8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Prorations divide a shared expense between buyer and seller as of the closing date; identify who owes which portion.
- Most exams use a 360-day banker's year (30 days per month) unless the problem states an actual-day basis.
- The seller typically owes expenses through (and including) the day of closing unless told otherwise.
- Transfer/recordation tax is a rate applied per dollar or per increment of the sale price, set by statute.
- Capitalization rate links income to value: Value = Net Operating Income ÷ Cap Rate.
Proration Basics
A proration splits a continuing expense — property taxes, HOA dues, prepaid rent, or interest — between buyer and seller based on the closing date. Two setup decisions drive every proration:
- Day basis. Most license exams use a 360-day banker's year (12 months × 30 days). A problem will say "use a 365-day year" or "actual days" if it wants the calendar basis. Do not assume.
- Who owes the closing day. The standard convention: the seller owns through the day of closing and is responsible for that day's expense.
The result becomes a debit to the party who owes money and a credit to the party owed. An item the seller has not yet paid (taxes paid in arrears) is a seller debit and buyer credit at closing.
Worked Tax Proration
Annual property tax is $3,600, unpaid, and closing is on April 30 using a 360-day year. The seller owned January through April (4 months). How is the tax prorated?
Step 1 — Daily rate: $3,600 ÷ 360 = $10 per day. Step 2 — Seller's days: Jan + Feb + Mar + Apr = 4 × 30 = 120 days. Step 3 — Seller's share: 120 × $10 = $1,200.
Because taxes are unpaid (in arrears), the seller's $1,200 is a debit to the seller and a credit to the buyer — the buyer will pay the full bill later and is reimbursed now.
The trap: counting April as 31 days. On a 360-day banker's year every month is 30 days regardless of the calendar. The second trap is reversing the debit/credit when taxes are paid in advance instead of in arrears.
Transfer and Recordation Tax
State and local transfer (and recordation) taxes are a rate applied to the sale price, often quoted per $500 or per $1,000 of value, or as a flat percentage. Read the increment carefully.
Worked Transfer-Tax Example
A state charges a transfer tax of $3.50 per $500 of sale price. A property sells for $360,000. What is the transfer tax?
Step 1 — Number of increments: $360,000 ÷ $500 = 720 increments. Step 2 — Tax: 720 × $3.50 = $2,520.
If instead the tax were a flat 0.7%, the math is $360,000 × 0.007 = $2,520 — the same answer, which is why $3.50 per $500 equals 0.7%. The exam tests whether you can switch between the per-increment and the percentage form. Rounding the increment count down when the price is not a clean multiple of $500 is the usual error; round up to the next full increment when statutes so require.
Investment and Capitalization Math
Income property is valued from its earnings. Net Operating Income (NOI) = effective gross income − operating expenses (NOT mortgage payments or depreciation). The capitalization formula is an IRV triangle:
- Value = NOI ÷ Rate
- Income (NOI) = Value × Rate
- Rate = NOI ÷ Value
Worked Cap-Rate Example
An apartment building produces $84,000 NOI and the market cap rate is 7%. What is its value?
Value = $84,000 ÷ 0.07 = $1,200,000.
If an investor wants an 8% return instead, Value = $84,000 ÷ 0.08 = $1,050,000 — a higher required rate lowers value. That inverse relationship is itself a tested concept.
The classic trap: subtracting the mortgage payment to get NOI. Debt service is a financing cost, not an operating expense; leave it out of NOI. Including it understates income and corrupts the value.
Insurance Prorations and the Mill-Rate Tax Bill
Two more proration-family skills round out the math: prorating a prepaid item and computing a property-tax bill from a mill rate or assessment ratio.
Prorating prepaid insurance
When the seller has prepaid an annual expense, the buyer reimburses the seller for the unused portion - the reverse direction of arrears taxes. A seller prepaid a $1,440 annual hazard-insurance policy and the buyer is assuming it. Closing is September 1 on a 360-day year; the seller owns the closing day, so the buyer's coverage starts September 2.
Step 1 - Daily rate: $1,440 / 360 = $4/day. Step 2 - Days remaining to the buyer: Sept 2-30 (29) + Oct, Nov, Dec (90) = 119 days... but on a banker's year count the four full remaining months (Sept 2 onward) carefully. Using full remaining months Oct-Dec = 90 days plus 29 days of September = 119 days. Step 3 - Buyer's reimbursement: 119 x $4 = $476, a debit to the buyer and a credit to the seller, because the seller already paid for coverage the buyer will enjoy.
Prepaid items credit the seller; arrears items credit the buyer. Confusing the two directions is the most common proration error.
Mill rates and assessed value
Property tax = assessed value x tax rate. Rates are often quoted in mills, where one mill = $1 per $1,000 of assessed value (0.001).
A home has a market value of $400,000, an assessment ratio of 80%, and a tax rate of 25 mills. Find the annual tax.
Step 1 - Assessed value: $400,000 x 0.80 = $320,000. Step 2 - Convert mills: 25 mills = 25 / 1,000 = 0.025. Step 3 - Tax: $320,000 x 0.025 = $8,000.
The traps: applying the rate to market value instead of assessed value (overstating the bill), and misreading mills as a percent (25 mills is 2.5%, not 25%). Read whether the question gives market or assessed value, and whether the rate is mills, dollars per hundred, or a flat percent.
Closing is June 30 on a 360-day year. Annual taxes of $4,320 are unpaid. The seller owned from January 1. What is the seller's prorated share (debit)?
An office building has a net operating income of $90,000. An investor requires a 9% capitalization rate. What is the most she should pay?