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 = $1,200 + $300 + $100 = $1,600 per month

Net to Seller and Cost to Buyer

$\text{Net to Seller} = \text{Sale Price} - \text{Seller Costs}$

$\text{Cost to Buyer} = \text{Sale Price} + \text{Buyer Costs}$

Table: Settlement and Investment Metrics

Prorations

Prorations allocate expenses between buyer and seller based on the closing date.

$\text{Daily Rate} = \frac{\text{Annual Cost}}{360 \text{ or } 365}$

Example:

Annual taxes = $3,600 Daily tax rate = $3,600 ÷ 360 = $10/day If closing is 90 days into the year, the seller owes $900 (90 × $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)

$\text{ROI} = \frac{\text{Annual Profit}}{\text{Investment}}$

Example:

Annual profit = $12,000 Investment = $120,000

ROI = $12,000 ÷ $120,000 = 10%

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 × 12
• Vacancy loss = Gross rent × 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/day Seller owes 100 × $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%.

Property Management Example

Monthly rent = $1,500 Annual rent = $18,000 Vacancy rate = 5% 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:

$\text{Break-even Occupancy} = \frac{\text{Operating Expenses}}{\text{Gross Income}}$

Example:

Operating expenses = $18,000 Gross income = $30,000 Break-even occupancy = $18,000 ÷ $30,000 = 60%

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.

$\text{GRM} = \frac{\text{Value}}{\text{Gross Annual Rent}}$

$\text{Value} = \text{GRM} \times \text{Gross Annual Rent}$

Example:

Gross annual rent = $60,000 GRM = 9 Value = $60,000 × 9 = $540,000

Cash-on-cash return - Annual before-tax cash flow divided by cash invested.

$\text{Cash-on-Cash Return} = \frac{\text{Annual Cash Flow}}{\text{Cash Invested}}$

Example:

Annual cash flow = $12,000 Cash invested = $100,000 Cash-on-cash return = $12,000 ÷ $100,000 = 12%

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.