8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Prorations divide an annual cost between buyer and seller based on the closing date and who owes which days.
- The seller typically owes expenses through the day of closing; confirm the method the question states.
- Transfer tax equals the taxable amount divided by the stated increment, times the rate per increment.
- Capitalization rate equals net operating income divided by value: Value = NOI / Cap Rate.
- Gross rent multiplier equals price divided by gross rent and is a quick, expense-blind screening tool.
Proration Basics
Proration fairly splits annual costs, mainly property taxes and prepaid items, between buyer and seller at closing. Two conventions appear on the exam:
- Statutory (banker's) year: 360 days, 30 days per month. Easiest math and most common on tests.
- Actual (calendar) year: 365 days. Used when a question says to count exact days.
The seller usually owes costs through the day of closing, and the buyer owes from the day after. Always determine: the daily rate, the number of days each party owns, and whether the item is a debit or credit.
Worked Tax Proration
Annual taxes of $3,600 are unpaid; closing is June 30 using a 360-day year. The seller owes January 1 through June 30 (6 full months).
- Monthly tax = $3,600 / 12 = $300.
- Seller's share = $300 x 6 = $1,800.
Because the taxes are unpaid, the seller's $1,800 is a debit to the seller and a credit to the buyer; the buyer will pay the full bill later but was reimbursed at closing. If the seller had already prepaid the year, the direction reverses and the buyer reimburses the seller for days after closing.
Annual property taxes are $4,800 and unpaid. Using a 360-day year, closing occurs on April 30 (seller responsible through closing). What is the seller's prorated share?
Transfer Tax
Transfer (or conveyance) tax is charged per a fixed increment of the sale or consideration. The formula is: Tax = (Taxable Amount / Increment) x Rate per Increment. A common increment is $500.
Example: A sale price of $325,000 at $0.50 per $500.
- Number of increments = $325,000 / $500 = 650.
- Tax = 650 x $0.50 = $325.
Watch the increment: $1.10 per $1,000 on the same $325,000 = 325 increments x $1.10 = $357.50. Read whether any existing assumed mortgage is excluded from the taxable amount, as some jurisdictions tax only new money.
Investment Math
Income-property questions convert rent into value. Build the income statement first, then apply a formula.
| Term | Definition |
|---|---|
| Gross Income | All potential rent |
| NOI | Gross income minus operating expenses (not debt service) |
| Cap Rate | NOI / Value |
| GRM | Price / Gross (annual or monthly) Rent |
Key rearrangements: Value = NOI / Cap Rate and NOI = Value x Cap Rate.
Example: A building nets $48,000 NOI and investors want an 8% cap rate. Value = $48,000 / 0.08 = $600,000. Lowering the required cap rate to 6% raises value to $48,000 / 0.06 = $800,000, showing value and cap rate move inversely.
Gross Rent Multiplier
GRM is a fast screening tool that ignores expenses. GRM = Price / Gross Rent. To value a property, multiply: Value = Gross Rent x GRM.
Example: Comparable fourplexes sell at a GRM of 110 on monthly gross rent. A subject property collects $4,200 per month.
- Value = $4,200 x 110 = $462,000.
Because GRM skips operating expenses, never confuse it with the cap-rate approach. A high-expense building can show an attractive GRM yet a poor cap rate, which is exactly the distinction the exam tests.
An apartment building generates $72,000 in net operating income. An investor requires a 9% capitalization rate. What is the indicated value?
Insurance, rent prorations, and the equity build-up idea
Prorations are not limited to taxes. Prepaid homeowner's insurance, HOA dues, and collected rent are split the same way, but the debit/credit direction depends on who prepaid. If a seller prepaid a $1,200 annual policy and closes after 4 months, the seller has 8 unused months coming back: $1,200 / 12 = $100/month x 8 = $800 credited to the seller, debited to the buyer (if the policy transfers).
Worked example: rent proration on a rental purchase
A duplex generating $2,400/month in rent closes on the 10th, and the seller already collected the full month. Using a 30-day month, the buyer owns days 11–30 = 20 days.
- Daily rent = $2,400 / 30 = $80.
- Buyer's share = $80 x 20 = $1,600, credited to the buyer and debited to the seller (the seller holds rent for days the buyer will own).
Equity, appreciation, and return
| Concept | Formula |
|---|---|
| Equity | Market value − loan balance |
| Appreciation rate | (New value − Old value) / Old value |
| Cash-on-cash return | Annual cash flow / cash invested |
Example: A property bought for $250,000 is now worth $300,000. Appreciation = ($300,000 − $250,000) / $250,000 = 20% total. If held 4 years, that is roughly 5% simple per year — the exam usually wants the total unless the item asks for an annual figure.
Profit, loss, and the percent-of-cost trap
Investment items also test simple profit and loss on a sale, and the exam plants its trap in the base of the percentage — profit percent is figured on the original cost, not the sale price.
Worked example: percent profit
An investor buys at $180,000 and sells at $216,000.
- Profit = $216,000 − $180,000 = $36,000.
- Percent profit = $36,000 / $180,000 = 20% (base = cost, not the $216,000 sale price).
Worked example: working backward from a loss
A property sells for $171,000, which represents a 10% loss. Find the original cost.
- Sale = cost x (100% − 10%) = cost x 0.90.
- Cost = $171,000 / 0.90 = $190,000.
The trap answer adds 10% to $171,000 ($188,100), under-stating the cost because the 10% should be taken on the larger original figure.
| Quantity | Formula | Base |
|---|---|---|
| Percent profit | Profit / cost | Original cost |
| Percent loss | Loss / cost | Original cost |
| Sale price | Cost x (1 ± rate) | Original cost |
Whenever a percentage of gain or loss appears, ask "percent of what?" — the answer on these problems is almost always the original purchase price.