8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration divides a shared expense between buyer and seller by ownership days; compute a daily rate, then multiply by each party's days.
- Under the seller-owns-day-of-closing convention, the seller pays through the closing date; prepaid items are credited to the seller, arrears are debited.
- Transfer tax equals the taxable price divided by the stated increment, rounded up, times the rate per increment.
- Profit/loss percentage is the gain or loss divided by the original cost (the base), not the sale price.
- Equity equals market value minus liens; appreciation and depreciation are percentages of the original or prior value.
Proration
Proration splits a continuing cost, property taxes, HOA dues, prepaid rent, between buyer and seller according to who owned the property each day. The method:
- Find the annual (or monthly) amount.
- Divide to get a daily rate (use the 360-day banker's year unless told otherwise: 30 days per month).
- Multiply the daily rate by each party's number of days.
Example: Annual taxes are $3,600. Daily rate = $3,600 / 360 = $10.00. Closing is on the 90th day of the year; the seller owned days 1-90.
| Party | Days | Calculation | Share |
|---|---|---|---|
| Seller | 90 | 90 x $10.00 | $900 |
| Buyer | 270 | 270 x $10.00 | $2,700 |
Debits, Credits, and Arrears vs. Prepaid
Whether a prorated item is a debit or credit depends on whether it was paid in arrears (after the period, like most property taxes) or prepaid (before, like insurance or HOA dues).
- Taxes in arrears: the seller has used the service but not yet paid. The seller's share is a debit to the seller and credit to the buyer, because the buyer will pay the full bill later.
- Prepaid items: the seller already paid beyond closing, so the unused portion is a credit to the seller and debit to the buyer.
Under the common convention, the seller owns the day of closing and pays through that date. Some questions specify the buyer owns the closing day instead, so read the convention stated in the problem rather than assuming.
To translate a calendar date into a day number on the 360-day year, count 30 days per completed month plus the days in the closing month. A closing on April 15 is 3 full months (Jan, Feb, Mar = 90 days) plus 15 days = day 105. Build the day count first, then apply the daily rate, so the proration and the debit/credit direction stay separate steps.
Worked proration with debit/credit direction
Annual taxes of $5,400 are paid in arrears; closing is day 150 of a 360-day year, and the seller owns the day of closing.
- Daily rate = $5,400 / 360 = $15.00.
- Seller's days = 150; seller's share = 150 x $15.00 = $2,250.
- Buyer's days = 210; buyer's share = 210 x $15.00 = $3,150.
Because taxes are in arrears (the bill comes later and the buyer will pay the full year), the seller's $2,250 is a debit to the seller and a credit to the buyer. Flip the direction for a prepaid item (insurance, HOA dues): the unused portion is a credit to the seller, debit to the buyer.
Transfer-tax rounding and equity, worked
Transfer tax at $0.55 per $500 on a $263,100 sale: $263,100 / $500 = 526.2, round up to 527 increments; 527 x $0.55 = $289.85. Forgetting to round up understates the tax.
Equity = market value − total liens. A home worth $420,000 with a $250,000 first mortgage and a $30,000 home-equity second has $280,000 in liens, leaving $140,000 equity. A question listing two loans is testing whether you summed them before subtracting.
Annual property taxes of $4,320 are paid in arrears. Using a 360-day year and a closing on the 120th day with the seller owning the day of closing, what is the seller's prorated share (a debit to the seller)?
Transfer and Recordation Tax
Transfer tax (and recordation tax) is charged per increment of value, commonly per $500 of price. The method:
- Divide the taxable price by the increment.
- Round up to a whole number of increments (a partial increment counts as a full one).
- Multiply by the tax rate per increment.
Example at $0.50 per $500 on a $182,750 sale: $182,750 / $500 = 365.5, round up to 366 increments; 366 x $0.50 = $183.00. The two traps are forgetting to round up and dividing by the wrong increment ($100 vs. $500). Read the stated increment carefully.
Some jurisdictions exempt a portion of the price (for example, the first $50,000 on an owner-occupied sale) before applying the per-increment tax. When the problem states an exemption, subtract it from the price first, then divide the remaining taxable amount by the increment and round up. Recordation tax on the mortgage, where it applies, is figured on the loan amount rather than the sale price, mirroring the points rule from the financing section: identify the correct base before you divide.
Profit, Loss, Appreciation, and Equity
Profit/Loss % = (Sale Price - Cost) / Cost. The base is always the original cost, not the sale price. A property bought for $200,000 and sold for $250,000 gained $50,000; $50,000 / $200,000 = 25% profit. Dividing by the $250,000 sale price (giving 20%) is the classic error.
To find an unknown original cost when you know the sale price and percent gain, treat the cost as 100% and the sale as (100% + gain%): Cost = Sale / (1 + gain%). A property sold for $253,000 at a 15% profit cost $253,000 / 1.15 = $220,000.
Appreciation/Depreciation are percentages of a base value; straight-line depreciation spreads cost evenly: a $300,000 building depreciated over 30 years loses $300,000 / 30 = $10,000 per year.
Equity = Market Value - Total Liens. A home worth $400,000 with a $260,000 mortgage balance carries $140,000 in equity. Add every lien, a first mortgage, a home-equity second, and any tax lien, before subtracting, because a question that lists two loans is testing whether you summed them.
Appreciation over multiple years compounds unless the problem says 'straight-line.' If a $250,000 home appreciates 4% in year one, its value becomes $260,000; a second 4% year is figured on $260,000, not the original. Simple (non-compounded) appreciation would apply both 4% amounts to the original $250,000. The exam signals which it wants with the words 'each year' (compound) versus 'per year of the original value' (straight-line), so read the phrasing before choosing your base.
An investor sells a property for $322,000, which represents a 15% profit over the original purchase price. What was the original cost?