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# Chapter 6

Chapter 6. Alternative Mortgage Instruments. 6-1. Chapter 6 Learning Objectives. Understand alternative mortgage instruments Understand how the characteristics of various AMIs solve the problems of a fixed-rate mortgage. Interest Rate Risk. 6-2. Mortgage Example:

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## Chapter 6

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1. Chapter 6 Alternative Mortgage Instruments

2. 6-1 Chapter 6 Learning Objectives • Understand alternative mortgage instruments • Understand how the characteristics of various AMIs solve the problems of a fixed-rate mortgage

3. Interest Rate Risk 6-2 • Mortgage Example: • \$100,000 @ 8% for 30 years, monthly payments • PMT = \$100,000 ( MC8,30) = \$733.76

4. 6-3 Interest Rate Risk • If the market rate goes to 10%, the market value of this mortgage goes to: • PV = \$733.76 (PVAF10/12,360) = \$83,613 • Lender loses \$16,387

5. Interest Rate Risk 6-4 • If the lender could automatically adjust the contract rate to the market rate (10%), the market value of the loan remains • Pmt = \$100,000 (MC10,30) = \$877.57 • PV = \$877.57 (PVAF10/12,360) = \$100,000

6. 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)

7. Adjustable-Rate Mortgage (ARM) • Designed to solve 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

8. 6-5 ARM Variables • Index • Margin • Adjustment Period • Interest Rate Caps • Periodic • Lifetime • Convertibility • Negative Amortization • Teaser Rate

9. 6-6 Determining The Contract Rate • Fully Indexed: • Contract Rate = i = Index + Margin • In general, the contract rate is • in= Index + Margin • or • in = in-1 + Cap • whichever is lower

10. 6-7 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%

11. 6-8 A. ARM Payment In Year One • Index0 = 5% • Pmt1 = \$100,000 (MC5,30) = \$536.82

12. 6-9 B. ARM Payment In Year Two • BalanceEOY1= 536.82 (PVAF5/12,348) = \$98,525 • Interest Rate for Year Two • IndexEOY1 = 6% • i = 6 + 2.50 = 8.5% • or • i = 5 + 2 = 7% • Payment2 = \$98,525 (MC7,29) = \$662.21

13. 6-10 C. ARM Pmt In Year 3 • BalanceEOY2 = \$662.21 (PVAF7/12,336) = \$97,440 • IndexEOY2 = 6.5% • i = 6.5 + 2.5 = 9% • i = 7 + 2 = 9% • Pmt3 = 97440 (MC9,28) = \$795.41

14. 6-11 Simplifying Assumption • Suppose Index3-30 = 6.5% • This means that i3-30 = 9% • Thus Pmt3-30 = \$795.41 • BalEOY3 = \$96,632

15. 6-12 ARM Effective Cost-Hold for 3 Years • \$100,000 = 536.82 (PVAFi/12,12) • + 662.21 (PVAFi/12,12) (PVFi/12,12) • + 795.41 (PVAFi/12,12) (PVFi/12,24) • + 96,632 (PVFi/12,36) • i = 6.89%

16. 6-13 ARM Effective Cost-Hold to Maturity • \$100,000 = 536.82 (PVAFi/12,12) • +662.21 (PVAFi/12,12) (PVFi/12,12) • +795.41 (PVAFi/12,336) (PVFi/12,24) • i = 8.40%

17. Graduated-Payment Mortgage • 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

18. Graduated-Payment Mortgage • 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

19. 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

20. Inflation 4% -3% 2% 0% EOY 1 2 3 4-30 6-14 PLAM Example Borrow \$100,000 for 30 years, monthly payments. Current Real Rate = 6% with Annual Payment Adjustments

21. 6-15 A. PLAM Pmt in year 1 • Pmt = \$100,000 ( MC6,30) = \$599.5

22. 6-16 B. PLAM Pmt in year 2 • BalEOY1 = \$98,772 (1.04) = \$102,723 • Pmt2 = \$102,723 (MC6,29) = \$623.53

23. 6-17 C. PLAM Pmt in year 3 • BalEOY2 = \$101,367 (.97) = \$98,326 • Pmt3 = \$98,326 (MC6,28) = \$604.83

24. 6-18 D. PLAM Pmt in year 4 • BalEOY3 = \$96,930 (1.02) = \$98,868 • Pmt4 = \$98,868 (MC6,27) = \$616.92

25. 6-19 E. PLAM Pmt in years 5-30 • BalEOY4 = \$97,356 (1.00) = \$97,356 • Pmt5-30 = \$97,356 (MC6,26) = \$616.92

26. 6-20 F. PLAM Effective Cost If Repaid at EOY3 • \$100,000 = 599.55 (PVAFi/12,12) • + 623.53 (PVAFi/12,12) (PVFi/12,12) • + 604.83 (PVAFi/12,12) (PVFi/12,24) • + 98,868 (PVFi/12,36) • i = 6.97%

27. G. PLAM Effective Cost If Held To Maturity 6-21 • \$100,000 = 599.55 (PVAFi/12,12) • + 623.53 (PVAFi/12,12) (PVFi/12,12) • + 604.83 (PVAFi/12,12) (PVFi/12,24) • + 616.92 (PVAFi/12,324) (PVFi/12,36) • i = 6.24%

28. 6-22 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

29. 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

30. 6-23 RAM Characteristics • Typical Mortgage - Borrower receives a lump sum up front and repays in a series of payments • RAM - Borrower receives a series of payments and repays in a lump sum at some future time

31. 6-25 RAM Characteristics • Typical Mortgage - “ Falling Debt, Rising Equity” • RAM - “ Rising Debt, Falling Equity” • Designed for retired homeowners with little or no mortgage debt • Loan advances are not taxable • Social Security benefits are generally not affected • Interest is deductible when actually paid

32. 6-26 RAM Characteristics • RAM Can Be: • A cash advance • A line of credit • A monthly annuity • Some combination of above

33. RAM Example 6-27 Borrow \$200,000 at 9% for 5 years, Annual Pmts.

34. 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

35. 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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