Appraisal Mathematics, Statistics, and Valuation Tools
Core tools
Key tools include compound interest, present value, direct capitalization (value equals NOI divided by cap rate), gross rent multipliers, percentage adjustments, and cash-equivalent analysis. Descriptive statistics such as mean, median, mode, range, and standard deviation summarize comparable data. Regression and paired analysis support adjustment derivation, while sensitivity analysis tests how value changes with a key input.
Traps
Median resists outliers better than mean; cap rates move inversely with value; NOI is before debt service; monthly and annual rates must match. A GRM applies to gross rent, not NOI. Percentage adjustments apply to the sale price, and order matters when adjustments compound. Do not confuse net operating income with cash flow after financing.
Worked example
NOI is $60,000 and the cap rate is 8 percent. Value equals $60,000 divided by 0.08, or $750,000. If the cap rate rises to 9 percent, value falls to $666,667. Rule of thumb: when asked for value, divide income by rate; when asked for rate, divide income by value.