8.3 Proration, Transfer Tax, and Investment Math

Proration basics

At closing, costs paid for the whole year (taxes, prepaid rent, interest) are divided between seller and buyer based on who owns the property each day. The method:

1. Find the annual (or monthly) amount.
2. Divide to a daily rate.
3. Multiply by the days owned by the party being charged or credited.

Many exams use a 360-day year (12 months of 30 days), the banker's year. The seller usually owns the day of closing unless the question states otherwise.

Worked example: tax proration

Annual taxes are $3,600, already paid by the seller. Closing is on the last day of April; the seller occupied Jan 1 through April 30 = 4 months.

• Daily/monthly: $3,600 / 12 = $300 per month
• Seller's share = 4 x $300 = $1,200
• Buyer reimburses the seller for the remaining $2,400 (prepaid year).

On the closing statement, a credit to one party is a debit to the other - the totals must balance. Read whether the closing date is charged to the buyer or the seller; conventions vary, and the exam will state which to use. When in doubt, the seller is responsible through the day of closing.

Formula Quick-Reference

Keep these proration and investment formulas straight; the exam rewards picking the right one for the question type:

The most common error is mixing a monthly rate with a daily day-count, or using a 365-day year when the problem specifies 360 (or vice versa). Always confirm the year convention before dividing.

Day-count detail

When the problem gives a daily rate, use a 360-day year unless told to use 365.

Worked example: unpaid taxes (debit seller, credit buyer)

Annual taxes $2,920 are unpaid at closing. Closing is on day 90 of the year (end of March, 30-day months). The seller owes for the days owned.

• Daily rate = 2,920 / 360 = $8.111 per day
• Seller's 90 days = 90 x 8.111 = $730.00
• This is a debit to the seller and a credit to the buyer (buyer will pay the full bill later).

Trap: Decide who pays based on whether the bill is prepaid or in arrears. Prepaid -> buyer reimburses seller. In arrears (unpaid) -> seller credits buyer.

Transfer and recordation taxes

State and local transfer taxes are charged as a rate per increment of price - commonly per $500 or per $100. Round the price up to the next full increment before applying the rate.

Worked example

A $268,000 property in a jurisdiction that charges $3.50 per $500 of price:

• Increments = 268,000 / 500 = 536
• Tax = 536 x 3.50 = $1,876

If the price were $268,200, divide by 500 = 536.4, round up to 537 increments: 537 x 3.50 = $1,879.50.

Trap: Watch whether the rate is per $100 or per $500 - using the wrong increment changes the answer fivefold. Some jurisdictions split the transfer tax between buyer and seller or exempt a first-time buyer; the exam will say so. Recordation tax (charged to record the deed or mortgage) is calculated the same bracket way but on a different base, so keep the two charges separate when a question lists both.

Investment math

Capitalization rate

The income (capitalization) approach ties value to net operating income (NOI):

• Value = NOI / cap rate
• NOI = effective gross income - operating expenses (excludes debt service and depreciation)

Worked example: a building with $84,000 NOI at an 8% cap rate is worth 84,000 / 0.08 = $1,050,000.

Gross rent multiplier (GRM)

• GRM = price / gross annual (or monthly) rent
• Value = GRM x gross rent

A fourplex grossing $60,000/year sold at a GRM of 9 is worth 9 x 60,000 = $540,000. When GRM is built from monthly rent instead of annual, the multiplier is roughly twelve times larger, so confirm which the question uses before applying it.

Percent profit or loss

Profit percent is measured against the original cost (the base):

• A home bought at $250,000 and sold at $287,500 gained 37,500 / 250,000 = 15%

Gross rent multiplier compares quickly across listings but ignores expenses, so a low GRM is not always the better buy; cap rate, which uses NOI after expenses, is the sharper measure of investment quality.

Trap: Dividing the gain by the sale price understates the percent - the base is always the original cost.

The same base rule applies to appreciation and depreciation. If a property is now worth 120% of its purchase price, the purchase price is the 100% base; divide today's value by 1.20 to recover the original cost. Cap rate and value move inversely: at fixed NOI, a higher required cap rate yields a lower value, which is why investors seeking safety accept lower returns and pay more. Memorize the IRV triangle - Income = Rate x Value - to rearrange for whichever variable the question hides.

Worked Example: Cap Rate Solved Three Ways

The income relationship Value = NOI / Cap Rate rearranges into all three exam variants. Given any two, solve the third.

• Find value: NOI $60,000, cap rate 7.5% -> $60,000 / 0.075 = $800,000.
• Find cap rate: NOI $60,000, price $750,000 -> $60,000 / $750,000 = 8%.
• Find NOI: value $800,000, cap rate 7.5% -> $800,000 x 0.075 = $60,000.

Remember NOI is income after operating expenses but before debt service and income tax. Mortgage payments are not subtracted to get NOI — a common trap answer subtracts the loan payment.

Worked Example: Profit, Basis, and Capital Gain

An investor buys at $250,000, spends $30,000 on a capital improvement, and sells for $360,000 with $25,000 in selling costs.

• Adjusted basis = $250,000 + $30,000 = $280,000.
• Amount realized = $360,000 - $25,000 = $335,000.
• Capital gain = $335,000 - $280,000 = $55,000.
• Percent return on the original price = $55,000 / $250,000 = 22%.

The exam distinguishes percent of profit on cost (gain / what you paid) from percent of the sale price (gain / what you sold for), and rewards adding capital improvements to basis while subtracting selling costs from the realized amount — repairs and routine maintenance do not adjust basis.