8.3 Proration, Transfer Tax, and Investment Math

Proration at closing

Proration splits a recurring expense (property taxes, HOA dues, prepaid rent, insurance) fairly between buyer and seller based on the closing date. The exam usually uses a 360-day banker's year (30 days per month) unless it states a 365-day year.

Step-by-step tax proration

Annual taxes are $3,600 and closing is on April 1 with the seller responsible through the day before closing. The seller has owned the property for January, February, and March (3 months).

1. Daily rate (360-day): 3,600 / 360 = $10 per day
2. Seller's days: 3 months x 30 = 90 days
3. Seller's share: 90 x $10 = $900

If the taxes are paid in arrears (not yet paid), the seller owes the buyer $900 as a credit to the buyer and a debit to the seller, because the buyer will pay the full bill later. Read carefully whether taxes are prepaid or in arrears — it flips the debit/credit direction.

Rent proration

Rent is usually collected in advance, so a seller who already received the month's rent owes the buyer the unearned portion. Monthly rent is $1,500 and closing is June 16, with the buyer owning from the closing date forward (15 days remaining in a 30-day month).

• Daily rent: 1,500 / 30 = $50
• Buyer's share (days 16-30 = 15 days): 15 x $50 = $750

The seller credits the buyer $750. The trap is counting the wrong party's days; mark on a calendar who owns each day before multiplying.

Transfer tax

Transfer (or conveyance/documentary) tax is charged on the sale price at a stated rate per dollar increment. A typical phrasing is $0.50 per $500 of price.

For a $360,000 sale at $0.50 per $500:

1. Number of $500 increments: 360,000 / 500 = 720
2. Tax: 720 x $0.50 = $360

If the rate were $1.00 per $1,000, you would compute 360,000 / 1,000 = 360 increments x $1.00 = $360. The trap is using the wrong increment size; always match the divisor to the stated unit ($500 vs. $1,000).

Investment math

Capitalization rate

The income approach values income property with: Value = Net Operating Income (NOI) / Cap Rate. NOI is income after operating expenses but before debt service.

A building has NOI of $48,000 and the market cap rate is 8%: Value = 48,000 / 0.08 = $600,000. Rearranged forms: Cap Rate = NOI / Value, and NOI = Value x Cap Rate. A lower cap rate produces a higher value for the same income.

Gross rent multiplier (GRM)

GRM = Price / Gross Annual Rent. If similar properties sell at a GRM of 9 and a subject earns $66,000 in gross annual rent: Value = 9 x 66,000 = $594,000. GRM uses gross rent (no expense deduction), unlike cap rate which uses NOI.

Property tax mills

One mill = $1 per $1,000 of assessed value = 0.001. With a 25-mill rate and a $240,000 assessment: tax = 240,000 x 0.025 = $6,000. To convert mills to a decimal, divide by 1,000 (25 mills = 0.025).

Building NOI from a rent roll

Many exam questions make you build NOI before capitalizing. Start with potential gross income, subtract vacancy, then subtract operating expenses. Do not subtract mortgage payments or depreciation — those are below the NOI line.

A fourplex rents for $1,200 per unit per month with a 5% vacancy allowance and $14,000 in annual operating expenses:

1. Potential gross income: 4 x 1,200 x 12 = $57,600
2. Vacancy loss: 57,600 x 0.05 = $2,880
3. Effective gross income: 57,600 - 2,880 = $54,720
4. NOI: 54,720 - 14,000 = $40,720

At a 7% cap rate, value = 40,720 / 0.07 = roughly $581,714. Subtracting the loan payment before reaching NOI is the classic error.

Return on investment and equity dividend

Cash-on-cash return = annual cash flow / cash invested. If an investor puts $120,000 down and nets $10,800 in annual cash flow after debt service: 10,800 / 120,000 = 9%. Distinguish this from the cap rate, which ignores financing entirely.

Profit and loss percentages

Seller and appreciation questions test percentage change. Percent gain or loss = (amount of change / original cost). A seller bought for $250,000 and sells for $300,000: gain = 50,000 / 250,000 = 20%.

Working backward: if a property sold for $300,000 at a 20% profit, the original cost is sale price / 1.20 = 300,000 / 1.20 = $250,000. The trap is taking 20% of the sale price instead of dividing; 300,000 x 0.80 = $240,000 is wrong because the percentage was based on the original cost, not the sale price.

Assessment and the tax bill

Property tax flows from assessed value, which may be a fraction of market value. If a home with a $400,000 market value is assessed at 60% of value, the assessed value is 400,000 x 0.60 = $240,000. At a 25-mill rate (0.025): tax = 240,000 x 0.025 = $6,000.