24.2 Real Estate Applications

This section connects the “basic math” skills to real real estate tasks—measurements, acreage from legal descriptions, commissions,
contract calculations, appraisal adjustments, finance ratios, investment returns, property taxes, and closing prorations.
The key is to write the formula first, then plug in the numbers.

Legal Descriptions (Chapter 9): Measures + Acreage from Fractions

Linear measures (U.S.):

• 1 foot = 12 inches
• 1 yard = 3 feet = 36 inches
• 1 mile = 5,280 feet = 1,760 yards = 320 rods
• 1 rod = 16.5 feet

Area measures:

• 1 square yard = 9 square feet
• 1 acre = 43,560 SF
• 1 section = 1 mile × 1 mile = 640 acres
• 1 township = 6 miles × 6 miles = 36 sections

Metric conversions (common):

• 1 inch = 2.54 cm
• 1 foot = 30.48 cm = 0.3048 m
• 1 mile ≈ 1.60 km
• 1 kilometer ≈ 0.621 mile

Listing Agreements (Chapter 12): Commissions

• Total commission: sale price × commission rate
• Co-brokerage commission: total commission × split rate
• Agent commission: broker’s commission × agent split rate

Brokerage Business (Chapter 13): Goodwill

Goodwill is the “extra” paid beyond tangible assets—often tied to brand, reputation, systems, and client relationships.

Sales Contracts (Chapter 14): Percent of List + Deposits + Rent Escalations + FIRPTA

• Percent of listing price: offer ÷ listing price
• Earnest money deposit: listing price × required percentage
• Rent escalation: new rent = current rent × (100% + escalation rate)(Example: 5% increase means multiply by 105% or 1.05.)
• FIRPTA withholding: gross proceeds × 15%

Appraisal (Chapter 16): Adjusting Comparables + CMA

A CMA typically involves selecting comparables, making adjustments to the comparables, and then reconciling/weighting the adjusted values
to estimate the subject’s value.

Income Capitalization (Value from Income)

• GRM: gross rent × multiplier = value
• GIM: gross annual income × GIM = value
• Net income capitalization: NOI ÷ cap rate = value

Finance (Chapter 17): Interest, LTV, Underwriting Ratios, Points

• Interest-only loans: Interest payment (I) = Principal (P) × Rate (R)Monthly interest = annual interest ÷ 12
• LTV: loan amount = market value × LTVor LTV = loan amount ÷ market value
• Income ratio (PITI): Conventional uses about 25–28%; FHA uses 31% (per chapter examples)
• Debt ratio: Conventional: (36% × income) − monthly debt; FHA: (43% × income) − monthly debt
• Points: 1 point = 1% of the loan amount

Investments (Chapter 18): Appreciation, Equity, Cash Flow, Returns

• Appreciation: current value − original price
• Equity: current value − current loan amount
• Pre-tax cash flow: NOI − debt service
• ROI: NOI ÷ price
• Cash-on-cash: cash flow ÷ cash invested
• ROE: cash flow ÷ equity

Taxation (Chapter 19): Millage, Tax Bills, Special Assessments

• Tax rate (millage): tax requirement ÷ tax base
• Taxable value: assessed value − exemptions
• Tax bill: taxable value × mill rate (for each authority), then add them up
• Special assessment: total cost × property’s prorated share

Closings (Chapter 21): Prorations (Advance vs. Arrears)

Prorations allocate income/expenses between buyer and seller based on the closing date.
The big exam trap is mixing up paid in advance vs. paid in arrears.

Quick Check-In (2 Questions)