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11 THE USE AND ABUSE OF RENTAL PROJECT 

MODELS 

Leonard E. Bunnan, Thomas S. Neubig, and D. Gordon Wilson 

I. INTRODUCTION 

During consideration of the Tax Refonn Act of 1986 (TRA86), housing 

analysts relied heavily on rental project models to support their arguments 

for more or less generous tax treatment of residential and commercial rental 

property. These models derive the rent level that would provide an investor 

with an assumed required rate of rerum given a set of assumptions about an 

investment's economic and tax characteristics. Despite the sophistication of 

these models. or perhaps because of it, analysts predicted widely varying 

effects of tax refonn proposals.1 How could analysts using similar models in 

evaluating a tax refonn bill whose characteristics were easy to represent 

parametrically produce such variant analyses? 

The purpose of this paper is threefold. First, we describe what rental 

project models are and discuss a particularly useful model that has been 

developed at the Office of Tax Analysis (OTA). Second. we show how these 

models can be used to gain valuable insights about how tax and non-tax factors 

affect individual investors. and about the implications for efficiency and 

equity of various tax policies. Finally . . we answer the question posed above. 

We show that the wide range of results is due to inherent and fatal flaws in 

rental project models as tools for forecasting market-wide responses to tax 

policies. 

Many otlrer economists lravv contribwed to devl'lopme/11 of rental projt•ct modds at OTA. Tlll!y 

are. in roughly clrronoloxical ordrr. Frank Dt•Lt•ettlv. Larry Ot.anm•. Harw.v Go/per. Eric Todcr. 

Larry DildiM . Steve Sllrlfrin. Jim Ntums. Joe Cordes. and Hudson Milner. Wt• art• grateful to 

Joe Cordes. Don Fulll!rtOII. Tim Goodspc•td. Hudso11 Mtlnc•r. Jim Ntnm!i . Jol!l Slmll'od. Marty 

Sulfi,·an. Eric Toder. and Jl!nny WaiJI for lrdpful conmu•llfl 011 t•arlirr droft!i a11d Vicky Conll'ay 

for assistana in tire preparation of tire manuscript and tabh•s. 

307 
308 Len Burman/Tom Neubig/Gordon Wilson 

II. WHAT IS A PROJECT MODEL? 

A. DEFINITION 

A project model simulates the cost and income streams that would be 

generated by a long-lived investment under a set of assumptions about taxes. 

the economic environment. and the characteristics of the investor. Early 

simple models were designed to help investors decide whether a particular 

investment was worthwhile. More sophisticated varianrs of this kind of 

analysis, such as the OT A model. can determine endogenously how long investors 

should hold properties, break-even rents. and sales price streams. Analysts 

at OTA have used project models to study the effect of tax changes on 

investments in real estate. timber. oil drilling. mining. and other assets. 

B. KINDS OF RENTAL PROJECT MODELS 

This section describes three kinds of rental project models that are used 

by investors and housing analysts: the spreadsheet model. the "initial 

investor" model, and a dynamic programming model. While the first two kinds 

of models are the most widely used. they are not well suited to representing 

the effects of anticipated future tax laws on the resale value of a property 

and may thus be misleading. Section Ill will describe the more sophisticated 

dynamic model that has been developed by OTA. 

l . Spreadsheet Models 

Table II . 1 illustrates a simple spreadsheet model for a hypothetical real 

estate investment. The spreadsheet provides a convenient way to evaluate a 

project under various assumptions about taxes and economic conditions. The 

left column lists the assumed parameters that underlie the analysis. It 

should be noted that. although this list of assumptions is extensive. more 

complicated models depend on even longer lists of assumptions. The advantage 

of this kind of model is that it is simple (models like this could be developed in any spreadsheet program on almost any microcomputer). easy to develop. 

and easy to use. 

The simple example in Table J I . I represents a low-income housing unit under 

conditions that might have prevailed in 1985 (pre-TRA86). The investor/ 

developer is assumed to hold the project for 15 years. which is the length of 

the ACRS low-income housing depreciation schedule.

2 

The nominal value of the 

land allocated to the property is assumed to increase at a constant rate <3 % 

per year) over the I 5 years. The nominal structure value is constant because 

inflation in structure values is assumed to just offset economic depreciation . 

The initial rent is assumed to be I 0 % of value ($4. I 00) and initial operating 

costs are assumed to be 2.5 % of the structure value. Both grow at a constant 

annual rate of 3 %. 

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.. • .. .. • • • • • .. .. .. .. .. .. 

Table 11.1 Sample Spread Sheet Calculator for ACRS Low-Income Housing 

lnve;unent A~>um~tions 

Purchase 

Land 

Structure 

Total Prit:e 

Rehahilitation 

Pcn:entage 

Dollar Cost 

New Bash 

T<llal Cost 

Mo•tgagl' 

lntl!re:.t Rate 

Tcnn (~earl>) 

'.t Borrowetl 

Ltmn Amount 

Ptt~IIICIII 

T1 :uhiiCII<lll C:ost~ 

Pct cn ~c 

D<'llao Co>t 

lnnwl ln t: ~lment 

Pu1 ;uncters 

D<·po \'dation Rate 

Operating CosllValue 

Initial Rent 

Rent lntla tion 

lanll lnllation 

Stt U\.turc lntlation 

Di ount Rule 

Doscount Factor 

Ta., Rate 

Capital Gains Rate 

ss.ooo 

530.000 

$35.000 

20 0% 

Sli.OOO 

S36.000 

$41 ,000 

II 0~ 

30 

90.0\11: 

536.900 

$4.244 

J .0\11: 

$1 .050 

S5, 150 

3.0% 

2.5% 

$4,100 

3 0% 

3.0% 

3.0% 

II 0~ 

92.6% 

50 0~ 

20.0% 

Generatal Stream of Income and Dedut:tions for Rental Pro~rt:r: 

Year 

I 

2 

3 

4 

5 

6 

7 

II 

9 

10 

II 

12 

13 

14 

IS 

16 

py, 

Operating Mortgage T;u 

Rent Costs Princ•eaJ lntere>"t Deerec. 

S4.100 $900 $36,900 $4.059 $5.100 

S4.223 $921 $36.715 $4.039 $4 ,1100 

S4.350 $955 $36.509 54 .016 $4 ,200 

$4,4110 59113 $36.280 $3.991 53.900 

S4.615 Sl .OIJ SJ6.027 $3,963 $3,600 

$4,753 $1.043 $35 .745 $3.932 $2,100 

$4 ,1196 $1,075 $35.433 53.1!911 Sl .l!OO 

$5,0-U $1.107 $35.0116 SJ.1159 SI.SOO 

SS. I94 $1 ,140 $34,701 $3,1117 SI.SOO 

SS.350 $1 ,174 $34.274 $3,770 SI.SOO 

SS .SIO $1 ,210 $33.1100 SJ.71K $1 ,200 

SS.67S $1.246 $33.273 $3.660 $1 .200 

SS.II46 $1.2113 $32.6119 $3.596 $1.200 

$6,021 $1,322 $32.040 $3.5:!4 $1.200 

S6.:!02 $1.361 $31.3~0 53 .445 $1.200 

$30.5:!1 

$41 ,727 $9.160 SJ3. 1 KK $24 .337 

Comoutation of Gam or Loss on Sale (Undiscountal) 

+- Sule Puce 

· Mortgage Pnncipal 

- Transaction Costs 

· Capital Guins Ta:o. 

= Net Return 

Present Value of Returns to Investment 

Initial Cost 

Income Stream 

Gatn on Sale 

Net Return 

Gross Return 

Coupon Equivalent 

·SS.ISO 

$8,716 

$2 .208 

$5,774 

$10.924 

$1 .0117 

$43.790 

·S30.S21 

-$1 ,31 4 

-S4.9S.l 

$7.003 

112.1 5I: 

212. 1% 

1.1~ 

Tax~tble Pre-Tax TIU 

Income Cash Aow Benefit 

-$5.959 -SI ,044 $2.9110 

-$5,543 -$941! $2,771 

·S·U121 -51150 $2.411 -$4.394 -$7411 $2.197 

·53.961 -Sii43 $1,9111 

-$1,311 -$535 $1 ,161 

-51 .877 -$423 S93R 

$1.424 ·S309 $712 

-$1.:!63 ·S191 $632 ·SI ,09S ·S69 $547 -$617 SS6 $309 -$430 SillS $215 

·S233 S31K $117 

-$25 $455 SIJ 

$195 $5% -S9R 

·S24.95H -$3 .763 $1~ 479 

.. • • -

Alter-Tal 

lncomt: 

Sl .935 

$1 .1123 

Sl.561 

$1.449 

SI .JJIC 

S6!6 

$515 

$403 

$441 

$4711 ;i $365 

S400 n 

$435 c 

$467 V> 

$4911 n 

SK.716 § 

0.. 

)> 

CT 

c 

V> 

n 

0 

....... 

::::0 

n 

:::3 

0) 

., 

.., 

0 

(ij 

(') 

-::: 

0 

0. 

!!. 

., 

w 

0 

\0 
310 Len Burman/Tom Neubig/Gordon Wilson 

Future values are risky. Rents and operating costs are affected by vacancy 

rates, how well the tenants care for the units, and actual inflation rates. 

The project model impHcitly assumes that the income and cost streams represent expected values and that risk may be accounted for in the discount rate 

(or rates

3

) at which the investor discounts future income. 

The simple model produces many of the outputs of other more complicated 

models. It summarizes the investor's cash flows through the assumed life of 

the project. It computes the present value of benefits. with detail about the 

value of tax incentives. This spreadsheet reports a variant on the internal 

rate of return-the "equivalent coupon rate"4 -which represents for a tax-exempt 

bond with the same face value. risk. and term as the project, the rate of 

interest that would generate the same present value. For this hypothetical 

project. the coupon equivalent is 13. 8%. 

The model is sensitive to a large number of assumed parameters. Results 

depend critically on the discount rate and the marginal tax rate of the 

investor. For example, accelerated depreciation and other tax deductions are 

most valuable to investors in high tax brackets. In tax-shelter investments. 

higher leverage (i.e., higher loan-to-value ratio) generates larger interest 

deductions. which increase the amount of income that can be sheltered from 

tax. Thus, the initial loan-to-value ratio as well as assumptions about 

refinancing are important. FinaJiy. with highly levera~ investments, the 

interest rate is more important than any other parameter. 

2. Initial Investor Models 

A drawback of the simple model as a policy tool is that it cannot determine 

the effect of tax policies on how long to hold the rental project. 6 Good tax. 

policy attempts to minimize tax-motivated distortions in taxpayers· decisions 

to buy or sell assets. But the simple spreadsheet provides no direct 

information about how investors· selling or holding decisions might respond to 

tax changes. In a seminal work. DeLeeuw and Ozanne ( 1979) developed a more 

complex model that included endogenous determination of the holding period. 

We call this kind of model the "initial investor" model because it simulates 

the economic decisions of the first investor to hold a rental project.

7 

An initial investor model is a straightforward extension of the simple 

model. Given an exogenous stream of sales prices for each year during the 

life of the project. the model solves for the holding period that maximizes 

the present value of after-tax cash flows. Initial investor models are 

especially useful for studying how capital gains taxes. depreciation recapture 

provisions. marginal tax rates. and innation affect chuming11 of real estate. 

3. Dynamic Models 

A shortcoming of initial investor models is that they cannot capture the 

effect of tax changes on future owners. To accomplish this. OTA has developed 

a dynamic programming model in which sales prices and holding periods are 

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The Use and Abuse of Rental Project Models 311 

determined endogenously and simultaneously.

9 An advantage of this kind of 

model is that it shows how future tax benefits can be capitalized into 

property values. 

III. THE OTA RENTAL HOUSING PROJECT MODEL 

The OT A rental housing project model is an extension of the types of models 

described above. The OTA model can run as either a dynamic model or as an 

initial-investor model (which allows easy comparison of the alternative 

methodologies). The model includes as options all of the major features of 

tax laws and proposals pertaining to rental housing made since the J 981 Tax 

Act. It allows for accounting peculiarities that help distinguish various tax 

laws. such as half-year accounting and variable len~th construction periods. 

The appendix describes the mechanics of the model. 0 

A. MEASURES OF RETURN ON INVESTMENT 

The model can compute one of three different summary measures of return on 

investments. By default. the calculator finds the user cost of rental housing 

capital, defined to be the initial period's rent as a proportion of value that 

sets the initial investor's net present value equal to zero. This measure is 

sometimes referred to as "required rent" .

11 The OTA model can also determine 

the internal rate of return on the first investor's equity. holding rates of 

return for subsequent investors constant. In another mode. the calculator can 

find the real after-tax rate of return that would drive the net present value 

for all investors (including the mortgagor) to zero given an exogenous rent 

level. This measure represents the equilibrium market rate of return given 

the assumed parameters. Finally. the calculator can simply compute the 

present value of the project to the initial investor given exogenous rents for 

the exogenous holding period. 

I. User Cost 

The user cost measure provides a concise summary of the effects of various 

tax and non-tax parameters in a single number. The model can thus be used to 

estimate. for a given tax law. how user costs are distorted among investors 

with different marginal tax rates and how tax shelter provisions affect user 

cost~. A sequence of model runs can detennine how much each of a set of tax 

provisions affects the cost of rental housing (for a given investor). and how 

those provisions interact. The model also shows how transaction costs and 

other non-tax factors affect user costs. 

2. Internal Rate of Return 

The internal rate of return ORR) ts another useful measure of capital 
312 Len Bunnan/Tom Neubig/Gordon Wilson 

costs for rental housing. Given a fixed rent stream. the IRR indicates how 

real after-tax rates of return for investments of comparable risk would have 

to change to make the particular investment attractive (or unattractive). 

This measure provides interesting insights into how rates of return vary 

across tax brackets. For example. it appears from the model that tax shelter 

investors may demand higher rates of return than small-scale landlords. 12 

This suggests that the tax shelter investors have higher opportunity costs of 

capital, perceive more risk in their investments. or have higher operating 

costs than the smaller investors. or. perhaps. some combination of the three . 

The IRR is used in the model to compute effective tax rates, as discussed 

below. 

3. Net Present Value 

The net present value (NPV) indicates how tax Jaw provisions might be 

capitalized into the value of the rental property, holding the rent stream and 

after-tax rates of return constant. This measure is more powerful than might 

appear at first glance because the model computes sales prices and holding 

period endogenously. Thus. net present value comparisons not only show the 

present value of direct tax benefits or costs incurred by the initial investor. but include how taxes are capitalized into the resale value of the 

property as well as how taxes affect the timing of sale. The initial investor 

model would ignore this latter component. 

The three measures may be used to infer ·the limits of tax incidence for a 

particular kind of housing held by a particular kind of investor. The user 

cost, IRR, and NPV. indicate the effect on renters. capital. or land holders 

in the case where each of them. respectively. is assumed to bear the entjre 

burden of a tax. Jf all other prices are constant and there is free entry and 

exit from the market. then rents for a new building held by the hypothetical 

type of investor would be driven to the level of the user cost in equilibrium 

(if the type of investor were participating in the market). Alternatively. if 

rents. land prices, and the amount of equity capital are fixed. th~n real 

after-tax returns on equity would equal the IRR. Finally. if the quantity of 

land is fixed and all other prices remain constant. then changes in the 

computed NPV represent chariges in land prices (subject to a nonnegativity 

constraint). 

B. EFFECfiVE TAX RATES 

J. Measuring Effective Tax Rates 

A logical extension of the rental project model is computation of effective 

tax rates on rental housing investment. The calculator prints three measures 

of effective tax rate defined by Bradford and Fullerton ( J 981) based on 

internal rates of return. The three measures are the effective gross rate 

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The Use and Abuse of Rental Project Models 313 

(t9 ) . the effective net rate (t0 ) . and the tax wedge (t.,). The gross rate is 

essentially taxes as a percentage of gross (before-tax) income, the net rate 

is taxes as a percentage of net (after-tax) income, and the wedge is taxes as 

a percentage of asset value. They are defined as follows: 

t li 

9 

t • n 

t !E w 

r - r b a 

r - r b a 

r 

a 

r - r b a 

(11.1) 

. and (11.2) 

(11.3) 

where rb and r are the before- and after-tax rates of return, respec- 13 a • 

tively. The property-tax rate is treated as a user charge (a la Tiebout), 

rather than as a tax. for purposes of computing rb . 

The effective gross rate. t . is the closest analogue to what is typically 9 

thought of as a tax rate. However. as Bradford and Fullerton point out, this 

measure yields peculiar results when the before-tax rate is close to zero or 

negative. When rb is zero. t

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is undefined. and when rb is negative. t

9 

has 

the wrong sign and can be very large. So what is. in fact. a large tax 

subsidy (which is why rb can be negative) is reponed as a large positive 

effective tax rate. 

Since the after-tax rate is usually positive. the effective net tax rate. 

t

0 • may be more appropriate. but care should be taken in its interpretation. 

Tax rates as a percentage of net income are always larger than gross rates 

whenever net rates of return are positive. For example, a 50% statutory rate 

of tax on gross income corresponds to a I 00% tax rate relative to net income 

because tax equals after-tax net income. 

The tax wedge, tw . may be the most robust estimator. in the sense that it 

is never undefined or HI-defined. But. again. care must be taken in 

comparing this measure to statutory tax rates. 

2. Implementation in the OTA Model 

It is both an advantage and a disadvantage of the approach taken here that 

the internal rate of return is used as a measure of returns to capital 

investment. The advantage is that the measure is independent of the assumed 

discount rate of the investors. The disadvantage is the general problem that 

internal rates of return do not always give consistent rankings of streams of 

income and expense when the internal rate varies greatly from the actual 

discount rate.

14 A related problem is that the IRR may be inconsistent with 

the user cost. sales prices. and holding periods that are derived assuming 

particular discount rates. Furthermore, some streams of income may have no 

internal rate of return . or the IRR may not be unique. A possible alternative 
314 Len Bunnan/Tom Neubig/Gordon Wilson 

approach would be to compute effective tax rates using before- and after-tax 

present values. 

The effective tax rates are computed for the equity portion of the investment as well as for all capital invested in the project. The effective rate 

on the whole investment is useful for analyzing the tax burden on rental 

housing capital and for comparison with tax rates on other forms of capital. 

This type of measure would typically be used in analysis of the efficiency 

aspects of a tax policy change. 

The effective tax rate on equity shows the effect of taxes on the equity 

part of an investment holding taxes on debt constant. This measure might be 

relevant if equity in rental housing is considered to be a different kind of 

financial instrument than debt, perhaps because of risk. Of course. in 

equilibrium. taxes on debt should be reflected in the cost of borrowing and 

thus affect the rate of return on equity. 

Effective tax rates are computed separately for each oWher and cumulatively 

for the project through each successive holding period. The separate 

computations by owner are helpful in comparing the tax treatment of new and 

used buildings. The cumulative effective tax rate provides a summary measure 

of the level of tax or subsidy for the project over its entire economic life. 

Finally, we should note that computation of effective tax rates as 

described above addresses the concerns of Summers ( 1987) in his recent 

working paper. He criticized Treasury's published effective tax rates on 

structures as being too high because they do not account for the capitalization of future tax benefits or the higher leverage that is possible with 

structures. But the OTA Rental Housing Project Model correctly accounts 

for both of these features. 

3. Effective Tax Rates for a Pre-TRA86 Investment 

Table I 1.2 illustrates the different effective tax rates computed by the 

OTA model for a rental housing investment made in 1985. The first section of 

the table displays internal rates of return for each of three owners of an 

ACRS rental housing investment assuming that rents are set so that all equity 

investors earn a 4% real after-tax rate of return. This requires that aftertax returns be positive and well defined. but the large tax incentives in 

pre-TRA86 law allowed a project with negative before-tax returns on equity to 

be profitable after taxes. The result is that for all but the last investor. 

the effective gross tax rate is not meaningful (indicated by NA. not applicable). The effective net tax rate and the tax wedge. however. provide 

consistent comparisons of the value of tax subsidies in each case. 

The table shows that in the case of a depreciating building with moderate 

inflation (the assumed project turns to dust after 50 years). the value of tax 

subsidies declines with each owner. The value of depreciation deductions 

falls as a percentage of each investor's purchase price as the value of land 

increases relative to structure value. The effective net rates in the table 

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The Use and Abuse of Rental Project Models 315 

Table 11.2 Three Measures of Effective Tax Rates for a 

Rental Housing Investment in 198sRates of Return Effective Tax. Rates 

Pre-Tax After-Tax. Gross Rate Net Rate Tax. Wedge 

For Each Owner 

Equity Only 

Owner l -.0073 .0400 NAb -1.183 -.047 

Owner 2 -.0007 .0400 NA -1.018 -.041 

Owner 3 .0115 .0400 -2.482 - .713 -.029 

Asset (Debt & Equity) 

Owner I .0422 .0400 .052 .055 .002 

Owner 2 .0460 .0400 . 131 . 15) .006 

Owner 3 .0593 .0400 .325 .482 .019 

Investment to Date 

Equity Only 

Through Owner 1 -.0073 .0400 NA -1.183 -.047 

Through Owner 2 -.0049 .0400 NA -1.124 -.045 

Through Owner 3 -.0041 .0400 NA -1.103 -.044 

Asset 

Through Owner I .0422 .0400 .052 .055 .002 

Through Owner 2 .0430 .0400 .069 .074 .003 

Through Owner 3 .0434 .0400 .079 .086 .003 

•Non-low-income ACRS housing investment. Rent set so all investors earn zero net present 

value. Default parameter values (see appendix): e.g .. discount rate- 4%, 80% Joan-to-value 

ratio, tax rate - 40% . inflation - 5%. interest rate • 12% . User cost is 9.23% : three owners' 

holding periods are 19. 19 and 12 years. respectively. bNA = not applicable. 

show that tax subsidies amount to ·118.3% of the first investor's net return, 

but only 71.3% of the last owner's. Looked at another way, the tax wedge 

shows that tax subsidies augmented the rate of return on investment by 4 . 7% 

for the first investor. but only 2.9% for the third. 

When considering the overall subsidy or tax on rental housing it is 

appropriate to include debt. The example that generated Table I I .2 was 80% 

debt-financed for each investor. Including debt. all three measures of 

effective tax rate are positive. The effective gross tax rates range from 

5.2% to 32.5%. 

The second section of Table 11.2 presents cumulative effective tax rates. 

The rates "through owner 3." represent the overall effective tax rates on the 

project through its entire life. The line in the equity-only portion shows 

that tax preferences account for more than I 00% of the return on equity. even 
316 Len Bunnan/Tom Neubig/Gordon Wilson 

accounting for the smaller subsidy on the last investor. The asset row. 

however. suggests that the investment as a whole is subject to a small 

positive effective tax rate on gross income (7. 9%). 

IV. APPLICATIONS OF RENTAL PROJECT MODEL ANALYSIS 

Like many of the tools in an economist's kit, rental project models are 

most useful for their qualitative results. Since the model represents a 

possible decision making strategy (based on maximizing expected present value) 

for a single investor considering a particular project in a hypothetical 

economic and tax environment. the model's quantitative results do not apply to 

the economy as a whole. However. it is very useful for tax policy purposes to 

be able to study how an existing or proposed policy would affect individuals· 

behavior in isolation from the myriad other factors that tend to confound 

analysis. Thus the model allows for a kind of controlled experiment. 

The model results can be generalized to market-wide phenomena in some 

cases. Certain qualitative results. such as higher user costs or longer 

holding periods, might prove to be robust when parameter values are varied 

between the extremes of their feasible ranges. However. even in these cases. 

conclusions about the market levels of economic variables (notably rents) 

cannot be made solely on the basis of rental project model results. Section V 

expands on the limitations of project model analysis. 

Nonetheless. a rental project model is very useful for evaluating tax 

policies on a micro level. This section illustrates some applications of the 

OTA Rental Project Model . 

A. TAXES AND CHURNING 

It would be inefficient and undesirable if the tax system were to encourage 

investors and landlords to sell rental real estate before they would have in 

the absence of taxes. A primary economic benefit of having a large and 

heterogeneous rental market is that it economizes on the very large costs that 

characterize real estate transactions. Landlords typically hold real estate 

much longer than the average tenant"s occupancy. so individuals who expect a 

short tenure in a home find it less expensive to rent than to own. 

In the absence of taxes. and assuming perfect credit markets (so that 

investors could borrow against the accumulated value of their real estate). 

the model predicts that transaction costs would prevent rental property 

holders from ever selling. Since transaction costs represent real resource 

costs. this kind of "lock-in " effect is efficient. However. as Tables 11.3A 

and 11 .3B show. before the passage of TRA86. investors would tend to choose 

shorter holding periods as tax rates increase. This result is qualitatively 

robust with respect to changes In assumed parameter values. 

Churning was profitable under the Economic Recovery Tax Act of 1981 

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The Use and Abuse of Rental Project Models 317 

Table l 1.3A Effect of Marginal Tax Rates on Rental Housing Investment 

(Pre-TRA86 Parameters •) 

Investor's User Percentage Holding Number Net Effective Tax Rate Average 

Tax Rate Cost of No Tax Period of Equity Investment Debt-Equity 

(%) (%) User Cost {Years~ Owners (%) (%2 ~%2 

b No Taxes 8.79% 100.0% 50 0.0% 0.0% 39. 1% 

0% 10.44% 18.8% 50 0 .0% 39.8% 41.2% 

15% 10.22% 116.3% 50 I -9.5% 34.4% 41.3% 

28% 9.94% 113. 1% 19 2 -70.5% 23.7% 62.4% 

33% 9.68% 110. 19' .. 19 3 -88.5% 16.9% 62.71o 

50% 8.39% 95.4% 19 3 -173.9% -16.2 % 63.9% 

70% 5 .48% 62.3% 18 3 NCC -99.9% 70. 1% 

•see Table 11 .8 for values. Tax rates vary as indicated. 

bTax rate on debt is also zero. Interest rate on debt falls to 9% to yield 4% real rate. 

c NC ... not computable. There is not internal rate of return for which the investor's beforetax present value equals zero (i.e. pre-tax income is negative in every year). 

Table I 1.38 Effect of Marginal Tax Rates on Rental Housing Investment 

(TRA86 Parameters •) 

Investor's User Percentage Holding Number Net Effective Tax Rate Average 

Tax Rate Cost of No Tax Period of Equity Investment Debt-Equity 

(%) ) User Cost ~Years2 Owners 2 (%2 ~%2 

b No Taxes 8.79% 100.0% 50 0.0% 0 .0 % 39. 1% 

0 % 10.02% 113.9% 50 0 .0% 29.6 % 40.7% 

15% 10.02% 113.9% 50 0 .2% 29.7% 40.9% 

28% 10.02% 113.9% 50 0 .4% 29.8% 41 .0% 

33% 10.02% 113.9% 50 0 .5% 29.9% 41.1% 

50% 10.02% 113.9 % 50 1.0% 30. 1% 41.5% 

70% 10.02% 113.9% 50 2.2% 30.7 % 42.7% 

• See Table 11.8 for values. Tax rates vary as indicated. 

bTax rate on debt is also zero. Interest rate on debt falls to 9 % to yield 4% real rate. 

(ERTA) and the 1982 and 1984 Tax Acts because of the greatly accelerated 

depreciation for residential real estate. Rental real estate owners in high 

tax brackets could earn valuable tax deductions in the early years of a 

project's life. Thereafter. the project became much more valuable to a new 

purchaser than to the original owner because each new owner could claim new 

accelerated depreciation deductions. Moreover. with inflation there would be 

a "step up in basis" each time the property changed hands. Were it not for 

recapture penaltjes.1 5 

owners would have sold even sooner. 

Capital gains taxes tend to distort holding patterns in the opposite 

direction. Hendershott and Ling ( 1985) used a project model to explore the 
318 Len Bunnan/Tom Neubig/Gordon Wilson 

effect of inflation and taxes on churning of real estate held as a tax 

shelter. They reported that capital gains taxes tended to reduce the incentive to sell real estate offsetting somewhat the perverse incentives of 

accelerated depreciation. As inflation increased (holding real after-tax 

interest rates constant). Hendershott and Ling found that the lock-in effect 

intensified, even for high tax bracket investors. This is because the effective tax rate on real capital gains increases with inflation, so investors 

find deferral of gain more profitable. 

In light of these findings. we would expect TRA86 to reduce churning 

significantly for residential (not low-income 16

) real estate. The Act 

lengthened the depreciation schedule from 19-year 175% declining-balance to 

27 .5-year straight-line, reduced tax rates, and repealed the partial exclusion 

of capital gains income from tax. The first part of Table 11.4A shows that, 

under one set of reasonable assumptions. rate reduction or repeal of the 

capital gains exclusion would be expected to end churning. which is optimal in 

the context of the rental model. 

The conclusion that tax refonn would result in optimal churning is not 

robust with respect to changes in parameter values, however. Under a set of 

assumptions that might be more characteristic of a tax-shelter investor. 

churning is reduced, but not ended. by the provisions of tax refonn. Table 

I I .4B considers a top-bracket investor who is more highly leveraged and who 

discounts future income at a higher rate than the hypothetical investor in · 

Table 11.4A. Table ll.4B also assumes somewhat lower interest rates. Under 

this scenario, tax rate reduction alone would not be sufficient to affect 

churning among individuals in the top brackets. Lengthening the depreciation 

schedule actually shortens the holding period for the first investor to 

fifteen years. However. repealing the exclusion for capital gains would 

lengthen the optimal holding period for the first investor from 19 to 26 

years. The TRA86 provisions. taken as a whole. result in a holding period of 

25 years. 

These results suggest two conclusions. First. the Tax Refonn Act of 1986 

should substantially reduce churning for most types of rental real estate.

17 

Assuming that refinancing is costly. these results are robust with respect to 

other assumptions about the characteristics of the taxpayer and the economy. 

The second important conclusion is that some kinds of results are very 

sensitive to smaJI changes in parameter assumptions. The sensitivity of model 

results is discussed in V. B. 

B. COMPARATIVE EFFECT OF TAX REFORM PROVISIONS 

ON RENTAL USER COSTS 

Table ll.4A and Figure II. I show how the non-low-income residential rental 

housing tax provisions affect the user cost for a hypothetical investor. They 

show both the effects of each provision separately as well as the incremental 

effect of adding one more provision (in a particular order) to the last. 

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Table I 1.4A Effect of Tax Reform Provisions on User Costs Stacked 

Separately and Together Compared to 1985 Law 

(Assumptions I) 

Stacked First Against 1985 law Stacked Against Previous Provisions 

Change Holding % Change Holding 

User from No. of Period User in User No. of Period 

Cost Baseline Owners of First Cost Cost Owners of First 

1985 law • 9 .23% 0.0% 3 19 9 .23% -- 3 19 

27.5 year stra ight-line depreciation 10. 10% 9.4% 3 19 10 10~ 9.4% 3 19 

Ta>. rate reduction b 10.08% 9 .2% I 50 10.39% ~ I 50 

Non-exclusion of capital gains 9.62% 4.2% I 50 10.40% 0. 1% I 50 

LO\.\Cr interest ratesc: 8.74% ·5.3% 3 19 9 .99% -3.9% I 50 

Capitalize CPIT 9.26% 0.3% 3 19 d 10.02% 0 .3% I 50 

Passive loss limitation • 11.08% 20.0% 2 29 10.36% 3.4% I 50 

• Assumes marginal tax rate of 40% for equity investors, 25~ on debt. discount rate of 4%. mortgage interest rate of 

ll%. innation rate of 5%, 80% leveraged. 

b Marginal tax rate is 22% for equity investors. 20% on debt. 

<= Interest rate = 11 .25% (yields ~ real after-tax return after rate reduction on debt). 

dTRA86. 

• Assumes no offsetting passive income so no losses are currently deducribl~. 

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Table 11.48 Effect of Tax Reform Provisions on User Costs Stacked 

Separately and Together Compared to 1985 Law 

(Assumptions m 

Slacked First Against 198.5 taw Scacked Against Previous Provisions 

%Change Holding % Change Holding 

User from No. of Period User in User No. of Period 

Cost Baseline Owners of First Cost Cost Owners of First 

• 1985 law 8.79% 0 .0 % 3 19 8.79% -- 3 19 

27.5 year straight-line depreciation 10.56% 20.2 '\ 3 15 10.56% 20.2% 3 15 

Tax rate reduction b 10.80% 22.9 % 3 19 11 .60% 9 .8% 3 21 

Non-ellclusion of capital gains 9.42% 7.2% 2 26 11.76% 1.4 % 2 28 

Lo"'a interest rates c 8.04% -8.5 % 3 18 10.97% -6.7% 2 25 

Capetalize CPIT 8.82% 0.3% 3 19 d 11.01 % 0.4 % 2 25 

Passh e loss limitation • 12.21 % 38.9 % 2 26 11.43% 3.8% 2 27 

a Assumes marginal taJt rate of 50% for equity investors, 25% on debt. discount rate of8% . mortgage interest rate of 

I 0%. inOation rate of 3% . loan-to-value = 90% 

bMarginal tax rate is 28% for equity investors. 20% on debt. 

c Interest rate = 9 % 

dTRA86. 

• Assumes no offsetting passive income so no losses are currently deductible. 

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Figure I I. I Effect of TRA86 on User Costs 

Percentage Change 

from Baseline 

5% 

~Stacked Separately 

~:~:~:~:~:~:~j Stacked Together 

0%:;:;:;:;:;:;:;:;:::::::::::::::::~ I ~ ho{:::::::::::::::::l ~ ..~~r:::::::::·: :~ W' ~::: ~·.·.w.·.·····t ··············· . .. ... ::::::::::::: y::::::::::::::J rrrl:::::~:::::::::l II%%J::::::::::::::::I . .... . ........ w.·. v77 ·:·:·:::::::::::: ::;:;:;:::;:;:;:; :::::::::::::;:: 

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322 Len Bunnan/Tom Neubig/Gordon Wilson 

Aside from the passive loss limitation. which will only affect certain 

investors. the most important single provision is the lengthening of the 

depreciation schedule. Were that the only reform. user costs for this 

hypothetical investor would increase by 9.4%. Reduction of marginal tax rates 

alone would increase user costs by 9.2% and repealing the exclusion for 

long-tenn capital gains would raise user costs by 4.2%. 

The total impact is far less than the sum of its parts. After lengthening 

the depreciation schedule. the decrease in marginal tax rates has a very small 

effect on user costs, raising them by only 2.9%. With depreciation more 

closely approximating economic depreciation and with higher rents. there are 

few "paper losses" to deduct, so the tax rate of the investor diminishes in 

importance. Similarly. with lower tax rates. repeal of the capital gains 

exclusion becomes virtually irrelevant. While repealing the exclusion alone 

would raise user costs by 4.2%. full taxation of capital gains adds only 0. I % 

to user costs after tax rate reduction. 

General equilibrium model analyses generally predict that TRA86will reduce 

equilibrium market interest rates. (See e.g .. Fullerton, Henderson, and 

Mackie. 1987). Table 11.4A shows that, in conjunction with other major 

provisions of TRA86. a 75 basis point decline in interest rates reduces user 

costs less than it would have under old law. Stacked on top of the other 

provisions. lower interest rates reduce user costs by 3.9% compared to 5.3% 

relative to the prior law baseline. 

This is an interesting. and perhaps counterintuitive. result that 

illustrates the subtle interactions of tax revisions in a dynamic context. 

Because TRA86 curtails churning of rental housing. rental housing investments 

become far less leveraged on average. As a result, interest becomes a much 

smaller part of total costs. Thus a reduction in interest rates has a smaller 

effect on costs under TRA86 than it would have had under prior law. 

One might expect that interest rate reduction would have a greater effect 

on user costs at lower tax rates. because the after-tax cost of debt 

increases. But user costs reflect before-tax rent levels. At the lower tax 

rates of TRA86. a one percent reduction in rents costs more after tax than 

before TRA86. Since lower tax rates raise both after-tax interest expense and 

after-tax rent. the direct effect of interest rate reduction should not depend 

on interest rates. Thus. the indirect effect through reduced churning 

dominates. 

Much has been made of the effect of the passive loss limitation on real 

estate investors. Tables 11.4A and 11.4B show that the passive loss limit has 

far less impact in the context of TRA86 than it would have if adopted under 

prior law tax rates. depreciation rules. and interest rates. The separate 

provision would have raised the 1985 user cost by 20% in the example . 

However. the passive loss limitation would add only 3.4 % when stacked on top 

of other TRA86 provisions. Under pre-TRA86 law. a passive loss limitation 

would have nullified the benefits of accelerated depreciation since tax losses 

would have been deferred until the time of sale. However. the refonns in 

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The Use and Abuse of Rental Project Models 323 

TRA86 combined with lower interest rates substantially reduce tax losses, so 

the passive loss limit has little effect. 

C. TAX RATES, TAX REFORM, AND USER COSTS 

Both ERTA and TRA86 significantly reduced top marginal tax rates. In 1988. 

when TRA86 is fully phased in, the top rate will be less than half of the 1980 

maximum. With the tax incentives in pre-TRA86·law, .investors in high tax 

brackets faced much lower user costs and effective tax rates for rental 

housing than investors in lower tax brackets. The Tax Reform Act of 1986. by 

scaling back the tax incentives and lowering marginal tax rates, removes those 

disparities. This provides both efficiency and equity gains. With approximately equal effective tax rates. high tax bracket investors will not be 

earning super-marginal returns. Furthermore, low and high bracket investors 

will have more equal access to real estate investments. Since accelerated 

depreciation provides the most valuable tax incentives to households in high 

tax brackets, tax rate reduction alone would have reduced much of the disparity in rates of return. 

Tables I J. 3A and 11. 3B show for 1985 law how the cost of capital as well as 

several other summary indicators vary with marginal tax rates. In 1985 (Table 

11.3A). a nontaxable investor faced the highest user cost of capital (10.44%) 

whiJe the same investor would have a user cost of 8.39% (19.6% lower) if he 

were in the top tax bracket. If the pre-ERTA top rate of 70% had applied in 

1985 the top-bracket investor's user cost would have been approximately half 

that of the non-taxable investor. Similarly. the net effective tax rate on 

equity varied from -173.9% for the 50% bracket investor to 0 for the nontaxable investor. 

Simply reducing the top tax rate would substantially reduce this disparity. 

At a top rate of 33%. the disparity in user costs is cut by nearly two-thirds 

to 7.3%. The lowest effective tax rate is increased in absolute value terms 

to -88.5% . 

Table 11.3B shows that the combination of residential real estate measures 

in the Tax Reform Act of 1986 obliterates the wide discrepancies between 

high-tax and low-tax investors. Effective tax rates become slightly positive 

for investors in every taxable income class. Because of longer depreciation 

and the repeal of the capital gains exclusion. the nontaxable investor becomes 

the least-cost investor by a small margin. If we were to further assume that 

the top-bracket investor were subject to the passive loss limitation. his or 

her user cost would become significantly greater than the untaxed investor's 

cost. 

These data are illustrated in Figure 11 .2. Before TRA86. user costs fell 

precipitously with marginal tax rates. But after TRA86. the relationship is 

virtually flat. (For comparison. the user cost that would apply in equilibrium if both lenders and real estate investors were exempt from tax is also 

shown.) At least for the baseline set of parameters. tax reform seems to have 
• 

Figure 11 .2 Effect of Tax Rates on User Cost 

User Cost 

11 .0 % 

10.0°/o 111111111111111111111111111111111111 1111'

111111111111• 111111111•••••••••••••••••••••••••••••••••••11111111 

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8.0% t- -Pre-TRA86 

7.0% 

6.0 % 

"""" Post-TRA86 

••••••No Tax 

L-----------~~----------~-------------L------------~------------- O% 15% 28% 33% 50% 70% 

Tax Rate 

- - - .. • • - - • - .. - - - - -

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The Use and Abuse of Rental Project Models 325 

succeeded dramatically in "leveling the playing field" among the various 

income classes of investors in rental housing. 

It is important to point out that the quantitative conclusions are dependent on parameter assumptions. At lower discount rates or higher inflation 

rates. for example. the effective tax rates and user costs would be different. 

However, the qualitative results about the disparity in user costs and rates 

of return are robust with respect to different parameter assumptions. It is 

clear that tax reform will tend to place investors in different tax brackets 

on a much more even footing than under pre- 1986 law.18 

D. THE VALUE OF LOW-INCOME HOUSING TAX INCENTIVES 

Table 11.5 compares the value of tax incentives for low-income rental 

housing before and after enactment of the Tax Reform Act of 1986. The table 

includes the value of tax -exempt bonds and the more generous A CRS depreciation 

schedule and expensing of construction period interest and taxes available in 

1985. After tax reform. a credit of 4 % per annum for ten years is available 

for low-income housing purchases and 9 % per annum for ten years for new 

investment. A certain percentage 

19 of units must be devoted to low-income 

tenants and abide by rent restrictions for a period of fifteen years. Rents 

are restrained to be no greater than 30% of "qualifying" income. 

For the 1985 law rows. the rent stream is that which would allow the 

particular investor to break even without special tax preferences. The first 

two columns are based on the dynamic model; the third and fourth are based on 

the initial investor model. A comparison of columns shows how initial 

investor models tend to underestimate the capitalized value of tax incentives 

for subsequent investors since sale price is set exogenously. For the TRA86 

columns. rents with the low-income housing credit are assumed to be limited to 

30% of qualifying income. adjusted annually by the rate of inflation. For the 

credit for existing housing (4%). it is assumed that rents and all parameters 

for the initial investor are the same as in the low-income housing base case 

in row 2. The subsequent investors face limited rents and the same tax 

provisions as in TRA86. 

Table 11 . .5 shows that before the Tax Reform Act of 1986. tax-exempt bonds 

were a very valuable subsidy. 

2 0 While greatly accelerated depreciation would 

have been worth $3.267 over the life of the project under the assumed parameters, tax-exempt bonds would have been worth more than twice as much ~$7. 632) 

assuming that each owner received new tax-exempt bond financing. 2 If the 

unit qualified for low-income accelerated depreciation , the present value of 

tax benefits and appreciation in property value increased to $12.672. With 

the lower interest rates. the optimizing investor would have found it worthwhile to seJI after only I 0 years. despite recapture penalties. to another 

investor who could claim the interest rate subsidy on the inflated value of 

the property. If the low-income units had to be rented at below-market rents. 

some or all of the value of the tax subsidy would be lost to the investor. 
326 Len Bunnan/Tom Neubig/Gordon Wilson 

Table 11 .5 Present Value of Low-Income Housing Tax Incentives 

Relative to 1985 Law 

D~namic Model Initial Investor Model 

Present Holding Present Holding 

Value Period Value Period 

1985 Law 

I. Baseline $0 19 $0 19 

2. Special depreciation $3.267 13 $2.167 15 

3. (2) + bonds $12,672 10 $6,327 18 

4. (J) + bonds $7.632 14 $4.499 19 

Tax Reform Act of 1986 

5. 4% credit $15.558 15 

6. 9% credit 

a. 20% low-income $9,968 15 $8.508 15 

b. 40% low-income $15.790 15 $14.721 50 

7. 4% credit + bonds 

a. 20% low-income $1,129 15 $1.100 15 

b. 40% low-income $7.699 15 $7,422 50 

Assumptions: 

I . $50.000 unit. newly constructed: all owners subject to 19·year ACRS: no tax-exempt bond 

financing. Rent stream is the same for (I) to (4). See Table 11 .8 for parameter list. 

2. Same unit as in (1). All owners subject to IS-year ACRS. Original owner expenses 

contruction period interest and taxes. 

3. Same as (2). but all owners receive tax·exempt bond financing at interest rate 20% below 

rate in (I) and (2). 

4 . Same as (1). but all owners receive tax-exempt bond financing. 

5 . Same as (3) for first owner. but subsequent owners receive the 4% per annum low-income 

housing credit and are subject to TRA86 depreciation rules. Rent for second and sub· 

sequent owners is constrained to be not greater than $3 .600 (approximately 30% of 50% of 

1986 median income) in 1986 dollars. 

6. First owner receives 9 % per annum low-income housing credit; subsequent owners receive 

4 % credit. All investors in (6) and (7) are subject to TRA86 depreciation rules. In ta). 

at least 20% of units have tenants with incomes not greater than 50% of area media.n income: 

rent is constrained to be not greater than $3.600 per year in 1986 dollars. In (b). at 

least 40% of units have tenants with incomes not greater than 60% of area median income : 

rent is constrained to be not greater than $4.320 per year in 1986 dollars. 

7. First owner receives 4% per annum lo"'··income ou~ing credit and rax·exempt bond 

financing: subsequent owners receive 4•-r credit. bur nor bond financing Otherwise. this 

is the same as (6). 

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The Use and Abuse of Rental Project Models 327 

This probably explains why most units financed with tax-exempt bonds were not 

claiming low-income depreciation. which had far tighter restrictions on 

tenants· incomes. 

The difference between the "dynamic" columns and the ''initial investor" 

columns represents the extent to which future tax subsidies might be capitalized into the value of the property. In rows 2 to 4, the present value of tax 

subsidies is increased by at least half because future owners would bid more 

based on anticipated tax benefits. 

Rows 5 to 7 in Table 11.5 represent the values of some of the tax subsidies 

for low-income housing in the Tax Reform Act of 1986. Row 5 shows the value 

of the 4% per annum credit for existing low-income housing applied to the ACRS 

low-income project. in row 3.22 The present value of $15.558 indicates that 

the 4% credit is more generous to the hypothetical investor than prior law. 

The other rows show the two credits available for newly constructed 

low-income rental housing. Row 6 shows that the 9% per annum credit (for lO 

years) could be worth between $9,968 and $15,790 to an investor in present 

value terms. In other words. the credits are equal to or more valuable than 

any tax preferences under pre-TRA86 law. From the table. it seems clear that 

the investor would be far better off using the higher qualifying percentage 

(40% low-income tenants) because that would allow him to charge 20% higher 

rents. However, this analysis does not account for possibly higher costs 

caused by having a larger percentage of low-income tenants. 

Finally. the last rows illustrate the value of· tax-exempt bond financing 

plus the 4% credit. After TRA86. units financed with tax-exempt bonds will be 

subject to meaningful restrictions on tenants' incomes combined with Limits on 

rents. This will tend to reduce the value of the bond-credit combination as a 

subsidy for new construction-to $7.699 assuming a qualifying percentage of 

low-income occupants of 40%. Nonetheless. this is still comparable in value 

to the most popular tax-exempt financing option before TRA86. 

v. LIMITATIONS OF PROJECT MODEL ANALYSIS 

The basic limitation of project model analysis is that the results apply 

specifically to a single project. Sometimes a particular kind of result seems 

to occur even when assumed parameters are altered over a range of values. as 

in the first two examples in the last section. In this case. it may be safe 

to generalize the qualitative result as a market-wide phenomenon. But project 

models are not models of markets. Great caution must be exercised in trying 

to infer anything specific about prices and quantities of remal housing in 

either the short or the long run based on project model analysis alone. 

A particular problem arises in using rental project models to predict 

changes in market rents. This interpretation of model results is. even under 

the best of circumstances. totally dependent on a set of assumptions that are 

guaranteed to be false . There is an obvious problem that complicated rental 
328 Len Bunnan/Tom Neubig/Gordon Wilson 

project models are dependent on a large number of parameters. The results 

shown in Table I 1.3

2 amply demonstrate that quantitative model results are 

very sensitive to reasonable changes in parameter values. However. more 

fundamentally. the assumptions that would be necessary to allow generalization 

of the optimal investment decisions for one representative investor to the 

rental housing market could simply not hold in practice, no matter how good 

the parameter values were. 

An analogy may be drawn with the corporate income tax. Arnold Harberger's 

( 1962) analysis showed that. in general equilibrium. the incidence of the 

corporate income tax may fall in whole or in part on any of the input factors 

as well as on consumers. In the last decade. a number of economists have 

reconsidered the incidence of the corporate tax in a variety of general equilibrium models. The general conclusion of these models is that the corporate 

tax is a tax on capital. (See Shoven and Whalley. 1984.) And yet, those who 

use rental project models to predict market rent responses are implicitly 

assuming that the entire incidence of taxes on rental housing capital falls on 

consumers, at least in the long run. This incidence assumption is no more 

credible in the rental market than it would be for corporations. 

To be sure, other kinds of analyses depend heavily on implicit assumptions. 

Bradford and Fullerton ( 1981) poimed out that effective tax rate calculations 

are sensitive to the assumed relationship between nominal interest rates and 

inflation (typically Fisher's Law or some variant). Hendershott and Ling's 

( 1984) conclusion that high inflation reduces churning depends heavily on 

their assumptions that real after-tax interest rates are constant (what 

Bradford and Fullerton refer to as "modified Fisher's Law") and that refinancing is costless. If. on the other hand, pre-tax interest rates are sticky 

and refinancing is costly. high inflation will reduce real interest rates. 

However. with high refinancing costs investors' debt-equity ratios will 

increase even as the cost of debt falls. In this case. inflation would tend 

to increase churning because the property is worth more to a purchaser at a 

high loan-to-value ratio and a low interest rate than to the seller if he 

holds. Thus. user costs could move in the opposite direction to that predicted by Hendershott and Ling assuming constant real interest rates. 

A. USING RENTAL PROJECT MODELS TO PREDICT 

RENT CHANGES 

Perhaps the most common use to which rental project model analysis has been 

applied is the prediction of the effect of tax policy changes on market rents. 

While a plausible argument can be made that the user cost estimate could 

represent long-run equilibrium rents in a simple microeconomic model. we 

believe that in practice this insight is likely to be of little relevance to 

estimating quantitative changes in rents. Generalizing rental project model 

results to infer the response of market rents requires a number of assumptions 

that have not been critically appraised in the literature. This section 

explores the implications of each of these assumptions. 

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The Use and Abuse of Rental Project Models 329 

1. A Model in Which User Costs are 

Long-Run Equilibrium Market Rents 

To see which assumptions are important, we can construct a hypothetical 

economy in which user costs would be good predictors of long-run required 

rents. This economy consists of a large number of identical investors. There 

are no barriers to entry or exit from the rental housing market. so when rents 

exceed their break-even levels, new rental housing is constructed which drives 

rents down to the level of user costs. Similarly. when rents are too low. the 

quantity of rental housing declines until rents cover costs. In other words, 

the market for rental housing is perfectly competitive. 

The model treats all input prices as exogenous. This is equivalent to 

assuming that the supply of inputs. such as land, is perfectly elastic in the 

long run. Furthermore, rental housing services are produced under conditions 

of constant returns to scale. 

Analysts typically compare "equiUbrium" states in which a particular tax 

policy is assumed to hold for the life of the project. So in our hypothetical 

economy. the tax policy and economic environment that is assumed to be the 

baseline has been in place or predictable for long enough that investors could 

adjust. The new tax policy is a permanent change in the tax system. or 

investors will believe that it is permanent for long enough that the market 

will achieve the new equilibrium. 

Finally. there is an issue of how investors would discount future returns. 

In the simple world hypothesized here. prices are either constant or evolve in 

such a way that investors can rationally plan for the future. Predictability 

is necessary for the market to converge to an equilibrium. 2 4 This means that 

real discount rates should be equal to the investors' real after-tax cost of 

funds. If future prices. costs, and taxes are random and investors are riskaverse. then we assume that investors discount future streams at the interest 

rate that would be charged in the market on an investment of comparable risk. 

2. Critical Assumptions 

Of course, the real world is different from the stylized model presented 

above. But it is not obvious that these deviations are more problematic than 

those required to generalize the results of other kinds of simulation models. 

However. we wiJI show that the following implicit assumptions underlying 

project model analysis tend to bias rent predictions. generally in the 

direction of overstatement of market rent changes. 

o Either all investors are the same. or there is one class of investor 

that is the marginal investor. or there exists an average or representative investor whose behavior approximates that of the market. 

Under the marginal or representative investor model. the marginal 

investor before the parameter change will remain the marginal investor 

after the change. 
330 Len Burman/Tom Neubig/Gordon Wilson 

o Either the supply for rental housing is perfectly elastic or demand is 

perfectly inelastic in the long run. 

o The market is in long-run equilibrium before the change that is being 

considered is undertaken. 

o Investors are myopic with respect to future policy or structural 

changes. 

o The parameter values chosen are correct for the representative 

investor. 

3. Is There a Marginal or Representative Investor? 

Housing analysts often assume that a particular kind of investor (such as 

the tax shelter syndicate) is the marginal investor. Under this assumption, 

for smaiJ changes. considering the behavior of the marginal investor would be 

sufficient to determine what will happen to the market. 

There are a number of reasons why this assumption is inappropriate. The 

real shoncoming of generalizing based on the "representative" investor is 

that there is no such animal. not even as an approximation. Refer again to 

Table 11.3, which compares investors in different marginal tax brackets. 

Residential rental real estate, with the possible exception of high-end units. 

is owned by significant numbers of individuals in each tax bracket. as well as 

by corporations and by government. See Gravelle, 1985. 

As Table 11.3 indicates, variation iri marginal tax rates differentiates 

investors' costs and optimal behavior in every significant respect. Thus we 

cannot assume that investors are identical. 

An alternative rationale is that there is a class of investors who are or 

who represent the marginal investor: that is, the source of new investment in 

real estate. There are three problems with this interpretation. First. 

economic theory suggests that all investors are "marginal" investors in the 

sense that they balance their ponfolios so that. on a risk

-adjusted basis. 

the expected marginal opponunity cost of additional investment in real estate 

just equals the expected additional revenue. 

25 Since all investors are on the 

margin. a change in prices should affect investors in all classes. It is 

possible that because of credit constraints and transaction costs. most 

investors would not adjust their portfolios in response to small changes in 

prices. However. this should hold for investors in all classes. 

Second, analysts often model the marginal investor as an individual or 

syndicate that is using real estate as a tax shelter. Tax shelter syndicates 

only represent a minority of investors in the residential real estate market. 

Funhennore. this application of "marginal" is somewhat peculiar in that the 

tax shelters seem to be the least-cost. rather than the highest-cost. 

investors in the market. Tax deductions are most valuable to high-bracket 

investors. But traditional economk anal

ysis would identify the highest-cost 

investor as the marginal investor. 

Alternatively. analysts could assume that there is some average or representative investor whose behavior accurately reflects the behavior of the 

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The Use and Abuse of Rental Project Models 331 

market. A logical choice would be to use an investor with the weighted 

average characteristics of all investors. However. Table 11.3A makes it clear 

that an average investor would not match the "market average" response of high 

and low tax investors to a policy or structural change. 

For example. suppose that 44% of the investors are non-taxable and 56% are 

in the 50% tax bracket. The average tax rate is 28%. Based on Table 11.4A, 

the average user cost would be 9.29%. the average holding period would be 32.6 

years. the average debt-equity ratio would be 0.54 , and the average effective 

net tax rate on the investment would be 8.3%. But looking at the "average" 

investor with a tax rate of 28%. the user cost is 9.94%26• the holding period 

is 19 years, the debt-equity ratio is 0.62, and the effective net tax rate is 

24%. The debt-equity ratio and the holding period are not even continuous 

functions of the tax rate. It is clear that the "typical" investor would not 

match market aggregates very closely at all. 

The third criticism of this approach is that tax policy changes rarely 

represent marginal change, even approximately. Every tax biU since 1978 has 

made significant changes in the way real estate was taxed. The Economic 

Recovery Tax Act of 1981 expanded opportunities for real estate tax shelters, 

and the composition of the market changed in response. The Tax Refonn Act of 

1986 generally discourages tax shelters. It would be naive to assume that 

there would not be a structural change in the market. 

Comparing Tables ll.3A and ll.JB. the user costs for investors in different 

tax brackets flip-flop based on the assumed parameterization of the effect of 

tax refonn. High tax bracket investors are the low-cost investors in the 

pre-1986 environment, and costs increase as the marginal tax rate falls. But 

after tax refonn. low tax-bracket investors face the lowest costs and high 

tax-bracket investors become the high-cost investors. although by a small 

margin. As Tables 11.4A and 11.4B showed, investors subject to the passive 

loss limitation will face much higher costs than other investors after TRA86. 

The result should be a shift in rental investment away from tax-shelter 

partnerships in favor of tax-exempt jnstitutions and other lightly-taxed 

investors. 

We conclude that any analysis based on a representative investor is likely 

to exaggerate predicted rent changes. even if all of the other assumptions 

underlying rental project model analysis were correct. ActuaJ market 

responses depend on the market dynamics. as investors in different classes 

become more or less important. While rental project model analysis might be a 

useful first stage in such an analysis. dynamic market analysis with many 

classes of investors is beyond the scope of available project models. 

4. Problems With a Static Competitive Model 

Assuming Regressive Expectations 

a . Is Supply Perfectly Elastic or Demand Perfectly Inelastic? 

Rental project model estimates of market rents require . at a minimum, that 
332 Len Bunnan/Tom Neubig/Gordon Wilson 

either long-run supply be perfectly elastic or that long-run demand be perfectly inelastic. Figures I I .3A and I I .38 show these cases. Suppose, for 

example. that the initial equilibrium rent or user cost is 

P0 and that the 

equilibrium market quantity of rental housing is 

Q0 • Then a tax policy change 

raises the after-tax user cost to P1 given the same input prices. 

If input prices do not depend on the quantity of rental housing. then the 

long-run supply will be perfectly elastic as in Figure 11.3A. If demand is 

not perfectly inelastic, the equilibrium quantity of rental housing will fall 

until market rents rise by the full amount of the increase in user costs. 

However, it does not seem reasonable to assume that input prices are fixed in 

the long run. Since land of a given quality and location is fixed. even in 

the long run. land prices will depend on the quantity of rental housing. As 

individuals respond to higher rents by renting smaller homes. the demand for 

the complementary good, land, will also decline. Even for those who switch 

tenure modes to owner-occupancy. their housing costs will increase and they 

will tend to consume less housing. Furthermore, zoning laws may limit the 

convertibility of Jand between uses. Thus. overall demand for residential 

land will decline. which will drive its price down. The result is that the 

long run supply of rental housing can not be totally elastic. 

However, if the demand for rental housing is perfectly inelastic, rents 

would also increase by the change in user costs. as Figure 1 1.38 shows. In 

this case, the quantity of rental housing remains fixed. 

While empirical evidence suggests that demand for rental housing is 

inelastic (see Mayo. 1981 ). there is no statistical evidence that the demand 

elasticity is zero. In the long run. market demand reflects changes in tenure 

choice as the relative price of rental housing increases relative to 

owner-occupied housing as well as a decrease in average quantity of housing 

services consumed by those who continue to rent. Furthermore. long-run demand 

elasticities will be greater than in the shon run when housing choices are 

limited by transaction costs of moving. 

Figure 11.3C shows the equilibrium in the case where long-run supply and 

demand both have constant elasticities of 0.5. The graph shows ttlat a 

parallel shift in the supply curve would increase equilibrium prices by less 

than half of the predicted change in the extreme models. While the actual 

level of price increase depends on long-run elasticities. it is unlikely that 

the long-run change in market equilibrium rents will be as great as the change 

in user costs. b. The Relevance of Static Analysis 

Even if one of the extreme models of long run supply and demand were 

accurate. that would not mean that the change in long run equilibrium rents 

would be a good predictor of how actual market rents would change. either in 

the short or the long run . If the user cost were an accurate measure of long-

run rents, it would generally not represent rents in the short run. The high 

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The Use and Abuse of RentaJ Project Models 333 

Figure 11 .3 Long-Run Supply and Demand 

A. Assuming Perfectly Elastic Supply 

Pnce 

~--------~r--------------------------------------- 5, 

B. 

a, Quantity 

Assuming Perfectly Inelastic Demand 

a. 

Quantity 
334 Len Bunnan/Tom Neubig/Gordon Wilson 

Figure J I . 3 (continued) 

C. Assuming Constant Elasticity Supply and Demand 

Ouanttly 

transaction costs of buying and selling rental housing. the lengthy construction period for new housing. and local rent controls mean that market rents 

would be very slow to adjust toward their long-run levels. This also means 

that in a dynamic environment where lax and non-tax shocks are common. current 

rents are not at equilibrium levels. 

Thus. the percentage change in long-run equilibrium rems as a result of 

adopting some policy could overstate or understate the actual change in rents. 

even if the model were perfectly specified. For example. several analysts 

predicted that equilibrium rents would increase from 1985 levels as a result 

of tax reform. But if rents in 1985 were above their equilibrium levels 

because of slow adjustment to the tax incentives in ERT A and the precipitous 

drop in interest rates of the past few years. the actual increase in equilibrium rents from their 1985 levels would be much less than predicted (or even 

negative). 

c. Are Investors Really Myopic? 

The assumption of myopia is also trouhlt!so m~ in trying to infer market rent 

changes from rental project models. Tax laws have changed about ev~ry two 

years over the last decade. and every new law has changed the depreciation 

treatment of rental housing. Rational investors would have to conclude that 

special tax incentives for rental housing are risky. Since tax benefits are 

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The Use and Abuse of Rental Project Models 335 

capitalized into property values, investors should also be able to figure out 

that the resale values for their properties are also risky. 

With pre-TRA86 depreciation deductions greatly in excess of economic 

depreciation, investors might have perceived more downside risk in resale 

prices than on the upside. The result would be that pre-TRA86 prices would 

not be as low as would be predicted by a model assuming perfect certainty. 

Thus. post-1986 price increases would be overstated by the model. This would 

be exacerbated if current investors expected that future tax bills would have 

a high probability of restoring tax shelter benefits, as has been suggested by 

some press reports. Finally, as Hendershott. Ling, and Follain ( 1986) pointed 

out. investors would have anticipated. at least in part, the effect of TRA86 

on rental real estate. and prices would have begun to adjust long before the 

bill became law. 

While it is common to account for risk through higher or lower discount 

rates. a model of how particular kinds of risk are reflected in market risk 

premia is really needed. This is a notable shortcoming of rental project 

models. 

B. SENSITMTY OF MODEL RESULTS TO 

PARAMETER CHANGES 

Every model is dependent on assumed parameters. A useful feature of 

sophisticated rental project models is the large range of parameters that may 

be selected and varied. However. model results are very sensitive to the 

assumed parameter values. Thus, even if all of the other assumptions used to 

justify generalizing model results were valid. model predictions would be very 

imprecise. 

I. Some Alternative Assumptions 

Table I I . 6 shows user costs based on tax parameters representing pre-TRA86 

law and TRA86 for a particular investor under a range of assumptions. The 

discount rate is probably the most commonly varied assumption, and it is very 

important. Raising the real after-tax discount rate from 4 % to 12 % exaggerates the effect of tax reform on user costs. The user cost increase (what 

some call a rent increase) as a result of TRA86 is 4 9. 4% greater at the high 

discount rate than at the lower one. Furthermore. while tax reform would 

still reduce churning at the higher discount rate. it would no longer be 

expected to end churning altogether. 

Hendershott and Ling ( 1985) showed how inflation can affect investor 

behav.ior and user costs. Higher inflation (holding real rates of return 

constant) lengthens optimal holding periods and raises user costs. as is shown 

in row 3 of Table 11.6. If we assume that Fisher's Jaw does not hold with 

respect to real after-tax interest rates. however. so that real rates of 

return decline as inflation increases. the results change substantially. 

Investors then would find it profitable to chum more often under pre- 1986 
336 Len Bunnan/Tom Neubig/Gordon Wilson 

Table 11.6 User Cost Estimates Under a Range of Parameter Values 

Pre-1986 TRA86 

User Holding User Holding % Change 

Cost Period Cost Period in User Cost 

I. Baseline 9 .23% 19 10.02 % 50 8.3% 

2. High Discount Rate 12.23% 12 13.41 % 18 9 .8% 

3. High Inflation w/ con st. real interest rate 9.79% 14 10.54% 50 7. 1% 

4 . High Inflation w/ lower real interest rate 6.52% 14 7.35% 50 13.8% 

5 . Constant Refinancing 8.91 % 50 9.95% 50 11 .8% 

6 . Retired Landlord (X) 10.27% 50 9.68% 50 ·5 .8% 

7. Pure Tax Shelter {Y) 10.37% 4 16.40% 25 58. 1% 

Assumptions: 

I. See Table 11 .8. 

2. Discount rate = I 2% 

3. Inflation rates for land. operating costs. and rent are 10%. Real after-tax interest rates 

are the same as in (1 ). 4%. 

4. Same as (3), except real after-tax interest rates fall by half of the increase in inflation 

(2.5 %). 

5. Mortgages are costlessly refinanced each year to keep the loan-to-value ratio at 80%. 

6 . Discount rate = 2%. inflation rate = 3%. tax rate = 15% . interest ratefalls from 12% before 

to 10.5% after TRA86. no capital gains tax (properry is held until death). 

7. Discount rate = 12 %. inflation rate = I 0%. tax rates at maximum level. interest rate = 

18 .57% with no reduction after TRA86. 10% syndication fee . passive loss limitation is 

binding after TRA86 . 

law. The real cost of debt falls and the debt-equity ratio declines rapidly 

with high inflation. so investors sell to others who can leverage the property. As a result. user costs are much lower than they would be in the 

absence of inflation. While the level of increase in user costs is only 

slightly greater than in the base case. the predicted percentage increase 

rises substantially. as shown on row 4 . 

The churning result with inflation and a decrease in real rates depends 

heavily on another assumption. that refinancing is prohibitively expt!ns'ive. 

If refinancing is allowed continuously. as Hendershott and Ling assumed. then 

there is no incentive to chum under this scenario. With constant refinancing, user costs are lower under each tax law. and the expected increase in 

user costs rises by 32 %. 

Table 11.3 showed that the results are sensitive with respect to tax rates. 

Other assumptions are also important. The cautionary tale is that predicted 

user cost increases and behavioral responses depend heavily on assumptions. 

upon which reputable analysts may have wide disagreements. 

2. Two Views of TRA86 

Rows 6 and 7 of Table I I . 6 show two views of the effect of tax refonn on 

rents. Row 6 shows an investor, X. who will be pleased with tax refonn. Her 

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The Use and Abuse of Rental Project Models 337 

required rent. as indicated by the user cost. falls by 5. 8% from pre-1986 law 

as a result of tax reform provisions. Jn contrast, row 7 shows an unhappy 

person. Y. who would require higher rents after 1986 than he would have in 

1985 to earn the same after-tax rate of return. Were the market made up 

entirely of investors like Y. both before and after tax-reform. rents might 

rise as predicted by some housing industry analysts. 

Individual X might be representative of a number of current owners of 

rental real estate. For example. a large number of small units are owned by 

individuals in low tax brackets (for example. retired persons). It might also 

be assumed that low tax bracket investors have a low opportunity cost of funds 

and thus a low real discount rate. These individuals got negligible benefit 

from accelerated depreciation and other front-loaded tax incentives under 

pre- 1986 law. Since we assume in Table 11 . 6 that tax reform will reduce 

interest rates by 0 . 75 percentage points. the benefit to X of lower interest 

rates exceeds the value of her lost tax benefits. 

For Y. on the other hand. tax preferences were very valuable under pre-1986 

law. Y might represent a typical partner in a tax-shelter syndicate. By 

making a highly leveraged investment and taking advantage of accelerated 

depreciation. he could generate tax losses that were very valuable at a tax 

rate of 50% . The front-loading of tax benefits was especially important to 

this investor because he has a high discount rate. Longer depreciation 

schedules. lower tax rates. a higher tax rate on capital gains. and the 

passive loss limitation combine to raise his user cost by 58 . I %. 

These views of the effect of tax reform on rents are completely contradictory and. of course. completely wrong. except as they pertain to particular 

kinds of individuals. The user cost changes could not both represent average 

rent changes. The only information about rents that might be gleaned from 

these polar cases is that the actual long-run rent change would probably be no 

greater than Y's user cost increase and no less than X's. This is not terribly 

useful given the range. 

However. the comparison is informative if we forget about market rents and 

think about the individuals. The example for X suggests that low-taxed and 

untaxed investors similar to X should become more important in the rental 

housing market after tax reform than they have been recently. Y's experience 

suggests that rental housing tax shelters will probably not be as viable after 

tax reform unless they change their structure. This, of course. was the point 

of the anti-tax shelter provisions. 

C. THE TRACK RECORD OF RENTAL PROJECT MODELS 

The previous section argued that the assumptions necessary to justify 

inferring market rents from rental project models are unlikely to be satisfied 

in practice. With the exception of the assumption that parameter values are 

accurate. the practical effect of the assumptions is that predicted rent 

swings tend to exaggerate actual market responses. There is no guarantee that 
338 Len Bunnan/Tom Neubig/Gordon Wilson 

the predicted change would have the ri.ght sign, even if parameters were right 

on average. 

Table 11.7 shows how user cost estimates. adjusted for changes in construction costs, tracked market rents as measured by the consumer price index for 

rents over the 1975-1985 period. Figure I I .4 illustrates the relationship 

graphically. The figure suggests that predicted rent changes bear only a weak 

relationship. If any, to short -tenn rent changes. 21 

Compared to actual rents there are large swings in the adjusted user cost 

variable. Actual rents increased steadily between 1975 and 1985. but never by 

more than 9% or by less than 5% in a year. User costs, on the other hand, 

decreased in four out of ten years. The absolute magnitude of the annual 

changes was greater than 9% in five out of ten years.

28 Finally, the 

predicted increase in rents over the eleven years was more than double the 

actual increase. 

This does not demonstrate that rental project models cannot predict rents 

in the long-run. It may be that actual rents can be explained by a distributed lag on predjcted user costs or that a different set of baseline assumptions would produce a stronger correlation. But the data suggest that, if 

there is a relationship between user cost estimates and actual rents. it may 

be too subtle to be useful. 

Figure I 1.4 Predicted versus Actual Rents, 1975 - 1985 

Rentl1975 • tOOl 

300 -userCo•t 

-•-Rent CPI 

1980 

I 

1981 1982 

I 

1983 1984 1985 

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The Use and Abuse of Rental Project Models 339 

Table 1 I . 7 Projec.t Model Estimates of Break-Even Rent Compared to the 

CPI for Urban Rents Using Historical Values- 1975 to l98sInOation Mortgage Construction Break-Even Rent CPJ9 Holding 

b Year Ratec: Rated Cost• Level %Change Level % Change Period -----

19751 9. 1% 9 .00% 89 100 100 9 

19761 5 .8 9.00 92 137 37% 105 5% 16 

19771 6 .5 9.02 100 146 7 112 6 14 

19782 7.7 9.56 113 141 -3 119 7 9 

19792 11.3 10.78 129 127 - 10 128 7 5 

19802 13.5 12.66 143 120 -6 140 9 4 

1981 3 10.4 14.70 152 178 48 152 9 7 

19823 6 . 1 15. 14 154 287 61 163 8 15 

19833 3.2 12 .57 157 326 14 173 6 50 

19844 4.3 12.38 164 307 -6 182 5 18 

19855 3 .6 lt .Sff 169 320 4 193 6 19 

• For non-low-income residential rental property. 

bTax law assumes marginal tax bracket of twice median income investor and: 

1 175% declining balance (DB) depreciation new property. 125% on used property with 

useful life over 20 years. 50% capital gain exclusion. 10-year amortizatjon of 

construction period interest and taxes. 2 Same as a. except 60% capital gains exclusion. 3

Same as b. except ACRS (175% DB). 15 year life on new and used property. 

• Same as b. except ACRS. 18 year life. 

5

Same as b. except ACRS. 19 year life. 

c: Consumer price index for all items. 

dNew home mortgage yields (p • preliminary). 

•Department of Commerce composite construction cost (1977 = 100). 

t Product of user cost and construction cost index normalized so 1975 = I 00. 9 Normalized so 1975 = 100. 

VI. CONCLUSION 

This paper has described the state of the art of rental housing project 

models. We have found that rental project model analysis is useful-almost 

essential-in studying the behavioral responses of individual investors to 

complicated tax policy changes that may affect current or future investors in 

rental housing. Rental project models can be used to study how special tax 

preferences are capitalized into land and property values as well as the 

direct effects of those policies on the costs and returns to investors. The 

OTA rental project model provides estimates of effective tax rates that take 

account of the special characteristics of the rental investment. especially 

leveraging and the effects of tax benefits on future investors when there is 

churning. 

However. rental project models cannot by themselves produce reliable estimales of changes in market rents as a result of tax policy changes. Virtually 
340 Len Bunnan/Tom Neubig/Gordon Wilson 

all of the assumptions necessary to generalize the results of rental project 

models to the market as a whole tend to predict grossly exaggerated market 

responses. No credible market analysis can rely solely on the predictions of 

rental project models. 

We have used the OTA model to look at the effects of the Tax. Reform Act of 

1986 on the behavior of residential rental real estate investors. It was 

found that tax. reform succeeds in greatly reducing the distortions in investor 

behavior that were prevalent under prior law.

29 TRA86 diminishes the incentive to chum real estate for tax reasons. It reduces the disparity in the 

costs and returns to real estate investment among different investors. As a 

result, residential real estate will no longer provide large tax shelters for 

high-income investors (except for low-income housing). Investors in all tax 

brackets will have to evaluate real estate investment based on the economic. 

rather than the tax, consequences. Further. we found that the most significant anti-tax shelter provisions in TRA86 were lengthening depreciation 

schedules and lowering marginal tax rates. not the passive loss limitatjon. 

even though the latter was the only explicitly tax shelter-oriented provision. 

This paper has focused on using the OT A model as a residential rental 

housing project model. but the scope of such analysis is much broader. OTA 

analysts have used the model to study the effects of tax provisions and 

proposals on commercial real estate. The model could also be used to study 

the effects of taxes on other capital assets. especiai1Y long-lived assets for 

which resale markets are reasonably well developed.

3 Farm machinery and 

equipment, for example. would provide logical applications. 

Several extensions of rental project model analysis would be worthwhile. 

The model presented here does not allow for rehabilitation. although tax. Jaws 

are important in certain kinds of rehabilitation projects. A better developed 

model of the role of uncertainty in rental housing investment decisions is 

clearly called for. While Hendershott and Ling's approach of discounting 

future streams of income and expense at different rates is an interesting 

extension, a full treatment of risk would have to explicitly account for the 

nature of the random disturbances that could affect future income. A model 

that assumed that investors maximize expected utility under some degree of 

risk aversion might provide results very different from the essentially 

perfect certainty model presented here. 

Finally, the question of how tax policy affects market rents is important. 

even if present models are not well suited to answering the question. A 

general equilibrium market model that incorporated the level of detail about 

tax policies in the OTA model would be a valuable tool. Such a model should 

include a variety of classes of investors and should integrate the various 

kinds of real estate: residential rental. commercial rental. and owneroccupied housing. Investors should choose between real estate and other kinds 

of capital investment. Consumers should. choose between rental and owneroccupied housing as well as other consumer goods. However, whether such a 

model is or will be technically feasible is an open question . 

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The Use and Abuse of Rental Project Models 34 J 

APPENDIX 

A. INTRODUCTION 

The OT A Rental Housing Project Model program was developed by the 

Treasury Department to simulate the effects of tax law changes on returns to 

rental housing investment. The model simulates the costs, returns, and tax 

consequences of a hypothetical real estate investment. The model includes tax 

provisions for housing under current and recent Federal statutes, as well as 

several reform proposals made over the past few years. 

An extensive set of data parameter assumptions is necessary to generate 

user costs. sales prices. and before and after tax returns for a hypothetical 

investment in a rental unit. The model requires specification of tax law 

parameters. the building's useful life. the mix of the original investment 

between land, structure. and construction period costs. interest rates and 

inflation rates, operating costs. competitive real rates of return and the 

marginal tax rates of current and potential future investors. and the economic 

rate of depreciation for the structure. All of these parameters may be 

changed by the model user. 

The program output may include (depending on print parameter settings) 

detailed information about the initial investment and period-by-period before 

and after tax returns for the original and subsequent investors. By default, 

the calculator computes the present value and internal rate of return, both 

before and after tax. earned by the original investor. The program can also 

be set to find the initial rent-to-value ratio that would give the initial 

investor an after tax present value of zero or compute the internal rate of 

return that would make all investors break even in present value terms. 

Table 11.8 lists the parameters used to simulate a rental housing investment both before and after enactment of the Tax Reform Act of 1986. The full 

list of possible parameters is much longer. Documentation is available upon 

request. For reference. Table I l . 9 briefly summarizes the key rental housing 

provisions in the Tax Reform Act of 1986. 

B. HOW THE CALCULATOR WORKS 

The flowchart in Figure I I .5 illustrates how the model computes before and 

after tax returns for all investors in a rental project over its useful life. 

The calculator inputs parameter values from a FORTRAN NAMELIST. 

The calculator can operate in several modes. In its basic mode. the 

calculator may be thought of as planning the optimal investment for a wellinformed hypothetical investor. This investor would want to know how much the 

investment will cost (see 2 on Figure 11 .5). the expected stream of rents and 

operating costs (3). the tax benefits that would accrue while the property is 

held (5). and sales prices and tax costs of sale at various dates (4 and 5). 

The investor could then find the holding period that maximized the present 
I 

342 Len Bunnan/Tom Neubig/Gordon Wilson I 

Table 11.8 Input Parameters and Baseline Values I 

1985 Law TRA86 

A. Economic Characteristics I . initial operating cost to value ratio .0250 

.0250 I 

2. true depreciation rate .0300 

.0300 

3. growth rate of prices I a) land .050 .050 

b) structure 

.050 .050 

c) CPI.050 

.050 

d) operating costs 

.050 .050 I 

4. length of construction period I I 5. amount spent on structure 44000. 44000. 

6. value of land when building placed in service 6000. 6000. 7. fraction of expenditures on structure by year I a) year I 1.000 1.000 

B. Financing Characteristics 

I . initial mortgage/value ratio 

.800 .800 I 

2. mortgage rate . 1200 .J 125 

3. initial mongage term (years) 30 30 4. frequency of refinancing (years) 

a) original owner NA NA I b) subsequent owner NA NA 

5. construction loan/value ratio .800 

.800 

6. construction loan rate .1200 . 1125 

C. Tax Characteristics 

I. income tax bracket of owner I 

a) 

original owner 

.40 .22 

b) subsequent owner 

.40 .22 I 

2. tax bracket of lender 

.25 

.20 

J. property tax rate .018 .018 

4. capital gains treatment 

a) structure I I) inclusion rate .40 1.00 

2) if indexed No No 

b) land 

I) inclusion rate .40 1.00 I 2) if indexed No No 

5. depreciation treatment 

a) schedule. ACRS I) if declining balance No No I 2) usefu l life 19 27 

3) whether indexed No No 

4) type of recapture Excess None 

6. CPIT treatment 

I a) fraction expensed . 10 .00 

b) fraction I 0 year amortization 

.90 .00 

c) fraction capitalized 

.00 1.00 

d) if indexed No No 

7. minimum tax 

a) rate .00 .00 I 

b) fraction of excess depreciation subject 

.00 

.00 

C) fraction of excluded gains subject 1.00 1.00 

8. tax-exempt financing 

a) whether tax-exempt financing No No I 

b) percent reduction from conventional rate 

:w. 20. 

NA = Not applicable. I 

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Table 11.9 COMPARISON OF REAL ESTATE TAX PROVISIONS BEFORE AND 

AFTER ENACTMENT OF THE TAX REFORM ACT OF 1986 (TRA86) 

hem 

Depreciation Low Income* 

Other 

Recapture 

LOw-income* 

Other 

Construction Period Interest and Taxes 

Low Income* 

Other Housing 

Rehabilitation Credit 

Historic Structures R~duction 

Nonhistoric Structures 

(nonresidental) 

Rapid Amortization 

Low Income* Rehabilitation 

lo~A Income Housing Credits 

Credit level 

Non-Federally Subsidized Units 

F~derally Subsidized 

(e .g . . tax-exempt bonds) C~rtain E"tisting Housini 

(HUD resyndications Additional Low Income nits 

Income Re~uirement 

General 

Existing Housing 

1985 Law 

15-year real property; 200% DB 

19-year real property: 175% DB 

Excess over SL: phased-out: I% per month after 100 months 

Excess over Sl 

Expensed 

I 0-year amortization 

25% tax credit: 1/2 reduces basis 

15% credit for 30-year old1 20% 

credit for 40-year old: rull 

basis reduction 

60-month amortization: $20.000 or $40.000 limit per unit 

No provision 

TRA86 

27.5-_year SL 

Resicfential: 27.5-:Year SL 

Commercial: 31 .5-year Sl 

Not relevant because there is no exclusion 

of capital gains 

Capitalized 

Capitalized 

20% tax credit: full basis reduction 

10% credit for buildings placed in service 

before 1936. 

Provision allowed to expire 12/31/86 

Credits with present value of 70% of basis over I 0 _years for new construction and 

qualifiecf rehabilitation ex~nditures Credits with present value of 30% of basis over 10 years Same as Federally subsidized 

Units added above the contracted level may receive credits at 2/3 the annual rate of 

base credits over the remaining years in 

the compliance period 

Same as for tax-exempt bonds 

At least 50% of units are very low income* 

;i 

~ 

c: 

~ 

~ 0.. 

> a' 

c 

~ 

0 

...,., 

~ :I 

[ 

"0 

a 

~r ... 

3: 

0 

0.. 

~ 

u;-

~ 

~ 

l..u 
Table 11 .9 COMPARISON OF REAL ESTATE TAX PROVISIONS (continued) 

Item 

Rent Limitation 

Compliance Period 

State Volume Cap Non-Federally Subsidized 

Federally Subsidized 

Compliance Penalty 

Expiration Date 

At-Risk Rules 

Deductibility of Losses 

Tax Exempt Bonds 

Multi· Family Rental 

Income Requirement 

Qualified Project Period 

Compliance Penalty 

Loss Limitation 

*Definitions 

Low Income 

1985 Law 

No limit for real estate 

TRA86 

Rent cao be no greater than 30% of qualifying income (either 50% or 60~ of area median) Income r~uirement and rent limitation 

must be met for 15 years 

New annual a.uthority of $ t .2~ per resid~nt per 

year, admtn. bY. state housmg authonty Not subjeCt to credit cap (although tax-exempt bond cap may apply) Accelerated portton of credit (relative to a 

15 year credit} is recaptured with interest 

December 3 t • 1989 

Repeal real estate exception. except Jrd-partY, 

non-recourse debt secured by real eslate is 

considered at risk 

Unlimited. tax-exempt bond Bond authority subject to private-purpose bond 

authonty state volume cap 20% of households (15% in target- Either 20~ of unirs are very low income-* or 

ed area.s). have incomes <80~ of 40% are low income• 

area median or 25% of fiouseholds 

have incomes <70% of area median 

Max {10 years. 50'% of loan term. Minimum period is 12 years ~riod of Section 8 Assistance~ Bonds retroactively taxable 

No provision 

Bonds retroactively taxable; interest not 

deductible 

Rental losses may _n_91 be used tO offset active 

income: $25,000 eJtception ror active rental 

losses by indtv .. phase-out at high incomes 

1985 Law - 85% of households have incomes ~ SO% of area median. adjusted for family size 

TR86 - Incomes 5 60% of area median. adjusted for family size 

Very Low Income 

TRA86 - Incomes 5 50% of area median. adjusted for family size 

~ 

~ 

~ 

~ ~ 

tD 

c 

§ 

g 

~ 3 

z 

n 

c 

~ 

...... 

a 

0 

a. 

0 

:;:, 

~ 

"' 0 

:;:, 

.............. ......... 
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The Use and Abuse of Rental Project Models 345 

Figure I 1.5 Flow Chart of Treasury Rental Investment Calculator 

I. Input Data 

NAMELJST input parameter~ override tlefauh vttluts. 

2. Initial Investment (period 0) 

Net ca~h flow .. · do~m payment 

• closing COStS 

+ initial tu benefit from CPJT 

3. Generate Flows 

Determined lly initi11l values or land and structure. 

renHo-value and opensting cost·to-va.lue ratios. 

and rates of inflation 

4. Generate Sales Prices and Holding Periods 

For a 11iven year; 

I. Find the sal~ pri~ for e11ch possible holding 

period that gives a typical Investor a competitive 

rate or return. 

2 The optimal holding period and 'ales pnce gtve 

madmum sales pr~ In (I) 

5. Compute the Consequences of 

Optimal Holding Pattern 

The optimal holding period for the orlgnal owner 

is computed as above. except that the purcha..e 

price Is fixed and the l8JI benefits of CPIT are 

included 11nd the original owner's tu nue is used 

6. Analysis of Investment (initjallnvestor) 

Present value is based on initial cost. 

and taJtes tRR is found Iteratively. 

7. Optional Search 

Vary initial rent-to-value ratio or target 

internal rate of return until aU PVs = 0 

(i.e .. everyone gets competitive rate of return) 

Done search? 

Marginal tax rates 

8. Output 

For each investor; 

Initial costs (including CPJT for first) 

Pre·tax cash now 

Ct~sh llow tax t>enetits 

After-tax cash Jlow 

Oosing <'OSIS, capital gain ta~es . recapture 

Either after-tax PV anti IRR tbr first investor 

or IRR for ftll investors or user cost. 

Input parameters 

Down "' payment and closing costs 

r+ Tax benefit from CPIT 

Net cash flow 

Land "' 

Operating Costs 

Rents 

Sales "' prices 

Holding periods 

Optimal holding pattern 

Depreciation and amortization of CPIT 

Closing costs. capital gains, recapture 

After-tax flow 

l 

PV of investment and IRR before· 

and after-tax for initial investor 

Search "' on target parameters? No 

_i_ 

Yes 

.. 

All PVs = 0? Yes I 

r 

No "' 

+ ~ Adjust Target Parameters j 

Display Output l 

["'"' 
346 Len Burman/Tom Neubig/Gordon Wilson 

value of the investment. The property would be purchased if the net present 

value of the investment were at least zero. 

Most real estate project models treat the sales price in each period as an 

exogenous stream (Hendershott and Ung, 1984, is the notable exception). The 

Treasury model computes the sales price in each period that would give a 

subsequent investor who behaves optimally the same rate of return as his/her 

best alternative investment (i.e.. net present value equals zero). The 

calculator iterates over possible holding periods and finds the bid price for 

each holding period. The sales price in any period is equaJ to the highest 

bid price, which corresponds to the optimaJ holding period. 

Computation of the optimal holding period requires knowledge of all future 

sales prices. At the terminal period (N), the structure is assumed to have 

totally deteriorated. so sales price would be equal to the value of the land. 

At period N-1, all future sales prices are known. The decision is whether to 

hold for one period or to sell the propeny for its land value. If the 

propeny is held, the sales price in period N-1 is the present value in period 

N-1 of cash flows in the last two periods. Working backwards, all future 

sales prices are thus always known. The calculator computes the sales price 

and holding period in each period by computing the optimal holding period for 

some sales price, then raising or lowering the sales price depending on whether the present value is positive or negative. and repeating the computation 

until the present value is driven to zero. 

The alternative modes of operation. which are set by parameter, provide a · 

way of altering some of the inherent assumptions in the basic mode computation. Using option J. the initial rent-to-value ratio is varied until the 

initial investor's net present value is driven to zero. This provides a measure of the user cost of rentaJ housing. In the second option. the calculator 

finds the change in the internal rate of return for all investors (i.e .. the 

rate of return such that all earn a net present value of zero). This gives a 

measure of how changes in policy or other parameters would affect the return 

on capital assuming that the supply of capital is fixed and aJI other prices 

remain constant. After a tax increase. for example. the change in the 

internal rate of return would indicate how much interest rates would have to 

fall to make the hypothetical investor just as well off as before the tax. 

The internal rate of return also allows measurement of effective tax rates. 

FOOTNOTES 

1 For example. some analysts predicted that residential ent ~ would increase by more than 

twenty percent. while others predicted long-run rent in :l ~e~ of s~ than ten percent. For 

low-income housing. the disparity in estimates was muc.: h wider. 2

This is arbitrary. In fact . because of the weak recapture provisions on low-income housing. 

investors would oflen find it profitable to sell before 15 years. See Table 11 .5 for examples. 

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The Use and Abuse of Rental Project Models 347 

3 Hendershott and Ling (I 985) argue that different income and expense streams should have 

different discount rates depending on their relative certainty. Nonetheless, there is no 

empirical evidence showing some future streams to be more certain than others. Summers (I 986) 

argues that business planners do not discount relatively sure streams of tax deductions at a 

lower rate than other risk.ier expenses and income. 4 Unlike the internal rate of return. which may only be calculated iteratively, the equivalent 

coupon rate can be computed based on a simple formula . 

The equivalent coupon rate is the value i that solves the equation. 

N -t -N 

tt•l iY(l +y) + Y(l +y) = X, 

where N is the holding period of the investment ( 15 years in the example), Y is the initial 

investment ($5 ,150). y is the discount rate (8%). and X is the gross present value of returns 

to the investment ($7 ,693). The equation simply requiresthatthe "equivalent" bond, which pays 

rate i. pay annual interest (the first part of the equation) and repay the principal at the end 

of year N (the second part) with present value equal to the present value of returns to the 

rental investment (X). 5 For example, the five percentage point drop in mortgage interest rates since 1981 almost 

certainly has had more effect on rents and returns to investors than any of the tax-shelter 

provision in the TaJt. Reform Act of I 986 will have. even under the most extreme assumptions about 

other parameter values. 6 The holding period is also important in determining the rate of return to the investor. 

which will generally depend on when the project is sold. 1 Endogenous determination of holding periods is the essential feature of timber. oil. and 

other resource models. In this k.ind of model, the analyst is interested in how long an investor 

will hold a tree (or oil well) before cutting (or drilling). 8

The term churning refers to the frequent sale of an asset in order to maximize the value of 

tax benefits. The primary tax benefit to churning, at least before TRA86, was that new 

investors would get a "step-up in basis. " while the seller would not be fully taxed on the gain 

due to weak recapture rules. In other words. each new purchaser would be able to take new 

accelerated depreciation deductions based on the purchase price of the asset. rather than the 

old depreciated basis. 9 Hendershott and Ling ( 1985) independently developed a model similar to the one described 

here. 10Technical documentation and FORTRAN 17 source code for the model is available upon 

re~uest. 1

The user cost is the most common. and most commonly misinterpreted. output of rental 

project models. Section V discusses the misinterpretation of user costs in detail. 

2 Holding other parameters constant, model simulations indicate that pre-TRA86 investors in 

hi~h taJt. brackets earned far higher rates of return than investors in low brackets. 3

The model uses computed internal rates of return for r and rb . 1 4 • See Musgrave and Musgrave, 1983. pp. 185- 186. 1 5 Recapture provisions penalized sale of the property before the end of the depreciation 

period ( 19 years in 1985) by subjecting capital gain which corresponded to deductions in excess 

of straight-line depreciation to taxation at ordinary rates rather than the lower capital gains 

rates. 1 6

Table II .9 compares the rental housing provisions in the Tax Reform Act of 1986 with those 

of pre- 1986law. TRA86 i net udes a new tax credit for low income housing. which may encourage 

churning if it is extended beyond its planned expiration date. 17 The low-income housing c redit provides a credit-equivalent of greatly accelerated 

depreciation with a harsh recapture provision during the first fifteen years after the c redit 

begins. This c redit will encourage churning of qualifying lo~ income properties every fifteen 

years. However. since the credit provision is temporary. the incentive to churn low-income 

housing will be sharply reduced if the credit is allowed to expire as scheduled in 1989. 18 

TRA86 may make effective tax rates quite different for individuals in the same tax bracket. 

For example. a high-income investor with !>ources of passive income will find investing in 
348 Len Burman/Tom Neubig/Gordon Wilson 

loss·producing real estate more advantageous than a similar investor with portfolio and labor 

income only. Since investors with incomes below $200,000 will only be able to currently claim 

low·income housing credits equal to their marginal tax rate times $25.000. individuals in the 

top bracket (33%) will be able to claim the most credits. 19 To qualify for the low· income housing credit, either 20% of rental units must be rented to 

households with incomes not greater than 50% of area median income or 40% of units must be 

rented to tenants with incomes not greater than 60% of area median income. 2 0 The value of tax~xempt bond financing includes a possibility for leveraging the value of 

the subsidy. In the case of elderly housing, for example, the non·low·income units might well 

be rented to tenants who can pay market rents. The result is that with a 20% low·income 

occupancy requirement, the valueoftax·exemptbond financing is leveraged by as much as four to 

one. In other words. since the bond financing is for the whole project, four non·low·income 

units are subsidized for every one low·income unit. However. in other C3Se$, rents might be 

depressed .. or risk might be higher for the entire housing project. which would mean that the 

leveraging argument would be less valid. The table assumes no leveraging. 21 To qualify for bond financing, subsequent owners would have to substantially rehabilitate 

the property. which was not reflected in the model runs. To the extent that rent increases 

would not cover the cost of rehabilitation. the value of future subsidies may be 

exayerated. 

The low· income housing credit is scheduled to expire after 1989. many years before any 

ACRS low·income housing would become eligible (since a project has to have been in service 

for at least 15 years to qualify for the credit). The low·income housing credit examples in 

Table 11.5 answer the question: "how would investors value a property under TRA86 if they 

expected the low· income housing credit to be extended permanentJy?" 

Note that there is no initial investor column in row (5) because the credit only applies to 

second and subsequent investors. 2 3 See also Table 11.7. which is discussed in section C. 2 4 Note that "predictability" does not mean that there can be no random shocks. A rational 

expectations equilibrium could exist if the optimizing behavior of economic agents conditional 

on their expectations produces market prices whose means are equal to those expectations. 

However, the rental project model would only produce user costs that represent market rents if 

investors were risk neutral and the investors' optimization problem satisfied the conditions for 

,. certainty equivalence" (Sargent, 1987). Proof of certainty equiva.lence is beyond the scope of 

thi~ ~~~ issue is reminiscent of Miller's (1977) model of the effect of taxes on ownership o£ 

debt and equity and subsequent analyses. In Miller's model. there is some marginal tax rate at 

which an investor is indifferent between holding debt and equity. Investors with higher 

marginal tax rates hold only equity. and investors in lower tax brackets hold debt. In this 

framework. the marginal investor determines the relative cost of debt and equity in 

equilibrium. 

Of course. as Miller noted . equity is held by non-taxable institutions and debt is held by 

high tax bracket investors. Subsequent general equilibrium models of portfolio choice under 

risk with many classes of investors have shown that portfolio diversification between debt and 

equity is rational. (See Stem rod . 1985. or Gal per. Lucke. and Toder. 1987 .) In a model with 

risk. every investor is a marginal investor. buying assets until marginal risk.·adjusted after· 

tax rates of return are equalized. Thus. the simple device of considering a single investor or 

class of investor as the marginal actor is inappropriate. 2 6 The average user cost would always be less than the user cost of the "average" investor. at 

least for the assumed pre· TRA86 parameters. Figure II . 2 shows that user costs were a concave 

function of marginal tax rates. which implies this result. 2 7 The hypothesis of no relationship between adjusted user cost and rents is not rejected at 

the 5% level. The estimated regression equation is 

CPI Rent = 0.819 + 

(38.8) 

0 .0867 

(15.2) 

Time + 0.0432 

(2. 1) 

User Cost. 

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The Use and Abuse of Rental Project Models 349 

T-ratios are in parentheses. The adjusted R2 with eight degrees offreedom is 0.993. However, 

if user cost is excluded, the adjusted R2 is 0.990. Note that the small sample size and obvious 

collinearity between user cost and the trend variable make this a dubious statistical test. It 

suggests. however. that if user cost has any contemporaneous effect on rents, it is likely to be 

dwarfed in importance by other factors. 28To keep things in perspective, one should note that non-tax factors contribute{! 

significantly to predicted changes. 29This is not true in the case of low-income housing. However, presumably low-income 

housing tax preferences are designed to distort behavior. 30 Note that a rental market is not absolutely necessary. The project model's "rents" are 

really imputed rents or the opportunity cost of capitaL 

REFERENCES 

Bradford, David F. and Don Fullerton (1981), "Pitfalls in the Construction and Use of Effective 

Tax Rates, • in C.R. Hulten, ed .. DepruiOTion. Inflation , and the Taxation of Income From 

Capital. Washington. DC: The Urban Institute Press. 

DeLeeuw. Frank and Larry Ozanne ( 1979). "The Impacts of the Federal Income Tax on Investment in Housing." Survey of Current Business. 59. December. 50-61 . 

Fullerton. Don, Yolanda Henderson, and James Mackie (1987). "Investment Allocation and 

Growth Under the Tax Reform Act of 1986." Chapter 6 in this volume. 

Galper. Harvey. Robert Lucke. and EricToder (1987). "General Equilibrium Model of Differential Asset Taxation." mimeo. 

Gravelle. Jane G. (1985). "U.S. Tax Policy and Rental Housing." Congressional Research 

Service Report No. 85-208E. 

Gordon. Roger H .. James R. Hines. Jr .• and Lawrence H. Summers (1986). "Notes on the Tax 

Treatment of Structures," NBER Work.ing Paper No. 1896. 

Harberger. Arnold C. (1962). "The Incidence of the Corporation Income Tax," Journal of 

Political Economy. 10. 215-240. 

Hendershott. Patrie H .• James R. Follain, and David C. Ling (1986). "Real Estate and the 

Tax Reform Act of 1986. " NBER Work.ing Paper No. 2098. 

Hendershott. Patrie H. and David C. Ling (1984). "Trading and the Tax Shelter Value of 

Depreciable Real Estate," National Tax Journal. 37. 213-223. 

Mayo. Stephen K. (1981). "Theory and Estimation in the Economics of Housing Demand. " 

Journal of Urban Economics. 10. 95-116. 

Miller. Merton H. (1977), "Debt and Taxes," The Journal of Finance. 32. 261-275. 

Musgrave, Richard A. and Peggy B. Musgrave (1984). Public Finance in Theory and Practice, 

New York: McGraw-Hill Book Company. 

Sargent. Thomas J. (1987). Dynamic Macroeconomic Theory. Cambridge: Harvard University 

Press. 

Shoven. John B .. and John Whalley ( 1984). "Applied General-Equilibrium Models ofTaxation 

and International Trade." Journal of Economic Literature. 22. 1007-1051 . 

Slemrod. Joel (1983). nA General Equilibrium Model of Taxation With Endogenous Financial Behavior. " in Martin Feldstein. ed .. Behavioral Simulation Methods in Tax Policy 

Analysis. Chicago: University of Chicago Press. 

Summers. Lawrence H. (1986). "Investment Incentives and the Discounting of Depreciation 

Allowances. • NBER Working Paper No. 1941 . 

Summers. Lawrence H. (1987). "Should Tax Reform Level the Playing Field?". NBER 

Working Paper No. 2132 . 

o U.S. COV£RNI'I'I£.NT PRINT INC OrF' IC£ :1987·181-903164713