Chapter 15 Mortgage Calculations and Decisions REAL ESTATE FIN 331

Chapter 15 Mortgage Calculations and Decisions REAL ESTATE FIN 331 Dr. David P. Echevarria All Rights Reserved 1

SEVEN VITAL FEATURES OF A MORTGAGE 1. Principal amount (PV) 2. Term to maturity (N) 3. Interest rate (I/Y or I%) 4. Monthly payment (PMT) (P/Y 12) 5. Amortization schedule (BA-II Amort, TI-83/83: bal, SPrn, SInt) 6. Points (based on Loan Amount) 7. Financing Costs (Fees) Dr. David P. Echevarria All Rights Reserved 2

BASIC MORTGAGE COMPUTATIONS A. Using the Texas Instrument BA II Plus financial calculator 1. Mortgage calculations require 4 of the six basic functions a. 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) Dr. David P. Echevarria All Rights Reserved 3

BASIC MORTGAGE COMPUTATIONS BA-II PLUS B. Example: 200,000 loan @ 4.50% for 30 years, 1.5 points, 2000 closing costs. 1. 2. 3. 4. Points to Lender: .015 * 200,000 3,000 Loan Origination Fees: 2000.00 Total Costs: 5,000 ( 3000 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: -1013.37 Dr. David P. Echevarria All Rights Reserved 4

BASIC MORTGAGE COMPUTATIONS TI-83/84 A. Using the Texas Instrument TI-83 / 84 [financial] calculator 1. 2. 3. 4. 5. 6. 7. 8. APPS – [ENTER] 1:Finance [ENTER] 1: TVM Solver [ENTER] N 360 [ENTER] I% 4.50 [ENTER] PV 200000 [ENTER] (cursor to PMT line) [ALPHA] – [ENTER] PMT -1013.37 Dr. David P. Echevarria All Rights Reserved 5

BASIC MORTGAGE COMPUTATIONS D. Preparing the Amortization Schedule 1. 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 BALance 5. Press the down key [ ] 6. Read the PRiNcipal 7. Press the down key [ ] 8. Read the INTerest 9. Press the down key [ ] 10.press the compute key (CPT): P1 and P2 values will increment to the next payment 11.repeat steps starting with “3” Dr. David P. Echevarria All Rights Reserved 6

BASIC MORTGAGE COMPUTATIONS TI-83/84 A. Preparing an Amortization Schedule 1. 2. 3. 4. 5. 6. 7. 8. 9. APPS – Finance [ENTER] Cursor down to 9: bal( [ENTER] Bal(1) [ENTER]: 199736.63 APPS – Finance [ENTER] Cursor down to 0: SPrn( [ENTER] SPrn(1,1) [ENTER]: -263.37 APPS – Finance [ENTER] Cursor down to 0: SInt( [ENTER] SInt(1,1) [ENTER]: -750.00 Dr. David P. Echevarria All Rights Reserved 7

BASIC MORTGAGE COMPUTATIONS TI-83/84 B. The amortization schedule is incremented based on the values entered inside the parens: 1. Bal(2), SPrn(2,2), SInt(2,2), etc. etc. 2. If you want to do a range of payments, say 1 through 12: a. Bal(12), SPrn(1,12), Sint(1,12) (note the “bal” value is for the last payment in the range. Dr. David P. Echevarria All Rights Reserved 8

Effective Borrowing Costs A. Loan Origination Fees: up-front expenses incurred by borrower but not paid to lender: 1. 2. 3. 4. 5. Mortgage insurance premium Taxes on the loan Lender’s title insurance Appraisal Survey B. Effect of Points on Lender’s Yield 1. Increases lender’s yield on loan Dr. David P. Echevarria All Rights Reserved 9

Effective Borrowing Costs B. Effect of Loan Fees: 1. Borrower net less at loan closing than lender’s actual net disbursement to borrower 2. Result? a. EBC lender’s yield C. Compute EBC to Borrower ( 5000 in fees) N 360, PV 195,000, PMT -1,013.37 CPT I/Y 4.717285% (vs 4.5% quoted rate) D. Compute Lender’s Yield (IRR) (1.5 points) 3. N 360, PV 197,000, PMT -1,013.37 4. CPT I/Y 4.629374% Dr. David P. Echevarria All Rights Reserved 10

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 PMT 2. Compute monthly PMT: -1,223.99 3. Compute Lenders Yield: PV 158,000 CPT I/Y 4.688783% 3. Compute Effective Borrowing Costs PV 156,000, CPT I/Y 4.880999% Dr. David P. Echevarria All Rights Reserved 11

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 charges 2.All compensation to originating brokers 3.All other charges controlled by lender 4.Premiums for any required insurance C. What inadequacy might you see in the APR as a measure of true borrowing cost? Dr. David P. Echevarria All Rights Reserved 12

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 98,524.09 TI-83/83: bal(84) 3. 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. Dr. David P. Echevarria All Rights Reserved 13

TI-83 Procedure A. APPS: 1: Finance, press ENTER key B. TVM Solver, press ENTER key 1. Set Values: N 180, I% 4.5%, PV 160000 2. Cursor to PMT, press ALPHA key, the ENTER key: PMT -1223.99 3. 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 Dr. David P. Echevarria All Rights Reserved 14

Effects of Additional Principal A. What happens when we add 100 to the monthly payment? 1. PMT -1323.99, solve N 161.27 2. Lender’s Yield: I% 4.28% (vs. 4.69%) 3. EBC: PV 156000, I% 4.50% (vs. 4.88%) Dr. David P. Echevarria All Rights Reserved 15

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 1,067.99 2. Lenders Yield: 4.66% 3. EBC 4.83% 4. Total Pmt.: 192,238.20 40,000 232,238.20 SInt 72,238.55 5. “Standard” Mortgage: Total Payments 220,318.20 SInt 60,317.93 Difference 11,920.00 Dr. David P. Echevarria All Rights Reserved 16

Adjustable Rate Mortgage A. Worst Case: 1-year ARM, 30-year term 1. 100,000 loan @ 3%: PMT 421.60 2. Bal(12) 97,912.24 3. Reset interest rate after first year to 4%: N 348, I/Y 4.00, PV 97912.24, PMT 475.83 4. Bal(12) 96,085.52 5. 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 Dr. David P. Echevarria All Rights Reserved 17

Some Cost Saving Strategies A. If you don’t plan to stay very long 1. 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. Dr. David P. Echevarria All Rights Reserved 18

HOMEWORK ASSIGNMENT A. Key terms: Annual Percentage Rate (APR), Discount points, Amortization B. Study Questions: 1, 2, 6, 7, 10, 16 1. Calculate the original loan size of a fixedpayment 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. Dr. David P. Echevarria All Rights Reserved 19

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 30year 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? Dr. David P. Echevarria All Rights Reserved 20

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? Dr. David P. Echevarria All Rights Reserved 21

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 Dr. David P. Echevarria All Rights Reserved 22

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? Dr. David P. Echevarria All Rights Reserved 23