14.3 Property Taxes, Prorations & Loan Calculations

14.3 Property Taxes, Prorations & Loan Calculations

Exam Focus: Financial settlement and lending calculations are heavily emphasized on the broker exam. Candidates must master ad valorem property tax assessments across multiple taxing jurisdictions, execute precise closing prorations using both statutory (360-day) and exact (365-day) calendar methods, apply Texas closing conventions, calculate Loan-to-Value (LTV) ratios based on appraised value versus sales price, compute upfront discount points, and break down monthly mortgage amortization payments into principal and interest.

1. Ad Valorem Real Property Tax Calculations

Real property taxes in Texas are ad valorem taxes (Latin for "according to value"). Under the Texas Tax Code, county appraisal districts (CADs) establish the market value of all real property within the county as of January 1 each year.

Key Definitions & Tax Formulas

1. Market Value: The price at which a property would transfer for cash in an open, competitive market.
2. Assessment Ratio: The percentage of market value subject to taxation (in Texas, properties are assessed at 100% of market value, subject to statutory exemptions).
3. Assessed Value (Taxable Value): Market Value minus allowable exemptions (e.g., General Residence Homestead, Over-65, Disabled Veteran): $\text{Assessed Value} = (\text{Market Value} \times \text{Assessment Ratio}) - \text{Exemptions}$
4. Annual Property Tax Formula: $\text{Annual Property Tax} = \text{Assessed (Taxable) Value} \times \text{Tax Rate}$

Understanding Tax Rate Expressions

Tax rates are expressed in three distinct formats across exam questions:

• Rate per $100 of Valuation (Texas Standard): Used by Texas school districts, cities, and counties.
  • Example: A tax rate of $2.45 per $100 assessed value equals $\frac{$2.45}{100} = 0.0245$ ($2.45%$).
• Percentage Rate: Direct percentage multiplier (e.g., $2.50% = 0.0250$).
• Millage Rate (Mills): Used in many national exam questions. One mill equals one-tenth of a cent ($0.001) or $1.00 per $1,000 of assessed value.
  • Conversion Formula: $\text{Tax Rate (Decimal)} = \frac{\text{Number of Mills}}{1,000}$
  • Example: 28 mills $= \frac{28}{1,000} = 0.0280$ ($2.80%$).

┌─────────────────────────────────────────────────────────────────────────────┐
│                      TAX RATE CONVERSION EQUIVALENTS                        │
├───────────────────┬─────────────────────┬───────────────────┬───────────────┤
│ Decimal Rate      │ Percentage          │ Rate per $100     │ Millage Rate  │
├───────────────────┼─────────────────────┼───────────────────┼───────────────┤
│ 0.0100            │ 1.00%               │ $1.00 per $100    │ 10 mills      │
│ 0.0225            │ 2.25%               │ $2.25 per $100    │ 22.5 mills    │
│ 0.0280            │ 2.80%               │ $2.80 per $100    │ 28 mills      │
│ 0.0350            │ 3.50%               │ $3.50 per $100    │ 35 mills      │
└───────────────────┴─────────────────────┴───────────────────┴───────────────┘

Worked Property Tax Example (Multi-Entity)

• Property Market Value: $450,000
• Exemptions: $100,000 State Homestead Exemption (applicable to School District only)
• Taxing Jurisdictions:
  • Independent School District (ISD): $1.15 per $100 ($0.0115)
  • County General Fund: $0.45 per $100 ($0.0045)
  • City Municipality: $0.55 per $100 ($0.0055)
  • Emergency Services District (ESD): $0.10 per $100 ($0.0010)
• Calculations:
  • ISD Taxable Value: $$450,000 - $100,000 = $350,000$
  • ISD Annual Tax: $$350,000 \times 0.0115 = $4,025.00$
  • Non-ISD Combined Rate: $$0.45 + $0.55 + $0.10 = $1.10 \text{ per } $100$ ($0.0110$)
  • Non-ISD Taxable Value: $$450,000$
  • Non-ISD Annual Tax: $$450,000 \times 0.0110 = $4,950.00$
  • Total Annual Ad Valorem Tax: $$4,025.00 + $4,950.00 = \mathbf{$8,975.00}$

2. Proration Calculations & Texas Closing Custom

Proration is the proportionate division and allocation of ongoing property expenses and income between buyer and seller as of the closing date.

Texas Promulgated Contract Convention

Under Paragraph 13 of the TREC One to Four Family Residential Contract (Resale), taxes for the current year, interest, maintenance fees, and rents are prorated through the closing date.

• Statutory Custom: The seller owns the property through and including the closing day. Therefore, the seller is charged (debited) for all expenses and credited for all revenue up to and including midnight of the closing date.

Accrued vs. Prepaid Items

┌─────────────────────────────────────────────────────────────────────────────┐
│                     ACCRUED ITEMS vs. PREPAID ITEMS                         │
├──────────────────────────────────────┬──────────────────────────────────────┤
│     ACCRUED ITEMS (Paid in Arrears)  │      PREPAID ITEMS (Paid in Advance) │
├──────────────────────────────────────┼──────────────────────────────────────┤
│ • Expenses incurred but not yet paid │ • Expenses paid in advance by seller │
│ • Examples: Real property taxes,     │ • Examples: Annual HOA dues, prepaid │
│   unpaid mortgage interest           │   hazard insurance, collected rent   │
│ • CLOSING DISCLOSURE ENTRY:          │ • CLOSING DISCLOSURE ENTRY:          │
│   ► DEBIT SELLER                     │   ► CREDIT SELLER                    │
│   ► CREDIT BUYER                     │   ► DEBIT BUYER                      │
└──────────────────────────────────────┴───────────────────────────────────────┘

360-Day Banker's Year vs. 365-Day Calendar Year

• 360-Day Banker's Year (Statutory Year): Assumes 12 equal months of 30 days each ($12 \times 30 = 360 \text{ days}$). Daily rate $= \frac{\text{Annual Amount}}{360}$.
• 365-Day Calendar Year (Exact Day Method): Uses actual calendar days in each specific month ($31, 28, 31, 30, \dots$). Daily rate $= \frac{\text{Annual Amount}}{365}$.

Property Tax & Proration Math Step-by-Step Table

Worked Proration Comparison

• Scenario: Closing occurs on April 18. Annual property taxes are $4,320 and will be paid in arrears by the buyer at year-end. The seller owns through the day of closing.
• Method A (360-Day Banker's Year):
  • Full months elapsed: Jan (30) + Feb (30) + Mar (30) = 90 days
  • Days in April: 18 days
  • Total Seller Days: $90 + 18 = 108 \text{ days}$
  • Daily Tax Rate: $$4,320 / 360 = $12.00 \text{ per day}$
  • Prorated Amount: $108 \text{ days} \times $12.00 = \mathbf{$1,296.00}$
  • Entry: Debit Seller $1,296.00; Credit Buyer $1,296.00
• Method B (365-Day Calendar Year):
  • Actual days elapsed: Jan (31) + Feb (28) + Mar (31) + Apr (18) = 108 days
  • Daily Tax Rate: $$4,320 / 365 = $11.835616 \text{ per day}$
  • Prorated Amount: $108 \text{ days} \times $11.835616 = \mathbf{$1,278.25}$
  • Entry: Debit Seller $1,278.25; Credit Buyer $1,278.25

3. Mortgage Loan Calculations & Amortization Mechanics

1. Loan-to-Value (LTV) Ratio

The Loan-to-Value (LTV) ratio expresses the relationship between the loan principal and the underlying property value.

$\text{LTV} = \frac{\text{Loan Amount}}{\text{Lesser of Appraised Value or Contract Sales Price}}$

Exam Trap (The Appraisal Shortfall Rule): If the appraised value comes in lower than the contract sales price, the lender will strictly base the maximum loan amount on the Appraised Value, not the purchase price. The buyer must provide additional cash out-of-pocket to cover the shortfall.

• Example: Purchase price is $380,000, but the appraisal comes in at $360,000. The buyer qualifies for an 80% LTV loan.
  • Maximum Loan Amount: $$360,000 \times 0.80 = \mathbf{$288,000}$ (NOT $$380,000 \times 0.80 = $304,000$)
  • Buyer Down Payment / Cash Required: $$380,000 - $288,000 = \mathbf{$92,000}$

2. Loan Discount Points & Origination Fees

• Discount Points: Upfront prepaid interest paid to the lender at closing to lower (buy down) the note interest rate over the life of the loan.
• Point Value: 1 Point = 1.0% of the LOAN AMOUNT (never the sales price!).
• Lender Yield Rule of Thumb: Each 1 discount point paid increases the lender's effective yield by approximately 1/8 of 1% (0.125%).
• Example: On a $300,000 loan, 2.5 discount points + a 1.0% origination fee equal: $\text{Total Points} = 3.5\% = 0.035$ $\text{Total Upfront Fee} = \$300,000 \times 0.035 = \mathbf{\$10,500}$

3. Simple Interest & Monthly Amortization Schedule Mechanics

In standard fully amortizing fixed-rate mortgages, interest is calculated using the simple interest formula applied to the remaining loan balance:

$\text{Annual Interest} = \text{Principal Loan Balance} \times \text{Annual Interest Rate}$

$\text{Monthly Interest} = \frac{\text{Annual Interest}}{12}$

$\text{Monthly Principal Reduction} = \text{Total Monthly P\&I Payment} - \text{Monthly Interest}$

$\text{New Principal Balance} = \text{Previous Balance} - \text{Monthly Principal Reduction}$

Loan Calculation Formulas Guide & Amortization Walkthrough

• Loan Terms: Principal Balance = $250,000; Interest Rate = 6.0%; Monthly Principal & Interest (P&I) Payment = $1,498.88.

┌─────────────────────────────────────────────────────────────────────────────┐
│                     MONTH 1 AMORTIZATION BREAKDOWN                          │
├─────────────────────────────────────────────────────────────────────────────┤
│ 1. Current Principal Balance                              $250,000.00       │
│ 2. Annual Interest ($250,000 × 0.06)                        $15,000.00       │
│ 3. Month 1 Interest Due ($15,000 / 12)                       $1,250.00       │
│ 4. Total Monthly P&I Payment                                 $1,498.88       │
│ 5. Month 1 Principal Reduction ($1,498.88 - $1,250.00)         $248.88       │
│ 6. New Principal Balance ($250,000 - $248.88)             $249,751.12       │
├─────────────────────────────────────────────────────────────────────────────┤
│                     MONTH 2 AMORTIZATION BREAKDOWN                          │
├─────────────────────────────────────────────────────────────────────────────┤
│ 1. Starting Principal Balance                             $249,751.12       │
│ 2. Annual Interest ($249,751.12 × 0.06)                     $14,985.07       │
│ 3. Month 2 Interest Due ($14,985.07 / 12)                    $1,248.76       │
│ 4. Total Monthly P&I Payment                                 $1,498.88       │
│ 5. Month 2 Principal Reduction ($1,498.88 - $1,248.76)         $250.12       │
│ 6. New Principal Balance ($249,751.12 - $250.12)          $249,501.00       │
└─────────────────────────────────────────────────────────────────────────────┘