460 ÷ 0.90 = $67,177.78
Cost Rule: Add the percentage of profit desired to 100%, then divide the selling price by the total percentage.
Example: Mayhem sold property for $90,000 and made 15% profit.
100% + 15% = 115%
$90,000 ÷ 1.15 = $78,260.87
Chapter 5: Interest and Loan Calculations
Simple Interest
Formula: I = PRT (Interest = Principal × Rate × Time)
Example: $1,200 loan at 8% for one year.
I = $1,200 × 0.08 × 1 = $96
Add-On Interest
Interest is computed on the total amount of the loan for the entire time period, then added to principal before calculating payments.
Example: $1,200 at 8% add-on for one year.
Total interest = $96
Total owed = $1,296
Monthly payment = $1,296 ÷ 12 = $108
Add-On Interest Rate Formula:
AIR = (2 × I × C) ÷ (P × (n + 1))
Where: I = number of installment payments per year; C = total loan charge; P = principal; n = number of installments
Example: $1,200 loan, $96 charge, 12 monthly payments.
AIR = (2 × 12 × $96) ÷ ($1,200 × 13) = $2,304 ÷ $15,600 = 14.77%
Nominal vs. Effective Rate
- Nominal Rate: The rate contracted for.
- Effective Rate: The actual rate paid by the borrower.
An 8% add-on rate has a nominal rate of 8% but an effective rate of approximately 15%.
Banker’s 12%-30 Day / 6%-60 Day Method
To find interest for 30 days at 12% or 60 days at 6%, move the decimal point two places to the left.
Example: $8,432.67 at 12% for 30 days = $84.33
Chapter 6: Compound Interest and the Time Value of Money
Compound Interest
Compound interest is interest paid on interest earned.
CS = BD(1 + i)n
Example: $1,000 for 10 years at 6% compounded annually.
CS = $1,000(1.06)10 = $1,000(1.79084) = $1,790.84
Compound Worth of an Annuity
A series of regular payments or receipts is an annuity.
Example: $1 deposited at beginning of each year for 3 years at 6%.
CS = $1[(1.06)2 + (1.06)1 + 1] = $1[1.1236 + 1.06 + 1] = $3.18
Present Worth of a Dollar
PW = A × 1/(1 + i)n
Example: $1,000 to be received 10 years from today at 6%.
PW = $1,000 × 0.55839 = $558.40
Present Worth of an Annuity
Example: $1 per year for 3 years at 6%.
PWA = $1[0.8396 + 0.8899 + 0.9433] = $2.67
Interest Factors (IF)
Tables of interest factors are available for various rates and periods.
| Formula | Equation |
|---|---|
| Compound sum of $1 | CS = BD(IF) |
| Compound worth of annuity | CA = RD(IF) |
| Present worth of $1 | PW = A(IF) |
| Present worth of annuity | PWA = RA(IF) |
Chapter 7: Amortization and Mortgage Payments
Amortization
The systematic repayment of a loan through regular level payments that include both principal and interest.
Annual Payments
RA = PWA / IF
Example: $7,360 loan at 6% for 10 years.
RA = $7,360 ÷ 7.3600 = $1,000 per year
Monthly Payments
Example: $20,000 loan at 6% for 300 months.
RA = $20,000 ÷ 155.20686 = $128.86 per month
Loan Constants
A loan constant expresses the relationship between regular level payments and the total loan amount as an annual percentage rate.
Example: $20,000 loan with $128.86 monthly payment.
Loan constant = ($128.86 × 12) ÷ $20,000 = 7.74%
Distribution of Principal and Interest
Example: $20,000 loan at 6% for 25 years, monthly payment $128.86.
- First payment: $100 interest, $28.86 principal
- Second payment: $99.85 interest, $29.01 principal
Total Interest Costs
Example: $100,000 loan at 8% for 30 years.
- Monthly payment = $734.17
- Total payments = $264,301.20
- Total interest = $164,301.20
Opportunity Cost
The cost of paying cash instead of investing.
Example: $100,000 invested at 5% for 30 years grows to $432,194.
Opportunity cost = $432,194 – $164,301 = $267,893
Chapter 8: Prequalifying Buyers
Prequalifying Worksheet
- Annual Income ÷ 12 = Gross Monthly Income (GMI)
- GMI × Housing Ratio % = Maximum Housing Payment
- GMI × Total Debt Ratio % = Maximum Total Debt Payment
- Total Monthly Debt Payments
- Subtract Line 4 from Line 3
- Enter lesser of Line 2 or Line 5 = Maximum Monthly PITI + Payment
- Escrow for Taxes and Insurance (TI)
- Multiply Line 6 by 25% (ave.) or use actual figures
- Subtract Line 7 from Line 6 = Maximum Principal and Interest Payment
- Divide Line 8 by rate factor
- Multiply Line 9 by $1,000 = Maximum Mortgage Amount
- Cash available for Down Payment
- Add Line 11 to Line 12 = Affordable Price Range
Chapter 9: Investment Property Analysis
Net Operating Income (NOI)
Rental income minus operating expenses.
Capitalization Rate (Cap Rate)
The rate of return an investor expects on their investment.
V = I / R
Where: V = Value; I = Net Annual Income; R = Rate
Example: $20,000 net annual cash flow at 10% cap rate.
V = $20,000 ÷ 0.10 = $200,000
Breakeven Analysis
The point at which gross income equals total fixed costs plus variable costs.
BE = FC ÷ (1 – VCR)
Example: Fixed costs $100,000, variable cost ratio 20%.
BE = $100,000 ÷ (1 – 0.20) = $125,000
Return on Investment (ROI)
The ratio of pre-tax net income to money invested.
Example: $0.20 return on $1 investment = 20% ROI
Net Present Worth (NPW) Method
A discounted cash flow technique to analyze the present value of an investment.
Example: $20,000 net annual income for 15 years, residual value $100,000, required return 15%.
NPW = $20,000 × 5.84737 + $100,000 × 0.122894
NPW = $116,947.40 + $12,289.40 = <strong
