Real Estate Mathematics and Valuation
Math that shows up
Real estate math rewards unit analysis. Know area (length × width), front-foot and square-foot value, commission (gross price × rate), loan-to-value (loan ÷ price or value), points (loan amount × point rate), and proration (annual amount ÷ 365 × days). Income capitalization uses value = net operating income ÷ cap rate; the gross rent multiplier uses price ÷ gross rent.
Valuation
Appraisers use three approaches: sales comparison (most common for homes), cost (replacement cost less depreciation plus land), and income (cap rate or GRM). Market value assumes a willing buyer and seller, no undue pressure, and reasonable exposure. Traps: using monthly income where annual is required; applying points to sale price instead of loan amount; prorating with a 360-day year when the problem says 365; and treating assessed value as market value. For commissions, compute on gross sale price, then split by brokerage agreement before applying salesperson splits.
Worked example
A property produces $48,000 annual net operating income. The market cap rate is 8%. Value = $48,000 ÷ 0.08 = $600,000. If the buyer pays $620,000, the implied cap rate is $48,000 ÷ $620,000 = 7.74%, a lower return. Rule of thumb: for income property, NOI ÷ cap rate = value; for prorations, annual ÷ 365 = daily unless stated otherwise.