FIN 331 Chapter 15

```Chapter 15
Mortgage Calculations and Decisions
REAL ESTATE
FIN 331
SEVEN VITAL FEATURES OF A
MORTGAGE
1.
2.
3.
4.
5.
6.
7.
Principal amount
Term to maturity
Interest rate
Monthly payment
Amortization schedule
Points
Financing Costs
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)
BASIC MORTGAGE COMPUTATIONS
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
3rd Party Loan Expense: \$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
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 []
5. Press the down key []
7. Press the down key []
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”
Effective Borrowing Costs
A.Third-party expenses: up-front expenses
incurred by borrower but not paid to
lender:
1.
2.
3.
4.
5.
Taxes on the loan
Lender’s title insurance
Appraisal
Survey
Effective Borrowing Costs
B. Effect of 3rd 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%
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%
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?
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
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.
TI-83 Procedure
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
TI-83 Procedure
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%)
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: 4.63%
3. EBC = 4.70%
4. Total Pmt.: \$232,238.55 →S Int = \$72,238.55
5. “Standard” Mortgage: S Int = \$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
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.
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.
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
has a large amount of credit card debt outstanding
at a rate of 15 percent?
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?
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
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?
```