Chapter 15Mortgage Calculations and Decisions

REAL ESTATEFIN 331

SEVEN VITAL FEATURES OF A MORTGAGE

1. Principal amount2. Term to maturity3. Interest rate4. Monthly payment5. Amortization schedule6. Points7. Financing Costs

BASIC MORTGAGE COMPUTATIONS

A. Using the Texas Instrument BA II Plus financial calculator1. Mortgage calculations require 4 of the six

basic functionsa. Number of payments (N)b. Interest rate per year (I/Y) (P/Y must be set to 12

for a standard mortgage)c. Loan amount (PV: present value equals about the

loan)d. Monthly payment (PMT)e. Value of the mortgage at maturity (FV)f. Compute (CPT)

BASIC MORTGAGE COMPUTATIONS

B. Example: $200,000 loan @ 4.50% for 30 years, 1.5 points, $2000 closing costs.

1. Points to Lender: .015 * 200,000 = $3,0002. 3rd Party Loan Expense: $2000.003. Total Costs: $5,000 ($3000 + $2000)4. Net Loan proceeds to Borrower: 195,000

C. Computing Monthly P&I1. N=360, I/Y = 4.5%, PV = 200,0002. CPT PMT: $-1013.37

BASIC MORTGAGE COMPUTATIONS

D. Preparing the Amortization Schedule1. Using the AMORTization function (a second function of the

PV key)2. Set the P1 and P2 values to 1: P1 = 1 [], P2 = 1 3. Press the down key []4. Read the BALance5. Press the down key []6. Read the PRiNcipal7. Press the down key []8. Read the INTerest9. Press the down key []10. press the compute key (CPT): P1 and P2 values will

increment to the next payment11. repeat steps starting with “c”

Effective Borrowing Costs

A.Third-party expenses: up-front expenses incurred by borrower but not paid to lender:1. Mortgage insurance premium2. Taxes on the loan3. Lender’s title insurance4. Appraisal5. Survey

Effective Borrowing Costs

B. Effect of 3rd party payments: 1. Borrower net less at loan closing than lender’s

actual net disbursement to borrower2. Result?

a. EBC > lender’s yield

C. Compute EBC to BorrowerN=360, PV = 195,000, PMT = 1,013.37CPT I/Y = 4.717285% (vs 4.5% quoted rate)

D. Compute Lender’s Yield (IRR)3. N=360, PV = 197,000, PMT = -1,013.374. CPT I/Y = 4.629374%

Lender’s Yield, EBC Example 2

A. 15 year mortgage, $160,000 loan @4.50%, $2000 in points, $2000 loan origination expense.1. N= 180, I/Y = 4.5, PV = 160,000: CPT

PMT2. Compute monthly PMT: $-1,223.993. Compute Lenders Yield: PV = 158,000

CPT I/Y = 4.688783%

3. Compute Effective Borrowing CostsPV = 156,000, CPT I/Y = 4.880999%

Truth in Lending Act (FILA)

A.Federal Truth in Lending Act requires disclosure of annual percentage rate (APR) on virtually all home mortgage loans

B.APR: Yield to maturity, after adjusting for:1.All loan finance charges2.All compensation to originating brokers3.All other charges controlled by lender4.Premiums for any required insurance

C.What inadequacy might you see in the APR as a measure of true borrowing cost?

Effects of Loan Prepayment

A.Suppose the previous loan is prepaid in 7 years. What are the effects on Lenders Yield and the EBC for Borrower?1. Loan Balance after 84 payments (7 * 12)2. AMORT: P1=84, P2=84: Bal = 98,524.093. Lender’s Yield: N = 84, PV = 158,000, FV = -

98524.03 (paying off loan balance. CPT I/Y = 4.75%

4. EBC: PV = 156,000, CPT I/Y = 5.01%5. Bottom line: Prepayment actually increases

Lender’s Yield and also EBC of loan.

TI-83 Procedure

A. APPS: 1: Finance, press ENTER keyB. 1: TVM Solver, press ENTER key

1. Set Values: N = 180, I% = 4.5%, PV = 1600002. Cursor to PMT, press ALPHA key, the ENTER

key: PMT = -1223.993. Compute Lender’s Yield: PV = 158000, cursor

to I%, press ALPHA key, the ENTER key: I% = 4.69%

4. Compute EBC: PV = 156000, cursor to I%, press ALPHA key, the ENTER key: I%=4.88

TI-83 Procedure

B. Effects of Prepayment: Lender’s Yield

1. APPS, cursor up to 9bal(, press ENTER, enter 84), press ENTER, bal(84) 98524.09

2. APPS, ENTER, ENTER: Set N = 84, PV = 158000, FV = -98524.09, cursor to I%, ALPHA ENTER, I% = 4.75

C. Effect of Prepayment: EBC1. PV = 156000, cursor to i%, ALPHA, ENTER, I%= 5.01

Effects of Additional Principal

A. What happens when we add $100 to the monthly payment?1. PMT = -1323.99, solve N = 161.272. Lender’s Yield: I% = 4.71% (vs. 4.75%)3. EBC: PV = 156000, I% = 4.92% (vs.

5.01%)

Effects of Balloon Payments

A. 15 year, $160,000 @ 4.5% mortgage, with a $40,000 balloon payment (a partially amortized mortgage) with $1600 in points and $800 in losing fees.1. N=180, I/Y= 4.50, PV = 160,000: FV = -

40,000 PMT = $1,067.992. Lenders Yield: 4.63%3. EBC = 4.70%4. Total Pmt.: $232,238.55 →S Int = $72,238.55

5. “Standard” Mortgage: S Int = $60,318.07

Adjustable Rate Mortgage

A. Worst Case: 1-year ARM, 30-year term1. $100,000 loan @ 3%: PMT = $421.602. Bal(12) = $97,912.243. Reset interest rate after first year to 4%:

N = 348, I/Y = 4.00, PV = 97912.24, PMT = $475.83

4. Bal(12) = $96,085.525. Reset interest rate after second year to 5%:

N = 336, I/Y = 5.00, PV = 96085.52, PMT = $531.90

B. If life-time cap = 5% - what can PMT rise to if rates go up 1% every year? $707.89

Some Cost Saving Strategies

A. If you don’t plan to stay very long1. Find a mortgage deal with the smallest

points (preferably none) and fees – which may result is a slightly higher rate.

2. If you plan to stay for a long period of time, consider larger down payment or consider paying points to lower the contract interest rate.

HOMEWORK ASSIGNMENT

A. Key terms: Annual Percentage Rate (APR), Discount points, Amortization

B. Study Questions: 1, 2, 6, 7, 10, 161. Calculate the original loan size of a fixed-

payment mortgage if the monthly payment is $1,146.78, the annual interest is 8.0%, and the original loan term is 15 years.

2. For a loan of $100,000, at 7 percent annual interest for 30 years, find the balance at the end of 4 years and 15 years assuming monthly payments.

HOMEWORK ASSIGNMENT

6. Give some examples of up-front financing costs associated with residential mortgages. What rule can one apply to determine if a settlement (closing) cost should be included in the calculation of the effective borrowing costs?7. A homeowner is attempting to decide between a 15-year mortgage loan at 5.5 percent and a 30-year loan at 5.90 percent. Assume the up-front costs of the two alternatives are equal. What would you advise? What would you advise if the borrower also has a large amount of credit card debt outstanding at a rate of 15 percent?

HOMEWORK ASSIGNMENT

10. Assume the following: Loan Amount: $100,000Interest rate: 10 percent annuallyTerm: 15 years, monthly payments

a. What is the monthly payment?b. What will be the loan balance at the end of nine years?c. What is the effective borrowing cost on the loan if the lender charges 3 points at origination and the loan goes to maturity?d. What is the effective borrowing cost on the loan if the lender charges 3 points at origination and the loan is prepaid at the end of year 9?

HOMEWORK ASSIGNMENT

16. Assume that you have purchased a home and can qualify for a $200,000 loan. You have narrowed your mortgage search to the following two options:

Mortgage ALoan term: 30 yearsAnnual interest rate: 6 percentMonthly paymentsUp-front financing costs: $5,000Discount points: 3

HOMEWORK ASSIGNMENT

Mortgage BLoan term: 15-yearsAnnual interest rate: 5.5 percentMonthly paymentsUp-front financing costs: $7,000Discount points: 3

Based on the effective borrowing cost, which loan would you choose?