Real Estate Mathematics

Exam rule

A percent means parts per hundred. Change 6 percent to 0.06 before multiplying. Every percent problem has a whole, a rate and a part. Part equals whole times rate. Whole equals part divided by rate. Rate equals part divided by whole. First identify the whole. Commission uses the sale price unless the facts name another base. Gross commission equals sale price times commission rate. A salesperson's share is then found from the gross commission, not from the sale price. Net after commission equals sale price minus gross commission when no other costs are included. Required sale price equals desired net divided by one minus the commission rate, again when other costs are ignored. Profit or loss equals selling price minus original cost. Percentage change equals the change divided by the original value. A later value after appreciation equals original value times one plus the rate. A later value after depreciation equals original value times one minus the rate. To work backward, divide the later value by the correct factor. Always label the base before using the calculator.

Exam rule

Simple interest does not compound. Interest equals principal times annual rate times time in years. Use the letters I, P, R and T if that helps. Principal equals interest divided by rate times time. Rate equals interest divided by principal times time. Time equals interest divided by principal times rate. Put parentheses around the two factors in the divisor. Convert months to years by dividing by 12. Use the day-count method stated in the question. For a 360-day year, divide days by 360. For an actual-year problem, use the stated 365 or 366 days. A point equals 1 percent of the loan amount, not the sale price. Points cost equals loan amount times the number of points times 0.01. An origination point is a lender charge. A discount point is paid in return for a reduced interest rate. Do not mix the one-time point charge with interest earned or paid over time.

Exam rule

Keep linear units separate from square units. Perimeter is the distance around a shape and stays in feet. Rectangle area equals length times width. Triangle area equals base times height divided by two. Trapezoid area equals the sum of the parallel sides times the height divided by two. For an L-shaped or irregular lot, split it into simple shapes. Add the pieces, or find a large rectangle and subtract the missing part. One acre is 43,560 square feet. One hectare is exactly 10,000 square meters and is about 2.471 acres. A front foot is one foot along the street or other stated frontage. Front-foot pricing equals price per front foot times frontage. It is not an area calculation. Price per square foot equals price divided by square feet. Price equals square feet times price per square foot. Square feet equals price divided by price per square foot. Write the unit beside every answer.

Exam rule

Loan-to-value, or LTV, equals loan amount divided by the value used by the lender. Loan amount equals value times LTV. Value equals loan amount divided by LTV. In a purchase question, use the lower of the price or appraised value when the facts say the lender follows that rule. If price and value match, down payment percent plus LTV equals 100 percent. Mortgage qualification usually starts with gross monthly income. Divide annual income by 12. The front ratio equals the proposed monthly housing expense divided by gross monthly income. Housing expense often includes principal, interest, property taxes and insurance, called PITI. Include association dues or another housing cost when the problem says to. The back ratio equals total monthly debt divided by gross monthly income. To find limits, multiply gross monthly income by each supplied ratio. Subtract existing monthly debt from the back-ratio limit. The allowed housing payment is the lower result. Ratio limits vary by loan and lender, so use the figures in the question.

Exam rule

A proration divides income or an expense as of closing. First decide whether the item is accrued or prepaid. An accrued expense is owed but not yet paid. The seller is usually debited for the seller's share, and the buyer is credited because the buyer will pay later. A prepaid expense was already paid by the seller. The buyer is usually debited for the buyer's future share, and the seller is credited. Rent collected in advance can reverse the direction because the seller may owe the buyer the rent for the buyer's ownership period. Next read the day-count rule. A statutory or actual method uses the actual days named in the problem. A 360-day method uses twelve 30-day months. Some questions assign the closing day to the buyer. Others assign it to the seller. Count it only as directed. Find the daily or monthly amount, multiply by the assigned period and keep debit and credit equal.

Exam rule

Real property tax is based on taxable assessment, not directly on sale price. In the usual exam model, assessed value equals market value times the level of assessment, or LOA. Taxable assessment equals assessed value minus allowed exemptions. A tax levy is the amount a taxing jurisdiction must raise after subtracting other revenue from its budget. A rate per $1,000 equals the levy divided by total taxable assessed value, then multiplied by 1,000. A parcel's tax equals its taxable assessment times the rate, divided by 1,000. Add town, county, school and other supplied rates before using a combined rate. New York generally requires a uniform percentage within an assessing unit. New York City and Nassau County are special assessing units that may use different fractional levels within property classes. An equalization rate compares a municipality's total assessed value with its total market value. It helps compare assessing units. For exam arithmetic, estimated full value equals assessed value divided by the equalization rate. That estimate is not an appraisal of one parcel.

Exam rule

New York State real estate transfer tax applies when consideration exceeds $500. The base rate is $2 for each $500, or fractional part of $500. Divide consideration by $500, round any fraction up and multiply by $2. At exact $500, the state tax does not apply because the law says exceeds $500. The base rate is often described as 0.4 percent, but rounding a fractional unit can make the exact tax slightly higher. The grantor, usually the seller, pays the base tax and any additional base tax. If the seller fails to pay or is exempt, the buyer must pay. An additional 1 percent mansion tax applies to qualifying residential property at $1 million or more. The buyer pays that additional tax unless the buyer fails to pay or is exempt. New York City has more state transfer taxes for certain large deals. The additional base tax starts at $3 million for residential property and $2 million for other property. A supplemental residential tax starts at $2 million and uses rates from 0.25 percent through 2.9 percent. Use the current rate supplied in a problem because the property type, location and price matter.

Exam rule

Mortgage recording tax is charged for recording a mortgage on New York real property. It follows the mortgage debt or obligation secured, not the purchase price. The statewide pieces are a basic tax of 50 cents per $100 and a special additional tax of 25 cents per $100. Another additional tax is 25 cents per $100, or 30 cents per $100 in the Metropolitan Commuter Transportation District. That additional tax does not apply where it has been suspended. New York City, Yonkers and various counties add local tax. Current combined rates therefore vary by location and, in New York City, by property type and mortgage amount. Use the combined rate supplied in the question. If the rate is quoted per $100, divide the debt by $100 and multiply by the rate. For a one-family or two-family residence, subtract the first $10,000 of principal only when computing the additional tax. Do not subtract it from the basic or special additional tax.

Exam rule

Start an income statement with potential gross income, or PGI. It assumes full occupancy and full collection. Add other property income when the facts include it. Subtract vacancy and collection loss to get effective gross income, or EGI. Subtract operating expenses to get net operating income, or NOI. Operating expenses can include management, repairs, utilities paid by the owner, insurance and property tax. Debt service, depreciation, capital improvements and the owner's income tax are not operating expenses in this formula. Use the IRV relationship for direct capitalization. Income equals rate times value. Value equals NOI divided by the capitalization rate. Rate equals NOI divided by value. A gross rent multiplier, or GRM, uses gross rent and ignores expenses. Value equals rent times GRM. GRM equals value divided by rent. Match the period. Monthly rent needs a monthly GRM, and annual rent needs an annual GRM. Vacancy rate equals vacant units or lost rent divided by the possible total. Operating expense ratio equals operating expenses divided by EGI.