8.3 Proration, Transfer Tax, and Investment Math

Proration Basics

Proration divides a shared expense between buyer and seller based on who occupies the property when. At closing, the seller is responsible for the period up to the closing date; the buyer takes over from there. Steps:

1. Find the annual amount of the item (taxes, insurance, HOA).
2. Compute the daily rate: annual / 360 (banker's year) or / 365 (calendar). The question tells you which.
3. Count the days the responsible party owes.
4. Multiply daily rate x days, then assign as a debit or credit.

Trap: mixing methods. If the problem says "use a 360-day year and 30-day months," do not switch to actual calendar days. Read the convention first.

Debit vs. Credit Direction

Direction trips up more candidates than arithmetic. Decide whether the item is paid in arrears or prepaid:

Example: annual taxes are $3,600, unpaid (arrears), 360-day year, closing on the 90th day.

• Daily rate: $3,600 / 360 = $10
• Seller owes 90 days: 90 x $10 = $900
• The $900 is a debit to the seller, credit to the buyer, who will pay the full bill later.

Worked Transfer Tax, Mills, and Cap-Rate Investment

Transfer tax (per $500): A state taxes $1.00 per $500 of price. On a $347,500 sale, divide first: 347,500 ÷ 500 = 695 taxable units × $1.00 = $695. Always divide before multiplying, and round the number of units up if the statute requires whole increments. (North Carolina's excise/"revenue" stamp tax is $1 per $500, i.e., $2 per $1,000, paid by the seller — a State-section overlap worth memorizing.)

Mill rate: Assessed value $280,000 at 18.5 mills. One mill = $1 per $1,000, so tax = 280 × 18.5 = $5,180. If the assessment ratio is 80% of a $350,000 market value, assessed value = 280,000 first, then apply the mills.

Cap rate / GRM: A fourplex nets $33,000 NOI and sells for $412,500. Cap rate = 33,000 ÷ 412,500 = 8%. If gross monthly rent is $4,400, the GRM = 412,500 ÷ 4,400 = 93.75. Investors compare a subject's GRM against market GRM to spot over- or under-pricing.

Worked Investment Return, Equity Buildup, and Rent Proration

Cash-on-cash return: An investor pays $500,000 with $125,000 down (rest financed) and clears $15,000 annual cash flow after debt service. Cash-on-cash = 15,000 ÷ 125,000 = 12%. This differs from the cap rate, which ignores financing and divides NOI by total price.

Appreciation and equity: A $300,000 property appreciating 4% annually is worth 300,000 × 1.04 = $312,000 after year one, and 312,000 × 1.04 = $324,480 after year two (compound, not 8% simple). Combined with loan paydown, equity grows from both appreciation and amortization.

Rent proration: Monthly rent is $1,800 and the property sells on the 10th with rent collected for the full month by the seller. The buyer owns days 10–30 = 21 days. Daily rent (30-day month) = 1,800 ÷ 30 = $60; buyer's share = 21 × 60 = $1,260, entered as a credit to the buyer, debit to the seller, since the seller holds rent for days the buyer owns.

Transfer and Stamp Taxes

States impose a transfer tax (also called documentary stamp or conveyance tax) when title transfers. It is typically quoted per $500 or per $100 of the sale price, so you must convert the price into the correct number of taxable units.

Formula: Tax = (Price / Unit) x Rate per Unit

Example: price $250,000, tax of $1.00 per $500.

• Units: $250,000 / $500 = 500 units
• Tax: 500 x $1.00 = $500

Trap: rounding. Many statutes round the price up to the next full $500 increment before taxing. A $250,250 sale is taxed as 501 units, not 500.5. The exam may also assign the tax to seller or buyer, so read who pays.

Property Tax and Mill Rates

Annual property tax is based on assessed value, which may differ from market value by an assessment ratio:

Tax = Assessed Value x Tax Rate

Rates are often stated in mills. One mill = $0.001, or $1 per $1,000 of assessed value. Convert mills to a decimal by dividing by 1,000.

Example: market value $400,000, assessment ratio 40%, tax rate 25 mills.

• Assessed value: $400,000 x 0.40 = $160,000
• Rate: 25 mills = 0.025
• Tax: $160,000 x 0.025 = $4,000

Trap: taxing the market value instead of the assessed value. Always apply the assessment ratio first when one is given, then apply the mill rate to the assessed figure.

Gross Rent and Income Multipliers

Investors use quick screening ratios. The Gross Rent Multiplier (GRM) uses monthly rent; the Gross Income Multiplier (GIM) uses annual income.

GRM = Price / Monthly Gross Rent

Example: a duplex sells for $360,000 and rents for $3,000 per month. GRM = $360,000 / $3,000 = 120. To value a comparable property renting for $3,200/month, multiply: $3,200 x 120 = $384,000.

Trap: mixing monthly and annual figures. GRM is monthly; GIM is annual. A GRM near 100-130 is normal, while a GIM is roughly one-twelfth of that. Confusing the two inflates or deflates the value by a factor of twelve, a favorite distractor.