8.3 Proration, Transfer Tax, and Investment Math

Proration: the two-step daily-rate method

Proration splits a recurring cost (property taxes, prepaid rent, HOA dues, interest) fairly between buyer and seller at closing. The method is always the same:

1. Find the daily rate = annual amount / number of days in the period.
2. Multiply the daily rate by the number of days each party is responsible.

Exams use either a statutory/banker's year of 360 days (12 months of 30 days) or an actual 365-day year; the question will tell you or imply which. A common phrasing is "prorate as of the day of closing," and unless told otherwise, the seller usually owns the closing day. Compute the daily rate to several decimals and round only the final dollar figure.

Worked proration: taxes paid in arrears

In most states property taxes are paid in arrears, meaning the bill for the year is paid after the period, so at closing the seller owes the buyer for the days the seller owned but has not yet paid.

Example: Annual taxes are $3,600. Closing is on the 90th day of the year using a 360-day year, seller responsible through closing day.

• Daily rate = $3,600 / 360 = $10.00 per day
• Seller's days = 90
• Seller's share = 90 x $10.00 = $900

Because taxes are in arrears and unpaid, this $900 is a debit to the seller and a credit to the buyer, since the buyer will later pay the full-year bill. If taxes had been prepaid, the direction reverses: the seller would be credited for the days after closing.

Transfer tax: read the increment

A transfer (conveyance) tax is charged on the sale price in fixed increments, commonly per $500 or per $100 of price. Read the increment carefully before computing, because using the wrong one is the built-in trap.

Example at $0.50 per $500: A $250,000 sale has $250,000 / $500 = 500 increments. Tax = 500 x $0.50 = $250.

Example at $1.10 per $1,000: A $250,000 sale has 250 increments of $1,000. Tax = 250 x $1.10 = $275.

If the price does not divide evenly, most statutes round the increment count up to the next whole increment. South Dakota imposes a real estate transfer fee of $0.50 per $500 of value (with certain statutory exemptions), so the first example mirrors the state's own rate.

Investment math: GRM, NOI, and cap rate

Income-property questions use a small set of formulas:

Gross Rent Multiplier: a property priced at $480,000 with $48,000 annual gross rent has a GRM of 480,000 / 48,000 = 10.

NOI excludes mortgage payments (debt service) and income tax but subtracts operating expenses like taxes, insurance, and maintenance. If gross income is $90,000 and operating expenses are $36,000, NOI = $90,000 - $36,000 = $54,000.

Cap-rate inversion and ROI

The cap-rate formula is the workhorse of investment questions because it moves in three directions. Given any two of value, NOI, and cap rate, solve for the third:

• Cap rate = NOI / value -> $54,000 / $600,000 = 9%
• Value = NOI / cap rate -> $54,000 / 0.09 = $600,000
• NOI = value x cap rate -> $600,000 x 0.09 = $54,000

When NOI rises and the market cap rate stays constant, value rises proportionally, which is why investors prize income growth.

Return on investment (ROI) measures return against the cash actually invested, not the full price: ROI = annual return / cash invested. An investor who nets $12,000 a year on $150,000 of cash invested earns $12,000 / $150,000 = 8% ROI. Choosing the correct day-count for prorations, the right transfer-tax increment, and inverting the cap-rate formula correctly will resolve the closing and investment questions in this section.

Choosing the day-count and arrears convention

Proration errors almost always trace to two decisions made at the start of the problem. The first decision is the day-count basis: a statutory or banker's year treats every month as 30 days for a 360-day year, while an actual-year basis uses 365 days and the true length of each month. The problem usually signals which to use; when it says "banker's year" or "30-day months," divide the annual amount by 360.

The second decision is the arrears versus prepaid direction. Taxes paid in arrears mean the seller has used time without paying, so the seller is debited and the buyer credited; prepaid items reverse that. The third small decision is who owns the closing day, which the problem states and which shifts the count by one day.

Lock in these three choices before you compute the daily rate, because a correct daily rate applied with the wrong direction or day-count still produces a wrong answer. Re-reading the convention sentence twice is faster than redoing the arithmetic.

Reading transfer-tax increments and investor ratios

Transfer-tax questions hinge on the increment the statute uses. A rate quoted "per $500" requires dividing the price by 500 before multiplying by the per-increment charge, while a rate "per $1,000" or "per $100" changes the divisor entirely. Misreading the increment is the built-in trap, so circle the increment first. When the price does not divide evenly, most statutes round the increment count up to the next whole unit, never down.

Investor questions reward fluency with a few ratios. The gross rent multiplier is a fast screen found by dividing price by gross rent, but it ignores expenses, so it is rougher than a cap rate. Net operating income subtracts operating expenses from effective gross income but never subtracts the mortgage payment or income tax. The capitalization rate then connects income and value in both directions, so given any two of value, NOI, and cap rate you can solve for the third.

Pairing the right increment with the right ratio, and remembering that NOI excludes debt service, answers the transfer-tax and investment questions in this section.