8.3 Proration, Transfer Tax, and Investment Math
Key Takeaways
- Proration divides shared annual costs by 365 (or 360) days to allocate them at closing.
- The seller typically owes costs through the day before closing; confirm which day convention the question states.
- Transfer tax equals the taxable amount divided by the stated increment, times the rate per increment.
- Capitalization rate equals net operating income divided by value; rearrange to solve for any term.
- Always read whether the buyer or seller is debited and credited for a prorated item.
Proration at Closing
Proration splits an annual cost between buyer and seller based on who owned the property each part of the year. The two conventions are the 365-day method (actual calendar, also called the exact method) and the 360-day method (a banker's 30-day month, also called the statutory method).
Process:
- Find the daily rate: annual amount / 365 (or 360).
- Count the days each party is responsible.
- Multiply daily rate by days.
The seller generally pays for the day of closing back to the start of the period; the buyer pays from closing forward. Always honor the day count the question specifies, then decide who is debited and who is credited.
Worked Tax Proration
Annual property taxes are $3,650, already paid by the seller for the full calendar year. Closing is on July 1 (day 182 of a 365-day year), and the buyer reimburses the seller for the remaining days.
- Daily rate: 3,650 / 365 = $10.00 per day.
- Days remaining (buyer's responsibility): 365 - 181 = 184 days.
- Buyer owes seller: 184 x $10.00 = $1,840.
Because the seller prepaid, the buyer is debited $1,840 and the seller is credited $1,840. If taxes were unpaid and owed in arrears, the seller would instead be debited for the days they owned. Direction depends on who already paid.
Transfer and Recordation Tax
Transfer taxes are usually charged per increment of value, such as $0.50 per $500, or as a flat percentage. The per-increment method is the tested one.
A property sells for $284,000 with a transfer tax of $0.55 per $500:
- Increments: 284,000 / 500 = 568.
- Tax: 568 x $0.55 = $312.40.
If the price does not divide evenly, round the number of increments up to the next whole increment before multiplying, because partial increments are charged in full. Confirm whether the rate is per $500, per $1,000, or per $100; using the wrong increment is the dominant error here.
Investment: Cap Rate and GRM
Income property uses the cap-rate triangle: Value = NOI / Cap Rate, NOI = Value x Cap Rate, Cap Rate = NOI / Value. NOI is net operating income (effective gross income minus operating expenses, before debt service).
A building has NOI of $48,000 and the market cap rate is 8%. Value = 48,000 / 0.08 = $600,000. A lower cap rate produces a higher value, which signals a less risky asset.
The Gross Rent Multiplier (GRM) = Price / Gross Annual Rent. A $600,000 property renting for $60,000 annually has a GRM of 10. Multiply a comparable's rent by the GRM to estimate value. GRM ignores expenses; cap rate accounts for them.
Depreciation and the Cost-Approach Numbers
The cost approach and income-tax problems both use straight-line depreciation: an equal amount each year over the asset's useful life. Only improvements depreciate; land never does (recall indestructibility).
Depreciation example. A building (excluding land) costs $400,000 with a 40-year useful life.
- Annual depreciation = $400,000 ÷ 40 = $10,000 per year (or 2.5% straight-line).
- After 6 years, accumulated depreciation = 6 × $10,000 = $60,000.
- Depreciated (book) value of the improvement = $400,000 − $60,000 = $340,000.
In the cost approach, value = land value + (reproduction/replacement cost of improvements − accrued depreciation). Add the land back at full value because it does not depreciate.
Appreciation, Equity Build-Up, and a Combined Investment Problem
Appreciation compounds on the growing value, unlike straight-line depreciation. The exam usually keeps it to one or two periods.
Appreciation example. A property worth $300,000 appreciates 4% in year one and 5% in year two.
- After year 1: $300,000 × 1.04 = $312,000.
- After year 2: $312,000 × 1.05 = $327,600.
Combined investment problem. An apartment building produces effective gross income of $90,000 with operating expenses of $34,000.
- NOI = $90,000 − $34,000 = $56,000.
- At an 8% cap rate, value = $56,000 ÷ 0.08 = $700,000.
- If the buyer pays $700,000 and rents total $87,500 annually, the GRM = $700,000 ÷ $87,500 = 8.
Cap rate uses NOI (after operating expenses); GRM uses gross rent (before expenses) — never mix the two.
Equity, Return on Investment, and a Net-Operating-Income Build
Investors track equity (value minus debt) and cash-on-cash return (annual cash flow ÷ cash invested). The exam keeps these arithmetic-light.
Equity example. A property worth $480,000 carries a $300,000 mortgage. Equity = $480,000 − $300,000 = $180,000.
Return on investment. An investor puts $120,000 cash into a property that yields $14,400 in annual pre-tax cash flow. ROI = $14,400 ÷ $120,000 = 12%.
Building NOI from the rent roll. A fourplex rents for $1,200 per unit per month, with a 5% vacancy allowance and $18,000 of annual operating expenses.
- Potential gross income = 4 × $1,200 × 12 = $57,600.
- Less 5% vacancy = $57,600 × 0.95 = $54,720 effective gross income.
- NOI = $54,720 − $18,000 = $36,720.
Use NOI (not gross rent) with the cap rate; vacancy is subtracted before expenses to reach effective gross income.
Annual taxes of $2,920 are unpaid and owed in arrears. Closing is at the end of day 90, using a 365-day year, and the seller owes through closing. How much is the seller debited?
An income property generates $72,000 in net operating income. Investors in the market expect a 9% capitalization rate. What is the indicated value?