8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration divides shared costs between buyer and seller as of the closing date
- The seller owns the day of closing in the most common exam convention; verify the stated rule
- Transfer and recording taxes are charged per increment of value, so round up to the next full increment
- Capitalization rate equals net operating income divided by value (V = NOI / Rate)
- Gross rent multiplier equals price divided by gross rental income
Proration at Closing
Proration splits an expense or income item between buyer and seller based on who benefits during which part of the period. Property taxes, prepaid rent, HOA dues, and accrued interest are the usual items.
Steps:
- Find the daily amount (annual figure / 360, or / 365 for actual-day method).
- Count the days that belong to each party up to or from closing.
- Multiply the daily rate by the days; debit and credit the correct party.
The common exam convention is a 360-day year, 30-day month, and the seller owns the day of closing. Always read which convention the question states.
Worked example: tax proration
Annual taxes are $3,600, paid in arrears. Closing is on September 1 (seller owns Jan 1 - Aug 31 = 8 months).
- Monthly tax = $3,600 / 12 = $300.
- Seller's share = 8 x $300 = $2,400.
Because taxes are paid in arrears (not yet paid), the seller owes their share to the buyer: $2,400 is a debit to the seller, credit to the buyer. If taxes were prepaid, the direction reverses and the buyer reimburses the seller.
Transfer and Recordation Tax
Transfer taxes are charged per increment of value (for example, per $500 of price). Round the price up to the next full increment before multiplying.
Worked example
A county charges $0.50 per $500 of sale price. The sale is $278,300.
- Increments = $278,300 / $500 = 556.6, rounded up to 557.
- Tax = 557 x $0.50 = $278.50.
Never round down: a partial increment is taxed as a full one. Watch for taxes quoted per $100 versus per $1,000 versus per $500; the per-increment unit changes the divisor.
Investment Math
| Formula | Meaning |
|---|---|
| NOI = Gross Income - Operating Expenses | Net operating income (before debt service) |
| Value = NOI / Cap Rate | Income approach to value |
| Cap Rate = NOI / Value | Return rate on the property |
| Gross Rent Multiplier = Price / Gross Rent | Quick comparison multiple |
Worked example: cap rate
A building produces $48,000 NOI and is valued at $600,000.
- Cap rate = $48,000 / $600,000 = 0.08 = 8%.
Reverse it: if a comparable trades at an 8% cap rate and earns $60,000 NOI, value = $60,000 / 0.08 = $750,000. Exclude debt service and depreciation from NOI; they are not operating expenses.
The proration workflow
Every proration follows the same four moves, and writing them out prevents direction errors. First, identify whether the item is paid in arrears (taxes, often interest) or prepaid (rent, some HOA dues). Second, choose the day count: the exam's default is a 360-day banker's year of twelve 30-day months, with the seller owning the day of closing unless the stem says otherwise.
Third, compute the daily or monthly rate and multiply by the correct party's days. Fourth, assign the debit and credit. Arrears items debit the seller (they used the time but the bill comes later); prepaid items credit the seller (they paid ahead for time the buyer will use).
Rent and interest proration
Prepaid rent is prorated the opposite way from arrears taxes. If a tenant paid $1,500 rent for a 30-day month and closing is on day 20, the seller used 19 days and the buyer owns 11 (seller owns closing day). Daily rent = $1,500 / 30 = $50. The buyer's 11 days = $550, which the seller, who already holds the rent, credits to the buyer.
Accrued mortgage interest on an assumed loan is prorated similarly: compute daily interest, count the seller's days in the period, and debit the seller for interest that accrued but is not yet paid.
Debits and credits at the table
A proration is meaningless until you assign direction. A debit is money a party owes; a credit is money owed to them. For taxes in arrears, the seller is debited and the buyer credited because the seller used the period but the bill arrives later. For prepaid items the seller is credited because they paid in advance for time the buyer will enjoy. The settlement statement must balance: total debits equal total credits for each party. Misreading arrears versus prepaid reverses the entry and is the single most common proration error on the exam.
Gross rent multiplier and gross income multiplier
The gross rent multiplier (GRM) uses monthly rent; the gross income multiplier (GIM) uses annual income. GRM = Price / Monthly Rent. A fourplex priced at $480,000 renting for $4,000 per month has a GRM of 120. To value a comparable renting at $4,500 per month at the same 120 multiplier: $4,500 x 120 = $540,000.
GRM is a quick screen, not a precise value, because it ignores expenses and vacancy. The cap-rate approach, which works from net operating income, is the more rigorous income method and the one tied to investor return.
Return on investment and equity
Return problems compare income to the cash invested. Cash-on-cash return = annual pre-tax cash flow / cash invested. An investor puts $150,000 down and nets $13,500 cash flow after debt service: $13,500 / $150,000 = 9% cash-on-cash. Distinguish this from the cap rate, which divides NOI (before debt service) by total value.
Equity grows two ways: appreciation and principal paydown. A property worth $400,000 with a $260,000 loan balance has $140,000 equity. If value rises to $440,000 and the balance falls to $250,000, equity becomes $190,000. Exam stems may ask for equity at a future point, so track both the value and the loan balance separately.
Annual property taxes of $4,800 are paid in arrears. Using a 360-day year with the seller owning the closing day, what is the seller's prorated share at a March 31 closing (3 months)?
An investor wants a 9% cap rate on a property generating $63,000 in net operating income. What is the maximum she should pay?