Topic 11:Mortgage Loan MechanicsIn this discussion, we look at the computational steps used in computing the payments, and some other relevant figures, for some common types of residential mortgage loans. I. Ways to classify mortgage loansA. By repayment methodThink about how loan payments could be arranged. We can do this in the context of the Laws of Financial Dynamics. What are some ways in which mortgage loan payments can be arranged without violating these “laws”?1. Negative amortization – initial payments are so low that they do not even cover interest owed for the respective time periods. The shortfalls are added to principal balance owed: negative amortization results (the amount the borrower owes after making the first payment is more than the amount initially borrowed). The graduated payment mortgage (GPM) loan is a type of negative amortization loan that sometimes might be well-suited to younger people with little money but much income growth potential. But the option-adjustable rate mortgage loan that gained popularity in the recent housing and mortgage lending crisis was a poorly conceived effort to keep payments low for cash-challenged borrowers, with the expectation (or at least the hope) that interest rates would stay low, borrower incomes (and credit scores) would rise, and home prices would continue rising. 2. No amortization – a straight term loan, with only interest paid during the loan’s life and a “balloon payment” for the full principal amount at maturity. This structure has not traditionally been used much in practice (especially for homes), but the concept should be easy to understand. Stock brokerage firms have at times promoted interest-only loans, touting the tax deductibility of the full payment (since it is all interest) and the accompanying ability to apply more money each month to other investments. One possibility put forth was to pair the interest-only loan with a life insurance policy whose cash value would be expected to grow tax-free and ultimately equal the loan’s principal. 3. Partial amortization – all interest is paid, and some principal is repaid during the loan’s life, but there is still a balloon payment owed at maturity. No current, commonly offered loan product offers this feature, but the lack of prepayment penalties on home mortgage loans would allow a borrower to synthetically create this arrangement, by getting a straight term loan and then paying enough extra each month to reduce, but not fully repay, principal over the loan’s life. 4. Full amortization – the old standby: fixed-payment, fixed interest rate mortgage loan (FRM). The payments and interest rate both remain unchanged throughout the life of the loan. A 30-year (360 month) repayment plan is most typical, although 15 years is also common; and 10, 20, and 25 year amortization periods are sometimes offered. In fact, as home prices rose in recent years some lenders even made 40-year loans, and 50-year terms were discussed. (Some lenders have extended payment periods from 30 to 40 years to forestall defaults in the recent financial crisis; other “loan modification” tools include reduced interest rates and deferred, or even forgiven, principal repayment; see “Mortgage Relief” handout on web site.) The FRM emerged in the 1930s with the creation of FHA. Earlier loans had been shorter term, such as five years, interest-only and with balloon payments.The FRM can be seen as being good for: - borrowers, because of cash flow benefits (ability to spread payments over a long period)- lenders, because the amortization feature reduced the likelihood that the borrower would default But the FRM can be bad for:- borrowers because of the “tilt” problem, in which rising incomes over time cause early-year payments to be very expensive in real dollar terms, but later payments to be more inexpensive in real dollar terms. So young buyers, in particular, face affordability problems (subsidizing their later, higher-earning years).- lenders because of interest rate risk, especially in light of the short-term nature of traditional lenders’ deposit base.FIL 260/Trefzger1Computing Payments for the Fixed Rate, Fixed Payment Mortgage LoanComputation of the payment is a present value of an annuity exercise (we are dealing with equal payments spaced equally through time). If we recall the formula Payment x PV of Annuity Factor = Total.Assume that we have a $120,000 loan with a 7.8% stated annual interest rate and an amortization period involving equal end-of-month payments over 30 years. The relevant number of (monthly) time periods is 30 x 12 = 360, and the relevant monthly interest rate is .078 ÷ 12 = .0065. Our computation formula isPayment x (1−(11+i)ni) = TotalPayment x (1−(11.0065)360.0065)= $120,000Payment x 138.913874 = $120,000or, more traditionally, we multiply the loan amount by a payment factor (reciprocal of the PV of annuity factor) to compute the payment:$120,000 x (.00651−(11.0065)360) = Payment$120,000 x .007199 = $863.84 For a fixed-payment loan, if the life is the typical 30 years and the interest rate is in the historically typical range of 7 – 10%, the payment factor is somewhere in the neighborhood of .007 (think of a famous spy). Note also that the monthly payment factor is a number slightly greater than the monthly interest rate (in the above example, the monthly interest rate is 7.8%/12 = .0065, and the monthly payment factor is the slightly larger .007199). Why? Because each monthly payment contains .0065 times the remaining principal balance to cover the month’s interest, plus a little bit more to chip away a little more at the remaining principal. [The loan payment factor actually consists of the interest rate for the period plus the sinking fund factor for accumulating a lump sum – the principal borrowed – over the loan’s amortization term and periodic interest rate.] 5. More than full amortization – each period, the borrower pays more than the amount that would be paid under a fixed-payment, fully amortizing arrangement. The added money paid directly reduces principal owed, and thereby shortens the period over which payments must be made. This arrangement is sometimes called a growing equity mortgage (GEM) loan. The extra payment can be an official part of the loan agreement, or can be done informally by the borrower because no prepayment penalty typically can be