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Chapter 4

Fixed Rate Mortgage Loans

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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)

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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

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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

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Components of the Mortgage Interest Rate – Continued

Default Risk Interest Rate Risk

Anticipated Inflation and Unanticipated Inflation

Prepayment Risk Liquidity Risk Legislative Risk

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Components of the Mortgage Interest Rate – Continued

r = Real Rate f1 = Inflation Rate p1 = Risk Premiums

111 fprit

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Constant Amortization Mortgage (CAM)

Loan Amount $60,000.00Interest Rate 12.00%Loan Term 30Payment per Year 12Number of Payments 360

MonthOpening Balance

Interest AmortizationMonthly Payment

Ending Balance

1 $60,000.00 $600.00 $166.67 $766.67 $59,833.332 $59,833.33 $598.33 $166.67 $765.00 $59,666.673 $59,666.67 $596.67 $166.67 $763.33 $59,500.004 $59,500.00 $595.00 $166.67 $761.67 $59,333.335 $59,333.33 $593.33 $166.67 $760.00 $59,166.676 $59,166.67 $591.67 $166.67 $758.33 $59,000.00

357 $666.67 $6.67 $166.67 $173.33 $500.00358 $500.00 $5.00 $166.67 $171.67 $333.33359 $333.33 $3.33 $166.67 $170.00 $166.67360 $166.67 $1.67 $166.67 $168.33 $0.00

Total $60,000.00

O

penin

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ala

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= P

revio

us

Peri

od E

ndin

g B

ala

nce

In

tere

st =

Openin

g B

ala

nce

× P

eri

odic

Rate

Peri

odic

Rate

= A

nnual R

ate

/ P

aym

ent

per

Year

A

mort

izati

on =

Ori

gin

al Lo

an B

ala

nce

/ N

um

ber

of

Paym

ents

M

onth

ly P

aym

ent

= Inte

rest

+ A

mort

izati

on

Endin

g B

ala

nce

= O

penin

g B

ala

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– A

mort

izati

on

8

Constant Amortization Mortgage

$0.00

$100.00

$200.00

$300.00

$400.00

$500.00

$600.00

$700.00

$800.00

$900.00

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360

Month

Am

oun

t ($

)

Interest Amortization Monthly Payment

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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 12 -60,000 617.17 0

10

Constant Payment Mortgage (CPM) – Continued

Loan Amount $60,000.00Interest Rate 12.00%Loan Term 30Payment per Year 12Number of Payments 360Monthly Payment $617.17

MonthBeginning

Loan Balance

Monthly Payment

Interest AmortizationEnding Loan

Balance1 $60,000.00 $617.17 $600.00 $17.17 $59,982.832 $59,982.83 $617.17 $599.83 $17.34 $59,965.493 $59,965.49 $617.17 $599.65 $17.51 $59,947.984 $59,947.98 $617.17 $599.48 $17.69 $59,930.295 $59,930.29 $617.17 $599.30 $17.86 $59,912.436 $59,912.43 $617.17 $599.12 $18.04 $59,894.38

357 $2,408.17 $617.17 $24.08 $593.09 $1,815.08358 $1,815.08 $617.17 $18.15 $599.02 $1,216.06359 $1,216.06 $617.17 $12.16 $605.01 $611.06360 $611.06 $617.17 $6.11 $611.06 $0.00

Total $60,000.00

Begin

nin

g L

oan B

ala

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= P

revio

us

Peri

od E

ndin

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ala

nce

M

onth

ly P

aym

ent

= D

ete

rmin

ed u

sing E

xce

l’s

PM

T

funct

ion

In

tere

st =

Begin

nin

g L

oan B

ala

nce

× P

eri

odic

Rate

Peri

od

ic R

ate

= A

nn

ual R

ate

/ P

aym

en

t p

er

Year

A

mort

izati

on =

Month

ly P

aym

ent

– In

tere

st

Endin

g L

oan B

ala

nce

= B

egin

nin

g L

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ala

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–

Am

ort

izati

on

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Constant Payment Mortgage

$0.00

$100.00

$200.00

$300.00

$400.00

$500.00

$600.00

$700.00

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360

Month

Am

oun

t ($

)

Monthly Payment Interest Amortization

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Constant Amortization/Payment Balances

$0.00

$10,000.00

$20,000.00

$30,000.00

$40,000.00

$50,000.00

$60,000.00

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360

Month

Am

oun

t ($

)

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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

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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

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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

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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

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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

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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 0

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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

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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 [58,598.16 × (1 + 0.03) =

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

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Yield and Prepayment TimeEffective Costs Year 1 - 30

6.00%

6.50%

7.00%

7.50%

8.00%

8.50%

9.00%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Year

AP

R

6.50%, 0.000 Points

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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: 0.934180 PV of payments to lender at the desired return:

The fees should total 100% - 94.53% = 5.47%

N I/Y P/Y PV PMT FV MODE

360 12 12 -1 0.010286

0

N I/Y P/Y PV PMT FV MODE

120 13 12 -0.9453 0.010286

0.934180

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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 12 -60,000

605.72 40,000

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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 $617.17 after 5 years?

N I/Y P/Y PV PMT FV MODE

360 12 12 -60,000 617.17 0

N I/Y P/Y PV PMT FV MODE

60 12 12 -60,000 400.00 76,334

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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 12 -60,000 600.00 60,000

N I/Y P/Y PV PMT FV MODE

240 12 12 -60,000 660.65 0

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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 0 1,220.44

-250,00

0

Three Loans when LTV < 20%

1. Conventional loan with PMI

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2. First and second loan

3. FHA insurance

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

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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 29

Authority to Assess Specially

Why a city would get into this type of an activity?

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Specials Example and Computations

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Specials Computations

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