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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

- Time Preference for Consumption
- Inflation Expectation
- Retain purchasing power

Components of the Mortgage Interest Rate

- Default Risk
- Interest Rate Risk
- Anticipated Inflation and Unanticipated Inflation

- Prepayment Risk
- Liquidity Risk
- Legislative Risk
- Option-adjusted spread

Components of the Mortgage Interest Rate

r = Real Rate

f1 = Inflation Rate

p1 = Risk Premiums/spread

Three Relationships for Fixed-income Securities

- Applicable to all fixed-income securities
- Interest payment at time t = loan balance at time t-1 X period interest rate
- Total payment = interest payment + principal (amortization) payment
- Principal payment at time t = Principal at time t-1 minus payment toward principal at time t

- Different debt security has different requirement for principal payment

Computing a Loan Balance

- Three methods
- “Rolling” principal balance period by period
- Convenient if principal payment is constant

- Compute the present value of the remaining payments
- More convenient if the payments are constant

- Compute the future value of the amortized loan amount, given initial loan value
- Convenient if total payment is constant

- “Rolling” principal balance period by period

Mortgage Payment Patterns

- Interest-only Mortgage (IO)
- Monthly payment constant
- Total principal stays constant as well

- Constant Amortization Mortgage (CAM)
- Loan Amortization Remains the Same
- Monthly Payment Changes

- Constant Payment Mortgage (CPM)
- Loan Amortization Changes
- Monthly Payment Remains the Same

Development of Mortgage Payment Patterns I

1.Short-term interest-only mortgage with large down payment requirement

- Interests paid based on constant principal amount
- No intermediate amortization

Development of Mortgage Payment Patterns I

Example 1: you are interested in a $75K house. The bank is willing to lend you at 12% 5-year interest only loan if you can put 50% down. What is the monthly payment and mortgage balance at the end of 5th year?

Development of Mortgage Payment Patterns II

2. Constant amortization mortgage (CAM)

- Constant amortization amount
Amort = total loan amount / number of months

- Interest computed on the loan balance at the end of previous month
Int(t) = OLB (t -1) * (mortgage rate / 12)

- Total pmt = constant amortization amount
+ monthly interest pmt

- OLB(t) = OLB(t-1) – amort(t)
Note: total payment will decrease over time

Development of Mortgage Payment Patterns II

Example 2: if you only need to put down 20% for the $75K property to qualify for a 30-year CAM, at 12% annual interest rate,

Q: what is mortgage balance by the end of 5th year?

Q: What is your 61st payment?

Q: How much of your 61st payment goes to principal?

Development of Mortgage Payment Patterns III

3. Constant payment mortgage (CPM)

- Constant total monthly payment
- Can be calculated using annuity PV formula

- Interest computed based on loan balance at the end of previous month
int(t) = OLB (t -1) * (mortgage rate / 12)

- Amount of amortization can be backed out by taking difference b/w total payment and its interest component
amort(t) = pmt(t) – int(t)

Development of Mortgage Payment Patterns III

3. Constant payment mortgage (CPM)

- Remaining balance can be calculated by deducting previous balance by payment toward principal in the current period (backward looking)
- Can also be calculated by discounting remaining payments at the mortgage interest rate
- Or follow a PV/PMT/FV calculation

Development of Mortgage Payment Patterns III

Example 3.

1. What is the monthly payment for a 30-year $60K CPM at 12%?

2. What is the loan balance by the end of 5th year?

3. How much does your 61st payment will go towards principal payment?

4. Over the life of the mortgage, what is the total amount of interest paid?

5. If inflation is 6%, what is the real value of the 60th payment today?

6. How much interest will you be paying in the 6th year?

Other Loan Patterns

- Partially Amortizing
- Balloon Mortgage

- Negative Amortization
- Graduated Payment Mortgage (GPM)

- Reverse Annuity Mortgages

Development of Mortgage Payment Patterns IV

4. Graduated payment mortgage (GPM)

- Mortgage payments are lower in the initial years of the loan
- GPM payments are gradually increased at predetermined rates for initial years, and then stay constant until maturity

GPM Example

- Loan amount $60,000
- Maturity 30 years
- Interest rate (yield) 12%
- Graduation time 5 years
- Graduation rate 7.5%
- Q: What is the initial payment?
- Q: What is the balance after 5 years?

Reverse AnnuityMortgage

- Residential property value $500,000
- Loan amount to be disbursed in monthly installments $250,000
- Term 10 years 120 months
- Interest Rate 10%
- Q: How much payment will the homeowner receive?

Reverse Annuity Mortgage Example Continued

- Calculator solution:
- FV=-250,000
- i=10%/ 12
- PMT= ?
- n=120
- Solve for payment $1220.44

Effective Interest Cost

- Fees and points are part of loan financing charges
- Should be taken into account in comparing loan cost or true interest costs

- Regulation - Truth in Lending Act
- What is the borrowing cost, called Annual Percentage Rate (APR, in %) if the loan is paid off at maturity?

Effective Interest Cost Example 1: APR

- Contractual loan amount $ 60,000
- Less organization fee(3%) $ 1,800
- Net cash disbursed by lender $ 58,200
- Interest rate= 12%
- Term 30 years

Effective Interest Cost Examples 1: APR Continued

- Calculator solution
- n=360
- PMT= -617.17
- PV= 58,200
- FV= 0
- i=1.034324 (12.41% annualized)

Effective Interest Cost Example 2:Early Termination

- Contractual loan amount $ 60,000
- Less organization fee(3%) $ 1,800
- Net cash disbursed by lender $ 58,200
- Interest rate= 12%
- Term 30 years
- Loan paid off in 5 years
Q: What is the true effective cost to the borrower/effective yield to the lender?

Effective Interest Cost Example 2:Early Termination

- 1. Find out loan balance after 5 years
- 2. Find out initial net cash outlay
- 3. Find out the interest rate that sets the present value of loan balance in 5 years (minus possible penalty/fess) and the mortgage payments in first 5 years to the initial net cash outlay (OLB0-Fees and points)

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