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Chapter 6
Alternative Mortgage Instruments
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Chapter 6 Learning Objectives
Understand alternative mortgage instruments (AMIs)
Understand how the standard mortgage terms are determined and how they are interrelated.
Understand how the characteristics of various AMIs solve the problems of a fixed-rate mortgage (FRM)
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Alternative Mortgage Instruments
Adjustable-Rate Mortgage (ARM)
Graduated-Payment Mortgage (GPM)
Price-Level Adjusted Mortgage (PLAM)
Shared Appreciation Mortgage (SAM)
Reverse Annuity Mortgage (RAM)
Pledged-Account Mortgage or Flexible Loan Insurance Program (FLIP)
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Adjustable-Rate Mortgage (ARM)
Most popular AMI designed to solve the interest rate risk problem
Allows the lender to adjust the contract interest rate periodically to reflect changes in market interest rates. This change in the rate is generally reflected by a change in the monthly payment
Provisions to limit rate changes Initial rate is generally less than FRM rate
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ARM Variables Index – CMT Index (e.g. 1-year T-bill); LIBOR; COFI; the 11th District Cost of
Funds Index
Margin – amount, in bps, added to the index to obtain the contract rate
Adjustment Period
Interest Rate Caps Periodic (or rate)
Life-of-loan or life
First adjustment
Convertibility (to FRM)
Negative Amortization – increase in the loan balance from one period to the next
Teaser Rate – initial period discount
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Determining The Contract Rate Fully Indexed:
Contract Rate (i) = Index + Margin
In general, the contract rate in time n is the lower ofin= Index + Margin
or
in = in-1 + Cap
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ARM Example Loan Amount = $100,000
Index = 1-Year TB Yield
One Year Adjustable
Margin = 2.50
Term = 30 years
2/6 Interest Rate Caps
Monthly Payments
Teaser Rate = 5%
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ARM Payment In Year 1 Index0 = 5%
Pmt1 = $100,000 (MC5/12,360) = $536.82
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ARM Payment In Year 2 BalanceEOY1= 536.82 (PVAIF5/12,348) = $98,525
Interest Rate for Year 2
IndexEOY1 = 6%
i = 6 + 2.50 = 8.5%
or
i = 5 + 2 = 7%
Payment2 = $98,525 (MC7/12,348) = $662.21
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ARM Payment In Year 3 BalanceEOY2 = $662.21 (PVAIF7/12,336) = $97,440
Interest Rate for Year 3
IndexEOY2 = 6.5%
i = 6.5 + 2.5 = 9%
or
i = 7 + 2 = 9%
Pmt3 = 97,440 (MC9/12,336) = $795.41
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Simplifying Assumption
Suppose Index3-30 = 6.5%
This means that i3-30 = 9% since the contract rate in year 3 is fully indexed
Thus Pmt3-30 = $795.41
BalEOY3 = $96,632
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ARM Effective Cost for a Three-Year Holding Period
$100,000 = 536.82 (PVAIFi/12,12)
+ 662.21 (PVAIFi/12,12) (PVIFi/12,12)
+ 795.41 (PVAIFi/12,12) (PVIFi/12,24)
+ 96,632 (PVIFi/12,36)
i = 6.89% The equation can be solved for i either by financial calculator
or by an iterative process of trial and error When using financial calculator, the cash flow mode is required since
payments are different each year
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ARM Annual Percentage Rate (APR)
$100,000 = 536.82 (PVAIFi/12,12)+662.21 (PVAIFi/12,12) (PVIFi/12,12)
+795.41 (PVAIFi/12,336) (PVIFi/12,24)
i = 8.40%
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Interest-Only ARM
Payment in the initial period is interest-only with no repayment of principal
After the initial period the loan becomes fully amortizing
Loan is designed to fully amortize over its stated term A 3/1 Interest-Only ARM is interest-only for the first
three years and then becomes a fully amortizing one-year ARM
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Interest-Only ARM
Suppose you take a 3/1 interest-only ARM for $120,000, monthly payments, 30-year term. The initial contract rate is 4.00% and the contract rate for year 4 is 6.00%. The lender charges two discount points.
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Interest-Only ARM
What is the monthly payment for the interest-only period?
$120,000 (.04/12) = $400.00
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Interest-Only ARM
What is the effective cost of the loan if it is repaid at the EOY3?
120,000 – 2,400 = 400 (PVAIFi/12,36) + 120,000 (PVIFi/12,36)
i = 4.72%
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Interest-Only ARM
What is the payment for year 4?
Pmt = 120,000 (MC6/12,324)
Pmt = $748.78
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Interest-Only ARM
What is the balance of the loan at the EOY4 of the 30-year term?
BalEOY4 = 748.78 (PVAIF6/12,312)
= $118,165
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Interest-Only ARM
If the loan is repaid at the EOY4, what is the effective cost?
120,000 – 2,400 = 400 (PVAIFi/12,36)
+ 748.78 (PVAIFi/12,12)
+ 118,165 (PVIFi/12,48)
i = 5.0145%
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Option ARM
Gives the borrower the flexibility of several payment options each month
Includes a “minimum” payment, an interest-only payment, and a fully Amortizing payment
Usually has a low introductory contract rate Minimum payment results in negative amortization
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Option ARM
Minimum payment can result in “payment shock” when payment increases sharply
Loan must be recast to fully amortizing every five or ten years
Negative amortization maximum of 125% of original loan balance
Loan payment increases to fully amortizing level
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Alt-A Loan
Alternative Documentation Loan or “No Doc” Loan Borrower may not provide income verification or
documentation of assets Loan approval based primarily on credit score In the mid-2000s, loans were popular with non
owner-occupied housing investors
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Flexible Payment ARM
Very low initial payment, expected to rise over time “Payment shock” with dramatic increase in payment Appeal is the very low initial payment designed to help
offset affordability problem Contract rate adjusts monthly with maybe no limits on
size of interest rate changes
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Graduated-Payment Mortgage (GPM)
Tilt effect is when current payments reflect future expected inflation. Current FRM payments reflect future expected inflation rates. Mortgage payment becomes a greater portion of the borrower’s income and may become burdensome
GPM is designed to offset the tilt effect by lowering the payments on an FRM in the early periods and graduating them up over time
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Graduated-Payment Mortgage (GPM)
After several years the payments level off for the remainder of the term
GPMs generally experience negative amortization in the early years
Historically, FHA has had popular GPM programs Eliminating tilt effect allows borrowers to qualify for
more funds Biggest problem is negative amortization and effect on
loan-to-value ratio
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Price-Level Adjusted Mortgage (PLAM)
Solves tilt problem and interest rate risk problem by separating the return to the lender into two parts: the real rate of return and the inflation rate
The contract rate is the real rate The loan balance is adjusted to reflect changes in
inflation on an ex-post basis Lower contract rate versus negative amortization
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PLAM Example
EOY Inflation1 4%
2 -3%
3 2%
4-30 0%
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Suppose you borrow $100,000 for 30 years, monthly payments. The current real rate is 6% with annual payment adjustments
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PLAM Example
Pmt in year 1 = $100,000 ( MC6/12,360) = $599.55
Pmt in year 2BalEOY1 = $98,772 (1.04) = $102,723
Pmt2 = $102,723 (MC6/12,348) = $623.53
Pmt in year 3BalEOY2 = $101,367 (.97) = $98,326
Pmt3 = $98,326 (MC6/12,336) = $604.83
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PLAM Example (Cont.)
Pmt in year 4BalEOY3 = $96,930 (1.02) = $98,868
Pmt4 = $98,868 (MC6/12,324) = $616.92
Pmt in year 5-30BalEOY4 = $97,356 (1.00) = $97,356
Pmt5-30 = $97,356 (MC6/12,312) = $616.92
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PLAM Effective Cost If Repaid at EOY3 $100,000 = 599.55 (PVAIFi/12,12)
+ 623.53 (PVAIFi/12,12) (PVIFi/12,12)
+ 604.83 (PVAIFi/12,12) (PVIFi/12,24)
+ 98,868 (PVIFi/12,36)
i = 6.97%
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PLAM Effective Cost If Held To Maturity (APR)
$100,000 = 599.55 (PVAIFi/12,12)+ 623.53 (PVAIFi/12,12) (PVIFi/12,12)
+ 604.83 (PVAIFi/12,12) (PVIFi/12,24)
+ 616.92 (PVAIFi/12,324) (PVIFi/12,36)
i = 6.24%
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Problems with PLAM
Payments increase at a faster rate than income
Mortgage balance increases at a faster rate than price appreciation
Adjustment to mortgage balance is not tax deductible for borrower
Adjustment to mortgage balance is interest to lender and is taxed immediately though not received
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Dual Index Mortgage (DIM) Uses more than one index for adjustment
Borrower’s rate tied to wage and salary index Lender’s rate tied to interest rate index If the borrower’s payment does not catch up with lender’s
payment – balance at maturity
From lender’s standpoint similar to the ARM From borrower’s standpoint not comparable to ARM
E.g. borrower’s initial payment low based on the a low interest rate, but rate due to lender higher – results in negative amortization
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Shared Appreciation Mortgage (SAM)
Low initial contract rate with inflation premium collected later in a lump sum based on house price appreciation
Reduction in contract rate is related to share of appreciation Amount of appreciation is determined when the house is sold or by
appraisal on a predetermined future date
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Reverse Mortgage Typical Mortgage
Borrower receives a lump sum up front and repays in a series of payments
“Falling Debt, Rising Equity”
Reverse Mortgage Borrower receives a series of payments and repays in a lump sum at some future
time
“Rising Debt, Falling Equity”
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Reverse Mortgage
Loan advances are not taxable
Designed for senior homeowners for little or no mortgage debt
Social Security benefits are generally not affected
Interest is deductible when paid
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Reverse Mortgage
Reverse Mortgage Can Be: A cash advance
A line of credit
A monthly annuity
Some combination of above
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Reverse Mortgage Example
Yr Beg. Bal. Pmt Interest End Bal.1 0 30659 2759 334182 33418 30659 5767 698443 69844 30659 9045 1095484 109548 30659 12619 1528265 152826 30659 16514 199999
Borrow $200,000 at 9% for 5 years, Annual Pmts.
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Pledged-Account Mortgage
Also called the Flexible Loan Insurance Program (FLIP) Combines a deposit with the lender with a fixed-rate
loan to form a graduated-payment structure Deposit is pledged as collateral with the house May result in lower payments for the borrower and
thus greater affordability
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Home Equity Loans Typically revolving credit lines in which the borrower’s
home serves as collateral Have specific credit limits based on the borrower’s quality Once the loan approved the borrower can draw any
amount up to the limit at any point of time Minimum payment required based on agreed
amortization period Generally, combined LTV of first and second mortgage
should not exceed 80% of the house value
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AMIs and Tax Deductibility of Interest Payments
With standard loan all interest payments are deducible With some AMIs borrowers (as cash-basis taxpayers)
may not use fully interest deductions E.g. with GPM: In initial years interest expense > payment The borrower cannot deduct the excess of interest charge
over the amount of payment. The deduction is deferred until positive amortization begins
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Mortgage Refinancing
Replaces an existing mortgage with a new mortgage without a property transaction
Borrowers will most often refinance when market rates are low
The refinancing decision compares the present value of the benefits (payment savings) to the present value of the costs (prepayment penalty on existing loan and financing costs on new loan)
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Mortgage Refinancing
Factors that are known to the borrower or can be calculated from the existing mortgage contract: Current contract rate
Current payment
Current remaining term
Current outstanding balance
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Mortgage Refinancing
Assumptions that must be made by the borrower: What will be the amount of the new loan?
Payoff of the existing loan?
Payoff of the existing loan plus financing costs of the new loan?
Payoff of the existing loan plus financing costs of the new loan plus equity to be taken out?
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Mortgage Refinancing
Assumptions that must be made by the borrower: What will be the term of the new loan?
Equal to the remaining term of the existing loan?
Longer than the remaining term of the existing loan?
Shorter than the remaining term of the existing loan?
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Mortgage Refinancing
Assumptions that must be made by the borrower: What will be the holding period of the financing?
Equal to the term (maturity) of the mortgage?
Shorter than the term (maturity) of the mortgage?
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Refinancing Example $100,000 30-year FRM at 10%, paid monthly, 3% prepayment penalty if
repaid in the first 8 years Consider refinancing in 5 yrs into 25-year FRM at 7.5%; 3% financing costs Calculations:
Current payment: $877.57
Payoff of existing loan =
= Balance + Prepayment Penalty = $96,574 + 2,897 = $99,471
New loan payment: $735.08
Monthly payment savings = $877.57 - 735.08 = $142.49
New loan financing costs = 3%*$99,471=$3,979
NPV of refinancing = $142.49 (PVAIF7.5/12,300) - $3,979 = $15,302
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