REAL ESTATE
FIN 331

SEVEN VITAL FEATURES OF A MORTGAGE
1. Principal amount
2. Term to maturity
3. Interest rate
4. Monthly payment
5. Amortization schedule
6. Points
7. Financing Costs

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)

B. Example: $200,000 loan @ 4.50% for 30 years, 1.5 points, $2000 closing costs.
1. Points to Lender: .015 * 200,000 = $3,000
2. 3 rd Party Loan Expense: $2000.00
3. Total Costs: $5,000 ($3000 + $2000)
4. 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

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 “c”

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

B. Effect of 3 rd party payments:
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
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. N=360, PV = 197,000, PMT = -1,013.37
2. CPT I/Y = 4.629374%

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%

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?

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
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.

A. APPS: 1: Finance, press ENTER key
B. 1: 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

B. Effects of Prepayment: Lender’s Yield
1. APPS, cursor up to 9
 bal(, 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: EBC
1. PV = 156000, cursor to i%, ALPHA, ENTER,
I%= 5.01

A. What happens when we add $100 to the monthly payment?
1. PMT = -1323.99, solve N = 161.27
2. Lender’s Yield: I% = 4.71% (vs. 4.75%)
3. EBC: PV = 156000, I% = 4.92% (vs. 5.01%)

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: 4.63%
3. EBC = 4.70%
4. Total Pmt.: $232,238.55 →
S I nt = $72,238.55
5. “Standard” Mortgage:
S I nt = $60,318.07

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

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.

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 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.

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 15year 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?

10. Assume the following:
Loan Amount:
Interest rate:
Term:
$100,000
10 percent annually
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?

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

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?