8.3 Proration, Transfer Tax, and Investment Math

Settlement math allocates costs fairly between buyer and seller and reports the taxes a transfer triggers. The mechanics are simple once you identify the day-count convention and who owes what.

Proration Basics

Proration divides a continuing expense (taxes, HOA dues, prepaid rent, interest) between buyer and seller as of the closing date.

1. Find the annual (or monthly) amount.
2. Divide to a daily rate.
3. Multiply by the number of days the responsible party owes.
4. Apply as a debit (charge) or credit to each side.

The seller is responsible through the closing date in most exam conventions, and the buyer owns the closing date forward.

Day-Count Conventions

Two systems appear on exams; read the problem to know which to use.

Unless told otherwise, default to the 360-day method, which makes the daily rate a clean number.

Tax Proration Example

Annual taxes are $3,600, unpaid, and closing is June 30 (seller responsible for 6 months on a 30-day calendar = 180 days). Daily rate = $3,600 / 360 = $10. Seller owes 180 x $10 = $1,800, shown as a debit to the seller and a credit to the buyer because the buyer will pay the full bill later.

Transfer Tax

A transfer tax (also called a documentary stamp or conveyance tax) is charged on the sale price, typically per $500 or per $1,000 of price.

$\text{Transfer Tax} = \frac{\text{Sale Price}}{\text{Unit Size}} \times \text{Rate per Unit}$

Transfer Tax Example

A property sells for $340,000 and the transfer tax is $1.50 per $500. Units = $340,000 / $500 = 680. Tax = 680 x $1.50 = $1,020.

Watch the unit size: a rate stated per $1,000 on the same sale would be $340,000 / 1,000 = 340 units, then multiplied by that rate. Misreading $500 versus $1,000 is a frequent error.

Property Tax and Mill Rates

Property taxes use assessed value, which often lags market value.

$\text{Property Tax} = \text{Assessed Value} \times \text{Tax Rate}$

Rates may be quoted in mills, where one mill equals one-thousandth of a dollar ($0.001) of tax per dollar of assessed value. Convert a mill rate to a decimal by dividing by 1,000.

Mill Rate Example

Assessed value is $250,000 and the rate is 22 mills. Decimal rate = 22 / 1,000 = 0.022. Tax = $250,000 x 0.022 = $5,500. If instead the rate were given as $1.25 per $100, units = $250,000 / 100 = 2,500, and tax = 2,500 x $1.25 = $3,125.

Investment Math

Investors evaluate property by return and growth.

• Equity = Market Value - Loan Balance. A $480,000 home with a $300,000 balance has $180,000 equity.
• Return on Investment (ROI) = Annual Net Income / Cash Invested. A property earning $24,000 net on $300,000 invested returns 24,000 / 300,000 = 8 percent.
• Appreciation: new value = original value x (1 + rate). A $400,000 property up 5 percent is $400,000 x 1.05 = $420,000.
• Depreciation (cost recovery) for tax uses the improvement value only, never the land, spread straight-line over the recovery period.

Distinguish ROI (a yield) from cap rate (a valuation tool): cap rate uses NOI and value, while ROI uses the investor's actual cash.

Worked Example - Cap Rate and Value

The capitalization rate ties net operating income to value: Value = NOI / Cap Rate, and rearranged, Cap Rate = NOI / Value.

A small apartment building produces $60,000 net operating income (income after operating expenses, before debt service). The market cap rate for similar buildings is 8%.

• Value = $60,000 / 0.08 = $750,000

If an investor instead paid $600,000 for that same $60,000 NOI, the implied cap rate = $60,000 / $600,000 = 10% - a higher return, because a lower price for the same income raises the rate.

Worked Example - Gross Rent Multiplier

The gross rent multiplier (GRM) is a quick screen: GRM = Price / Gross Rent. If comparable buildings sell at a GRM of 9 and a property collects $80,000 annual gross rent, its indicated value = 9 x $80,000 = $720,000.

Exam Trap: GRM uses gross rent (no expenses removed); cap rate uses net operating income. Mixing the two produces a badly wrong value.

Debits and Credits at Closing

A debit is a charge to a party; a credit is money owed to a party. Getting the direction right is half of every proration question.

The rule of thumb: whoever benefited from a service they did not pay for is debited, and whoever pre-paid for time they will not own is credited. Rent collected in advance for the closing month is split, with the unearned portion credited to the buyer.

Putting It Together: A Settlement Snapshot

Suppose a sale closes June 30 on a 360-day year. Annual taxes of $3,600 are unpaid, and the buyer will pay them later. The seller used January through June (180 days).

• Daily rate: $3,600 / 360 = $10.
• Seller's share: 180 x $10 = $1,800, a debit to the seller, credit to the buyer.

Add a transfer tax of $1.50 per $500 on a $300,000 price: $300,000 / 500 = 600 units x $1.50 = $900, usually a seller debit. Tracking each figure as a debit or credit to the correct party is exactly how a settlement statement reconciles to zero.