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**Chapter 15 Mortgage Calculations and Decisions**

REAL ESTATE FIN 331

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**SEVEN vital features of a mortgage**

Principal amount Term to maturity Interest rate Monthly payment Amortization schedule Points Financing Costs

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**basic mortgage computations**

Using the Texas Instrument BA II Plus financial calculator Mortgage calculations require 4 of the six basic functions Number of payments (N) Interest rate per year (I/Y) (P/Y must be set to 12 for a standard mortgage) Loan amount (PV: present value equals about the loan) Monthly payment (PMT) Value of the mortgage at maturity (FV) Compute (CPT)

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**basic mortgage computations**

B. Example: $200, % for 30 years, 1.5 points, $2000 closing costs. Points to Lender: .015 * 200,000 = $3,000 3rd Party Loan Expense: $ Total Costs: $5,000 ($ $2000) Net Loan proceeds to Borrower: 195,000 C. Computing Monthly P&I 1. N=360, I/Y = 4.5%, PV = 200,000 2. CPT PMT: $

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**basic mortgage computations**

D. Preparing the Amortization Schedule Using the AMORTization function (a second function of the PV key) Set the P1 and P2 values to 1: P1 = 1 [], P2 = 1 Press the down key [] Read the BALance Read the PRiNcipal Read the INTerest press the compute key (CPT): P1 and P2 values will increment to the next payment repeat steps starting with “c”

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**Effective Borrowing Costs**

Third-party expenses: up-front expenses incurred by borrower but not paid to lender: Mortgage insurance premium Taxes on the loan Lender’s title insurance Appraisal Survey

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**Effective Borrowing Costs**

B. Effect of 3rd party payments: Borrower net less at loan closing than lender’s actual net disbursement to borrower Result? EBC > lender’s yield C. Compute EBC to Borrower N=360, PV = 195,000, PMT = 1,013.37 CPT I/Y = % (vs 4.5% quoted rate) D. Compute Lender’s Yield (IRR) N=360, PV = 197,000, PMT = -1,013.37 CPT I/Y = %

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**Lender’s Yield, EBC Example 2**

15 year mortgage, $160,000 $2000 in points, $2000 loan origination expense. N= 180, I/Y = 4.5, PV = 160,000: CPT PMT Compute monthly PMT: $-1,223.99 Compute Lenders Yield: PV = 158,000 CPT I/Y = % 3. Compute Effective Borrowing Costs PV = 156,000, CPT I/Y = %

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**Truth in Lending Act (FILA)**

Federal Truth in Lending Act requires disclosure of annual percentage rate (APR) on virtually all home mortgage loans APR: Yield to maturity, after adjusting for: All loan finance charges All compensation to originating brokers All other charges controlled by lender Premiums for any required insurance What inadequacy might you see in the APR as a measure of true borrowing cost?

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**Effects of Loan Prepayment**

Suppose the previous loan is prepaid in 7 years. What are the effects on Lenders Yield and the EBC for Borrower? Loan Balance after 84 payments (7 * 12) AMORT: P1=84, P2=84: Bal = 98,524.09 Lender’s Yield: N = 84, PV = 158,000, FV = (paying off loan balance. CPT I/Y = 4.75% EBC: PV = 156,000, CPT I/Y = 5.01% Bottom line: Prepayment actually increases Lender’s Yield and also EBC of loan.

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**TI-83 Procedure APPS: 1: Finance, press ENTER key**

1: TVM Solver, press ENTER key Set Values: N = 180, I% = 4.5%, PV = Cursor to PMT, press ALPHA key, the ENTER key: PMT = Compute Lender’s Yield: PV = , cursor to I%, press ALPHA key, the ENTER key: I% = 4.69% Compute EBC: PV = , cursor to I%, press ALPHA key, the ENTER key: I%=4.88

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**TI-83 Procedure B. Effects of Prepayment: Lender’s Yield**

APPS, cursor up to 9bal(, press ENTER, enter 84), press ENTER, bal(84) APPS, ENTER, ENTER: Set N = 84, PV = , FV = , cursor to I%, ALPHA ENTER, I% = 4.75 C. Effect of Prepayment: EBC 1. PV = , cursor to i%, ALPHA, ENTER, I%= 5.01

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**Effects of Additional Principal**

What happens when we add $100 to the monthly payment? PMT = , solve N = Lender’s Yield: I% = 4.71% (vs. 4.75%) EBC: PV = , I% = 4.92% (vs. 5.01%)

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**Effects of Balloon Payments**

15 year, 4.5% mortgage, with a $40,000 balloon payment (a partially amortized mortgage) with $1600 in points and $800 in losing fees. N=180, I/Y= 4.50, PV = 160,000: FV = -40,000 PMT = $1,067.99 Lenders Yield: 4.63% EBC = 4.70% Total Pmt.: $232, →S Int = $72,238.55 “Standard” Mortgage: S Int = $60,318.07

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**Adjustable Rate Mortgage**

Worst Case: 1-year ARM, 30-year term $100,000 3%: PMT = $421.60 Bal(12) = $97,912.24 Reset interest rate after first year to 4%: N = 348, I/Y = 4.00, PV = , PMT = $475.83 4. Bal(12) = $96,085.52 5. Reset interest rate after second year to 5%: N = 336, I/Y = 5.00, PV = , PMT = $531.90 B. If life-time cap = 5% - what can PMT rise to if rates go up 1% every year? $707.89

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**Some Cost Saving Strategies**

If you don’t plan to stay very long Find a mortgage deal with the smallest points (preferably none) and fees – which may result is a slightly higher rate. 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.

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homework assignment Key terms: Annual Percentage Rate (APR), Discount points, Amortization Study Questions: 1, 2, 6, 7, 10, 16 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. 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.

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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?

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**homework assignment 10. Assume the following: Loan Amount: $100,000**

Interest rate: 10 percent annually Term: 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?

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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 A Loan term: 30 years Annual interest rate: 6 percent Monthly payments Up-front financing costs: $5,000 Discount points: 3

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homework assignment Mortgage B Loan term: 15-years Annual interest rate: 5.5 percent Monthly payments Up-front financing costs: $7,000 Discount points: 3 Based on the effective borrowing cost, which loan would you choose?

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