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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.
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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
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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.
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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
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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.
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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!.’’
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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.
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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
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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
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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
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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
2.5 5 7.5 10 12.5 15 17.5 20
Life Ex
p
ectanc
y
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Return
4% Growth
6% Growth
FIGURE 11-4 Remainderman returns with different growth rates.
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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.
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Index
Advertising, see Commercial advertising
Agency problemd
collected rent calculation, 197–198
correction of model, 204–207
data issues, 201–202, 205–207
net profit
building size influences, 193–194
function, 190–191
property manager profit, 192–193
no vacancy rate approach in modeling,
195–197
property owner’s dilemma, 195
quality of property management, 190
reconciliation of property owner and

property manager problems,
198–201
transaction cost modeling, 191
vacancy factor, 197–198
Appraisal
capitalization rate approach, 210–212
mortgage equity approach, 210–212
Bargaining, discounted cash flow
analysis, 87–90
Before-tax cash flow, discounted cash
flow analysis, 75, 85, 87
Bid rent curve
bid rent surface for entire city, 7–8
calculation
several competing users in different
industries, 5–6
two competing users in same
industry, 3–5
linearity, 7–8
BTCF, see Before-tax cash flow
Bubble market
lenders as governors, 217, 221–222
number of unit effects in Tier II
properties, 214–215
positive leverage modeling, 219
private lender strategies, 239–240
Tier I versus Tier III properties,
213–214
Capital gains
discounted cash flow analysis, 76, 85

tax deferral, see Tax deferral; Tax
deferral exchange
Capitalization rate
appraisal approach by lenders,
210–212
assumptions in use, 49–50
components, 136
definition, 41
discounted cash flow analysis, 50–51
monotonic growth modeling, 52–53
relationship with interest rate and
inflation, 216
value relationship, 54–55, 137
Cash-on-cash return
applications, 67
comparative analysis, 67–69
conflict between debt coverage ratio
and borrower’s cash-on-cash
return
data issues, 231–235
excess debt coverage ratio, 223–224,
226–227
overview, 222–223
three-dimensional illustrations,
227–231
two-dimensional illustrations,
224–227
definition, 41
277
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Cash-on-cash return (continued)
leverage modeling
amoritizing debt, 220–221
growth assumption, 222
simple, 218
regression analysis, 69–71
C/C, see Cash-on-cash return
CDF, see Cumulative distribution
function
Certainty equivalent, risk analysis,
107–110
Coin toss experiment
marriage comparison, 128, 138, 153
St. Petersburg Paradox, 101–104
Collected rent, calculation in agency
problem, 197–198
Commercial advertising
community disutility, 31–32
land use regulation modeling
graphic illustration, 28–32
implications, 32
optimization and comparative
statics, 27–28, 37–38
overview, 24–27
Comparative statics, land use regulation
optimization, 27–28, 37–38
CR, see Capitalization rate
Creative financing, see Home Equity

Conversion Mortgage; Life
Estate; Retirement
Cumulative distribution function
expense and vacancy rates, 59
random variable derivative, see
Probability distribution
function
DCF, see Discounted cash flow
DCR, see Debt coverage ratio
Debt coverage ratio
conflict between debt coverage ratio
and borrower’s cash-on-cash
return
data issues, 231–235
excess debt coverage ratio, 223–224,
226–227
overview, 222–223
three-dimensional illustrations,
227–231
two-dimensional illustrations,
224–227
definition, 42
Debt service, discounted cash flow
analysis, 75, 86
Determinism, risk analysis
house prices, 131–134
overview, 128–130
real estate investment, 135–138
Discounted cash flow
after-tax cash flow, 75, 85–87

analysis using capitalization rate,
50–51
bargaining effects, 87–90
data issues in analysis, 93–98
deterministic inputs affecting gross
rent multiplier, 82–83
due diligence in hot markets, 215–216
modified logistic growth function,
90–93
monotonic growth modeling, 52–53
multi-year analysis, 78–79
net present value determination, 81
sale variables relationships, 79–80
single year analysis, 76–78
variables in analysis
equity reversion variables, 76
financing variables, 75–76
income tax variables, 76
operating variables, 75
performance variables, 75
Due diligence level
number of unit effects in Tier II
properties, 214–215
Tier I versus Tier III properties,
213–214
Economic topography maps, 12–13
Environmental protection, land use
regulation modeling, 24–27
Equity reversion, discounted cash flow
analysis, 76, 84–85

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EVR, see Expense and vacancy rate
Excess debt coverage ratio, see Debt
coverage ratio
Expense and vacancy rate
calculation, 55
cumulative distribution function, 59
data analysis, 55–60
gross rent multiplier relationship, 55
linear transformations of data, 62, 64
normal and Stable distributions of data,
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
discounted cash flow analysis,
82–83
equilibrium of ratio of value to gross
income, 45–46
field work supplementation, 44
market equilibrium, 43
property size limitations in 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
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 lenders
Interest rate
components, 136
relationship with capitalization rate
and inflation, 216
Internal rate of return, IRR

buy-and-hold example, 183–185
private lender loan evaluation, 252
purchase–hold–sell base case, 163
purchase–hold–sell base case with
growth projection modification,
165–167
tax deferred exchange example,
172, 174
Irrational exuberance, see Bubble market
Jarque Bera test, normality testing, 61
Land use regulation, see Regulation,
land use
Lenders
appraisal, see Appraisal
bubble market control, 217, 221–222
conflict between debt coverage ratio
and borrower’s cash-on-cash
return
data issues, 231–235
excess debt coverage ratio, 223–224,
226–227
overview, 222–223
three-dimensional illustrations,
227–231
two-dimensional illustrations,
224–227
private, see Private lenders
qualification of desired borrowers, 213
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Lenders (continued)
rules, 209–210
threshold performance measures,
41–42
Leverage
modeling
appreciation, 219
assumptions, 218
bubble market, 219
cash-on-cash return
amoritizing debt, 220–221
growth assumption, 222
simple, 218
debt service, 219
positive leverage versions, 217–218
Life Estate
principles, 260–261
Remainderman, 263, 271–272, 274
Loan-to-value ratio, definition, 41
Location theory
assumptions, 2, 13–14, 16
data sources, 16
economic topography maps, 12–13
empirical verification, 8–9, 11
examples
several competing users in different
industries, 5–6
two competing users in same

industry, 3–5
notation, 2–3
profit equation, 3
rent decay rate versus distance, 11
transportation costs, 3, 5
LTV, see Loan-to-value ratio
Market rent, definition, 44
Maximum likelihood estimation, MLE,
data fitting in risk analysis,
150–152
Modified logistic growth function,
discounted cash flow analysis,
90–93
Municipal services, land use regulation
modeling, 24–27
Net operating income
discounted cash flow analysis, 75, 86
equations, 55
no vacancy rate approach in agency
problem modeling, 195–197
reconciliation of property owner
and property manager
problems, 199
sale-and-repurchase strategy, 176
Net present value
buy-and-hold example, 183–185
calculation, 81
data issues, 185–186
private lender loan evaluation, 249
purchase–hold–sell base case with

growth projection modification,
165–167
tax deferred exchange example, 172
Net profit
agency problem function, 190–191
building size influences, 193–194
property manager profit, 192–193
reconciliation of property owner and
property manager problems,
199–203
NOI, see Net operating income
NPV, see Net present value
Payment factor, discounted cash flow
analysis, 86
PDF, see Probability distribution function
PMF, see Probability mass function
PPU, see Price per unit
Present value, equation, 51
Price per unit, definition, 41
Private lenders
bubble market strategies, 239–240
buyer evaluation of financing
internal rate of return test, 252
net present value test, 249
tax blind test, 252–253
competent counseling importance,
256–257
diversification problem, 238–239
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foreclosure rights, 241–242
future value function for property,
240–241
hard money loan versus purchase
money loan, 238
installment sale transaction, 248
lending versus owning as interest rates
rise, 240–242
motivations
buyer, 244–245
seller, 237, 245–248
prepayment penalties, 253–255
rules, 238–239
tax deferral advantages, 242–244, 248
Probability distribution function
expense and vacancy rates, 58, 63
generation, 112
random variables, 123
specification for continuos variables,
112–113
stable function production in risk
analysis, 123–126, 152
Probability mass function
dice rolling, 141, 143–144
modification in real estate, 145–147
Profit, equation in location theory, 3
Property manager, see Agency problem
Regulation, land use

aesthetic regulation case study, 32–36
community objections, 21–22
externalities, 20–23
modeling
environmental protection versus
advertising, 26
graphic illustration, 28–32
implications, 32
notation, 25
optimization and comparative
statics, 27–28, 37–38
rational models, 22
variables, 24–25
Problem of Social Cost, 20
utility concept, 23–24
Remainderman
Life Estate, 263, 274
position 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 position,
271–272
reverse amoritization mortgage,
265–266
Reverse mortgage, see Home Equity
Conversion Mortgage
Risk
certainty equivalent approach,
107–110
coin flipping game and St. Petersburg
Paradox, 101–104
continuous normal case analysis,
112–116
continuous stable case analysis,
121–123
data issues in analysis, 150–152
determinism in analysis
house prices, 131–134
overview, 128–130
real estate investment, 135–138
dice experiment, 141–145
multiple outcomes analysis, 111
non-normality in real estate
investment, 117, 119–121
objective, 100–101
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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 analysis,
73–74
St. Petersburg Paradox, coin flipping
game example, 101–104
Stable Paretian distribution
expense and vacancy rate data, 62–63
origins, 121
Tax deferral
modeling
buy-and-hold, 182–185
purchase–hold–sell base case
growth projection modification,
161, 163, 165–167
overview, 161–163
tax deferred exchange strategy,
161, 167–173

sale-and-better repurchase strategy,
161, 178–182
sale-and-repurchase strategy, 161,
176–178
variables, 160
private lender advantages, 242–244,
248
real estate advantages, 158–160
value, 173–175
Tax deferred exchange
add labor strategy, 158
buy-and-hold example, 182–185
data issues, 185–186
definition, 158
example
carryover basis for second property,
169–170
data for exchange of tax basis, 169
data input, 167–168, 170–171
outcomes, 171–173
overview, 161
threshold performance measures,
170–171
variable definitions, 168–169
policy 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
limitations, 42
linear transformations of data, 62, 64
loan-to-value ratio, 41
normality of data, 60–62
price per unit, 41, 67–69
statistical considerations, 71–72
tax deferred exchange example,
170–171
Tiers, investment real estate market,
94–95, 98
Transportation, costs in location theory,
3, 5
Uncertainty, see Risk
Utility
land use regulation modeling, 23–27
production function, 23
risk and utility function, 104–107
Weibull distributions, risk analysis,
126–127
Zero coupon bond, overview, 261

282 Index