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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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