Re Academic Press Private Real Estate Investment_10

276 Creative Financing 263 imposed maximum payment-to-income ratio, pti, can repay over a full amortization period, t.1 loan ¼ 1 ÿ ð1 þ iÞt incpti ð11-1Þ The maximum value of the house he can purchase, v, is equal to the amount he can borrow, plus the value of his old residence used as a down payment, dp. v ¼ dp þ 1 ÿ ð1 þ iÞt incpti ð11-2Þ The balance of the loan, balance (n), at the end of any particular year, n, is a function of the interest rate, term, and the initial balance.2 balanceðnÞ ¼ loanð1 þ iÞtÿð1 þ iÞ12n ð11-3Þ The sale price, s, at death is the value, v, increased by growth, g, compounded over the life expectancy, le. 0 1 s ¼ ÿ1 þ gleBdp þ 1 ÿ ð1 þ iÞt incptiC ð11-4Þ The bequest, b, is then merely the remaining equity, the difference between the value at sale and the loan balance. b¼dpÿ1þgleiþð1þiÞtÿ1þgleÿ1ÿð1þiÞtÿÿ1þgleþð1þiÞ12leincpti ð11-5Þ 1In the interest of simplicity, we ignore other home ownership operating costs at this stage. 2Note that this is not the equation for Ellwood Table #5. 276 264 Private Real Estate Investment TABLE 11-1 Three Datasets data1 data2 data3 Downpayment Growth Interest rate Term of loan Life expectancy Operating cost Income Payment-to-income ratio Value Loan-to-value ratio Payment dp $135,000 g 0.04 i 0.06/12 t 360 le 6 oc 0.04 inc $3,750 pti 0.4 val $300,000 ltv 0.6 pmt $1,500 $135,000 0.00 0.06/12 360 8 0.04 $3,750 0.4 $300,000 0.6 $1,500 $135,000 0.04 0.06/12 360 7 0.04 $3,750 0.4 $300,000 0.4 $1,500 Table 11-1 shows three datasets to be used as input values for the examples in this chapter. The second and third datasets are used only in the reverse amortization mortgage section and only differ in life expectancy, growth rate, and loan-to-value ratios. Note that the variable for value, v, provided in Equation 11-2 is a computed value, but val in the datasets is a fixed given value. Using data1 we obtain the following values for what we are calling the conventional arrangement, as shown in Table 11-2. The above example ignores the fact that operating costs for the house may increase, but also ignores the fact that retirement income may be indexed. In the interest of simplicity, these are assumed to cancel. TABLE 11-2 Values for the Convention Arrangement Purchase price Downpayment Loan Sale price Loan balance at life expectancy Bequest $385,187 $135,000 $250,187 $487,385 $228,666 $258,719 276 Creative Financing 265 THE REVERSE AMORTIZATION MORTGAGE We now consider a retiree who owns a larger house free of debt and wishes to generate monthly income from his home equity without selling the home. The lender will grant the loan based on his life expectancy, le, the value of the house, val, interest rate, i, and payment amount, pmt. Ellwood Table #2 handles the way $1 added each period at interest grows. The lender sets a maximum loan amount based on the loan-to-value ratio, ltv. hecmbalðnÞ ¼ minð1 þ iÞ12nÿ1pmt,ltvvalÿ1 þ gn ð11-6Þ Thus, given data1 and using le for n, the loan balance at life expectancy is $129,613. As this is less than ltvval(1 þ g)n, payments occur throughout the full life expectancy of the retiree. By incorporating growth into the model, we assume that the lender is willing to lend against future increases in value (g>0). Should that not be the case, in data2 where g ¼ 0 and le ¼ 8, the loan reaches its maximum (ltvinitial value) at 94 months and payments stop short of life expectancy. From a lender’s risk perspective, the imposition of a cap is an essential underwriting decision. How the cap is computed is also important. It can be based, as above in data1, on a fixed property value and permit a larger initial loan-to-value ratio or it can allow for growth in value but allow a lower loan-to-value ratio as in data3. Clearly, the lender does not want the loan balance to exceed the property value. Because the loan documents are a contract, the lender must perform by making payments regardless of the change in value. Thus, different assumptions impose different burdens and benefits, respectively, on the lender and borrower. When we permit the growth assumption, but reduce the loan-to-value ratio as in data3, the payments stop in 85 months. If the dollar amount of appreciation in house value grows faster than the balance of the loan, it is possible that the house could once again ‘‘afford’’ more payments and payments would resume.3 The sample amounts are not represented to be any sort of standard; they are arbitrary and merely serve as an illustration. The plot in Figure 11-1 demonstrates the importance to both parties of estimating life expectancy correctly, obviously not an easy task. The type of loan contract most desirable differs depending on how long one expects to need the income. 3From a loan servicing standpoint, this is an unappetizing prospect for the lender. 276 266 Private Real Estate Investment Balance 175000 150000 125000 100000 75000 No Growth − Hi LTV 50000 Growth − Low LTV 25000 2 4 6 8 10 Years FIGURE 11-1 Reverse amortization mortgages under different growth assumptions. Using Equation (11-7), one can approach the question from the standpoint of the maximum payment, mopmt, allowed under the three data scenarios offered in Table 11-1, each requiring one to know life expectancy exactly. mopmtðnÞ ¼ ð1 þ iÞ12nÿ1ltv valÿ1 þ gn ð11-7Þ Table 11-3 shows the maximum payments under the three datasets of Table 11-1. We see in Figure 11-2 that in the choice between a plan with a larger loan-to-value ratio but no growth assumption (data2) and one with a growth assumption but a smaller loan-to-value ratio (data3), the decision changes when one’s life expectancy is ten years or more. Not surprisingly, the most TABLE 11-3 Data data1 data2 data3 Maximum Payment under Different Assumptions Maximum payment $2,635.81 $1,465.46 $1,517.30 Creative Financing 267 Payment 2000 1500 1000 data 1 500 data 2 data 3 Years 5 10 15 20 FIGURE 11-2 Payment under different sets of assumptions. permissive arrangement (allowance for growth and high loan-to-value ratio) in the original dataset (data1) provides the highest payment. INTRA-FAMILY ALTERNATIVES The above examples represent ways to approach the problem using institutional lenders. We now turn to intra-family methods where economics only partially control. We shall focus on modifications to conventional arrangements. That is, we shall assume the reverse annuity mortgage option is not available because the retiree does not own a home of sufficient size to produce the desired results. There are two ways to approach such a financing scheme. 1. Should someone be willing to purchase a house for our retiree to live in for his lifetime with no right to devise by will, the retiree would have an additional $1,500 per month discretionary income. This, which we will call the Income Viewpoint, considerably enhances his retirement lifestyle. 2. Alternatively, the retiree could live in a house he could not otherwise afford if he is unconstrained by the loan qualifying payment-to-income ratio. We will call this the Larger House Viewpoint. This variation is just ... - tailieumienphi.vn