8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration divides shared costs at closing between buyer and seller based on days of ownership.
- The 360-day banker's year (30 days per month) is the most common proration convention on exams.
- Transfer tax is charged per a stated dollar increment of the sale price; round up per local rule before multiplying.
- Profit/loss percentage uses the original cost as the base: percent change = (new - old) / old.
- Capitalization and gross rent multiplier are quick investment-screening tools, not appraisals.
Proration at Closing
Proration splits an annual cost (taxes, HOA dues, prepaid rent) between seller and buyer based on who owned the property each day. Most exams use a 360-day year, 30 days per month unless told otherwise.
Steps:
- Find the daily rate: annual amount / 360.
- Count the seller's days of ownership (closing day usually charged to buyer).
- Multiply daily rate by the relevant days.
Tax Proration Example
Annual property tax is $3,600, paid in arrears. Closing is on May 1 (seller owned Jan 1 through Apr 30 = 4 months = 120 days under 30-day months).
- Daily rate = 3,600 / 360 = $10/day
- Seller's share = 120 x $10 = $1,200 (credit to buyer, debit to seller)
The trap is the direction of the entry. With taxes paid in arrears, the seller owes for time already used, so the seller is debited and the buyer credited.
Rent proration and the closing-day convention
Rent is usually paid in advance, so at closing the seller credits the buyer for the unused, already-collected portion.
Problem: Monthly rent of $1,500 was collected on the 1st; closing is the 16th of a 30-day month. Days the buyer owns = 15. Daily rent = 1,500 / 30 = $50. Buyer's share = 15 x $50 = $750, entered as a credit to buyer / debit to seller. The seller already has the cash, so it must be handed over for the days the buyer owns.
Worked cap-rate and value problems
The income relationships chain three ways — solve for whichever is missing.
| Find | Formula | Example |
|---|---|---|
| Value | NOI / Cap rate | $48,000 / 0.08 = $600,000 |
| Cap rate | NOI / Value | $48,000 / $600,000 = 8% |
| NOI | Value x Cap rate | $600,000 x 0.08 = $48,000 |
Worked NOI build-up: A fourplex grosses $72,000/year, has 5% vacancy ($3,600) and $20,400 operating expenses. Effective gross = $68,400; NOI = 68,400 − 20,400 = $48,000. At an 8% market cap rate, value = 48,000 / 0.08 = $600,000. Note operating expenses exclude mortgage payments and depreciation — including the mortgage is the most common NOI error.
GRM vs. cap rate and a transfer-tax recap
GRM = Price / Gross Annual (or monthly) Rent ignores expenses and is a rough screen; cap rate uses NOI and reflects true return — never mix the bases. Transfer tax: round the price up to the next increment, then multiply. At $0.50 per $500 on a $241,250 sale: 241,250 / 500 = 482.5 → 483 increments x $0.50 = $241.50. Forgetting to round up undercounts by one increment, the standard trap.
Profit, loss, and the original-basis trap
Percent-change problems always use the original value as the base, and the exam tests the reverse form to catch shortcut errors. Forward: a property bought for $250,000 sells for $290,000; profit = $40,000; percent = 40,000 / 250,000 = 16%. Reverse (the trap): "A home sold for $276,000 at a 15% profit — what was the cost?" The cost is not 276,000 minus 15%. Because $276,000 represents 115% of cost, cost = 276,000 / 1.15 = $240,000.
Likewise a 15% loss means the sale price is 85% of cost, so cost = sale / 0.85. Dividing by the percentage (0.15) or subtracting it from the sale price are the two distractor answers the exam plants for this question type.
Annual taxes are $2,400, paid in arrears, using a 360-day year. Closing is July 1. What is the seller's prorated share for January 1 through June 30?
Transfer / Conveyance Tax
Transfer tax is stated as a dollar amount per increment of price, commonly per $500 or per $1,000. Round the price up to the next full increment first, then multiply.
Example: Rate is $0.50 per $500 of price; sale price $241,250. Increments = 241,250 / 500 = 482.5, round up to 483 increments. Tax = 483 x $0.50 = $241.50. Forgetting to round up undercounts by one increment.
Transfer Tax per $1,000
If the rate is $1.10 per $1,000 on a $350,000 sale: 350,000 / 1,000 = 350 increments. Tax = 350 x $1.10 = $385.
| Sale Price | Rate | Increments | Tax |
|---|---|---|---|
| $200,000 | $0.75 / $500 | 400 | $300.00 |
| $350,000 | $1.10 / $1,000 | 350 | $385.00 |
| $241,250 | $0.50 / $500 | 483 | $241.50 |
Always match the increment in the question; mixing $500 and $1,000 bases doubles or halves the answer.
Profit and Loss Percentage
Percent change always uses the original value as the base: Percent = (New - Old) / Old.
Example: A home bought for $250,000 sells for $290,000. Profit = 40,000. Percent = 40,000 / 250,000 = 0.16 = 16% gain.
Reverse problem: 'A property sold for $276,000 at a 15% profit. What was the cost?' Cost = 276,000 / 1.15 = $240,000. The trap is dividing by 0.15 or subtracting 15% of the sale price; you must divide the sale price by 1.15.
Investment Screening Ratios
Two quick tools appear on the exam:
- Capitalization rate = NOI / Value. A $600,000 building with $48,000 NOI has a cap rate of 0.08 = 8%.
- Gross Rent Multiplier (GRM) = Price / Gross Annual Rent. A $360,000 property renting for $36,000/year has a GRM of 10.
GRM uses gross rent (no expenses) and is a rough comparison tool; cap rate uses net income and reflects true return. Do not mix the two bases.
A rental property is priced at $480,000 and produces $40,000 in gross annual rent. What is its gross rent multiplier (GRM)?