Xem mẫu
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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.
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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
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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 à 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 à 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.
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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 à 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
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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
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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!.’’
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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
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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
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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.
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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
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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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