# L3

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```					LECTURE 3: MORTGAGE MARKETS I                                  A Basic Mortgage Scenario

Overview                                                       • You want to purchase a residential property.
• You do not have sufficient funds to pay for it.
•   A basic mortgage scenario
• You borrow money or take a loan from a financial
•   The mortgage instrument                                      institution(FI).
•   Mortgage mathematics                                       • The FI will demand a collateral for granting you the loan.
•   Fixed rate mortgages                                       • Your property will be the collateral.
•   Adjustable rate mortgages                                  • Such a loan (where your property is the collateral) is
called a mortgage.
•   CPF financing                                              • You buy the property and service the mortgage.

The Mortgage Instrument                                        The Mortgage Instrument - Elements

• A mortgage is created in a transaction whereby one           •   Loan Amount or Principal
party pledges real property to another party as security     •   Interest Rate or Coupon
for an obligation owed to that party.                        •   Loan Maturity Period or Duration
• A mortgage involves a transfer or conveyance of an           •   Method and Timing of Debt Service/Amortisation
interest in real estate with a provision for redemption.
•   Loan-to-value Ratio
• The FI is the creditor/lender/mortgagee. It has a legal or
equitable interest on your property.                         •   Debt Coverage Ratio
• You are the debtor/borrower/mortgagor.                       •   Other Special Provisions       - Fees
• Redemption is the repayment to discharge the loan                                        - Early Repayment
outstanding.                                                                             - Others

Mortgage Mathematics                                           Fixed Rate Mortgages (FRMs)

• Suppose you take out a mortgage for \$60,000 for 30           • Two types:
years at a fixed interest rate of 12% p.a. What is the           – Constant Amortisation Mortgage (CAM) where the principal is
annual mortgage debt service (assuming annual                      reduced by a constant amount each period
compounding)?                                                    – Fully Amortising, Constant Payment Mortgage (CPM) where a
constant amount is repaid each period but the principal reduction
Principal = PVA = \$60,000                                      is not constant
Interest rate = i = 0.12                                 • FRMs which are CPMs have
Number of payments = n = 30                                  – constant monthly payments based on an original loan amount at
Annual debt service = \$60,000 (MC12%,30yrs)                    a fixed interest rate for a given term
– payment comprises interest and some (though not a constant)
= \$60,000 (0.124143657)                 repayment of principal
= \$7,448.62
FRMs - An Example                                              FRMs - Loan Amortisation Pattern

\$60,000 loan at 12% for 30 years, monthly
rest./compounding
Monthly debt service based on a CPM uses PVA/MC                   Period Beginning     Debt Interest (\$)   Principal          Ending
formula                                                                Balance (\$) Service (\$)         Amortisation (\$)   Balance (\$)
ANN1%,360 mths = PVA (MC1%,360mths)                               1     60,000.00 617.17       600.00      17.17           59,982.83
⎡          ⎤
⎢    i     ⎥                           2     59,982.83 617.17       599.83      17.34           59,965.49
= \$60,000 ⎢⎣1− (1+ i) ⎥⎦
⎢       −n ⎥
3     59,965.49 617.17       599.65      17.51           59,947.98
.         .           .         .           .                .
.         .           .         .           .                .
=    \$60,000 (0.01028613)
.         .           .         .           .                .
=    \$617.17
360     611.06     617.17      6.11      611.06               0

FRMs - Graph of Amortisation Pattern                           FRMs - Mortgage Balance

• Mortgages may be repaid before they mature for various
Payment                                       Debt               reasons.
Service          • Suppose you want to repay the loan after 10 years. What
is the outstanding mortgage balance at the end of year
Principal                10?
• Compute the mortgage balance using the PVA formula
Interest                               where the annuity is the monthly payment and n is the
term remaining until loan maturity.
Mortgage Balance         = ANN (PVAF1%, 240mths)
Time                       = \$617.17 (90.81941635)
= \$56,051.02

FRMs - Loan Origination/Closing Fees                           FRMs - Effective Borrowing Cost

• Generally, closing costs include statutory costs, third-     Suppose the lender charges 3%(points) upfront on the
party charges and additional finance costs/charges.            loan.
• Finance fees cover the “fixed cost” elements of
mortgages and are additional income received by the          • 3% of \$60,000 = \$1,800
lender.                                                      • Borrower receives only \$58,200 rather than contractual
• Fees are charged upfront to the borrower and result in a       sum of \$60,000. (Hence, the term “discount”)
discount on the loan.                                        • Debt service is still based on principal of \$60,000.
• Significance:                                                • Because the borrower receives only 97% of principal
– increase the cost of borrowing to the borrower              sum but makes payment based on 100% of principal
– increase the yield/return to the lender                     amount, the actual borrowing cost to the lender is more
than 12%.
FRMs - Effective Borrowing Cost                             FRMs - Rationale for Loan Fees

To determine the effective cost of the loan to the        • Increase the yield or return on mortgage loans
borrower or the effective interest return to the lender     for lenders.
denoted r, equate the PV of \$58,200 with the PV of 360
monthly payments of \$617.17 at the rate r.                • Marketing tool.
• Protect lenders against “sticky” mortgage rates:
\$617.17(PVAr%,360mths) = \$58,200                            upward movement in market interest rates may
PVAr%,360mths = \$58,200/\$617.17 = 94.30140804               occur but mortgage rates may still be
r = 1.03% per month (12.41%) > 1% per month (12%            unchanged.
p.a.)                                                     • In U.S., lenders must disclose the APR (Annual
Why is the effective interest rate higher?                  Percentage Rate) being charged on the loan.

FRMs - Loan Fees and Early Repayment                        Loan Fees and Early Repayment

• Mortgages are sometimes repaid before the full            • Say you repay the loan at the end of 5 years.
term/maturity of the loan.                                • Mortgage Balance still outstanding at the end of
• Early loan repayment may be because of                      5 years = PV of 300 monthly payments of
–   divestment/sale of property                             \$617.17 at 12% p.a. = \$58,597.93.
–   death                                                 • Solve for r, the effective interest rate per month:
–   divorce                                                 \$58,200 = \$617.17(PVAFr%,60mths) + \$58,597.93
–   disability
(PVFr%,60mths)
–   dislocation
r = 1.069% p.m > 1.03% p.m.

Loan Fees and Early Repayment                               Prepayment Penalty

• When loan fees are charged upfront and the                • Borrowers mistakenly assume a loan can be prepaid in
loan is repaid before maturity, the effective               part or in full anytime before maturity.
interest cost of the loan is even higher.                 • Most FIs impose a prepayment penalty, notice of partial
prepayment &/or notice of redemption.
• Why? What if you repaid the very next day?
• Rationale:
• What if there were no upfront loan fees? Would               - allows the lender to recover loan origination costs
you care if you had to prepay?                               - compensates lender for risk that he may not be able to
• Moral Hazard Issue: The lender doesn’t know                     reinvest the funds from prepayment to earn similar
when you will prepay but you have some idea.                    yields if interest rates have fallen since origination
- compensates lender for promotional /preferential rates
Prepayment Penalty                                    FRMs - Cash Flow Time Line

• Say the prepayment penalty is 3% on the                                          Payment at
outstanding mortgage balance or 3% of                                            EOY 5 = DS
Debt Service
\$58,597.93 (= \$1757.94).                                                         + MB + PP
of \$617.17 p.m.
• If the loan is prepaid at the end of 5 years, the
Time
effective interest cost r is solved as follows:
\$58,200 = \$617.17(PVAFr%,60mths) + \$60,355.87
(PVFr%,60mths)                          \$58,200
at time EOY 0
r = 1.104% p.m > 1.069% p.m.

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 views: 16 posted: 6/25/2011 language: English pages: 4