I I I I 11 THE USE AND ABUSE OF RENTAL PROJECT MODELS I Leonard E. Bunnan, Thomas S. Neubig, and D. Gordon Wilson I I I. INTRODUCTION I 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 I 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 I investment's economic and tax characteristics. Despite the sophistication of these models. or perhaps because of it, analysts predicted widely varying 1 effects of tax refonn proposals. How could analysts using similar models in I 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 I 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 I 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 I rental project models as tools for forecasting market-wide responses to tax I policies. I 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 I 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 I for assistana in tire preparation of tire manuscript and tabh•s. 307 I I 308 Len Burman/Tom Neubig/Gordon Wilson I II. WHAT IS A PROJECT MODEL? I A. DEFINITION A project model simulates the cost and income streams that would be I 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 I investment was worthwhile. More sophisticated varianrs of this kind of analysis, such as the OTA model. can determine endogenously how long investors I 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. I B. KINDS OF RENTAL PROJECT MODELS I 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 I 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 I dynamic model that has been developed by OTA. l . Spreadsheet Models I Table II . 1 illustrates a simple spreadsheet model for a hypothetical real I 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 I 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 devel­ I oped 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 I 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 2 the ACRS low-income housing depreciation schedule. The nominal value of the I 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 I inflation in structure values is assumed to just offset economic depreciation. The initial rent is assumed to be I 0 % of value ($4. I00) and initial operating costs are assumed to be 2.5 % of the structure value. Both grow at a constant I annual rate of 3 %. I .. • .. .. • • • • • .. .. .. .. .. .. .. • • - Table 11.1 Sample Spread Sheet Calculator for ACRS Low-Income Housing lnve;unent A~>um~tions Generatal Stream of Income and Dedut:tions for Rental Pro~rt:r: Operating Mortgage T;u Tax~tble Pre-Tax TIU Alter-Tal Purchase Year Rent Costs Princ•eaJ lntere>"t Deerec. Income Cash Aow Benefit lncomt: Land ss.ooo Structure 530.000 I S4.100 $900 $36,900 $4.059 $5.100 -$5.959 -SI ,044 $2.9110 Sl .935 Total Prit:e $35.000 2 S4 .223 $921 $36.715 $4.039 $4 ,1100 -$5,543 -$941! $2,771 $1 .1123 Rehahilitation 3 S4 .350 $955 $36.509 54 .016 $4 ,200 ·S·U121 -51150 $2.411 Sl.561 Pcn:entage 20 0% 4 $4 ,4110 59113 $36.280 $3.991 53.900 -$4.394 -$7411 $2.197 $1.449 Dollar Cost Sli.OOO 5 S4 .615 Sl .OIJ SJ6.027 $3,963 $3,600 ·53.961 -Sii43 $1,9111 SI .JJIC New Bash S36.000 6 $4 ,753 $1.043 $35 .745 $3.932 $2,100 -$1,311 -$535 $1 ,161 S6!6 T<llal Cost $41 ,000 7 $4 ,1196 $1,075 $35.433 53.1!911 Sl .l!OO -51 .877 -$423 S93R $515 II $5,0-U $1.107 $35.0116 SJ.1159 SI.SOO $1.424 ·S309 $712 $403 Mo•tgagl' 9 SS. I94 $1 ,140 $34,701 $3,1117 SI.SOO -$1.:!63 ·S191 $632 $441 lntl!re:.t Rate II 0~ 10 SS .350 $1 ,174 $34.274 $3,770 SI.SOO ·SI ,09S ·S69 $547 $4711 ;i Tcnn (~earl>) 30 II SS .SIO $1 ,210 $33.1100 SJ.71K $1 ,200 -$617 SS6 $309 $365 '.t Borrowetl 90.0\11: 12 SS.67S $1.246 $33.273 $3.660 $1 .200 -$430 SillS $215 S400 n Ltmn Amount 536.900 13 SS.II46 $1.2113 $32.6119 $3.596 $1.200 ·S233 S31K $117 $435 c Ptt~IIICIII $4.244 14 $6,021 $1,322 $32.040 $3.5:!4 $1.200 -$25 $455 SIJ $467 V>n IS S6.:!02 $1.361 $31.3~0 53 .445 $1.200 $195 $5% -S9R $4911 T1 :uhiiCII<lll C:ost~ 16 $30.5:!1 py, § Pct ccn t~c J .0\11: $41 ,727 $9.160 SJ3. 1KK $24 .337 ·S24.95H -$3 .763 $1~ . 479 SK.716 0.. D<'llao Co>t $1 .050 lnnwl lnvt: ~lment S5 , 150 )> Comoutation of Gam or Loss on Sale (Undiscountal) CTc V>n +- Sule Puce $43.790 0 Pu1 ;uncters · Mortgage Pnncipal ·S30.S21 ....... - Transaction Costs -$1 ,31 4 ::::0 n D<·po \'dation Rate 3.0% · Capital Guins Ta:o. -S4.9S.l :::3 Operating CosllValue 2.5% = Net Return $7.003 0) Initial Rent $4,100 Rent lntlation 3 0% .,.., lanll lnllation 3.0% 0 (ij Stt U\.turc lntlation 3.0% Present Value of Returns to Investment (') Di~ount Rule II 0~ Doscount Factor 92.6% Initial Cost ·SS.ISO -::: Ta., Rate 50 . 0~ Income Stream $8,716 0 0. Capital Gains Rate 20.0% Gatn on Sale $2.208 !!. Net Return $5,774 112.1 5I: ., Gross Return $10.924 212. 1% w Coupon Equivalent $1 .0117 2 1.1~ 0 \0 I 310 Len Burman/Tom Neubig/Gordon Wilson I 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. I The project model impHcitly assumes that the income and cost streams repre­ sent expected values and that risk may be accounted for in the discount rate 3 I (or rates ) 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 I value of tax incentives. This spreadsheet reports a variant on the internal 4 rate of return-the "equivalent coupon rate" -which represents for a tax-exempt I 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%. I 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 I 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 I tax. Thus, the initial loan-to-value ratio as well as assumptions about refinancing are important.