8.3 Proration, Transfer Tax, and Investment Math

Closing-Day and Investment Calculations

The final math cluster covers prorations at closing, government transfer taxes, and the investment ratios that value income property. These reward a disciplined step-by-step method more than memorized formulas, because the trap is almost always who owes what and for how many days.

Proration Fundamentals

Proration divides a shared expense or income between buyer and seller by time of ownership. The exam usually uses a statutory year of 360 days and 30-day months (the banker's year) unless it says otherwise.

The method:

1. Find the annual amount.
2. Divide by 360 for a daily rate (or by 12 for a monthly rate).
3. Multiply by the number of days each party owns.

The seller pays through the day of closing in most exam conventions; read the problem for the stated cutoff.

Worked Example: Property Tax Proration

Annual taxes are $3,600, paid in arrears, and closing is on March 31 (90 days into the year under a 360-day calendar). The seller owes for the time owned.

Step 1: Daily rate = $3,600 ÷ 360 = $10. Step 2: Seller's days = 90 (Jan, Feb, Mar at 30 each). Step 3: Seller's share = $10 × 90 = $900.

Because taxes are paid in arrears, the seller's $900 is a credit to the buyer and a debit to the seller at closing.

Transfer (Conveyance) Tax

Many jurisdictions impose a transfer tax stated as a dollar amount per increment of the sale price. The national exam tests the arithmetic, not any specific state rate.

Worked example: A transfer tax of $1.00 per $500 of price (or any fraction thereof) on a $327,400 sale.

Step 1: Divide price by the increment: $327,400 ÷ $500 = 654.8. Step 2: Round UP to the next whole increment because partial increments are taxed: 655. Step 3: 655 × $1.00 = $655.

Trap: forgetting to round up the partial increment understates the tax.

Reading Proration Debits and Credits

The number is only half the answer; the exam also asks who is debited and who is credited. Two patterns cover most questions:

• Expenses paid in arrears (taxes due later): the seller owes for time owned, so the seller's share is a debit to the seller and a credit to the buyer, who will pay the full bill later.
• Expenses prepaid (insurance, annual fees): the seller already paid past the closing date, so the buyer reimburses the seller, a credit to seller and debit to buyer.

Decide arrears versus prepaid first, then the direction follows automatically.

Worked Example: Prepaid Rent Proration

A rented duplex closes June 16. The tenant prepaid $1,800 in rent for all of June (30 days). The seller collected rent the buyer is entitled to keep for days owned after closing.

Step 1: Daily rent = $1,800 ÷ 30 = $60. Step 2: Buyer owns June 16 through 30 = 15 days (assume seller owns the closing day). Step 3: Buyer's share = $60 × 15 = $900.

Because the seller holds rent belonging to the buyer's ownership period, the $900 is a credit to the buyer and a debit to the seller at closing.

Investment Math: Cap Rate, NOI, and Value

Income property is valued with the IRV triangle:

Value = NOI ÷ Cap Rate (and NOI = Value × Rate; Rate = NOI ÷ Value)

Net Operating Income (NOI) = Effective Gross Income − Operating Expenses. NOI excludes debt service (mortgage payments) and depreciation.

Worked example: A building generates $120,000 effective gross income with $45,000 in operating expenses. NOI = $75,000. At a 7.5 percent cap rate, Value = $75,000 ÷ 0.075 = $1,000,000.

Cash Flow and Return Ratios

Two more ratios appear regularly:

Worked example: A property priced at $900,000 with $100,000 annual gross rent has a GRM of 9. If annual cash flow after debt service is $18,000 on $200,000 invested, cash-on-cash return = $18,000 ÷ $200,000 = 9 percent.

Trap: do not subtract the mortgage payment when computing NOI for cap rate, only when computing cash flow.

Building NOI Step by Step

Many investment questions hand you the raw rent roll and expect you to assemble NOI yourself. Follow the income statement order:

1. Potential Gross Income (all units fully rented).
2. Subtract vacancy and collection loss to get Effective Gross Income.
3. Subtract operating expenses (taxes, insurance, management, maintenance) to get NOI.

Worked example: An eight-unit building rents for $1,200 per unit per month, so PGI = $1,200 × 8 × 12 = $115,200. Apply 5 percent vacancy: $115,200 × 0.95 = $109,440 EGI. Subtract $40,000 operating expenses for NOI = $69,440. Reserves and debt service are excluded from NOI.

Proration Methods, Transfer Tax, and Investment Returns

Two proration conventions: A statutory (banker's) year uses 360 days and 30-day months; an actual (calendar) year uses 365 days. The question always tells you which. Daily rate = annual amount / (360 or 365).

Worked tax proration (365-day, seller pays through day before closing): Annual tax $4,380; closing on day 90. Daily = $4,380 / 365 = $12. Seller's share = 90 x $12 = $1,080, entered as a debit to the seller and a credit to the buyer because Nebraska taxes are typically paid in arrears.

Nebraska documentary stamp tax: $2.25 per $1,000 of value. On a $315,000 sale: $315,000 / 1,000 = 315 units x $2.25 = $708.75, paid by the grantor.

Investment Math

Capitalization (value from income): Value = NOI / Cap rate. NOI $69,440 at a 9% cap rate = $69,440 / 0.09 = $771,556 (rounded).

Return on investment: A buyer pays $500,000 cash and nets $45,000 NOI. ROI (cap rate) = $45,000 / $500,000 = 9%.

Equity and appreciation: A property bought for $400,000 appreciates 5%/year for 2 years (simple): gain = $400,000 x 0.05 x 2 = $40,000, value $440,000. If the loan balance is $300,000, owner equity = $440,000 - $300,000 = $140,000. The exam tests each piece separately, so label every dollar as value, loan, equity, income, or expense before computing.