8.3 Proration, Transfer Tax, and Investment Math

Proration, transfer tax, and investment math

Closing-statement math allocates shared costs fairly between buyer and seller and assigns government charges. Investment math values income property. Both reward orderly, labeled steps. Decide your day-count convention first: many exams use a statutory or banker's year of 360 days (12 months of 30 days each), while some use the exact 365-day year. The question usually tells you; if it does not, the 360-day method is the conventional default.

What proration does

Proration splits an expense between the party who used the period and the party who will use the rest. Annual property taxes, prepaid insurance, HOA dues, and collected-in-advance rent are common. The owner pays for the days they own the property.

Step one: find the daily or monthly rate. Step two: count the days each party owns. Step three: multiply and assign as a debit or credit.

Tax proration example

Annual taxes are $3,600, paid in arrears, and closing is June 30 (the seller owned exactly 6 months). Using a 360-day year, the daily rate is 3,600 ÷ 360 = $10 per day. The seller owned 180 days (6 × 30), so the seller owes 180 × $10 = $1,800.

Because taxes are paid in arrears, the seller has not yet paid; the buyer will pay the full bill later. So the seller's $1,800 share is a debit to the seller and a credit to the buyer at closing.

Debit and credit logic

On a closing statement, a debit is money a party owes (reduces what they walk away with) and a credit is money in their favor. Prorated items create paired entries.

For rent collected in advance: the seller already received money for days the buyer will own, so the seller must hand that portion to the buyer — a debit to the seller and a credit to the buyer.

Rent proration example

A tenant paid $1,500 rent for a 30-day month; closing is on the 20th, so the buyer owns the last 10 days. Daily rent = 1,500 ÷ 30 = $50. Buyer's share = 10 × $50 = $500. The seller collected it, so $500 is debited to the seller and credited to the buyer. Counting days carefully — and confirming whether the closing day belongs to buyer or seller per the problem's instruction — prevents off-by-one errors.

Transfer and recordation tax

Transfer tax is a government charge on conveying real property, stated as a rate applied to the sale price or to a taxable unit (often per $500 or per $1,000 of price). Read the unit carefully.

If the rate is $0.50 per $500 of price on a $300,000 sale: divide price by the unit, 300,000 ÷ 500 = 600 units, then multiply by the rate, 600 × $0.50 = $300. If instead the rate is simply 0.5% of price, then 300,000 × 0.005 = $1,500. The two methods give different numbers, so match the calculation to how the rate is quoted. Wrong answers often mix the per-$500 method with the flat-percentage method.

Some jurisdictions round the price up to the next whole taxable unit before applying the rate. On a $300,250 sale taxed per $500, divide and round up: 300,250 ÷ 500 = 600.5, which rounds to 601 units, then 601 × $0.50 = $300.50. When the problem says "or fraction thereof," always round the unit count up, never down. Forgetting to round is a common one-cent-to-a-few-dollars error the exam may test deliberately.

Capitalization and value

Income property is valued by the income (capitalization) approach: Value = Net Operating Income (NOI) ÷ Capitalization rate. NOI is effective gross income minus operating expenses, and it excludes mortgage debt service.

A property with $90,000 NOI and a market cap rate of 9% is valued at 90,000 ÷ 0.09 = $1,000,000. Rearrange to find the rate: Cap rate = NOI ÷ Value. If that same property is offered at $1,200,000, the cap rate is 90,000 ÷ 1,200,000 = 0.075, or 7.5% — a lower return for the higher price.

Building NOI correctly

NOI errors come from including the wrong items. Start with potential gross income, subtract vacancy and collection loss to get effective gross income, then subtract operating expenses. Do not subtract mortgage payments, depreciation, or capital improvements — those are not operating expenses.

• Potential gross income: $120,000
• Less 5% vacancy: −$6,000 → effective gross income $114,000
• Less operating expenses $44,000 → NOI $70,000

At a 10% cap rate, value = 70,000 ÷ 0.10 = $700,000. If a candidate wrongly subtracts a $24,000 annual mortgage payment, NOI falls to $46,000 and value to $460,000 — a large, tempting wrong answer. Debt service belongs to cash-flow analysis, not NOI.

Gross rent multiplier

A quicker screening tool is the gross rent multiplier (GRM): Value = Gross rent × GRM, and GRM = Value ÷ Gross rent. If comparable sales show a GRM of 8 and a property's annual gross rent is $85,000, estimated value is 85,000 × 8 = $680,000. GRM uses gross rent and ignores expenses, so it is a rough estimate, while the cap-rate method using NOI is more precise.

Watch the rent period the GRM was built from. A monthly GRM multiplies monthly rent, and an annual GRM multiplies annual rent; the two differ by a factor of 12. If comparables show a monthly GRM of 96 and a property rents for $7,000 per month, value is 7,000 × 96 = $672,000. Mixing a monthly GRM with annual rent — or the reverse — produces an answer off by a factor of 12, which is a deliberate distractor on the income-property questions.