8.3 Proration, Transfer Tax, and Investment Math

Proration, Transfer Tax, and Investment Math

Proration splits a recurring cost between the buyer and seller so each pays only for the period they own the property. The two recurring questions are: who has used the service, and who has already paid.

Proration mechanics

1. Find the daily (or monthly) rate of the item.
2. Count the days each party is responsible. The seller usually owns through the day of closing.
3. Decide direction:
   • Accrued / unpaid (e.g., taxes paid in arrears): seller owes the buyer -> credit buyer, debit seller.
   • Prepaid (e.g., insurance, HOA already paid): buyer reimburses seller -> credit seller, debit buyer.

Unless told otherwise, use a 360-day year (12 months of 30 days). A problem that says "actual/365" wants the calendar-day method.

Worked example: property tax proration

Annual taxes are $3,600, paid in arrears. Closing is on April 30, and the seller owns through the closing day.

1. Daily rate (360-day): $3,600 / 360 = $10/day.
2. Seller's days: Jan, Feb, Mar, Apr = 4 months x 30 = 120 days.
3. Seller's share = 120 x $10 = $1,200.

Because taxes are paid in arrears (not yet paid), the seller owes the buyer this $1,200: debit seller, credit buyer.

Trap: Reverse the direction if taxes were prepaid. Read whether the bill is already paid.

Transfer and recordation taxes

Transfer taxes are charged per increment of the sale price or loan amount. A typical phrasing: "$0.50 per $500 of value."

Worked example

Sale price $320,000; transfer tax of $0.50 per $500.

1. Number of increments = $320,000 / $500 = 640.
2. Tax = 640 x $0.50 = $320.

If the rate is stated per $1,000, divide by 1,000 instead. Trap: Match the increment to the rate's stated unit ($500 vs $1,000 vs $100); using the wrong increment is the most common error.

Investment math

Income property is valued by its net operating income (NOI) - effective gross income minus operating expenses (NOT including debt service or depreciation).

Worked example: cap rate to value

A building produces $48,000 NOI. Investors in the area expect an 8% cap rate. Value = $48,000 / 0.08 = $600,000.

If the same building's price were $600,000 and gross annual rent were $75,000, the GRM = $600,000 / $75,000 = 8.0. Note that GRM uses gross rent while the cap rate uses NOI - never mix them.

Trap: Debt service and depreciation are excluded from NOI. Including the mortgage payment in operating expenses understates NOI and distorts the cap rate.

Calendar-day (actual/365) prorations

When a problem specifies actual/365, count the real days in each month rather than using 30-day months. The daily rate is the annual amount divided by 365.

Worked example: insurance proration, actual/365

A seller prepaid a $1,460 annual hazard policy. Closing is on the 200th day of the policy year, and the seller owns through closing day.

1. Daily rate = $1,460 / 365 = $4/day.
2. Buyer's days remaining = 365 - 200 = 165 days.
3. Buyer reimburses seller = 165 x $4 = $660: a prepaid item, so debit buyer, credit seller.

Capitalization and the income approach in depth

Cap-rate problems flow in three directions from V = I / R (value = income / rate). Rearrange to find any missing term.

Worked example: building the NOI first

A 10-unit building rents for $1,200/unit/month with 5% vacancy and $46,800 annual operating expenses. Potential gross = 10 x $1,200 x 12 = $144,000. Effective gross = $144,000 x 0.95 = $136,800. NOI = $136,800 - $46,800 = $90,000. At an 8% cap rate, value = $90,000 / 0.08 = $1,125,000.

Trap: Debt service (the mortgage payment) and depreciation are never subtracted to reach NOI. Cap-rate value is a property-level figure independent of how any single buyer finances it; including the loan payment understates NOI and inflates the apparent value.

Gross rent multiplier and equity build

Two more income tools round out investment math. The gross rent multiplier (GRM) values small rentals off gross rent without expenses: GRM = price / gross rent. If comparable duplexes sell at a GRM of 9 and a subject property grosses $30,000/year, indicated value = 9 x $30,000 = $270,000. GRM uses gross rent; the cap rate uses net operating income — never interchange them.

Equity is market value minus debt owed. A $500,000 building with a $310,000 loan balance carries $500,000 - $310,000 = $190,000 of equity. As the owner pays down principal and the property appreciates, equity grows on both ends.

Trap: A higher cap rate signals higher risk / lower price for the same income, while a low cap rate reflects a premium, low-risk asset. Candidates often invert the relationship between cap rate and value.