8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration divides shared costs between buyer and seller as of the closing date.
- Many exams use a 360-day banker's year of twelve 30-day months for prorations.
- Transfer tax is the tax rate applied per a stated dollar increment of the sale price.
- Profit and loss percentages are figured against the original cost (the base), not the new value.
- Equity equals market value minus the remaining loan balance.
Proration Fundamentals
Proration divides a continuing expense or credit between buyer and seller so each pays only for the time they own the property. Common prorated items include property taxes, prepaid rent, HOA dues, and interest.
The seller is typically responsible through the day of closing (check the exam's stated convention). The four steps:
- Find the annual or monthly amount.
- Compute the daily rate.
- Count the days owed by each party.
- Multiply the daily rate by the days.
Statutory vs. Banker's Year
Exams use one of two day-count conventions, and the problem will tell you which:
| Method | Year length | Month length |
|---|---|---|
| Banker's / statutory | 360 days | 30 days each |
| Actual / calendar | 365 days | actual days |
Unless told otherwise, use the 360-day banker's year: divide the annual amount by 360 for the daily rate. A $3,600 annual tax bill yields a $10 daily rate (3,600 / 360). If the seller owns the property for 90 days into the year, the seller's share is 90 x $10 = $900.
Debits and Credits
Whether a proration is a debit (charge) or credit depends on who already paid. If taxes are paid in arrears (after the period), the seller owes their share and is debited, while the buyer is credited. If a cost was prepaid, the seller is credited for the unused portion. Identifying the direction is worth as many points as the arithmetic, so name the paying party before computing.
Annual property taxes are $4,320, paid in arrears, on a 360-day basis. Closing is at the end of the fourth month, with the seller responsible through closing. What is the seller's prorated share?
Transfer Tax
Transfer tax (also called documentary or conveyance tax) is charged when title changes hands, stated as a rate per a fixed dollar increment of the sale price.
Transfer tax = (Sale price / Increment) x Rate per increment
If the tax is $0.50 per $500 of price on a $250,000 sale: 250,000 / 500 = 500 increments, times $0.50 = $250. Always round the number of increments up if the statute requires it. Confirm whether the tax applies to the full price or only the amount financed.
Profit, Loss, and Percentage Change
Investment questions test the base of a percentage change. Profit or loss is always measured against the original cost, not the new value.
Percent change = (New value - Original cost) / Original cost
A property bought for $200,000 and sold for $250,000 gained $50,000, or 50,000 / 200,000 = 25% profit. The classic trap divides by the sale price (20%). When a problem says a property sold "at a 20% profit," the sale price equals cost x 1.20, so cost = sale price / 1.20.
Equity and Net to Seller
Equity is the owner's stake: market value minus debt.
Equity = Market value - Remaining loan balance
A $400,000 home with a $310,000 mortgage has $90,000 of equity. Net to seller (seller's proceeds) subtracts commission, payoff, and closing costs from the sale price. When a seller states a desired net, solve backward: Required sale price = (Net + fixed costs) / (1 - commission rate). This reversal, dividing by 1 minus the rate, is the most-missed investment calculation on the national exam.
Net-to-Seller, Worked Both Directions
The seller-net formula confuses candidates because commission is a percentage of the unknown sale price, not of the net.
Forward (find the net). Sale price $350,000, 6% commission, $4,000 closing costs, $180,000 loan payoff.
- Commission = $350,000 x 6% = $21,000.
- Net = $350,000 − $21,000 − $4,000 − $180,000 = $145,000.
Backward (seller wants a target net). A seller must net $200,000 after a 6% commission and $5,000 in fixed costs (ignore any payoff). You cannot just add 6% to $205,000 — the commission is charged on the sale price, which is larger than the net.
- Required sale price = ($200,000 + $5,000) / (1 − 0.06) = $205,000 / 0.94 = $218,085 (round up to clear the net).
- Check: $218,085 x 6% = $13,085 commission; $218,085 − $13,085 − $5,000 = $200,000. Correct.
Trap: dividing by 1.06 instead of 0.94 understates the price. Always divide the required gross by (1 − commission rate).
Profit, Appreciation, and Transfer-Tax Cross-Check
Percentage-change problems hinge on choosing the right base — almost always the original cost, not the new value.
| Question type | Setup | Solve |
|---|---|---|
| Percent profit | Bought $200,000, sold $250,000 | $50,000 / $200,000 = 25% |
| Find original cost | Sold $250,000 at a 25% profit | $250,000 / 1.25 = $200,000 |
| Find sale price | Bought $200,000, sold at 15% loss | $200,000 x 0.85 = $170,000 |
Appreciation over time. Simple (non-compounded) appreciation adds the same dollar amount each year: a $300,000 home appreciating 4% simple for 3 years gains 3 x ($300,000 x 0.04) = $36,000, reaching $336,000. Read carefully whether the problem wants simple or compound growth.
Wisconsin transfer-fee cross-check. Wisconsin's transfer fee is $3 per $1,000 (0.30%) of value. On a $250,000 sale that is $250,000 / 1,000 x $3 = $750, paid by the seller. National exams may instead give an arbitrary "$0.50 per $500" rate — read the increment the problem states and divide the price by that increment before multiplying. Mixing up the per-$500 and per-$1,000 bases is the classic transfer-tax error, so confirm the increment first, then count increments (rounding up if the statute requires).