8.3 Proration, Transfer Tax, and Investment Math

Proration, Transfer Tax, and Investment Math

Proration splits a recurring cost - property taxes, HOA dues, prepaid rent, or insurance - fairly between buyer and seller as of the closing date. The national exam typically uses a 360-day banker's year with 30-day months unless the question states a 365-day actual year, so read carefully.

The method: find the daily (and monthly) cost, count the days each party owns the property, and assign each their share. For an item the seller has already PAID (prepaid, like insurance), the buyer reimburses the seller. For an item paid in ARREARS (taxes owed but not yet paid), the seller credits the buyer for time the seller owned.

Worked Proration

Annual taxes are $3,600, paid in arrears. Closing is September 1; the seller owned January through August (8 months) and is responsible for that period.

1. Monthly tax = 3,600 / 12 = $300
2. Seller's share = 300 x 8 = $1,800 (credit to buyer)
3. Alternatively, daily = 3,600 / 360 = $10/day; 8 months x 30 = 240 days; 240 x 10 = $1,800

Exam convention: the seller usually OWNS the day of closing in most jurisdictions, but follow the question's stated rule. A credit to the buyer is a debit to the seller on the settlement statement - the dollar amount is the same regardless of label.

Transfer Tax and Conveyance Fees

Transfer (conveyance, documentary, or stamp) taxes are charged per increment of sale price. A typical structure is a set dollar amount per $500 of price.

Example: a $250,000 sale at $0.50 per $500.

1. Number of $500 increments = 250,000 / 500 = 500
2. Transfer tax = 500 x $0.50 = $250

If the rate is stated per $1,000, divide the price by 1,000 instead. Trap: the question may say the tax applies only to the amount ABOVE an exemption, or that the increment rounds UP to the next full $500. Round increments up unless told otherwise, then multiply by the per-increment charge.

Investment: Cap Rate and NOI

Income property is valued from Net Operating Income (NOI), which is gross income minus vacancy and operating expenses - but NOT mortgage debt service or income tax.

The IRV triangle ties it together:

Example: NOI = $48,000, market cap rate = 8%. Value = 48,000 / 0.08 = $600,000. A LOWER cap rate yields a HIGHER value, which trips up many candidates. Always strip debt service out before computing NOI.

Return, Equity, and Profit

A few more investment measures appear:

• Cash-on-cash return = Annual cash flow / Cash invested. If you invest $100,000 and net $9,000 cash flow, return = 9,000 / 100,000 = 9%.
• Equity = Value - Loan balance. A $600,000 property with a $420,000 loan has $180,000 equity.
• Percent profit = Profit / Original cost. Buy at $200,000, sell at $250,000: profit $50,000 / 200,000 = 25% gain.

Trap: percent change uses the ORIGINAL number as the denominator, never the new sale price. Dividing by the wrong base produces a plausible but wrong answer choice.

Reversing a Percentage Change

The hardest percent questions give you the result and ask for the starting figure. If a property increased 25% to a current value of $250,000, do not subtract 25% of $250,000. The current value is 125% of the original, so divide:

• Original = $250,000 / 1.25 = $200,000

Likewise, a value that dropped 15% to $170,000 was $170,000 / 0.85 = $200,000 originally. The recurring trap multiplies the new figure by the same percentage instead of dividing by (1 + rate) for gains or (1 - rate) for losses. Whenever a problem says a number is already higher or lower 'by X%', divide the known result by the appropriate factor to recover the base.

Mill Rates and Property-Tax Computation

Property tax problems often supply a mill rate, where one mill = $0.001 of assessed value (or $1 per $1,000). Tax = Assessed Value x Mill Rate, after subtracting any exemption.

Worked example: a home is assessed at $280,000, qualifies for a $50,000 homestead exemption, and the rate is 22 mills.

1. Taxable value = $280,000 - $50,000 = $230,000
2. Tax = $230,000 x 0.022 = $5,060

If the rate is quoted per $100 instead, divide the taxable value by 100 first. The signature trap applies the rate before subtracting the exemption, which overstates the bill. Always apply the exemption first, then multiply by the rate.

Assessed Value, Equalization, and Working Backward

Many jurisdictions assess at a fraction of market value using an assessment ratio. Assessed Value = Market Value x Assessment Ratio. If a home worth $400,000 is assessed at a 40% ratio, its assessed value is 400,000 x 0.40 = $160,000, and the tax is then computed on $160,000.

The exam also reverses this: given a tax bill and the rate, recover the assessed or market value. If a property is taxed $3,200 at a rate of 20 mills (0.020), the assessed value is $3,200 / 0.020 = $160,000; at a 40% ratio, the implied market value is $160,000 / 0.40 = $400,000.

Keep the order straight: ratio converts market to assessed, exemptions reduce the assessed base, then the rate produces the tax.