CHAPTER 4
FIXED RATE MORTGAGES
 DETERMINANTS OF MORTGAGE INTEREST
RATES:
– MORTGAGE INTEREST RATES ARE BASED ON A
“DERIVED DEMAND” -- THE DEMAND FOR HOUSING
AND ALSO SUPPLY SIDE FACTORS.
– THE MORTGAGE MARKET IS PART OF A LARGER
CAPITAL MARKET - i.e., THE SUPPLY OF MORTGAGE
MONEY IS IN COMPETITION WITH OTHER TYPE OF
LOANS/INVESTMENTS (CAPITAL MARKETS)
INTEREST RATES
 REAL RATE OF INTEREST - MINIMUM RATE
REQUIRED TO DIVERT FUNDS FROM PRESENT
CONSUMPTION TO FUTURE CONSUMPTION
– USUALLY MEASURED AS A SHORT-TERM INTEREST
RATE
– A NOMINAL (CURRENT DOLLARS) RATE CORRECTED
FOR ACTUAL (OR ANTICIPATED) CHANGES IN
INFLATION
Continued
INTEREST RATES
– USUALLY THOUGHT OF AS A “RISKLESS” RATE
– HISTORICALLY ABOUT 3 PERCENT
NOMINAL RATE - INFLATION RATE = REAL RATE
NOMINAL INTEREST RATE
(CONTRACT RATE)
=i
= REAL INTEREST RATE
+ ANTICIPATED INFLATION PREMIUM
+ DEFAULT RISK PREMIUM
+ PREPAYMENT RISK PREMIUM
+ LIQUIDITY RISK PREMIUM
+ LEGISLATIVE RISK PREMIUM
NOMINAL INTEREST RATE
(CONTRACT RATE)
 PRICING DECISIONS BY LENDERS ARE
RENDERED COMPLEX BECAUSE MOST
MORTGAGE LOANS ARE MADE AT FIXED
INTEREST RATES FOR LONG PERIODS OF TIME.
NOMINAL INTEREST RATE
(CONTRACT RATE)
 IF LENDERS FORMED EXPECTATIONS OF WHAT
INTEREST RATES WOOULD BE ON A SERIES OF
ONE-YEAR LOANS OVER THE MATURITY OF A
GIVEN LOAN - THEY WOULD CALCULATE IT AS
FOLLOWS:
(1+it)n = (1+i1)(1+i2)(1+i3) … (1+in)
NOMINAL INTEREST RATE
(CONTRACT RATE)
 EXAMPLE: IF YOU FORECASTED THE FOLLOWING
SERIES OF INTEREST RATES
(8%, 9%, 9%, 10%, 8%)
(1+it) =
(1+.08)(1+.09)(1+.09)(1+.10)(1+.08)
= (1.5244)
NOMINAL INTEREST RATE
(CONTRACT RATE)
 AND,
it = n 1.5244 - 1
= 5 1.5244 - 1
= 1.087977 - 1
= .087977 = 8.7977%
(HP10B) 1.5244, shift, yx, 1/5 = 0.2,
= 1.0880 and 1.0880 - 1 = .088 = 8.8%
Continued
NOMINAL INTEREST RATE
(CONTRACT RATE)
 THIS IS THE CONTRACT RATE THAT WOULD BE
CHARGED IF THE FUTURE ANTICIPATED WERE
AS FORECASTED ABOVE.
 IT IS ALSO THE COMPOUND ANNUAL RATE
NECESSARY TO GROW $1 TO $1.5244 IN 5
YEARS
MORTGAGE PAYMENT PATTERNS
 PRIOR TO GREAT DEPRESSION:
–
–
–
–
HIGH DOWN PAYMENTS (50%)
SHORT MATURITY (5 YEARS)
INTEREST ONLY LOANS
BALLOON PAYMENTS
MORTGAGE PAYMENT PATTERNS
 THEREFORE,
– FEW COULD AFFORD HOME PURCHASE
– SHORT MATURITY/ BALLOON PAYMENT CREATED
REPAYMENT DANGER
– R.E. AS COLLATERAL WAS NOT HIGHLY REGARDED
MORTGAGE PAYMENT PATTERNS
 MID 1930’s - 1970’s
–
–
–
–
“NEW DEAL” PROGRAMS
FHA/VA LOANS, LOW DOWN PAYMENTS
SELF - AMORTIZING LOANS
MONTHLY PAYMENTS
SELF - AMORTIZING LOANS
 AMORITIZATION - THE PROCESS OF LOAN
REPAYMENT OVER TIME
 1. CONSTANT AMORTIZATION MORTGAGE
(CAM)
MONTHLY PAYMENT = CONSTANT
AMORTIZATION OF PRINCIPAL + INTEREST DUE
ON OUTSTATNDING LOAN BALANCE (OLB)
SELF - AMORTIZING LOANS
 EXAMPLE: $100,000 LOAN, 10% INTEREST,
30YEARS (360 PAYMENTS)
MONTH 1 PAYMENT = $100,000/360= 277.78
+100,000(.10/12)= 833.33
$1,111.11
SELF - AMORTIZING LOANS
MONTH 2 PAYMENT
= 277.78 + ((100,000-277.78)(.10/12)
= 277.78 + 827.69
= $1,105.47
 BORROWERS DIDN’T CARE FOR CHANGING
MONTHLY PAYMENTS
SELF - AMORTIZING LOANS
 2. CONSTANT PAYMENT MORTGAGE (CPM)
– MONTHLY PAYMENT IS CONSTANT OVER LIFE OF
LOAN
– LOAN IS FULLY AMORTIZED AT MATURITY
– PORTION OF PAYMENT THAT IS PRINCIPAL VERSUS
INTEREST CHANGES IN EVERY PAYMENT
– EASIER TO QUALIFY FOR THAN CAM BECAUSE
INTIAL PAYMENT IS LOWER
– MORE INTEREST IS PAID OVER LIFE OF LOAN
SELF - AMORTIZING LOANS
CONSTANT PAYMENT =
ORIGINAL LOAN AMOUNT




i


m


1
1 



i
 (1  m )nm 
SELF - AMORTIZING LOANS
 WHERE:
– i IS ANNUAL INTEREST RATE
– m IS NUMBER OF TIMES COMPOUNDING OCCURS
PER YEAR
– n IS NUMBER OF YEARS FOR LOAN TO MATURE
Self-Amortizing Loans
Example:
$100,000 Loan, 10% Interest, 30 Years
Payment =




.10


12

$100,000 
1
1 
.30.12 


.10
(
1

)


12
= $877.57
SELF - AMORTIZING LOANS
 INSERT CHARTS AND GRAPHS
CACULATING OUTSTANDING LOAN
BALANCES (OLB)
 HP10B
– 1. CALCULATE MORTGAGE PAYMENT
– 2. RECORD PAYMENT IN QUESTION, IMPUT
– 3. SHIFT, AMORT
= INTEREST EXPENSE
= PRINCIPAL REDUCTION
= OLB
CACULATING OUTSTANDING LOAN
BALANCES (OLB)
 OLB = PV OF REMAINING PAYMENTS
DISCOUNTED AT CONTRACT RATE
 EXAMPLE:
$100,000 LOAN, 10% INTEREST, 30 YEARS
PMT = $877.57
OLB357 = $2,589.37 HP10B
= $2,589.43 PV OF PMTS METHOD
CLOSING COSTS
 EXPENSES IN ADDITION TO THE PURCHASE
PRICE OF THE PROPERTY WHICH MUST BE PAID
BY THE PURCHASER OR DEDUCTED FROM THE
PROCEEDS OF THE SALE TO THE SELLER AT THE
TIME OF CLOSING. THESE COSTS CAN
GENERALLY BE PLACED IN ONE OF THREE
CATEGORIES: STATUTORY COSTS, THIRDPARTY CHARGES, AND ADDITIONAL FINANCE
CHARGES.
CLOSING COSTS
 STATUTORY COSTS - LEGAL REQUIREMENTS
PERTAINING TO TITLE TRANSFERS, RECORDING
DEEDS, TAX STAMPS, ETC... THESE COSTS
SHOULD NOT BE CONSIDERED PART OF
FINANCING COSTS.
CLOSING COSTS
 THIRD-PARTY COSTS - ATTORNEY’S FEES,
APPRAISALS, SURVEYS, BUILDING INSPECTION,
TERMITE INSPECTION, TITLE INSURANCE,
BROKER COMMISSIONS. NOT TO BE
CONSIDERED PART OF FINANCING COSTS.
CLOSING COSTS
 FINANCE COSTS (LOAN FEES) - THESE CHARGES
CONSTITUTE ADDITIONAL INCOME TO THE
LENDER AND SHOULD BE INCLUDED AS A PART
OF THE COST OF BORROWING. TWO TYPES:
– 1. LOAN ORIGINATION FEES - THESE CHARGES
COVER THE ADMINISTRATIVE COSTS INCURRED BY
THE LENDER AND ARE TYPICALLY STATED AS A
PERCENTAGE OF THE LOAN.
CLOSING COSTS
– 2. LOAN DISCOUNT OR POINTS - A FEE CHARGED BY
A LENDER AT CLOSING OR SETTLEMENT THAT
RESULTS IN INCREASING THE LENDER’S EFFECTIVE
YIELD (IRR) ON THE MONEY LOANED. EACH
DISCOUNT POINT REPRESENTS A ONE-TIME
CHARGE BY THE LENDER EQUAL TO 1% OF THE LOAN
PRINCIPAL.
EFFECTIVE YIELD
(EFFECTIVE BORROWING COSTS)
 THE INTEREST RATE THE LENDER EARNS.
 NORMALLY, THE EFFECTIVE YIELD IS THE SAME AS
THE CONTRACT RATE OF INTEREST ON WHICH THE
LOAN PAYMENTS ARE CALCULATED.
 CERTAIN MODIFICATIONS TO LOANS ALTER THE
“TRUE” RATE OF INTEREST THE LENDER EARNS.
THESE MODIFICATIONS ARE LOAN DISCOUNTS, LOAN
ORIGINATION FEES, AND PREPAYMENT PENALITIES.
EFFECTIVE YIELD
(EFFECTIVE BORROWING COSTS)
 TRUTH-IN-LENDING ACT REQUIRES APR (ANNUAL
PRECENTAGE RATE) WHICH ACCOUNTS FOR
ORIGINATION FEES AND DISCOUNT POINTS. APR
CALCULATION ALLOWS COMPARISION OF LOANS
WITH DISSIMILAR CONTRACT RATES, FEES, AND
MATURITIES. PREPAYMENT EFFECT IS NOT
CONSIDERED IN APR CALCULATION.
Calculating Effective Yield
The basic idea:
The present value of forecasted stream
of income + PV of any reversion amount
should be equal to the disbursement
[orig. loan] when discounted at the
appropriate rate [Effective Yield/Cost].
IRR (Internal Rate of Return]
= the discount rate that caused the
PV of CFs to equal the initial cost
= The i that causes NPV = 0
Think of a loan disbursement as the
lender’s investment.
The CFs equal the loan payment.
Examples:
Loan Amount $100,000
Interest Rate
8%
Maturity Term 30 years- monthly payment
Calculate monthly payment = $733.76
Calculate effective yield (YTM or IRR) = 7.99999
= 8%
What if an origination fee or discount
points are charged ?
Assume same loan term as above, however 2
discount points and 1 origination point are
charged .
Disbursement = $100,000
-3,000 ( .03 X 100,000)
$ 97,000
CFS = $733.76/mo.
IRR = 8.3237%
What happens when a loan is prepaid ?
1. Assume no origination fees or discount
points. Loan prepaid at end of year 15 (after
180 payments)
Calculate OLB = $76,781.55
CFs
Time
(100,000)
0
733.76
1
733.76
2
.
.
.
.
733.76 + 76,781.55 180
IRR = 8%
• IRR will equal contract rate at any
prepayment date if there are no
orig. or discount points, and there is
no prepayment penalty.
2. Assume no points, but a prepayment
penalty of 3% of OLB. Loan prepaid at end
of year 15.
$76,781.55
Calculate prepayment penalty = X.03
$ 2,303.45
CFs
Time
(100,000)
0
733.76
1
733.76
2
.
.
.
.
733.76 + 76,781.55+2,303.45 180
IRR = 8.0853%
3. Assume 3 points, 3% prepayment penalty.
Loan prepaid at end of year 15.
IRR = 8.4628%
4. Assume same as #3, but prepayment
occurs at end of year 5.
IRR = 9.2278%
• The earlier a loan is prepaid that has
origination or discount points, or a
prepayment penalty, the higher the effective
yield.
Mortgage Tilt
 Tilting describes the high nominal mortgage
payments required in the early life of a
mortgage when interest rates include a large
inflation premium. Tilt results because inflation
expectations are included in the interest rate
and therefore expense estimate but not in the
loan applicants’ income estimate.
Mortgage Tilt
 Tilt creates on affordability problem when
traditional loan underwriting standards are
used. Explains the inability of home buyers
to obtain homes whose actual economic
costs they could afford.
 If inflation does occur incomes and home
prices should rise, therefore most families
should be able to more easily cover the
fixed monthly mortgage payment (the
payment becomes a smaller portion of
their income).
Effect of Inflation of Real Payment of Fixed-rate Mortgage
$80,000, 30-year mortgage; $3,000/month initial income
Year
Monthly Payment Real Payment Payment/Income
Case A: 0% inflation; 3% interest rate
1
5
10
20
30
$335.36
335.36
335.36
335.36
335.36
$335.36
335.36
335.36
335.36
335.36
11.18%
11.18
11.18
11.18
11.18
Case B: 2% inflation; 5% interest rate
1
5
10
20
30
$429.45
429.45
429.45
429.45
429.45
$421.03
388.97
352.30
289.01
237.09
13.76%
11.74
9.60
6.40
4.36
Case C: 8% inflation; 11% interest rate
1
5
10
20
30
$761.86
761.86
761.86
761.86
761.86
$705.42
518.51
352.89
163.45
75.71
23.05%
15.65
9.65
3.67
1.39
Graduated Payment Mortgage (GPM)
Another approach to the inflation problem.
Lower initial payments than on CPMs with
same i & n. Payments stabilize after 5-10
years of gradual increases.
• Combats Tilt Effect
• Makes initial qualifying easier
What about GPMs in non inflationary
periods ? Yes for homebuyers who have
careers that offer future (substantial) wage
increases.
Because GPM payments are lower than
those of comparable CPMs in the early
years, GPM payments must eventually
exceed the level payments of CPMs to
“catch up”.
OLBS - Since early year GPM payments are
lower than similar GPM payments - not
enough is being repaid to meet full
principle + interest expense required to
amortize the loan. Therefore, negative
amortization will occur.
Higher OLBs are not good for lenders - it
reduces their “Safety margin”; LTV goes up.
Therefore, GPMs is riskier than CPMs.
Lenders probably would /should charge
slightly higher nominal rates on GPMS.
What is a reverse mortgage loan?
 A reverse mortgage is a special type of loan available
only to older homeowners with full or nearly full equity
in their homes. Such owners can borrow against the
equity they have built up over the years, but no
repayment is necessary until the borrower sells the
property or moves elsewhere. If the borrower dies
before the property is sold, the estate repays the loan
(plus any interest that has accrued
Common Features of Reverse
Mortgages
 RMs are rising-debt loans. This means that the interest is added
to the principal loan balance each month, because it is not paid
on a current basis. Therefore, the total amount of interest you
owe increases significantly with time as the interest
compounds.
 All three plans (FHA-insured, lender-insured, and uninsured)
charge origination fees and closing costs. Insured plans also
charge insurance premiums, and some impose mortgage
servicing charges. Your lender may permit you to finance these
costs so you will not have to pay for them in cash. But remember
these costs will be added to your loan amount
Common Features of Reverse
Mortgages
 RMs use up some or all of the equity in your home,
leaving fewer assets for you and your heirs in the
future.
 You generally can request a loan advance at closing
that is substantially larger than the rest of your
payments.
 Your legal obligation to pay back the loan is limited by
the value of your home at the time the loan is repaid.
This could include increases in the value
(appreciation) of your home after your loan begins.
Common Features of Reverse
Mortgages
 RM loan advances are nontaxable. Further, they do not affect
your Social Security or Medicare benefits. If you receive
Supplemental Security Income, RM advances do not affect your
benefits as long as you spend them within the month you
receive them. This is true in most states for Medicaid benefits
also. When in doubt, check with a benefits specialist at your
local area agency on aging or legal services office .
 Some plans provide for fixed rate interest. Others involve
adjustable rates that change over the loan term based upon
market conditions .
 Interest on RMs is not deductible for income tax purposes until
you pay off all or part of your total RM debt.