6.3 Real Estate Math and Calculations

Commissions, Area, and Acreage

Most real estate math is the percentage relationship Part = Total x Rate. Cover the unknown in the T-bar to find it.

Commission example. A home sells for $360,000 at a 6% total commission. Total commission = $360,000 x 0.06 = $21,600. If the listing and selling brokers split 50/50, each brokerage gets $10,800. If the selling agent then keeps 70% of their brokerage's share: $10,800 x 0.70 = $7,560.

Area and acreage. Memorize 1 acre = 43,560 square feet. To find area of a rectangle: length x width.

• A lot measures 220 ft x 198 ft = 43,560 sq ft = exactly 1 acre.
• A 5-acre parcel = 5 x 43,560 = 217,800 sq ft.
• A lot of 130,680 sq ft / 43,560 = 3 acres.

For square footage of a rectangular building 40 ft x 60 ft = 2,400 sq ft; at a construction cost of $145/sq ft, that is 2,400 x $145 = $348,000.

Prorations, LTV, and Discount Points

Prorations split recurring costs at closing. The exam uses two day-count conventions:

Proration example (banker's). Annual taxes are $3,600, unpaid, and closing is on the last day of April (4 months elapsed: Jan-Apr). Daily rate = $3,600 / 360 = $10/day. Seller owes 4 x 30 = 120 days x $10 = $1,200, debited to the seller and credited to the buyer.

Loan-to-value (LTV) and down payment. LTV = loan / value. A buyer puts $60,000 down on a $300,000 home: loan = $240,000, so LTV = 240,000 / 300,000 = 80%. If a lender allows 90% LTV on a $250,000 purchase, the maximum loan is $225,000 and the down payment is $25,000.

Discount points. One point = 1% of the LOAN amount (not the sale price). On a $240,000 loan, 2 points = $240,000 x 0.02 = $4,800. Points are prepaid interest that buy down the rate. A common trap: applying the point percentage to the purchase price instead of the loan.

Profit, Loss, Percentage Change, and Transfer Taxes

Profit/loss and percentage of change use the made/paid relationship: New = Old x (1 +/- rate).

• An investor buys at $200,000 and sells at $250,000. Profit = $50,000; percent gain = 50,000 / 200,000 = 25%.
• A property appreciated 20% to a value of $360,000. Original value = 360,000 / 1.20 = $300,000 (divide by 1 + rate to undo the increase).
• A home worth $400,000 lost 15%: 400,000 x 0.85 = $340,000.

Transfer taxes (documentary stamps) are charged per increment of price. If the rate is $0.50 per $500 of price on a $300,000 sale: $300,000 / $500 = 600 increments x $0.50 = $300.

Equity is value minus debt. A home worth $420,000 with a $260,000 mortgage balance has equity = 420,000 - 260,000 = $160,000. As the loan amortizes and value appreciates, equity grows—useful for refinance and LTV questions.

Income-Property Math and Property Taxes

Income-property questions revolve around Net Operating Income (NOI) = effective gross income - operating expenses (NOI excludes debt service and income tax).

Capitalization rate. The relationship is Value = NOI / Cap Rate, and rearranged, Cap Rate = NOI / Value.

• A building has NOI of $48,000 and the market cap rate is 8%. Value = 48,000 / 0.08 = $600,000.
• If that building is listed at $800,000 with the same $48,000 NOI, cap rate = 48,000 / 800,000 = 6% (a lower cap rate means a higher price for the same income).

Gross Rent Multiplier (GRM). GRM = price / gross (annual or monthly) rent. A $480,000 property renting for $4,000/month: GRM = 480,000 / 4,000 = 120 (monthly GRM). To value a comparable renting at $3,800/month: 3,800 x 120 = $456,000.

Property taxes and mills. A mill is $1 per $1,000 of assessed value, i.e., 0.001. Divide the millage rate by 1,000 before multiplying.

• Assessed value $250,000 at 30 mills: 250,000 x (30 / 1,000) = 250,000 x 0.030 = $7,500/year.
• A $4,500 annual tax bill on a $300,000 assessment implies a rate of 4,500 / 300,000 = 0.015 = 15 mills.

Assessed Value vs. Market Value

Property tax is levied on assessed value, which can differ from market value. Many jurisdictions assess at a fraction of market value called the assessment ratio. If a $400,000 market-value home is assessed at a 40% ratio, the assessed value is $160,000, and the tax applies to that figure—not the full $400,000. Exemptions (such as a homestead exemption) are subtracted from assessed value before applying the rate.

A Quick Word Problem Workflow

For any exam math item: (1) identify what is asked—area, dollars, percent, or rate; (2) write the matching formula; (3) convert units (months to days, percent to decimal, mills divided by 1,000, acres to square feet); (4) plug in and compute; (5) sanity-check the magnitude. For instance, a question asking the monthly payment from an annual figure requires dividing by 12, and an interest question converts the annual rate to the period in question. Watching units prevents the most common errors—applying a point percentage to the price instead of the loan, or forgetting that one acre is 43,560 square feet.