Real Estate Mathematics and Valuation
The Three Approaches
Sales comparison (most reliable for residential), cost approach (reproduction/replacement cost less depreciation plus land value; best for special-purpose or new property), and income approach (capitalization; best for income property). Know that appraised value is an opinion, not a guarantee.
Income Approach
Value = Net Operating Income ÷ Capitalization Rate. NOI = effective gross income − operating expenses (excluding debt service and income taxes). Traps: including mortgage payments in NOI, and confusing gross rent multiplier (GRM = price ÷ gross rent) with cap rate.
Depreciation and Costs
Distinguish physical deterioration (curable/incurable), functional obsolescence, and external/economic obsolescence. Cost approach: value = replacement cost − depreciation + land value.
Commission and Percentage Math
Commission = sale price × rate. If a broker splits with a cooperating broker, total commission still equals the rate on the price. Understand proration for taxes and rent (usually based on days in the month or year) and the difference between assessed value and market value.
Worked Example
A property produces $48,000 NOI; the market cap rate is 8%. Value = 48,000 ÷ 0.08 = $600,000. If a 6% commission is paid, the broker receives $36,000, split per the agreement.
Rule of Thumb
Identify what is being asked (value, rate, or income) and rearrange the formula before computing.