8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration: find the daily rate (annual / 360 or / 365), multiply by the days owned; arrears taxes create a seller debit and buyer credit.
- Confirm whether the problem uses a 360-day banker's year (30-day months) or a 365-day calendar and stay consistent throughout.
- Transfer tax = (price / increment) x rate per increment; round increments up when the rule says 'or fraction thereof.'
- Income value = NOI / cap rate, where NOI is gross income minus operating expenses (before debt service); higher cap rate means lower value.
- Profit or return percentages use the original cost as the denominator, and equity equals market value minus debt owed.
- Land is never depreciated; straight-line tax depreciation = building value / useful life, separate from cost-approach accrued depreciation.
Proration: Splitting Shared Costs at Closing
Proration divides an expense or income item between buyer and seller based on the portion of the period each one owns the property. The classic items are property taxes, HOA dues, prepaid rent, and interest. The method: find the daily rate, then multiply by the number of days that belong to the responsible party.
The 360-Day Versus 365-Day Method
Many exams use the banker's (statutory) year of 360 days with 30-day months for simplicity; others use the actual 365-day calendar. The question or its answer choices reveal which. Daily rate = annual amount / 360 (or / 365). Always state your assumption and stay consistent through the whole problem.
Worked Proration Example
Annual taxes are $3,600, unpaid, and closing is on the last day of April (the buyer owns the day of closing). Using a 360-day year: daily rate = 3,600 / 360 = $10 per day. The seller owned January through April: 4 months x 30 days = 120 days.
Seller's share = 120 x $10 = $1,200, credited to the buyer (because the buyer will pay the full bill later). This is the most-tested arrangement: arrears taxes generate a seller debit / buyer credit.
Debits and Credits Direction
| Item | Status | Effect at closing |
|---|---|---|
| Taxes in arrears | Unpaid | Seller debit, buyer credit |
| Taxes paid in advance | Prepaid | Buyer debit, seller credit |
| Rent collected by seller | Buyer's month | Seller debit, buyer credit |
| Buyer's new loan interest | Accrued to date | Buyer debit |
The seller pays for the days they owned; the buyer pays for days they will own. Misdirecting the credit is the single most common proration error.
Transfer Tax and Recording Fees
Transfer tax (also called documentary stamp or conveyance tax) is charged on the sale price, usually per a fixed dollar increment. If the rate is $0.50 per $500 of price, a $300,000 sale incurs (300,000 / 500) x 0.50 = 600 x 0.50 = $300.
Read the increment carefully: 'per $500 or fraction thereof' means you round the count of increments up. A $300,250 sale would round 600.5 increments up to 601, giving 601 x 0.50 = $300.50. Who pays (buyer or seller) varies by state and contract.
Investment Math: Capitalization and Return
Income property value is driven by the capitalization (cap) rate: value = net operating income (NOI) / cap rate. NOI is gross income minus operating expenses, before debt service and income tax.
If a building produces $48,000 NOI and investors require a 8% cap rate, value = 48,000 / 0.08 = $600,000. Rearranged, cap rate = NOI / value, and NOI = value x cap rate. A higher required cap rate produces a lower value, which is why riskier properties sell at higher cap rates.
Other Return Measures
- Gross rent multiplier (GRM) = price / gross (often monthly) rent; a $360,000 property renting at $3,000/month has a GRM of 120.
- Cash-on-cash return = annual pre-tax cash flow / cash invested.
- Equity = market value minus debt owed.
- Profit/loss percent = (sale price - cost) / cost, expressed as a percent.
For a percentage of profit, the denominator is always the original cost (the 'whole' you started with), not the sale price.
Worked Example: Transfer Tax
Transfer (documentary) tax is charged on the sale price, usually per a stated dollar increment. Suppose the rate is $4 per $1,000 of value on a $285,000 sale. Round the price up to the next full $1,000 if the problem requires it (here it is already even), then 285,000 / 1,000 = 285 increments, and 285 x $4 = $1,140. If a problem gives a percentage instead, multiply directly: a 1.5% state transfer tax on $285,000 is 285,000 x 0.015 = $4,275. Read whether the tax is split between buyer and seller; many problems assign half to each, so the seller's share above would be $570 in the per-thousand example.
Worked Example: Capitalization and Value
Income property uses the IRV relationships: Value = NOI / Cap Rate, NOI = Value x Cap Rate, Cap Rate = NOI / Value. A building producing $48,000 net operating income that comparable sales price at a 8% cap rate is worth 48,000 / 0.08 = $600,000. If an investor pays $600,000 and wants a 10% return, the required NOI is 600,000 x 0.10 = $60,000. NOI excludes debt service and depreciation: start with gross income, subtract a vacancy and collection loss, then subtract operating expenses (taxes, insurance, management, repairs) to reach NOI.
As the cap rate rises, value falls for the same income, an inverse relationship the exam tests directly.
Annual property taxes of $4,320 are unpaid. Closing is June 30 using a 360-day year with the seller responsible through the day before closing. What is the seller's prorated share?
An office building has gross income of $90,000 and operating expenses of $36,000. If investors demand a 9% cap rate, what is the indicated value?
Depreciation for Cost Approach and Taxes
Two depreciation concepts appear. Straight-line depreciation for income-tax purposes spreads the building's basis (land is never depreciated) over a fixed recovery period: annual depreciation = building value / useful life. A $275,000 building depreciated over 27.5 years yields 275,000 / 27.5 = $10,000 per year.
In the cost approach, accrued depreciation is subtracted from reproduction cost. If a structure cost $400,000 to build and has lost 25% to physical and functional depreciation, the depreciated improvement value is 400,000 x 0.75 = $300,000, to which land value is then added.
Final Exam-Day Reminders
State the day-count convention before prorating and keep the credit pointed at the party who will ultimately pay. For transfer tax, round increments up when the statute says 'or fraction thereof.' For investment value, compute NOI first (no debt service), and remember that value and cap rate move in opposite directions.
For depreciation, never depreciate the land, and separate the income-tax straight-line figure from the cost-approach accrued-depreciation deduction. Keep a clean line between operating expenses, which reduce NOI, and debt service and depreciation, which do not. These distinctions decide several of the harder investment questions on the national portion.