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# Academic Press, Private Real Estate Investment - Data Analysis and Decision Making

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- 276 263 Creative Financing imposed maximum payment-to-income ratio, pti, can repay over a full amortization period, t.1 1 1À inc pti ð1 þ iÞt loan ¼ ð11-1Þ i 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. 1 1À inc pti ð1 þ iÞt v ¼ dp þ ð11-2Þ i 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 ð1 þ iÞt Àð1 þ iÞ12n balanceðnÞ ¼ loan ð11-3Þ ð1 þ iÞt À1 The sale price, s, at death is the value, v, increased by growth, g, compounded over the life expectancy, le. 0 1 1 1À t inc ptiC Ále B À ð1 þ iÞ s ¼ 1 þ g Bdp þ C ð11-4Þ @ A i The bequest, b, is then merely the remaining equity, the difference between the value at sale and the loan balance. 1 À Ále À À Ále ÁÀ Ále 1 þ g À1 ð1 þ iÞt À 1 þ g þ ð1 þ iÞ12 le incpti dp 1 þ g i þ t ð1 þ iÞ b¼ 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.
- 276 264 Private Real Estate Investment 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 6 8 7 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 11-1 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 $385,187 Downpayment $135,000 Loan $250,187 Sale price $487,385 Loan balance at life expectancy $228,666 Bequest $258,719
- 276 265 Creative Financing 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. ! ð1 þ iÞ12n À1 À Án hecmbalðnÞ ¼ min pmt,ltv val 1 þ g ð11-6Þ i Thus, given data1 and using le for n, the loan balance at life expectancy is $129,613. As this is less than ltv Ã val(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 Ã initial 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.
- 276 266 Private Real Estate Investment Balance 175000 150000 125000 100000 75000 No Growth − Hi LTV Growth − Low LTV 50000 25000 Years 2 4 6 8 10 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. À Án i mopmtðnÞ ¼ ltv Ã val 1 þ g ð11-7Þ 12n ð1 þ iÞ À 1 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 Maximum Payment under Different Assumptions Data Maximum payment data1 $2,635.81 data2 $1,465.46 data3 $1,517.30
- 267 Creative Financing Payment 2000 1500 1000 data 1 data 2 500 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
- 276 268 Private Real Estate Investment 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). 1 1À inc pti ð1 þ iÞ12 le pv ¼ ð11-8Þ i 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!.’’
- 276 269 Creative Financing 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). ! b Max ,pv ð11-9Þ ð1 þ iÞ12 le 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.
- 270 Private Real Estate Investment 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. 12inc pti lg hse ¼ ð11-10Þ oc 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. 2 3 6 7 b 6 7 Max6lg hse À v, ð11-11Þ 12 le 7 4 5 :18 1þ 12 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
- 271 Creative Financing 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). Log½s=loan retInc ¼ ð11-12Þ le 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
- 276 272 Private Real Estate Investment 0.5 0.4 0.07 Return 0.3 0.2 0.06 0.1 Growth 5 0.05 10 15 Life Expectancy 20 0.04 FIGURE 11-3 Return based on growth and life expectancy. 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. " Ále # À lg hse 1 þ g Log lg hse À dp retLghse ¼ ð11-13Þ le 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.
- 273 Creative Financing 0.4 0.35 0.3 Return 6% Growth 0.25 4% Growth 0.2 0.15 0.1 0.05 2.5 5 7.5 10 12.5 15 17.5 20 Life Expectancy FIGURE 11-4 Remainderman returns with different growth rates. CONCLUSION We have been rather cavalier about assuming a ﬁxed value for life expectancy. One must be cautioned about using the mortality tables for inputs in the equations above. Mortality tables are based on a large pool of people and report the portion of those that can be expected to die during or survive until the end of any one year. For individuals the ‘‘expectation’’ is far less precise. Variance from expectation can be considerable and dependent on a host of personal factors that may or may not be representative of actuarial results in a large pool. This analysis could stand for the reason many seniors rent. The 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 variety of property rights that can be combined in very 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 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 it with no tax due on gains up to $500,000 ($250,000 if ﬁling 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. If so, beneﬁts not measured in dollars could enhance the ﬁnancial decision in ways not available via conventional lending arrangements. Nonetheless, if the transaction is framed in economics offering a baseline of reasonable ﬁnancial merit, family members can proceed in a way that minimizes the possibility of one becoming 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 for the elderly. Journal of Housing for the Elderly, 2(2), 27–40. 4. DiVenti, T. R. and Herzog, T. N. (1990). Modeling home equity conversion mortgages. Actuarial Research Clearing House, 2. 5. Fratantom, M. C. (2001). Homeownership, committed expenditure risk, arid the stockholding puzzle, Oxford Economic Papers, 53:241–259. 6. Fratantom, M. C. (1999). Reverse mortgage choices: A theoretical and empirical analysis of the borrowing decisions of elderly homeowners. Journal of Housing Research, 10(2), 189–208. 7. Keynes, J. M. (1923). A Tract on Monetary Reform. Macmillan, London. 8. Pastalan, L. A. (1983). Home equity conversion: A performance comparison with other-housing options. Journal of Housing for the Elderly, 1(2), 83–90. 9. Phillips, W. A. and Gwin, S. B. (1992). Reverse Mortgages Transactions of the Society of Actuaries, 44, 289–323. 10. Rasmussen, D. W., Megbolugbe, I. F., and Morgan, B. A. (1997). The reverse mortgage as an asset management. Tool Housing Policy Debate, 8(1), 173–194 11. Rasmussen, D. W., Megbolugbe, I. F., and Morgan, B. A. (1995). Using 1990 public use microdata sample to Estimate Potential Demand for Reverse Mortgage Products. Journal of Housing Research,6(1), 1 Venti, S. F. and Wise, D. A. 23. 12. Venti, S. F. and Wise, D. A. (1989). Aging, moving and housing wealth. (Wise, D. A., Editor). The Economics of Aging. Chicago, IL, The University of Chicago Press, pp. 9–48.
- 282 Index Advertising, see Commercial advertising number of unit effects in Tier II Agency problemd properties, 214–215 collected rent calculation, 197–198 positive leverage modeling, 219 correction of model, 204–207 private lender strategies, 239–240 data issues, 201–202, 205–207 Tier I versus Tier III properties, net proﬁt 213–214 building size inﬂuences, 193–194 function, 190–191 Capital gains property manager proﬁt, 192–193 discounted cash ﬂow analysis, 76, 85 no vacancy rate approach in modeling, tax deferral, see Tax deferral; Tax 195–197 deferral exchange property owner’s dilemma, 195 Capitalization rate quality of property management, 190 appraisal approach by lenders, reconciliation of property owner and 210–212 property manager problems, assumptions in use, 49–50 198–201 components, 136 transaction cost modeling, 191 deﬁnition, 41 vacancy factor, 197–198 discounted cash ﬂow analysis, 50–51 Appraisal monotonic growth modeling, 52–53 capitalization rate approach, 210–212 relationship with interest rate and mortgage equity approach, 210–212 inﬂation, 216 value relationship, 54–55, 137 Bargaining, discounted cash ﬂow Cash-on-cash return analysis, 87–90 applications, 67 Before-tax cash ﬂow, discounted cash comparative analysis, 67–69 ﬂow analysis, 75, 85, 87 conﬂict between debt coverage ratio Bid rent curve and borrower’s cash-on-cash bid rent surface for entire city, 7–8 return calculation data issues, 231–235 several competing users in different excess debt coverage ratio, 223–224, industries, 5–6 226–227 two competing users in same overview, 222–223 industry, 3–5 three-dimensional illustrations, linearity, 7–8 227–231 BTCF, see Before-tax cash ﬂow two-dimensional illustrations, Bubble market 224–227 lenders as governors, 217, 221–222 deﬁnition, 41 277
- 282 278 Index Cash-on-cash return (continued) overview, 222–223 leverage modeling three-dimensional illustrations, amoritizing debt, 220–221 227–231 growth assumption, 222 two-dimensional illustrations, simple, 218 224–227 regression analysis, 69–71 deﬁnition, 42 C/C, see Cash-on-cash return Debt service, discounted cash ﬂow CDF, see Cumulative distribution analysis, 75, 86 function Determinism, risk analysis Certainty equivalent, risk analysis, house prices, 131–134 107–110 overview, 128–130 Coin toss experiment real estate investment, 135–138 marriage comparison, 128, 138, 153 Discounted cash ﬂow St. Petersburg Paradox, 101–104 after-tax cash ﬂow, 75, 85–87 Collected rent, calculation in agency analysis using capitalization rate, problem, 197–198 50–51 Commercial advertising bargaining effects, 87–90 community disutility, 31–32 data issues in analysis, 93–98 land use regulation modeling deterministic inputs affecting gross graphic illustration, 28–32 rent multiplier, 82–83 implications, 32 due diligence in hot markets, 215–216 optimization and comparative modiﬁed logistic growth function, statics, 27–28, 37–38 90–93 overview, 24–27 monotonic growth modeling, 52–53 Comparative statics, land use regulation multi-year analysis, 78–79 optimization, 27–28, 37–38 net present value determination, 81 CR, see Capitalization rate sale variables relationships, 79–80 Creative ﬁnancing, see Home Equity single year analysis, 76–78 Conversion Mortgage; Life variables in analysis Estate; Retirement equity reversion variables, 76 Cumulative distribution function ﬁnancing variables, 75–76 expense and vacancy rates, 59 income tax variables, 76 random variable derivative, see operating variables, 75 Probability distribution performance variables, 75 function Due diligence level number of unit effects in Tier II properties, 214–215 DCF, see Discounted cash ﬂow Tier I versus Tier III properties, DCR, see Debt coverage ratio 213–214 Debt coverage ratio conﬂict between debt coverage ratio and borrower’s cash-on-cash Economic topography maps, 12–13 return Environmental protection, land use data issues, 231–235 regulation modeling, 24–27 excess debt coverage ratio, 223–224, Equity reversion, discounted cash ﬂow 226–227 analysis, 76, 84–85
- 282 279 Index EVR, see Expense and vacancy rate lender’s risk, 265 Excess debt coverage ratio, see Debt life expectancy estimation, 265–266 coverage ratio principles, 260 Expense and vacancy rate calculation, 55 Inﬂation cumulative distribution function, 59 relationship with capitalization rate data analysis, 55–60 and interest rate, 216 gross rent multiplier relationship, 55 Tier II investor activity as linear transformations of data, 62, 64 predictor, 235 normal and Stable distributions of data, Installment sale, see Private lenders 60–63 Interest rate Expense ratio components, 136 deﬁnition, 41 relationship with capitalization rate expense and vacancy rate, 55–60 and inﬂation, 216 net income dependence, 54 Internal rate of return, IRR relationships buy-and-hold example, 183–185 age of property, 64 private lender loan evaluation, 252 gross rent multiplier, 66 purchase–hold–sell base case, 163 number of units, 66 purchase–hold–sell base case with size of property, 66 growth projection modiﬁcation, 165–167 Foreclosure, rights of private lenders, tax deferred exchange example, 241–242 172, 174 Future value function, 240–241 Irrational exuberance, see Bubble market GRM, see Gross rent multiplier Jarque Bera test, normality testing, 61 Gross rent multiplier accuracy, 43 Land use regulation, see Regulation, applications, 43 land use deﬁnition, 41 Lenders deterministic inputs affecting in appraisal, see Appraisal discounted cash ﬂow analysis, bubble market control, 217, 221–222 82–83 conﬂict between debt coverage ratio equilibrium of ratio of value to gross and borrower’s cash-on-cash income, 45–46 return ﬁeld work supplementation, 44 data issues, 231–235 market equilibrium, 43 excess debt coverage ratio, 223–224, property size limitations in use, 47 226–227 rent per square foot calculation, 45 overview, 222–223 required rent raise calculation, 46–47 three-dimensional illustrations, Gross scheduled income, discounted cash 227–231 ﬂow analysis, 75, 83–84 two-dimensional illustrations, 224–227 Home Equity Conversion Mortgage, private, see Private lenders HECM qualiﬁcation of desired borrowers, 213
- 282 280 Index Lenders (continued) Net operating income rules, 209–210 discounted cash ﬂow analysis, 75, 86 threshold performance measures, equations, 55 41–42 no vacancy rate approach in agency Leverage problem modeling, 195–197 modeling reconciliation of property owner appreciation, 219 and property manager assumptions, 218 problems, 199 bubble market, 219 sale-and-repurchase strategy, 176 cash-on-cash return Net present value amoritizing debt, 220–221 buy-and-hold example, 183–185 growth assumption, 222 calculation, 81 simple, 218 data issues, 185–186 debt service, 219 private lender loan evaluation, 249 positive leverage versions, 217–218 purchase–hold–sell base case with Life Estate growth projection modiﬁcation, principles, 260–261 165–167 Remainderman, 263, 271–272, 274 tax deferred exchange example, 172 Loan-to-value ratio, deﬁnition, 41 Net proﬁt Location theory agency problem function, 190–191 assumptions, 2, 13–14, 16 building size inﬂuences, 193–194 data sources, 16 property manager proﬁt, 192–193 economic topography maps, 12–13 reconciliation of property owner and empirical veriﬁcation, 8–9, 11 property manager problems, examples 199–203 several competing users in different NOI, see Net operating income industries, 5–6 NPV, see Net present value two competing users in same industry, 3–5 Payment factor, discounted cash ﬂow notation, 2–3 analysis, 86 proﬁt equation, 3 PDF, see Probability distribution function rent decay rate versus distance, 11 PMF, see Probability mass function transportation costs, 3, 5 PPU, see Price per unit LTV, see Loan-to-value ratio Present value, equation, 51 Price per unit, deﬁnition, 41 Market rent, deﬁnition, 44 Private lenders Maximum likelihood estimation, MLE, bubble market strategies, 239–240 data ﬁtting in risk analysis, buyer evaluation of ﬁnancing 150–152 internal rate of return test, 252 Modiﬁed logistic growth function, net present value test, 249 discounted cash ﬂow analysis, tax blind test, 252–253 90–93 competent counseling importance, Municipal services, land use regulation 256–257 modeling, 24–27 diversiﬁcation problem, 238–239
- 282 281 Index foreclosure rights, 241–242 Remainderman future value function for property, Life Estate, 263, 274 240–241 position in creative ﬁnancing hard money loan versus purchase income case, 271–272 money loan, 238 large house case, 272 installment sale transaction, 248 tax considerations, 274 lending versus owning as interest rates Rent rise, 240–242 decay rate versus distance, 11 motivations location theory, see Location theory buyer, 244–245 Retirement seller, 237, 245–248 parameters in creative ﬁnancing, prepayment penalties, 253–255 261–262 rules, 238–239 modeling of real estate disposition tax deferral advantages, 242–244, 248 conventional arrangement of Probability distribution function downsizing, 262–264 expense and vacancy rates, 58, 63 intra-family alternatives generation, 112 income viewpoint, 268–269 random variables, 123 larger house viewpoint, 269–271 speciﬁcation for continuos variables, overview, 267–268 112–113 Remainderman’s position, stable function production in risk 271–272 analysis, 123–126, 152 reverse amoritization mortgage, Probability mass function 265–266 dice rolling, 141, 143–144 Reverse mortgage, see Home Equity modiﬁcation in real estate, 145–147 Conversion Mortgage Proﬁt, equation in location theory, 3 Risk Property manager, see Agency problem certainty equivalent approach, 107–110 coin ﬂipping game and St. Petersburg Regulation, land use Paradox, 101–104 aesthetic regulation case study, 32–36 continuous normal case analysis, community objections, 21–22 112–116 externalities, 20–23 continuous stable case analysis, modeling 121–123 environmental protection versus data issues in analysis, 150–152 advertising, 26 determinism in analysis graphic illustration, 28–32 house prices, 131–134 implications, 32 overview, 128–130 notation, 25 real estate investment, 135–138 optimization and comparative dice experiment, 141–145 statics, 27–28, 37–38 multiple outcomes analysis, 111 rational models, 22 non-normality in real estate variables, 24–25 investment, 117, 119–121 Problem of Social Cost, 20 objective, 100–101 utility concept, 23–24
- 282 282 Index Risk (continued) data for exchange of tax basis, 169 payoff expectations, 148–150 data input, 167–168, 170–171 probability mass function modiﬁcation outcomes, 171–173 in real estate, 145–147 overview, 161 stable distributions, 123–126 threshold performance measures, subjective, 100–101 170–171 uncertainty relationship, 138–141 variable deﬁnitions, 168–169 utility function, 104–107, 116 policy ramiﬁcations, 173, 186–187 Weibull distributions, 126–127 United States tax code, 159, 187 Rules of thumb, see Threshold value, 173–175 performance measures Threshold performance measures basic income property model, Software, role in real estate analysis, corporations versus real estate 73–74 investment, 40–41 St. Petersburg Paradox, coin ﬂipping capitalization rate, 41, 49–53 game example, 101–104 cash-on-cash return, 41, 67 Stable Paretian distribution debt coverage ratio, 42 expense and vacancy rate data, 62–63 expense ratio, 41, 54–56, 64–66 origins, 121 gross rent multiplier, 41, 43–47 investor reliance in hot markets, Tax deferral 215–216 modeling investor rules, 41 buy-and-hold, 182–185 lender rules, 41–42 purchase–hold–sell base case limitations, 42 growth projection modiﬁcation, linear transformations of data, 62, 64 161, 163, 165–167 loan-to-value ratio, 41 overview, 161–163 normality of data, 60–62 tax deferred exchange strategy, price per unit, 41, 67–69 161, 167–173 statistical considerations, 71–72 sale-and-better repurchase strategy, tax deferred exchange example, 161, 178–182 170–171 sale-and-repurchase strategy, 161, Tiers, investment real estate market, 176–178 94–95, 98 variables, 160 Transportation, costs in location theory, private lender advantages, 242–244, 3, 5 248 real estate advantages, 158–160 Uncertainty, see Risk value, 173–175 Utility Tax deferred exchange land use regulation modeling, 23–27 add labor strategy, 158 production function, 23 buy-and-hold example, 182–185 risk and utility function, 104–107 data issues, 185–186 deﬁnition, 158 Weibull distributions, risk analysis, example 126–127 carryover basis for second property, Zero coupon bond, overview, 261 169–170

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