Settlement and Investment Math
This section covers closing costs, prorations, and basic investment calculations.
PITI and Monthly Payment
PITI includes principal, interest, taxes, and insurance.
Example:
Principal and interest = $1,200 Taxes = $300 Insurance = $100
PITI = $1,600 per month
Net to Seller and Cost to Buyer
- Net to seller = Sale price - seller costs
- Cost to buyer = Sale price + buyer costs
Table: Settlement and Investment Metrics
| Metric | Formula | Notes |
|---|---|---|
| Net to seller | Sale price - seller costs | Costs include commission and fees |
| Cost to buyer | Sale price + buyer costs | Add closing costs and prepaids |
| Proration daily rate | Annual cost / 360 or 365 | Use stated method |
| ROI | Annual profit / investment | Percent return |
| Break-even occupancy | Operating expenses / gross income | Percent |
Prorations
Prorations allocate expenses between buyer and seller based on the closing date.
Example:
Annual taxes = $3,600 Daily tax rate = $3,600 / 360 = $10 If closing is 90 days into the year, the seller owes $900 (90 x $10) and the buyer owes $2,700.
Debits and Credits
In closing statements:
- Debits increase what a party owes.
- Credits reduce what a party owes.
Transfer Taxes and Recording Fees
Transfer taxes and recording fees are often charged at closing and allocated by contract.
Investment Calculations
Return on Investment (ROI)
ROI = Annual Profit / Investment
Example:
Annual profit = $12,000 Investment = $120,000
ROI = 10 percent
Appreciation and Depreciation
Appreciation is an increase in value. Depreciation is a decrease in value (or a tax deduction for investment property).
Property Management Calculations
- Gross rent = Monthly rent x 12
- Vacancy loss = Gross rent x vacancy rate
- Effective gross income = Gross rent - vacancy loss
Proration Practice
If annual taxes are $3,650 and closing occurs on day 100 of a 365-day year:
Daily rate = $3,650 / 365 = $10 Seller owes 100 x $10 = $1,000 Buyer owes the remaining $2,650
Investment Return Example
If an investor puts $100,000 down and earns $12,000 net per year, ROI = 12 percent.
Property Management Example
Monthly rent = $1,500 Annual rent = $18,000 Vacancy rate = 5 percent Vacancy loss = $900 Effective gross income = $17,100
Exam Application Check
- To find daily proration, divide annual cost by 360 or 365 (use the method given).
- To calculate ROI, divide annual profit by investment.
- To find net to seller, subtract seller costs from sale price.
Net Sheet Example
Sale price = $400,000 Seller costs (commission, fees, taxes) = $28,000
Net to seller = $400,000 - $28,000 = $372,000
Buyer costs (loan fees, title, escrow) = $9,500
Cost to buyer = $400,000 + $9,500 = $409,500
Debits and Credits Practice
If the seller has prepaid taxes of $1,200 for the year and the buyer closes halfway through, the buyer owes a $600 credit to the seller. The seller receives a credit; the buyer receives a debit.
Exam Application Check
If a question asks which side receives a credit for prepaid items, the answer is the seller.
Property Management and Investment Metrics
Gross rent is the total rent before vacancy. Effective gross income accounts for vacancy loss. Operating expenses include maintenance, taxes, and insurance but exclude mortgage payments.
A simple break-even occupancy calculation is:
Break-even occupancy = Operating Expenses / Gross Income
Example:
Operating expenses = $18,000 Gross income = $30,000 Break-even occupancy = 60 percent
Exam Application Check
If a question asks for break-even occupancy, divide operating expenses by gross income.
Proration Methods and Interest Adjustments
Closing prorations often use either a 360-day year (30-day months) or a 365-day actual method. The method must be stated in the question, so look for that detail first.
Two proration types appear often:
- Accrued expense - Seller owes the buyer because the bill has not been paid yet. Seller gets a debit, buyer gets a credit.
- Prepaid expense - Buyer owes the seller because the seller already paid. Buyer gets a debit, seller gets a credit.
Mortgage interest is usually paid in arrears. At closing, the buyer is charged interest from the closing date through the end of the month. That amount appears as a buyer debit.
Exam Application Check
If the question says taxes are unpaid, treat them as accrued and charge the seller. If it says taxes are prepaid, credit the seller.
Gross Rent Multiplier and Cash-on-Cash Return
Gross rent multiplier (GRM) - A quick valuation tool that compares price to gross annual rent.
GRM = Value / Gross Annual Rent Value = GRM x Gross Annual Rent
Example:
Gross annual rent = $60,000 GRM = 9 Value = $60,000 x 9 = $540,000
Cash-on-cash return - Annual before-tax cash flow divided by cash invested.
Example:
Annual cash flow = $12,000 Cash invested = $100,000 Cash-on-cash return = 12 percent
Exam Application Check
Use GRM when the problem gives gross rent. Use cash-on-cash when the problem gives annual cash flow and the cash invested.
Closing Cost Allocation
Closing costs are allocated by contract and local custom. Typical seller costs include commission and some transfer taxes. Typical buyer costs include lender fees, appraisal, and prepaid escrows.
Rent and Security Deposit Proration
If a property has tenants and the closing occurs mid-month, rent is prorated between buyer and seller. Security deposits are typically credited to the buyer, who will return them at lease end.
Exam Application Check
If a question asks who receives the security deposit credit, the answer is the buyer.
PITI stands for:
If annual taxes are $2,400 and the closing is 6 months into the year, the seller owes:
Net to seller is calculated as:
ROI is calculated as:
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