File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan /cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 263/ 276 imposed maximum payment-to-income ratio, pti, can repay over a full amortization period, t. 1 loan ¼ 1 À 1 1 þ iðÞ t  inc pti i 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 À 1 1 þ iðÞ t  inc pti i ð11-2Þ The balance of the loan, balance (n), at the end of any particular year, n,isa function of the interest rate, term, and the initial balance. 2 balance nðÞ¼loan 1 þ iðÞ t À 1 þ iðÞ 12n 1 þ iðÞ t À1 ð11-3Þ The sale price, s, at death is the value, v, increased by growth, g, compounded over the life expectancy, le. s ¼ 1 þ g ÀÁ le dp þ 1 À 1 1 þ iðÞ t  inc pti i 0 B B @ 1 C C A ð11-4Þ The bequest, b, is then merely the remaining equity, the difference between the value at sale and the loan balance. b ¼ dp 1 þg ÀÁ le i þ 1 1 þiðÞ t 1 þg ÀÁ le À1  1 þiðÞ t ÀÁ À 1þg ÀÁ le þ 1 þiðÞ 12le  incpti i ð11-5Þ 1 In the interest of simplicity, we ignore other home ownership operating costs at this stage. 2 Note that this is not the equation for Ellwood Table #5. Creative Financing 263 File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 264/ 276 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 11-1 Three Datasets data1 data2 data3 Downpayment dp $135,000 $135,000 $135,000 Growth g 0.04 0.00 0.04 Interest rate i 0.06/12 0.06/12 0.06/12 Term of loan t 360 360 360 Life expectancy le 687 Operating cost oc 0.04 0.04 0.04 Income inc $3,750 $3,750 $3,750 Payment-to-income ratio pti 0.4 0.4 0.4 Value val $300,000 $300,000 $300,000 Loan-to-value ratio ltv 0.6 0.6 0.4 Payment pmt $1,500 $1,500 $1,500 TABLE 11-2 Values for the Convention Arrangement Purchase price $385,187 Downpayment $135,000 Loan $250,187 Sale price $487,385 Loan balance at life expectancy $228,666 Bequest $258,719 264 Private Real Estate Investment File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 265/ 276 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. hecmbalðnÞ¼min 1 þ iðÞ 12n À1 i pmt,ltv val 1 þ g ÀÁ n ! ð11-6Þ Thus, given data1 and using le for n, the loan balance at life expectancy is $129,613. As this is less than ltv Ãval(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 (ltv Ãinitial 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. 3 From a loan servicing standpoint, this is an unappetizing prospect for the lender. Creative Financing 265 File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 266/ 276 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. mopmtðnÞ¼ i 1 þ iðÞ 12n À1 ltv Ãval 1 þ g ÀÁ n 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 2 4 6 8 10 Years 25000 50000 75000 100000 125000 150000 175000 Balance No Growth − Hi LTV Growth − Low LTV FIGURE 11-1 Reverse amortization mortgages under different growth assumptions. TABLE 11-3 Maximum Payment under Different Assumptions Data Maximum payment data1 $2,635.81 data2 $1,465.46 data3 $1,517.30 266 Private Real Estate Investment File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 267/276 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 5 101520 Years 500 1000 1500 2000 Payment data 3 data 2 data 1 FIGURE 11-2 Payment under different sets of assumptions. Creative Financing 267 File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 268/ 276 a special case of lifestyle enhancement in which the larger residence is how one elects to apply larger disposable income arising from the life estate arrangement. THE INCOME VIEWPOINT In the conventional example, our retiree essentially ‘‘purchases’’ the satisfaction of leaving a bequest by incurring the obligation to make loan payments and foregoing the benefits associated with more discretionary income he would have had during his lifetime if he did not have loan payments to make. The income viewpoint amounts to ‘‘selling’’ that satisfac- tion in return for the enhanced present income. The interesting question is: How much of one is the other worth? The tradeoff is between leaving a bequest, b, and current income, inc. 4 A rational retiree chooses based on his calculation of the greater of these two. Such a calculation involves assumptions that can, at times, be uncomfort- able to make. Using Equation (11-5), the value of the bequest in Table 11-2 for data1 circumstances is $258,719. To make a fair comparison we need to know the present value of the income foregone in order that a bequest may be left. If our retiree is able to live in a house without paying loan payments, he enjoys that income for the remainder of his life. The present value of this income is computed via Equation (11-8). pv ¼ 1 À 1 1 þ iðÞ 12 le  inc pti i ð11-8Þ If we value that income at the same interest rate as the bank and accurately predict life expectancy (recall we said some uncomfortable assumptions would be necessary), using data1 the present value of those payments is $90,509. As the $258,719 bequest is larger than the present value of the foregone income, if one takes the simple (too simple!) position that the investor chooses the largest of these, he buys a house, makes payments, and leaves a bequest. Why is this too simple? It is naive to equate the nominal value of money left to someone else in the future with the present value of dollars one may 4 This is popularized by the bumper sticker adorning many recreational vehicles that reports, ‘‘We’re spending our children’s inheritance!.’’ 268 Private Real Estate Investment File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 269/ 276 personally consume. Merely incorporating the time value of money and using the same rate as the bank, a present value calculation performed on the bequest seems at least reasonable. Thus, the decision rule becomes Equation (11-9). Max b 1 þ iðÞ 12 le ,pv ! ð11-9Þ But under data1, at bank interest rates the discounted value of the bequest, $180,664, is larger than the $90,509 present value of the foregone income, so this retiree still buys a house and leaves a bequest. Present value may imperfectly adjust for the difference between the value our retiree places on his own consumption and the value he places on financing the future consumption of others. One way to deal with this is to increase the discount rate on the bequest. Suppose we arbitrarily value bequest dollars considerably less than present consumption dollars by making the discount rate thrice the interest rate. Now, for data1 the present value of the bequest, $88,567, is below the present value of the foregone income. Under these conditions our retiree opts to have someone else buy him a house, someone who will receive the house at his death. 5 So for the Income Viewpoint and given data1, the decision turns on how dollars the retiree may consume are valued versus how he values dollars he leaves behind. This means the retiree carefully selects a discount rate that adjusts future dollars others receive to equal the value of dollars he may otherwise consume. THE LARGER HOUSE VIEWPOINT One point illustrates how this may, indeed, be creative financing. An institutional lender evaluates risk based on the probability of repayment taking place over the investor’s lifetime. As there is a cap on his dollar return (all interest payments plus the principal), the lender makes a loan governed by the realities of (a) the income the retiree has during his lifetime to make payments and/or (b) the liquidation value of the property needed to retire any balance remaining at the retiree’s death. The Remainderman as lender has a different perspective. Since he captures the entire (uncertain) value of the property at death, the Remainderman’s payoff prospects are different. Also, it is possible that an older relative’s care of a larger property for the 5 We are reminded that we assumed the ‘‘someone’’ who buys the retiree a house is not his heir. If this were not the case the retiree would be, in a sense, merely deciding the form of the bequest. Creative Financing 269 File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator:iruchan /cipl-un1-3b2-1.unit1.cepha.net Date/Time:22.12.2004/3:28pm Page:270/27 6 Remainderman can produce positive results for the Remainderman that are not included in these computations. Let us begin by noting how the retiree will approach the possibility of a larger house. Remember that ‘‘larger’’ is just a metaphor for ‘‘better’’ in some tangible way. The house may be better located, newer, have a better view, be larger, or otherwise in some sense be more desirable than the house the retiree might purchase. We assume that all of these desirable attributes will be captured in a higher price, making possible the measurement of larger or better. Suppose that the retiree’s self-imposed limit on the portion of his income he will spend on housing is the same fraction a lender will allow. That is, he wishes to have the most house he can support, paying in operating costs, oc, the same amount as his loan payment would have been had he purchased the property. The point is that our retiree has a housing budget that is a self-imposed constraint on the size of house he is willing to ‘‘support,’’ whether that support is in the form of loan payments, upkeep, or some combination of the two. Clearly, ‘‘bigger’’ or better is more feasible without loan payments. We will suppose that annual operating costs on an expensive residence run 4% of its purchase price. Thus, he can ‘‘carry’’ a house the value of which is equal to the ratio of his annual housing budget to operating costs. Using Equation (11-10) and data1, our retiree acquires a house valued at $300,000. lg hse ¼ 12inc pti oc ð11-10Þ If we assume, naively, that the utility of different houses is represented by the difference in their values, using Equation (11-11), the retiree chooses the greater of this difference or the bequest, again requiring an ‘‘appropriate’’ discount, which we have again set three times bank interest rate. Max lg hse À v, b 1 þ :18 12  12 le 2 6 6 6 4 3 7 7 7 5 ð11-11Þ Under data1 conditions, the larger of these alternatives, $88,567, is the bequest. Setting the two equations in Equation (11-11) equal and solving for payment-to-income ratio, we can find an indifference point based on the 270 Private Real Estate Investment File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 271/276 portion of the retiree’s income he is willing to devote to housing. Using data1 inputs we find that, if all else is equal and the retiree uses only 17.73% of his income for housing rather than the 40% the lender would allow, he is indifferent between the large house and the bequest. This provides planning flexibility in that under these circumstances the retiree may choose to use an additional 22.27% of his income either for housing or for other retirement comforts. The qualifier ‘‘if all else is equal’’ is important. Combining the variables using different values provides an infinite number of permutations. For instance, leaving the discount rate at the bank interest rate, i, moves the indifference point of the payment-to-income ratio to 28.57%, again making the choice of discount rate critical. The case shown here is a template for further reflection following some simulation using the Excel workbook that accompanies this chapter. THE REMAINDERMAN’S POSITION The Remainderman’s position is conceptually much simpler. He may be viewed as buying a zero coupon bond with an uncertain payoff date and amount. We assume that the Remainderman buys the house for its value, v, and concurrently sells a life estate to the retiree for the amount the retiree realizes from the sale of his old residence, dp. In that way the Remainderman really is providing financing, creative or not, for he takes the place of the lender. His net investment is the amount of the loan. The payoff is the sale price of the property, an unknown amount, at the death of the retiree, on an unknown date. THE INCOME CASE Given data1, the Remainderman’s investment would be a loan of $250,187 on which he computes an annual return of 11.11% using Equation (11-12). retInc ¼ Log s = loan ½ le ð11-12Þ Figure 11-3 shows that, as one might expect, the return is negatively related to life expectancy and positively related to growth. Because higher returns occur in the early years, the choice of which relative to stand in as lender is critical. One does not want to create a perverse incentive in such an arrangement. Measuring the utility our Remainderman gains from his Creative Financing 271 File: {Elsevier}Brown/Revises-II/3d/Brown-ch011.3d Creator: iruchan/cipl-un1-3b2-1.unit1.cepha.net Date/Time: 22.12.2004/3:28pm Page: 272/ 276 relations’ longevity (or lack of it!) is at best an unsavory task that even an economist would not relish. THE LARGER HOUSE CASE The larger house alternative may be less attractive for the younger family member. One reason is that in our example the retiree’s purchase price for the life estate is limited to the value of his former residence. So even though the growth takes place on a bigger number, unless the larger house comes with a larger growth rate, because of the larger investment this alternative yields less, 9.87% per annum using data1, to the junior member of the family. retLghse ¼ Log lg hse 1 þg ÀÁ le lg hse À dp "# le ð11-13Þ The longer the arrangement continues, the lower the yield. At le ¼ 20 years, the yield drops to 5.71%. The return is again negatively related to life expectancy. Figure 11-4 shows that if a larger house comes with higher growth, the return is respectable across the likely range of the investment time horizon. 5 10 15 20 0.04 0.05 0.06 0.07 Growth 0.1 0.2 0.3 0.4 0.5 Return Life Expectancy FIGURE 11-3 Return based on growth and life expectancy. 272 Private Real Estate Investment [...]... non-normality in real estate investment, 117, 119–121 objective, 100–101 282 282 Risk (continued) payoff expectations, 148–150 probability mass function modification in real estate, 145–147 stable distributions, 123–126 subjective, 100–101 uncertainty relationship, 138–141 utility function, 104–107, 116 Weibull distributions, 126–127 Rules of thumb, see Threshold performance measures Software, role in real estate. .. question in states that 274 Private Real Estate Investment reassess on transfer of title Estate tax questions hinge on the size of the estate, the size of the exemption, and other factors Finally, the capital gains taxes must not be ignored Under present U.S tax law, when the life estate falls the Remainderman can move into the property for a short time, establishing it as his primary residence, and then sell... single) These are powerful benefits and costs that should be included in the decision Due to personal considerations, there are usually non-economic issues at work here Hopefully, these are positive Numerous family benefits may be realized when older relations are close by (although opposite results can occur) It is assumed that this sort of transaction only takes place among stable, harmonious relations... specific ways A talented estate planning attorney and a careful real estate analyst can craft an ownership arrangement tailored to individual needs Through this entire chapter we have deliberately ignored taxes This should not be done when a transaction of this type is contemplated The ordinary income tax questions include who gets the deduction for paying property taxes There is a property tax/valuation... the dependent of the other REFERENCES 1 Capozza, D R and Megbolugbe, I F., Editors (1994) Journal of the American Real Estate and Urban Economics Association, Vol 22 2 Case, B and Schnare, A B (1994) Preliminary evaluation of the HECM reverse mortgage program Journal of the American Real Estate and Urban Economics Association, 22(2), 301–346 3 Grossman, S M (1984) Mortgage and lending instruments designed... use, 47 rent per square foot calculation, 45 required rent raise calculation, 46–47 Gross scheduled income, discounted cash flow analysis, 75, 83–84 Home Equity Conversion Mortgage, HECM 279 lender’s risk, 265 life expectancy estimation, 265–266 principles, 260 Inflation relationship with capitalization rate and interest rate, 216 Tier II investor activity as predictor, 235 Installment sale, see Private. .. in creative financing income case, 271–272 large house case, 272 tax considerations, 274 Rent decay rate versus distance, 11 location theory, see Location theory Retirement parameters in creative financing, 261–262 modeling of real estate disposition conventional arrangement of downsizing, 262–264 intra-family alternatives income viewpoint, 268–269 larger house viewpoint, 269–271 overview, 267–268 Remainderman’s... complexities of this chapter are bewildering enough to anyone not dealing with the challenges of aging There are even more alternatives that approach the task differently A shared appreciation mortgage or simple joint tenancy are just two other possibilities that can achieve similar goals The important general point is that the United States has an economic system capable of precisely describing a large... 60–63 Expense ratio definition, 41 expense and vacancy rate, 55–60 net income dependence, 54 relationships age of property, 64 gross rent multiplier, 66 number of units, 66 size of property, 66 Foreclosure, rights of private lenders, 241–242 Future value function, 240–241 GRM, see Gross rent multiplier Gross rent multiplier accuracy, 43 applications, 43 definition, 41 deterministic inputs affecting in... ramifications, 173, 186–187 United States tax code, 159, 187 value, 173–175 Threshold performance measures basic income property model, corporations versus real estate investment, 40–41 capitalization rate, 41, 49–53 cash-on-cash return, 41, 67 debt coverage ratio, 42 expense ratio, 41, 54–56, 64–66 gross rent multiplier, 41, 43–47 investor reliance in hot markets, 215–216 investor rules, 41 lender rules, 41–42 . concurrently sells a life estate to the retiree for the amount the retiree realizes from the sale of his old residence, dp. In that way the Remainderman really is providing financing, creative. 123–126 subjective, 100 101 uncertainty relationship, 138–141 utility function, 104 107 , 116 Weibull distributions, 126–127 Rules of thumb, see Threshold performance measures Software, role in real estate. Equation (11 -10) and data1, our retiree acquires a house valued at $300,000. lg hse ¼ 12inc pti oc ð11 -10 If we assume, naively, that the utility of different houses is represented by the difference