Fixed Rate Mortgage Loans

1
Fixed Rate Mortgage Loans

• Lecture Map
• How/why loans are priced and structured as they
  are
• Impact of pricing and structuring on real estate
  returns
• Evolution of the modern real estate mortgage
  market
• Mortgage math

2
Fixed Rate Mortgage Loans

• What determines interest rates on real estate
  loans?
• Macro and Micro factors
• Real estate is part of the larger capital market
• Interest rates help to allocate capital among
  investment alternatives
• In theory, interest rates are the equilibrium
  price between what borrowers are willing to pay
  and the return lenders require to lend to them

3
The Real Rate of Interest

• In economics, the real rate is equated to the
  underlying, risk free rate of interest
• The minimum, least risk alternative rate
  available
• Fed funds, LIBOR, etc.
• These real rates also referred to as base
  rates - are the starting point for determining
  the all-in cost of mortgage money

4
What is the Real Cost of a Real Estate Loan?

• The real cost to a borrower equals the underlying
  base rate plus a spread, fees and other lender
  charges
• Dont forget the effect of compound interest!
• The real cost is a function of risk
• Lenders perception of risk factors
• How they charge for those risk factors

5
Mortgage Risk Factors

• Basic Risks from the Lenders Perspective
• Default Risk
• Interest Rate Risk
• Prepayment Risk
• Liquidity Risk
• Legislative Risk (change in legal rules)

6
How Do Lenders Charge for Taking these Risks?

• Interest Rates
• Real Rate plus premiums charged as the price of
  these risks
• Non-monetary terms
• Loan to appraised value and/or cost
• Debt service coverage ratios
• Other covenants and conditions

7
Whats the Effect of Changes in Perceived Risk?

• Changes in terms reflect tightening or loosening
  of credit
• Debt becomes more costly, or
• Debt amounts decrease
• Result ? Required returns to equity will change
  based on equitys perception of mortgage risk

8
Whats the Effect of Changes in Perceived Risk?

• Changing debt and equity costs flow through over
  time to change market conditions
• Changing debt requirements
• ?
• changing equity requirements
• ?
• changing return requirements
• ?
• changing cap rates
• ?
• changing values in the markets

9
The Mortgage Market

• How is the mortgage market different today than
  30 years ago?
• Greater reliance on the underlying physical
  collateral value of real estate
• Increased size and liquidity
• Larger number of participants
• Increased sophistication in pricing, structuring
  and legal governance

10
Mortgage Market History

• Pre-WWII
• High downpayments, fast repayment
• Little reliance on underlying physical asset
• Post WWII
• Introduction of constant amortizing mortgages
• Constant principal, declining interest payments
• Lender recognition that borrowers could repay
  loans over time as economy grows

11
Mortgage Market History (cont.)

• Today
• Basic mortgage vehicle is the constant payment
  mortgage
• Declining interest, increasing principal payments
• Important changes in market
• More people qualify for loans based on
  development, standardization of underwriting
  criteria
• Volume of loans has increased dramatically
• Risk has shifted to lenders in the aggregate as a
  result

12
The Constant Payment Mortgage

• Monthly payment includes p i
• As principal amortizes, interest due on
  outstanding balance declines
• Therefore, each payment includes more principal
  and less interest
• Payment stream is designed to amortize the loan
  balance to zero (0) at maturity

13
Calculating a Constant Mortgage Payment

• 10 million loan, 25 years amortization, 8
  interest rate
• PV - 10,000,000
• FV 0 (loan balance at maturity)
• N 25 years x12 monthly periods
• I 8 12 monthly periods
• Solve for PMT
• 77,181.62 per month

14
Calculating Outstanding Loan Balances

• The outstanding balance at any point in time PV
  of the remaining payment stream
• Time value of money
• Lenders will only lend money today if the present
  value of what they will get back is at least
  equal to the amount of the loan
• Structure of the payments
• Since each payment includes principal and
  interest, a remaining outstanding balance must
  equal the PV of that balance plus the compound
  interest on the balance

15
Calculating Outstanding Loan Balances (cont.)

• Whats the balance on our 10 million loan at the
  end of 10th year?
• We are solving for PV
• PMT 77,181.62
• I 8 12 monthly periods
• N 15 x 12 (Remaining of years x 12 monthly
  compounding periods)
• FV 0 (the remaining payments will amortize the
  loan in full
• Remaining Balance PV 8,076.330

16
Mortgage Constants

• A mortgage constant is the interest factor used
  to determine payments on fixed rate, constant
  payment mortgages
• Not the same as the effective rate of interest
• Equates the sum of annual pi into a single
  interest factor
• Used frequently as a shorthand method of
  determining required mortgage payments

17
Calculating the Mortgage Constant

• What is the mortgage constant on our 10 million
  loan?
• PMT 77,181.62 per month
• X 12 926,179 per year
• Constant Total annual payments principal
  balance
• 926,179 10,000,000
• 9.262

18
Effective Borrowing Costs

• The effective cost of a loan includes fees and
  charges imposed by lenders
• These fees and charges
• Increase effective yield to lender
• Effective cost to borrower effective yield to
  lender
• Represent additional compensation for lender risk
  

19
Effective Borrowing Costs (cont.)

• What items increase borrowing costs?
• Points and closing expenses
• Decrease actual proceeds received by borrowers
• Cost increases because payment is still
  calculated on the original loan balance
• Points are finance charges
• represent early amortization of principal
• Compensate for prepayment liquidity, interest
  risk
• Closing Costs
• Statutory fees and expenses
• Third party fess and expenses

20
Effective Borrowing Costs (cont.)

• Effective costs can also be changed by back-end
  loaded fees and charges
• Prepayment, late and default penalties
• Increase interest cost because they are added to
  payments
• Compensation for interest, prepayment, default
  risks
• These fees and charges are incurred as a result
  of borrower action
• More manageable than up front increases to
  effective borrowing costs

21
Calculating Effective Borrowing Costs

• 10 million loan, 8 interest, 25 year
  amortization, 2 points up front
• What is the effective cost?
• Step 1 Solve for the payment
• Step 2 Solve for the effective interest cost of
  that payment on actual loan dollars received at
  closing

22
Calculating Effective Borrowing Costs (cont.)

• PMT 77,181.62 (from earlier slide)
• Solve for effective cost
• PV - (10,000,000 x .98)
• FV 0
• N 25 12
• PMT 77,181.62
• I 8.237

23
Effective Borrowing Costs Impact on Equity

• As lending costs go up, borrowers face
• Higher equity requirements
• Points and other loan fees reduce actual loan
  proceeds at transaction closing
• Greater cash flow risk
• Mortgage payment claims on cash flow go up
  relative to the actual percentage of the
  transaction financed with debt

24
Effective Borrowing Costs Impact on Equity
(cont.)

• Assume we have a 13 million warehouse under
  contract
• Total investment
• Purchase price plus closing expenses
• Debt Equity
• If points and closing expenses reduce loan
  proceeds, more equity is require to complete the
  transaction

25
Closing Statement Example
26
More Effective Cost Calculations

• Suppose you prepay the loan at the end of the 5th
  year?
• Looking for the real cost of what youve paid
  over the last five years
• Step 1 Solve for the remaining balance of the
  loan
• FV 0
• N 20 12
• I 8 x 12
• PMT 77,181.62
• PV 9,227,394

27
More Effective Cost Calculations (cont.)

• Step 2 Determine the effective cost based on
  the initial proceeds and this remaining balance
• PV (10,000,000 x .98) 9,800,000
• PMT 77,181.62
• FV 9,227, 394
• N 5 12
• I 8.509
• The effective cost is higher because the lender
  is getting principal back much early than
  projected
• Higher PV to the lender must indicate higher
  yield to them

28
Calculating Effective Borrowing Costs (cont.)

• Suppose our 10 million loan has a prepayment fee
  of 2, and we prepay at the end of the 5th year?
• Step 1 Calculate the revised remaining
  balance
• Outstanding balance in year 5, plus 2 (of
  balance) fee
• Step 2 Solve for effective borrowing cost
• In this case, we are looking for what the
  payments you have made to date have really cost
  you
• the effective cost will be higher
• Addition of the prepayment penalty decreases the
  amount of principal you have amortized to date

29
Calculating Effective Borrowing Costs (cont.)

• PMT 77,181.62
• PV (10,000,000 .98) 9,800,000
• FV PV of the remaining payments in year 5 plus
  the 2 prepayment fee 9,411,942
• FV 0
• N 20 12
• I 8 x 12
• PMT 77,181.62
• PV 9,227,394
• N 5 x 12 (we have made payment for 5 years)
• The effective interest cost (I) 8.818

30
Comparing the rates

• Our loan example
• 10 million loan, 8 interest rate, 25 year
  amortization, 2 points, 2 prepayment fee
• Nominal rate 8
• Effective rate with points 8.237
• W/points, if prepaid early 8.509
  
• W/points, prepaid w/penalty 8.818

31
Inflation and Mortgages

• Interest rates reflect the markets assessment of
  inflation at a point in time
• Both lenders and borrowers worry about inflation
  because of its effect on the value of payment
  streams
• tilt effect on borrowers
• As inflation rises and borrower incomes decline
  in real current value, mortgage payments take a
  greater percentage of borrowers real incomes
• Loss of real economic value to lenders
• Outstanding mortgages represent assets that
  lenders could be lending today at higher rates,
  reflecting an increase in the inflation premium

32
Other Types of Mortgages

• Graduated Payment Mortgage
• Mitigates the tilt effect on borrowers
• Payments increase over loan period
• Borrowers initial cost is lower, allowing them
  to keep more of their PV dollars today
• Puts more risk on appreciation of the property to
  maintain value of the pledged physical asset
• GPMs are negative amortization mortgages
• Balance actually increases as a result of accrued
  interest
• Accrue what would be paid under the CPM and what
  is actually paid
• We will study negative amortization later in
  semester

33
Other Types of Mortgages (cont.)

• Reverse Annuity Mortgages
• Borrowing against the equity in a home
• Lender actually makes payments to the borrower
• The loan balance builds up over time advances are
  made and interest accumulates
• Why is this an interesting value proposition for
  the lender?