1. Fixed Rate Mortgage Loans
Chapter 4
Fixed Rate Mortgage Loans

2. Overview Mortgage Interest Rates
Components of the Mortgage Interest Rate
Constant Amortization Mortgage (CAM)
Constant Payment Mortgage (CPM)
CAM and CPM Payment Patterns
Computing a Loan Balance
Loan Closing Costs
Pricing a Loan
Other Loan Patterns
Partially Amortizing Loan
Negative Amortization
Option Mortgages
Reverse Annuity Mortgage (RAM)

3. Mortgage Interest Rates
What will borrowers pay for the use of funds?
What are lenders willing to accept for the use of funds?
Housing Demand Factors: Income & Demographics
Mortgage Funds Supply Factors: Alternative Investments

4. Components of the Mortgage Interest Rate
Real Rate of Interest
Time Preference for Consumption
Compensation to delay a purchase
Production Opportunities in the Economy
Competition for funds when there are other investment opportunities
Inflation Expectation
Retain purchasing power

5. Components of the Mortgage Interest Rate – Continued
Default Risk
Interest Rate Risk
Anticipated Inflation and Unanticipated Inflation
Prepayment Risk
Liquidity Risk
Legislative Risk

6. Components of the Mortgage Interest Rate – Continued
r = Real Rate
f1 = Inflation Rate
p1 = Risk Premiums

7. Constant Amortization Mortgage (CAM)
Amortization = Original Loan Balance / Number of Payments
Opening Balance = Previous Period Ending Balance
Ending Balance = Opening Balance – Amortization
Periodic Rate = Annual Rate / Payment per Year
Interest = Opening Balance × Periodic Rate
Monthly Payment = Interest + Amortization

9. Constant Payment Mortgage (CPM)
FRM payments are structured as an ordinary annuity
PV of the annuity is the amount borrowed
The monthly payment on a 30-year, 12%, $60,000 loan is:
Notes:
To get the answer press CPT and then what you are trying to get
To clear the calculator memory use 2nd CLR TVM
To change P/Y, press 2nd P/Y, enter the amount and press ENTER. To get out of this mode use 2nd QUIT
Annuity due setting is BGN (for beginning): 2nd BGN, 2nd SET, 2nd QUIT N
I/Y
P/Y PV
PMT FV
MODE
360 12
-60,000
617.17

10. Constant Payment Mortgage (CPM) – Continued
Monthly Payment = Determined using Excel’s PMT function
Beginning Loan Balance = Previous Period Ending Balance
Interest = Beginning Loan Balance × Periodic Rate
Ending Loan Balance = Beginning Loan Balance – Amortization
Periodic Rate = Annual Rate / Payment per Year
Amortization = Monthly Payment – Interest

13. CAM and CPM Payment Patterns
Comparing the CAM & CPM
Higher initial monthly payments for the CAM
More difficult for a borrower to qualify for a loan
Amortization of CPM is slower than CAM
CAM payment declines over time

14. Computing a Loan Balance
The outstanding loan balance is the PV of the remaining loan payments discounted at the original loan rate
After computing the PMT of the original loan just change N to number of remaining payments then CPT PV
Alternatively, to determine the outstanding balance of the loan in the previous example after 10 years:
Compute PMT (617.17)
2nd AMORT
120 ENTER 120 ENTER This will allow you to see loan information (self explanatory) at that point in time
You can change P1 and P2 to get the data for the specified payment range

15. Computing Payment Components
How much interest do you pay during the second year?
$7,160.67
How much principal do you pay during the second year?
$245.34
What is the interest component of 72nd payment?
$582.37

16. Loan Closing Costs There are three categories of loan closing costs:
Statutory Costs: These charges are associated with the legal transfer of title and other fees. They are paid for services by governmental agencies
Third Party Charges: Payments for legal fees, appraisals, surveys, inspection, and title insurance
Additional Finance Charges: These charges provide additional income to the lender and therefore should be included as a part of cost of borrowing
Loan Origination Fees
Cover origination expenses
Loan Discount Fees – “Points”
Used to raise the yield on the loan
Borrower trade-off: points vs. contract rate
1 Point = 1% of the loan amount

17. Loan Closing Costs – Continued
Why Points?
Sticky mortgage rates
Price in the risk of a borrower
Early repayment of a loan does not allow recovery of origination costs
Earn a profit on loans sold to investors at a yield equal to the loan interest rate

18. Loan Closing Costs – Continued
If there are fees and points, then the effective interest cost is higher
If the previous loan has 3 points, then the lender will disburse: [60,000 – (60,000 X 0.03)] = –58,200
Loan payments are based on $60,000 and the borrower receives less, increasing the return to lender
Note that fees and points work the same way
We also assume that the loan is not prepaid
Lenders are required to disclose by law (Truth-in-Lending Act) an annual percentage rate (APR) computed in a similar manner
The effective interest cost is N
I/Y
P/Y PV
PMT FV
MODE
360
12.41 12
-58,200
617.17

19. Loan Closing Costs and Prepayment
What would be effective interest cost if the loan is paid early
Assume that after 5 years (60 payments), the loan is paid off
We need to determine the outstanding balance of the loan after 60 payments
Make sure that calculator has the original loan data without fees and points
2nd AMORT
60 ENTER 60 ENTER This will allow you to see loan information at that point in time (58,598.16)
Loan balance becomes an entry for future value N
I/Y
P/Y PV
PMT FV
MODE 60
12.82 12
-58,200
617.17
58,598.16

20. Loan Closing Costs and Prepayment Penalty
What would be effective interest cost if the loan is paid early
Assume that after 5 years (60 payments), the loan is paid off
We need to determine the outstanding balance of the loan after 60 payments
Make sure that calculator has the original loan data without fees and points
2nd AMORT
60 ENTER 60 ENTER This will allow you to see loan information at that point in time (58,598.16)
Apply 3% prepayment penalty [58, × ( ) = 60,356]
Loan balance becomes an entry for future value N
I/Y
P/Y PV
PMT FV
MODE 60
13.25 12
-58,200
617.17
60,356

21. Yield and Prepayment Time

22. Pricing a Loan
How can a lender earn 13% return on a 12% interest rate, 30-year fixed rate mortgage that is expected to prepay in 10 years?
This is same as asking for points to be charged to achieve the desired yield
Payment on the loan:
Balance of the loan after 120 payments:
PV of payments to lender at the desired return:
The fees should total 100% % = 5.47% N
I/Y
P/Y PV
PMT FV
MODE
360 12 -1 N
I/Y
P/Y PV
PMT FV
MODE
120 13 12

23. Partially Amortizing Loan
What is the payment on a $60,000 loan with 12% interest rate, 30-year term, monthly payments, and $40,000 balloon payment at maturity? N
I/Y
P/Y PV
PMT FV
MODE
360 12
-60,000
605.72
40,000

24. Negative Amortization
What is the payment on a $60,000 loan with 12% interest rate, 30-year term, and monthly payments?
What is the balance of this loan if the lender and borrower agree on a monthly payment of $400 rather than $ after 5 years? N
I/Y
P/Y PV
PMT FV
MODE
360 12
-60,000
617.17 N
I/Y
P/Y PV
PMT FV
MODE 60 12
-60,000
400.00
76,334

25. Option Mortgages
In a simple case, a borrower pays interest only for a certain period and then converts the loan into a fixed rate fully amortizing loan
What is the interest only payment for the first ten years on a $60,000 loan with 12% interest rate, 30-year term, and monthly payments?
What is the monthly payment when the loan converts into a fixed rate fully amortizing loan? N
I/Y
P/Y PV
PMT FV
MODE
120 12
-60,000
600.00
60,000 N
I/Y
P/Y PV
PMT FV
MODE
240 12
-60,000
660.65

26. Reverse Annuity Mortgage (RAM)
A RAM is a raising debt falling equity mortgage
It requires large payment later in its life
It is designed for retired home owners who have little debt on their home
It allows owners to take out equity
What is the payment on a $250,000 RAM with 10% interest rate, 10-year term, monthly payments? N
I/Y
P/Y PV
PMT FV
MODE
120 10 12
1,220.44
-250,000

27. Three Loans when LTV < 20%
1. Conventional loan with PMI
2. First and second loan
3. FHA insurance

28. Not So Special Specials
A land developer purchases land, or purchases on option on land, with the intention of developing or enhancing the value of the property through improvements
With an option the developer ties up less cash than with an outright purchase. A developer may be able to “control” property worth many millions of dollars with an option that may cost only in the thousands
The developer makes a profit not through the appreciation in the value of the land but through the value added from the improvements

29. Not So Special Specials – Continued
Zoning compliance – making sure that there are no legal restrictions to the type of development that is contemplated. If there are, then efforts must be made to have the zoning changed if possible, or the development modified to meet the existing zoning regulations
Engineering and surveying – specialists in this field must be employed to make sure that the types of structures that are contemplated can be built on the land. The land may have to be modified to accommodate certain types of structures. In extreme cases it may be impossible to build certain types of structures on the available land
Subdividing – the large land parcel is divided into smaller parcels. The smaller parcels are sold to other developers or to the final consumer who, in turn, constructs a structure
Physical work – the actual grading of the land, landscaping, installation of utilities, and so forth

30. Authority to Assess Specially
Why a city would get into this type of an activity?

31. Specials Example and Computations

32. Specials Computations