Court Opinion

ID: 4332858
Source: CourtListenerOpinion
Date Created: 2018-11-14 00:54:16.670475+00
Date Added: 2024-06-11T14:19:52.502649
License: Public Domain

ESTATE OF FRED O. GODLEY, DECEASED, FRED D. GODLEY, ADMINISTRATOR CTA, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, RespondentGodley v. CommissionerNo. 19880-94United States Tax CourtT.C. Memo 2000-242; 2000 Tax Ct. Memo LEXIS 284; 80 T.C.M. (CCH) 158; T.C.M. (RIA) 53984; August 4, 2000, Filed *284  Decision will be entered under Rule 155.  C. Wells Hall III, for petitioner.James E. Gray, for respondent.  Gale, Joseph H.GALEMEMORANDUM FINDINGS OF FACT AND OPINIONGALE, JUDGE: Respondent determined a deficiency of $ 696,554 in petitioner's Federal estate tax.Unless otherwise noted, all section references are to the Internal Revenue Code in effect for the date of decedent's death, and all Rule references are to the Tax Court Rules of Practice and Procedure.After concessions, we must decide the fair market value of decedent's interest in five partnerships as of November 11, 1990.FINDINGS OF FACTSome of the facts have been stipulated and are so found. We incorporate by this reference the stipulation of facts, the supplemental stipulation of facts, and the attached exhibits.Decedent was a resident of Charlotte, North Carolina, when he died testate on May 11, 1990. Lisa G. Gilstrap, Gregory Godley, and Kimberly E. Godley, all of whom are grandchildren of decedent, were appointed coexecutors of the Estate of Fred O. Godley (estate). At the time of filing of the petition in this case, the address of the coexecutors was in Charlotte, North Carolina. After*285  the filing of the petition, the original coexecutors of the estate resigned, and Fred D. Godley (Fred Jr.), one of decedent's sons, succeeded as administrator c.t.a. of the estate. A Federal estate tax return was timely filed, under extension, on or about August 14, 1991. The estate elected to use the alternate valuation date of November 11, 1990.At the time of his death, decedent owned a 50-percent interest in each of the five general partnerships in issue, with the remaining 50-percent interest in each owned by Fred Jr. Four of these partnerships, which were formed in 1978, owned and operated housing projects for elderly tenants known as: Monroe Housing for the Elderly (Monroe); Clinton Housing for the Elderly (Clinton); Rocky Mount Housing for the Elderly (Rocky Mount); and Charlotte Housing for the Elderly (Charlotte), collectively referred to the housing partnerships.For each of the housing partnerships, Fred Jr. was permanently established as the managing partner. The partnership agreements for the housing projects contained the following provisions:     Section 2.02 MANAGEMENT OF PARTNERSHIP. The overall   management and control of the business and*286  affairs of the   Partnership shall be vested in the managing Partner (the   "Managing Partner") designated herein, provided, however, no act   shall be taken or sum expended or obligation incurred by the   Partnership, or any Partner, with respect to a matter within the   scope of any major decision ("major decision") affecting the   Partnership, unless such major decision has been approved by   Partners holding collectively a 75% interest in the Partnership.   * * *"Major decisions" included the acquisition and sale of land or partnership property, financing, expenditures in excess of $ 2,500, entering into major contracts, or any other decision or action "which materially affects the Partnership or the assets or operation thereof."   Section 2.03 DAY TO DAY MANAGEMENT.     (a) Subject to the limitations set forth in this Article   II, the day to day management of the Partnership's business   shall be conducted by the Managing Partner, Fred D. Godley, Jr.,   and his agents and designees. Such Managing Partner subject to   the limitation set forth in Section 2.02 above shall implement*287     the major decisions of the Partners. * * *Day-to-day management included duties such as effecting property acquisitions as decided by the partnership, protecting title, paying debts, and setting aside reserves for replacement of assets or to cover contingencies.   Section 4.05 DISTRIBUTION OF NET CASH FLOW.     (a) The net cash flow of the Partnership shall be   distributed to the Partners annually or at such more frequent   intervals as the Managing Partner shall determine. The "net cash   flow" of the Partnership as used herein shall mean the net   profits derived from the property owned by the Partnership as   computed in accordance with normal and accepted accounting   principles except that (i) depreciation of buildings,   improvements, furniture, fixtures, furnishings and equipment   shall not be taken into account, (ii) mortgage amortization paid   by the Partnership shall be considered a deduction; and (iii)   any amounts expended by the Partnership in the discretion of the   Partners for capital improvements or set aside by the Managing   Partner as a reserve for the replacement*288  of assets of the   Partnership or other contingencies shall be considered a   deduction. Borrowings of the Partnership shall be excluded in   computing net cash flow.Although Fred Jr. was managing partner, decedent was actively involved in the housing partnerships. He regularly visited the housing projects to inspect the property and to attend to tenants' concerns, maintenance, and the like. He made his own decisions, without consulting with Fred Jr., when such issues arose. Moreover, decedent had a long history as a businessman in the field of construction and brought his sons into the business. Finally, when he was engaged in a business enterprise, he was almost always the person in charge.Upon the formation of Monroe, Clinton, and Rocky Mount, decedent and Fred Jr. each owned a 45-percent general partnership interest and a third party, Frank M. McCool (McCool), owned the remaining 10-percent general partnership interest. McCool was an engineer and worked as a general manager for a company that Fred Jr. operated. Decedent and Fred Jr. each owned 50 percent of Charlotte from inception. McCool predeceased decedent, and in 1985, decedent and Fred Jr. purchased*289  McCool's three 10-percent general partnership interests from his widow for a total of $ 65,000. Thereafter and until decedent's death, decedent and Fred Jr. each owned a 50-percent general partnership interest in each of the housing partnerships.The housing partnerships held multifamily rental housing projects operated and maintained under Housing Assistance Payments contracts (HAP contracts) with the U.S. Department of Housing and Urban Development (HUD) pursuant to the United States Housing Act of 1937, ch. 896, 50 Stat. 888, currently codified at 42 U.S.C. secs. 1437-1437x (1994), and the Department of Housing and Urban Development Act, Pub. L. 89-174, 79 Stat. 667 (1965), currently codified at 42 U.S.C. secs. 3531-3547 (1994). The HAP contracts were executed by HUD in order to provide, through local public housing agencies, financial assistance to eligible families of lower income in renting housing. Pursuant to these HAP contracts, the Government pledged to pay a certain annual contribution to the applicable public housing agency on behalf of the contracting housing partnership. Housing assistance payments made to the housing partnerships*290  covered the difference between the contract rental rates agreed to under the HAP contracts (contract rents) and that portion of the rent payable by eligible families determined in accordance with HUD-established schedules and criteria. The term of the HAP contracts for Monroe, Charlotte, and Rocky Mount was 30 years and for Clinton was 20 years.Also, in general the HAP contracts entitled the owner to housing assistance payments in the amount of 80 percent of the contract rent for a period not exceeding 60 days (i) in the event a unit covered under the HAP contract (covered unit) was not leased within 15 days of the effective date of the HAP contract or (ii) upon the vacancy of a covered unit by an eligible family. In the event a covered unit remained vacant for a period exceeding 60 days, the owner could, in general, request additional payments in an amount equal to the principal and interest payments required to amortize that portion of the debt service attributable to the vacant unit for up to 12 additional months.On March 1, 1980, after the formation of the housing partnerships, a fifth general partnership, Godley Management Association (GMA), which was owned 50 percent each*291  by decedent and Fred Jr., was formed for the purpose of managing the operations of the housing partnerships. The formation of GMA for this purpose was required by HUD. As of the valuation date, GMA held no real estate or other fixed assets and served only as a management company for the housing partnerships to oversee leasing, maintenance, and repair in compliance with HUD requirements. GMA received a management fee from each of the housing partnerships equal to 10 percent of rental income.On the Federal estate tax return, decedent's interests in the five partnerships were reported at a fair market value of $ 10,000 each. At the time of decedent's death, the partnership agreement for each housing project contained a provision granting Fred Jr., or his personal representatives, heirs or assigns, the option to purchase decedent's interest in said partnership for the sum of $ 10,000.  1 This option provision was contained in each of the original partnership agreements. On December 31, 1990, Fred Jr. exercised these options to purchase decedent's interests in the four housing partnerships for the payment of the option price of $ 10,000 for each partnership interest, or $ 40,000. On*292  March 12, 1990, decedent and Fred Jr. executed a similar option with respect to decedent's interest in GMA. The estate also accepted a cash payment in the amount of $ 10,000 from Fred Jr. for decedent's 50-percent interest in GMA.  2*293  From 1985 through 1994, Fred Jr. was the defendant in an equitable distribution suit brought by his former spouse, Jean H. Godley. An Equitable Distribution Judgment was filed by the District Court of Mecklenburg County, North Carolina, on January 1, 1991. In the equitable distribution proceedings, the nature of the foregoing option provisions was in issue, and testimony was presented concerning the same. Also, depositions were taken of Fred Jr. and decedent in connection with the equitable distribution proceedings on the same issue. Fred Jr. testified by deposition and at trial that the options "[were] done for the purpose of circumventing inheritance taxes" and "[were] a gift". Decedent testified by deposition that the options "would simplify at my death the closing of my estate, and also would help establish to the government our worth whereby he [i.e., Fred Jr.] could buy it * * * at a reasonable price"; and in answer to the question whether the options "[were] a gift that you made to him [i.e., Fred Jr.] at the time you signed the contract", decedent replied "That's right." The Judgment of Equitable Distribution held as follows:     239. All of the evidence*294  indicates and the Court finds that   there was no consideration for Defendant's father giving to   Defendant options to acquire Defendant's father's interest in   the five partnerships. Both Defendant and his father testified   UNEQUIVOCALLY that the options were gifts to Defendant from   Defendant's father. The Court finds such testimony to be   credible and further finds that these options were gifts to   Defendant from his father. [Emphasis added.]At issue in the equitable distribution litigation was the value of Fred Jr.'s 50-percent general partnership interest in the partnerships. In this regard, Fred Jr. was asked whether the idea of HUD-subsidized projects originated with him or decedent, and he testified that he could not recall. As part of the litigation, both the plaintiff (Fred Jr.'s former spouse) and the defendant (Fred Jr.) produced expert witnesses and reports regarding the value of Fred Jr.'s 50-percent general partnership interest in the partnerships as of December 1989. The court accepted the plaintiff's expert appraisal of GMA prepared by Mitchell Kaye (Kaye). In his appraisal, Kaye estimated the net fair market value*295  of GMA as of December 31, 1989, to be $ 450,000 and concluded that Fred Jr.'s 50-percent interest in GMA had a net fair market value of $ 225,000 as of December 31, 1989. The court also accepted the expert appraisals of Robert O. Beck III (Beck), who relied on David A. Dvorak (Dvorak) in valuing the improved real estate held by Monroe and Charlotte, and Tom J. Keith (Keith) in valuing the improved real estate held by Clinton and Rocky Mount. Beck valued decedent's housing partnership interests as follows:             Total Value of     Fred Jr.'s      Entity     the Partnership    50% Interest      ______     _______________    ____________     Monroe       $ 469,307      $ 234,653     Clinton        158,391       79,196     Rocky Mount      187,287       93,643     Charlotte       198,005       99,003Dvorak and Keith both qualify as experts on valuation of real estate, and Kaye and Beck qualify as experts on the valuation of businesses.On August 2, 1994, respondent mailed*296  a notice of deficiency for Federal estate tax. The values of decedent's 50- percent partnership interests determined by respondent in the notice were derived by averaging values of decedent's interests as determined under a net asset approach and an income approach after applying a 10-percent discount for lack of marketability to each.  3 The values were as follows:Partnership    Income Value    Asset Value     Average___________    ____________    ___________     _______Monroe       $ 577,689     $ 337,125     $ 457,407Clinton        186,039      72,933      129,484Rocky Mount      439,960      320,782      380,371Charlotte       390,087      309,692      349,890GMA          431,356      230,020      330,688In calculating income value, respondent applied a capitalization*297  rate of 10 percent.In a report prepared for this Court in valuing decedent's interests, Beck concluded that a lack of marketability discount of 25 percent and a lack of control discount of 15 percent should apply to the values derived in his valuation of Fred Jr.'s interests in the housing partnerships, which would result 4 in values as follows:     Partnership            Value     ___________            _____     Monroe             $ 149,591     Clinton              50,487     Rocky Mount            59,697     Charlotte             63,114In addition to the partnerships in issue, at the time of his death, decedent and Fred Jr. each owned 50 percent of the stock of Godley Realty, *298  Inc. (Godley Realty), and decedent owned a 25- percent interest and Fred Jr. owned a 75-percent interest in Concrete Panel Systems, Inc., of North Carolina (CPSI). In the notice of deficiency, respondent determined that the value of decedent's interest in Godley Realty was $ 225,048 as of the valuation date and the value of decedent's interest in CPSI was $ 34,271 as of the valuation date.  5 Respondent's valuations of Godley Realty and CPSI were based, in part, upon the November 11, 1990, balance sheets, which reflect accounts payable to the five partnerships in issue at full face value as of that date as follows:   Partnership     Godley Realty      CPSI   ___________     _____________      ____   Monroe        $ 376,078       $ 38,750   Charlotte        237,753        16,500   Rocky Mount       278,528        9,000*299     Clinton         75,399        None   GMA            None         1,550             ________       _______    Total         967,758        65,800As of December 31, 1989, adjusted balance sheets of Godley Realty and CPSI showed accounts receivable of the housing partnerships, with Godley Realty and CPSI as payors, as follows:   Project       Godley Realty       CPSI   _______       _____________       ____   Monroe        $ 359,487       $ 32,750   Charlotte       241,222        11,500   Rocky Mount      284,103         None   Clinton         81,049         None             ________        _______   Total         965,861        44,250In order to finance the acquisition and construction of Charlotte, Monroe, and Rocky Mount, bonds were issued by the local public housing agency as the construction lender. *300  To secure the payment of the bonds, the housing partnerships, the local nonprofit housing development corporation, and a trustee entered into trust indentures requiring the creation of various trust funds, including:     (a) THE MORTGAGE ACQUISITION FUND, which shall be disbursed   for the purpose of paying in full the Construction Note and   acquiring an assignment of or satisfying and releasing the   Construction Deed of Trust * * * or which shall be applied to   the redemption of the Bonds * * * in the event of the failure to   satisfy those requirements.     (b) THE REVENUE FUND, into which all Revenues shall be   paid, except as otherwise provided * * *     (c) THE PRINCIPAL AND INTEREST FUND, to be funded monthly,   and which shall be held by the Trustee for disbursal by the   Trustee * * * from time to time solely for the purpose of paying   the principal of an interest on the Bonds * * * and * * * to pay   the Trustee's fees from earnings thereon;     (d) THE DEBT SERVICE RESERVE FUND, which shall be funded   upon Completion of Construction from*301  the Mortgage Acquisition   Fund, in an amount equal to the Debt Service Reserve Requirement   ($ 167,100), and shall, subsequent to the Completion of   Construction, be disbursed by the Trustee solely to pay the   principal of, premium, if any, and interest on the Bonds. * * *     (e) THE INSURANCE AND TAX ESCROW FUND, to be funded   monthly, from which the Trustee shall pay the premiums of all   insurance on the Project required by this Indenture and all   taxes, assessments or governmental charges except utility   services * * *     (f) THE MAINTENANCE FUND, to be used upon the written   request of the Owner, with the concurrence of the Trustee, for   extraordinary maintenance * * *     (g) THE REPLACEMENT FUND, to be used upon written request   of the Owner with the concurrence of the Trustee, for   extraordinary repair and replacement * * *     (h) THE OPERATING FUND, to be funded monthly, which shall   be disbursed to make monthly payments to the Owner for operation   of the Project pursuant to the requirements of its then current*302     Budget. * * *     (i) THE PROJECT RESERVE AND SURPLUS FUND, to receive any   monies not required to be disbursed to any other fund or account   * * *     (j) THE BOND REDEMPTION FUND, which shall be held in escrow   and disbursed by the Trustee solely for the purpose of paying   the principal of and interest and redemption prices or premiums,   if any, on the Bonds called for redemption in advance of   maturity * * *As of December 31, 1989, the balances of these trust funds were as follows:1. MONROE   Current trust funds  1         $ 49,360   Noncurrent trust funds     Debt service fund          138,862     Maintenance and replacements     55,970                       _______   Total trust fund accounts         244,1922. CHARLOTTE   Current trust funds  2         $ 68,108   Noncurrent trust funds     Debt service fund          170,684     Maintenance and replacements     33,170*303       Project reserves           35,851                       _______   Total trust fund accounts         307,8133.  Rocky Mount   Current trust funds  3         $ 70,073   Noncurrent trust funds     Debt service fund          135,043     Maintenance and replacements     72,988                       _______   Total trust fund accounts         278,104*304  Clinton was not financed by bond issuance and is not subject to these same reserve requirements. However, Clinton was financed by a loan issued by the Farmers Home Administration of the U.S. Department of Agriculture, and the loan agreement required a maintenance and replacements reserve, which as of December 1989 contained $ 8,920.OPINIONThe issue in this case is the fair market value for Federal estate tax purposes of decedent's interests in the five partnerships. Under the regulations, the value of property includable in decedent's gross estate is its fair market value at the alternate valuation date with adjustments prescribed under section 2032. See sec. 20.2031-1(b), Estate Tax Regs. Fair market value is defined for these purposes as "the net amount which a willing purchaser * * * would pay for the interest to a willing seller, neither being under any compulsion to buy or to sell and both having reasonable knowledge of relevant facts." Sec. 20.2031-3, Estate Tax Regs. Fair market value is determined on the basis of the interest that passes at death. See Ahmanson Found. v. United States, 674 F.2d 761">674 F.2d 761 (9th Cir. 1981); United States v. Land, 303 F.2d 170">303 F.2d 170 (5th Cir. 1962).*305 Petitioner introduced the expert report of Beck prepared for purposes of the present proceeding. In addition, the parties stipulated into evidence the expert reports that were prepared for the equitable distribution proceedings. Finally, Beck, Dvorak, Kaye, and Keith all testified as expert witnesses at trial. Expert opinion sometimes aids the Court in determining valuation; other times, it does not. See Laureys v. Commissioner, 92 T.C. 101">92 T.C. 101, 129 (1989). We evaluate such opinions in light of the demonstrated qualifications of the expert and all other evidence of value in the record. See Estate of Newhouse v. Commissioner, 94 T.C. 193">94 T.C. 193, 217 (1990). We are not bound, however, by the opinion of any expert witness when that opinion contravenes our judgment. See id. We may accept the opinion of an expert in its entirety, see Buffalo Tool & Die Manufacturing Co. v. Commissioner, 74 T.C. 441">74 T.C. 441, 452 (1980), or we may be selective in the use of any portion thereof, see Parker v. Commissioner, 86 T.C. 547">86 T.C. 547, 562 (1986). OptionsWe must first decide whether the value of each interest is limited by the option provision contained in each partnership*306  agreement. Petitioner claims that the fair market value of each partnership interest is limited to the $ 10,000 option price, or in the alternative, that the option provision otherwise affects the value to some degree. Respondent takes the position that the option provision should be disregarded in determining the fair market values of decedent's interests.It is well settled that an option agreement may fix the value of a business interest for Federal estate tax purposes if the following conditions are met: (i) The price must be fixed and determinable under the agreement; (ii) the agreement must be binding on the parties both during life and after death; and (iii) the agreement must have a bona fide business purpose and must not be a substitute for a testamentary disposition. See Estate of Bischoff v. Commissioner, 69 T.C. 32">69 T.C. 32, 39 (1977); see also sec. 20.2031-2(h), Estate Tax Regs.  6 Respondent does not dispute that petitioner meets the first two conditions but challenges whether the option provision had a bona fide business purpose and whether it was a substitute for testamentary disposition. According to petitioner, the option provision was inserted in each of the*307  partnership agreements for the purpose of allowing Fred Jr. to maintain control of the businesses without the possibility of interference from other family members. The maintenance of family ownership and control constitutes a bona fide business purpose. See Estate of Bischoff v. Commissioner, 69 T.C. at 39-40. However, even if we find that the option had a bona fide business purpose, it will be disregarded if it served as a device to pass decedent's interest to the natural objects of his bounty and to convey that interest for less than full and adequate consideration. See Bommer Revocable Trust v. Commissioner, T.C. Memo 1997-380">T.C. Memo 1997-380; Estate of Lauder v. Commissioner, T.C. Memo 1992-736">T.C. Memo 1992-736; see also sec. 20.2031-2(h), Estate Tax Regs. We find that the option provision in each of the partnership agreements represents a testamentary device to convey decedent's interest to his son for less than full and adequate consideration, and therefore we disregard it in determining the value of those interests.*308  Petitioner argues that the options were not a testamentary device because they were exchanged for full and adequate consideration. Petitioner claims that the options were granted in exchange for allowing decedent to participate as a 45- or 50-percent partner in the partnerships without a substantial contribution, either of cash or in kind, and that, therefore, decedent's agreement to concede to Fred Jr. all future appreciation exceeding $ 10,000 was the product of a bona fide, arm's-length transaction. That is, Fred Jr. testified at trial, and petitioner argues on brief, that Fred Jr.'s contribution to the partnerships substantially outweighed decedent's; namely, that Fred Jr. had the original idea of seeking HUD contracts; that Fred Jr. mastered the HUD bureaucracy and regulations encountered in the undertaking; and that, as managing partner, Fred Jr. did the lion's share of the work in developing and managing the housing projects, whereas decedent served merely as a "sounding board". Thus, petitioner's argument goes, decedent's agreement to give the options to Fred Jr. -- in which decedent effectively gave up any future appreciation in the value of his interests exceeding the $ *309  10,000 option price and settled for a share of each partnership's current operating income -- was arm's length and bona fide, given the vastly unequal contributions of father and son.When both parties to the agreement are members of the same family and circumstances indicate that testamentary considerations influenced the creation of the option agreement, we do not assume that the price as stated in the agreement was a fair one. See Bommer Revocable Trust v. Commissioner, supra; Estate of Lauder v. Commissioner, supra.We first note that the fixed price of the option, without any adjustment mechanism to reflect changing conditions, invites close scrutiny. If decedent and Fred Jr. really engaged in an arm's-length transaction in which it was decided that Fred Jr.'s greater contribution required decedent to give an option, we believe the price of the option would have included an adjustment mechanism to account for future appreciation. See Bommer Revocable Trust v. Commissioner, supra.The fact that the price was set at $ 10,000, combined with the fact that the agreement was between a father and son, strongly suggests that there was no arm's-length*310  bargain for the option price, but rather that the option was a testamentary device designed to pass decedent's interest for less than adequate consideration.Moreover, the foregoing picture of the partners' relative contributions is based almost entirely on Fred Jr.'s self-serving testimony at trial.  7 In contrast to Fred Jr.'s efforts to portray the options in the instant proceeding as the product of an arm's- length bargain, in their sworn testimony in the equitable distribution proceedings, Fred Jr. and decedent both characterized the options as "gifts", suggesting that both thought it was decedent who was giving something of value to Fred Jr., not the other way around. We note also that decedent's second wife provided detailed, credible testimony concerning decedent's frequent trips (on which she accompanied him) to inspect each partnership property and attend to problems thereby discovered; that decedent had an entire career's worth of experience in the construction business; and that Fred Jr.'s brother testified credibly that when decedent entered into a business venture, he was almost always in charge -- all of which tend to rebut Fred Jr.'s characterization of decedent's*311  role in the enterprise as minimal.On balance, we believe the evidence that the options were a substitute for a testamentary device outweighs any evidence of their bona fide business purpose. In an unusual circumstance, we have the sworn testimony of the grantor-decedent himself as to the options' *312  essentially testamentary purpose, as well as the sworn testimony of the grantee to the same effect, albeit a grantee who now testifies in changed circumstances that the options had a bona fide business purpose.Alternatively, petitioner argues that even if the option provisions do not control the values of the partnership interests, they nonetheless should be given "significant weight" in determining the values of decedent's interests. The regulations state that the option price shall be "disregarded" in determining the value of a business interest unless it is determined that the option represents a bona fide business arrangement and not a substitute for testamentary disposition. Sec. 20.2031-2(h), Estate Tax Regs. Because we have determined that the option provision represents a substitute for testamentary disposition, the provision will be disregarded and shall have no effect on the valuation of decedent's interest for purposes of the Federal estate tax.VALUATION OF THE HOUSING PARTNERSHIPSPetitioner offered into evidence the expert report and testimony of Beck regarding the fair market value of decedent's interests in the housing partnerships. Beck applied a net asset approach*313  under which the value of each partnership was estimated to equal each partnership's equity in its real estate assets, plus cash and accounts receivable, net of liabilities. Beck adopted the valuations of Keith and Dvorak of the real estate and subtracted the mortgage balances as of December 1989 to determine each partnership's equity in the real property it held.Respondent did not present any expert testimony as to the value of the housing partnerships. Instead, respondent called as a fact witness David Archer (Archer), the revenue agent who had calculated the values used in respondent's determination in the notice of deficiency, to testify regarding his calculations. There is no expert testimony in the record to support Archer's method of computing the asset and income values of the partnerships or his decision to average the two approaches in reaching his valuation conclusion. Respondent also called Dvorak and Keith, the real estate appraisers who valued the partnerships for the equitable distribution proceedings and who were relied upon by Beck, to testify as to their valuations of each partnership's real property. On brief, respondent challenges certain aspects of Dvorak's appraisal*314  and argues for adjustments that would increase the value of the real estate. Keith's real estate valuations are not challenged. Finally, respondent challenges, and proposes adjustments to, various aspects of Beck's appraisal of the partnership entities.VALUE OF THE HOUSING PARTNERSHIPS' REAL ESTATEKeith's valuation estimates for the real estate held by Clinton ($ 665,000) and Rocky Mount ($ 1,400,000) are not disputed, and we accept them for purposes of this case. Respondent does challenge various aspects of the approach used by Dvorak to value the real property held by Monroe and Charlotte. We consider each.DVORAK'S REPORTDvorak applied three general approaches in valuing the improved real estate: (i) The cost approach, (ii) the direct sales comparison (market) approach, and (iii) the income approach. The cost approach consisted of valuing the land of the subject property by examining comparable sales and valuing the improvements on the land by considering cost of construction, taking into account depreciation and obsolescence. The market approach consisted of examining sales of comparable properties to estimate the cost of the subject property. The income approach consisted*315  of discounting to present value the future income stream of the subject property for a number of years into the future and then capitalizing the residual or reversionary value, using appropriately derived discount and capitalization rates. The values determined by Dvorak with respect to Charlotte and Monroe were as follows:   Housing       Cost     Market      Income   Project      Approach   Approach  1    Approach   _______      ________   ____________    ________   Charlotte    $ 1,070,000   $ 1,137,500   $ 1,480,000   Monroe      1,240,000    1,337,500    1,370,000Dvorak believed that the income approach was the correct method for valuing the*316  real estate in question and relied on the other approaches only to confirm his income-based value. Thus, his final appraised values for Charlotte and Monroe were $ 1,480,000 and $ 1,370,000, respectively.RESPONDENT'S CHALLENGES(a) VACANCY RATEIn calculating cash-flow, Dvorak reduced gross income of the housing partnerships by 3 percent as a vacancy allowance. Respondent challenges Dvorak's use of a 3-percent vacancy allowance, arguing that in light of the HUD guaranty to pay 80 percent of the contract rent for 2 months after a tenant vacates, the 3-percent vacancy allowance is too high and that 1 percent is appropriate. We agree. According to Dvorak's appraisals, a vacancy allowance represents a reduction in potential rental income due to vacancies or uncollectibility. Dvorak normally would have used a 5-percent rate, but he reduced it to 3 percent because the risk of uncollectibility was low, given that the Federal Government was the obligor with respect to most of the rent. However, although Dvorak testified that he understood the actual vacancy rates were low and that there were usually waiting lists of tenants at Monroe and Charlotte, he admitted that he was unaware of the*317  HUD guaranty to pay 80 percent of the rent for 2 months following a vacancy when he made the determination to use a 3-percent vacancy rate.  8 In light of Dvorak's view that the reduced risk of uncollectibility required a 2-percent adjustment to the vacancy rate, we believe that the reduced risk of loss from short-term vacancies provided by the HUD guaranty requires another 2- percent reduction in the vacancy rate assumption, resulting in a vacancy rate adjustment of 1 percent. We note that a vacancy rate assumption of 1 percent was used by Keith, whose expert reports are not disputed by either party in this proceeding.(b) RENTAL RATESRespondent disputes Dvorak's use of an estimated figure for 1989 rental receipts, on the grounds that it is less than actual 1989 rents. Because actual 1989 figures were not available to him when he did his appraisal (originally for use in the equitable distribution proceedings), Dvorak used*318  actual rental income from 1985, and estimated expenses for the same period, and then inflated his net income amounts at 1.5 percent per year to produce estimates for 1989. This resulted in 1989 net operating income for Charlotte of $ 187,531 and for Monroe of $ 176,350. The record in the instant case contains 1989 income statements for Charlotte and Monroe, including actual rents and expenses. Using actual rents, as respondent urges, but also using actual expenses -- since both would presumably have been available to a hypothetical buyer and seller on the November 11, 1990, valuation date -- results in 1989 net operating income of $ 189,319 for Charlotte and $ 175,905 for Monroe. In comparison with Dvorak's estimated amounts, the difference is negligible, and we see no need to modify Dvorak's results on the basis of this factor.(c) CAPITALIZATION RATEFinally, respondent contends that net income multipliers 9 applied by Dvorak are erroneous because they exceed the range of multipliers identified from comparable sales. We first note that Dvorak's method did not consist of a simple application of net income multipliers. Dvorak calculated a discount rate to apply to cash-flow year*319  by year for 4 years, and a capitalization rate to apply to cash- flow in the fifth year, which he termed a reversionary value. He first calculated the reversionary value, using the reversionary capitalization rate. He then subtracted costs of sale, then added this result to the cash-flow figure for year 4. He then discounted to present value the cash-flow figure for each of 4 years following the date of valuation, using the discount rate.Dvorak applied different discount and capitalization rates depending on whether he was assuming the existence of HUD subsidies. For Charlotte, the discount rate without the HUD subsidies was 13 percent, and with the HUD subsidies was 15 percent. The capitalization rate for the reversionary interest was 11 percent without, and 12 percent with, HUD subsidies. For Monroe, the discount rate was 13 percent without, and 14 percent with, the HUD subsidies.*320  The capitalization rate for the reversionary interest was 11.25 percent without, and 11.75 percent with, HUD subsidies. He used higher rates for the HUD-subsidized housing because he believed an investor would demand a greater rate of return due to the risk of losing the HUD subsidies.Rather than attacking the specific method by which Dvorak generated his discount and capitalization rates, respondent argues that the rates should match the rates of the properties that Dvorak used as comparables for his market method value. In other words, respondent looks at the market comparables, examines their rates of return, and criticizes Dvorak's income method because his rate does not fall within the range of these amounts. Using net income multipliers rather than discount or capitalization rates, respondent calculates Dvorak's net income multiplier for Charlotte to be 7.78 and argues that the correct net income multiplier would fall in the range of 9.22 to 9.6. For Monroe, respondent calculates Dvorak's net income multiplier to be 7.77 and argues that the correct net income multiplier would fall in the range of 9.31 to 9.84.There is no evidence in the record suggesting that the small sample*321  of comparables used in Dvorak's market approach could be used to generate a reliable net income multiplier, or capitalization rate, for purposes of an income valuation of the subject properties. Indeed, the evidence shows just the opposite. In his market approach, Dvorak found virtually all of the comparables to be superior to the subject. In his income approach, Dvorak himself used a broad-based survey of investors to derive the required rate of return for an investor in the subject properties, rather than simply looking at the rates of return for the very small sample of actual sales relied on by respondent. In addition, the dates of the sales used in the market approach ranged from 1983 to 1989.  10For the foregoing reasons, we do not believe respondent's criticisms of Dvorak's capitalization rates are well taken. However, our review of Dvorak's analysis causes us to question*322  whether Dvorak was justified in his use of higher discount and capitalization rates for HUD-subsidized properties than for properties operating without HUD subsidies. We do not believe he was. In Dvorak's view, an investor in the subject properties would require a higher rate of return because of the risk of loss of the HUD subsidies and the above-market rental income stream that such subsidies produced. However, Dvorak offered no evidence or analysis to support the existence of, or quantify the extent of any, risk that HUD subsidies on properties of this type might be lost. The HUD contracts covering the subject properties were generally for 30 years, yet Dvorak asserted the purported risk only in conclusory fashion. Even if we were to accord some weight to his unsupported opinion regarding this risk, we believe any such increase in risk would be offset by the decreased risk (in comparison to non-HUD-subsidized rental properties) provided by (i) the status of the Federal Government as obligor for most of the contract rents, and (ii) the mandated trust fund accounts, which provided for reserves for a broad range of project expenditures, including routine and extraordinary maintenance, *323  insurance, taxes, debt service, etc. Dvorak acknowledged that he did not consider the trust funds in his valuation analysis. On balance, we believe the Federal Government's liability for the rents and the existence of the trust funds provide support for a lower, not a higher, capitalization rate. On this record, therefore, we conclude that the most appropriate capitalization rate is the lower one used by Dvorak for the subject properties in the absence of HUD subsidies. 11FINAL VALUES BASED ON ADJUSTMENTS TO DVORAK'S REPORTIncorporating the adjustments above, *324  we find that the value of the real estate held by Charlotte was $ 1,720,000, and the value of the real estate held by Monroe was $ 1,690,000. The following tables show the derivation of these values:CHARLOTTE   DVORAK'S REPORT         Year 1   Year 2   Year 3     Year 4    Year 5         ______   ______   ______     ______    ______Net operating income     $ 190,344 $ 193,199 $ 196,097    $ 199,039 $ 202,024Cash-flow      190,344   193,199   196,097   1 1,815,235Present value  2 165,517   146,086   128,937    1,037,867*325     COURT'S ADJUSTMENTS          Year 1   Year 2   Year 3      Year 4   Year 5          ______   ______   ______      ______   ______Net operating income  1    $ 195,948 $ 198,887 $ 201,871    $ 204,899 $ 207,972Cash-flow      195,948  198,887   201,871   2 2,028,313Present value  3  173,405  155,758   139,907    1,243,941Sum of present values: $ 1,713,011Estimated value: $ 1,710,000*326  MONROE   DVORAK'S REPORT          Year 1   Year 2   Year 3     Year 4   Year 5          ______   ______   ______     ______   ______Net operatingincome  1    $ 176,350 $ 176,350 $ 176,350    $ 176,350 $ 176,350Cash-flow      176,350   176,350   176,350 2 1,617,165Present value  3  154,693   135,696   119,031     957,491Sum of present values: $ 1,366,910Estimated value: $ 1,370,000*327     COURT'S ADJUSTMENTS         Year 1   Year 2   Year 3   Year 4   Year 5         ______Net operating income  1    $ 195,386 $ 198,317 $ 201,292    $ 204,311 $ 207,376Cash-flow      195,386   198,317   201,292   22 1,987,619Present value  3  172,909   155,311   139,505    1,219,044Sum of present values: $ 1,686,769Estimated value: $ 1,690,000*328  VALUE OF DECEDENT'S INTEREST IN THE HOUSING PARTNERSHIPSBeck valued decedent's partnership interests using only the net asset approach under the theory that rental real estate was the primary asset of the housing partnerships and the income- producing value of the partnerships is contained in the net asset value. We agree. The hypothetical investor would seek the income stream from the partnerships as going concerns, but, because the partnerships hold rental properties, the income stream of the partnerships is reflected in the net asset value, or income stream, of the underlying properties. See, e.g., Estate of Andrews v. Commissioner, 79 T.C. 938">79 T.C. 938, 944 (1982); Estate of Smith v. Commissioner, T.C. Memo 1999-368">T.C. Memo 1999-368. A value based principally on the income stream is especially appropriate in this case, we believe, because the HUD subsidies produced above-market rents and also, in our view, affect the capitalization rate that should be used to value the properties. The impact of the subsidies is thus only captured in an income-based approach to valuation. Accordingly, we find that an income-based value, which takes into account the HUD subsidies, is the most*329  appropriate method to value the housing partnerships. We therefore believe that Beck's reliance on Dvorak's appraisals, which used an income approach to value the real estate, was, in general, proper.BECK'S REPORTAs earlier noted, under Beck's net-asset approach, the value of the partnerships was estimated to equal each partnership's equity in its real estate assets (as appraised by Dvorak and Keith), plus cash and accounts receivable, net of liabilities.  12 Beck's appraisals of decedent's interests in the housing partnerships, before discounts, were as follows:CHARLOTTEReal estate value (per Dvorak appraisal)      $ 1,480,000Less*330  outstanding mortgage balance   1,380,000                  __________Real estate equity                 100,000Plus cash and accounts receivable          259,343Less (nonmortgage) liabilities           161,338                         _______Partnership value                  198,005Value of 50% interest                99,003MONROEReal estate value (per Dvorak appraisal)      $ 1,370,000Less outstanding mortgage balance   1,220,000                  __________Real estate equity                 150,000Plus cash and accounts receivable          436,751Less (nonmortgage) liabilities           117,444                         _______Partnership value                  469,307Value of 50% interest                234,653ROCKY*331  MOUNTReal estate value (per Keith appraisal)       $ 1,400,000Less outstanding mortgage balance   1,380,000                  __________Real estate equity                  20,000Plus cash and accounts receivable          339,952Less (nonmortgage) liabilities           172,665                         _______Partnership value                  187,287Value of 50% interest                93,643CLINTONReal estate value (per Keith appraisal)        $ 665,000Less outstanding mortgage balance    587,500                   ________Real estate equity                  77,500Plus cash and accounts receivable          113,709Less (nonmortgage) liabilities            32,818                         _______Partnership value              *332      158,391Value of 50% interest                79,196Beck then applied discounts to the values of the 50-percent interests in the housing partnerships for lack of control (15 percent) and for lack of marketability (25 percent), which would result in discounted values as follows:              Value Before    Discounted      Project       Discounts      Value      _______      ____________    __________     Charlotte      $ 99,003      $ 63,114     Monroe        234,653      149,591     Clinton        79,196       50,487     Rocky Mount      93,643       59,697There are disputes concerning various aspects of Beck's analysis, which we consider in turn.(a) ACCOUNTS RECEIVABLEThe first issue to decide is whether it is appropriate to discount intercompany accounts receivable. Petitioner argues that the value of certain accounts receivable from Godley Realty and CPSI should be discounted in valuing the underlying assets of the housing*333  partnerships. Petitioner's theory is that discounting is required to reflect the risk of nonpayment, in particular because there were no promissory notes or collateral for the partnerships' receivables.We believe petitioner's argument for discounting the accounts receivable is unpersuasive. The accounts receivable in question were not secured because they were from related parties. Generally speaking, accounts receivable and payable between related parties are disregarded in a valuation of the commonly controlled entities; that is, they are either all counted at face value or all eliminated, producing in either case a wash. Beck, petitioner's own expert on valuation of business entities, so testified. Moreover, Beck valued the accounts receivable of each housing partnership at face value in his expert report, which petitioner has submitted under Rule 143(f) in support of its position. In conformance with the general rule, respondent allowed the corresponding accounts payable of Godley Realty and CPSI at full face value in reaching an agreement with petitioner as to the valuations of those entities for Federal estate tax purposes, which valuations the parties have stipulated are correct. *334  Accordingly, we conclude that the accounts receivable of the housing partnerships should be valued at face value, and we make no adjustment to Beck's report in this respect.  13*335  (b) TRUST FUND ACCOUNTSBeck assigned no value to the trust funds established and maintained under the financing arrangements of the housing partnerships, on the grounds that maintenance of the funds was essentially a prerequisite for the HUD subsidies and therefore the funds were not available to a purchaser of decedent's interest. It is respondent's contention that the trust funds are includable in the net asset value of the partnerships at their full face value as of December 31, 1989. Although we disagree with respondent's approach, we also do not believe that Beck has fully accounted for the value supplied by the trust funds. We believe respondent is correct in arguing that the trust funds would have some value to a purchaser of an interest in the housing partnerships, as the existing funds could eventually be used to defray expenses that the partnerships would otherwise incur. However, viewed from this perspective, the funds would have to be discounted to present value, because the circumstances and timing for their use are subject to strict controls. The appropriate discounting would vary with each fund, depending upon the terms governing its use; and the record in this case*336  provides an insufficient basis on which to estimate such discounting.In these circumstances, we think the trust funds are best viewed as analogous to working capital. The trust funds had to be maintained by the partnerships in order to retain the HUD subsidies. The funds were thus essential to producing the above-market rental income stream earned by the partnerships, not unlike the working capital necessary for any going concern to produce an income stream. Since we are valuing the partnerships as operating businesses, we consider the trust accounts not as liquid assets (which might be proper if we were considering liquidation value), but rather as components of working capital, necessary to continue the income stream of the partnerships, but otherwise unavailable to an investor in the partnerships. However, the trust funds have some value to an investor; as reserves, they make the housing partnerships less risky than other partnerships similarly situated that do not have such trust funds. Thus, we believe an investor would require a lower rate of return from the partnerships with the trust funds. For this reason, we believe the trust funds are best accounted for by means of a reduction*337  in the otherwise applicable capitalization rate. We have done so earlier in this analysis, where we rejected Dvorak's position that an increase in the capitalization rate was warranted by the risk of loss of the HUD subsidies. We concluded there that any such risk was offset by a reduction in risk produced by the trust funds. On this record, we believe such an adjustment to the capitalization rate is the best means to account for the effect that the trust funds would have on the price that a hypothetical buyer would pay for decedent's interest in the housing partnerships. 14*338  (c) DISCOUNTSThe final issue we must resolve is the extent to which discounts may apply to the interests being valued. Beck applied a lack of control discount of 15 percent to decedent's interests in the housing partnerships because of the irrevocable designation of Fred Jr. as managing partner thereof. In Beck's opinion, this irrevocable designation effectively surrenders a degree of control which would otherwise be held by a 50-percent general partner, and therefore places decedent's interest in the position of a minority partner interest. We disagree.A minority discount will apply where a partner lacks control, indicated by such factors as the inability to participate in management, to direct distributions, or to compel liquidation or withdraw from the partnership without the consent of the controlling interest. See Estate of Bischoff v. Commissioner, 69 T.C. 32">69 T.C. 32, 49 (1977). Degree of control is the critical factor in deciding whether the minority discount applies and the amount of the discount, if any. See id.We find that the terms of the partnership agreements do not reduce decedent's interests to the level of minority interests. The partnership agreements for*339  the housing partnerships contain restrictions on a partner's right of liquidation, termination, and withdrawal, but the restrictions apply equally to all partners. Day- to-day management decisions are in the hands of the managing partner, but major decisions require approval of partners owning 75 percent of the partnership's interests. The term "major decisions" is broadly defined under the partnership agreements so as to include nearly any decision other than routine daily operational matters, including the acquisition and sale of partnership property, financing, expenditures in excess of $ 2,500, entering major contracts, or any other decision or action "which materially affects the Partnership or the assets or operation thereof." Also, annual distributions of net cash-flow are required under the partnership agreements, giving the holder of decedent's interest the right to require distributions. Beck argues that the partnership agreements give the managing partner, Fred Jr., "absolute discretion in establishing 'reserves for replacement of assets or to cover contingencies'", essentially allowing him to nullify the provision requiring annual distributions of cash. We believe Beck*340  gives an overly expansive reading of the managing partner's discretion regarding reserves. Although Fred Jr. had discretion, we do not believe the other partners would lack recourse if this discretion were used to cut off otherwise available cash distributions. Moreover, the discretion to establish such reserves was listed as an item of day-to-day management, suggesting a limited scope to that right. When read in the context of the entire partnership agreement, we do not believe the managing partner's discretion to establish reserves confers the absolute power suggested by Beck. Thus, we conclude that the terms of the agreements do not restrict control to the extent of a minority interest.Petitioner argues, in the alternative, that Fred Jr. had virtual control over the housing partnerships because of his options to buy decedent's interests. As previously discussed, the options must be disregarded in valuing those interests.Beck also determined that a lack of marketability discount of 25 percent should apply because there was no ready market for the housing partnership interests and a seller would necessarily suffer a period of illiquidity. Respondent concedes on brief that a lack*341  of marketability discount of 15 to 20 percent is appropriate, but only where the income approach to valuation is employed. However, as previously discussed, in this case the income and net asset values are intertwined. Moreover, to calculate the values in the notice of deficiency, Archer used a lack of marketability discount for both asset and income-based values of the housing partnerships. Further, we believe that Beck makes a persuasive case that decedent's interests would not be readily marketable. He notes that they would be subject to the irrevocable designation of Fred Jr. as managing partner. Beck also cited the provisions in the partnership agreements that grant a right of first refusal to nonselling partners and give them 60 days to accept or reject the offer to sell, which he interpreted as forcing a period of illiquidity on every selling partner. In light of all the facts and circumstances and respondent's concession, we find that a 20-percent lack of marketability discount is appropriate.For the reasons previously outlined, we believe Beck's analysis should be modified: (i) To include our adjustments to Dvorak's appraisals of the Charlotte and Monroe real estate; (ii) *342  to eliminate his 15-percent minority discount; and (iii) to apply a 20- rather than 25-percent marketability discount. Using Beck's methodology, as modified, results in the following values, which we find are correct:CHARLOTTEReal estate value (per modified Dvorak appraisal)    $ 1,710,000Less outstanding mortgage balance     1,380,000                    __________Real estate equity                   $ 330,000Plus cash and accounts receivable            259,343Less (nonmortgage) liabilities              161,338                           ________Partnership value                    428,005Value of 50% interest                  214,003Less 20% marketability discount              42,801                            _______Correct value                      171,202MONROEReal*343  estate value (per modified Dvorak appraisal)    $ 1,690,000Less outstanding mortgage balance     1,220,000                    __________Real estate equity                   $ 470,000Plus cash and accounts receivable            436,751Less (nonmortgage) liabilities              117,444                           ________Partnership value                    789,307Value of 50% interest                  394,654Less 20% marketability discount              78,931                           ________Correct value                      315,723ROCKY MOUNTReal estate value (per Keith appraisal)         $ 1,400,000Less outstanding mortgage balance     1,380,000                    __________Real estate equity      *344               $ 20,000Plus cash and accounts receivable            339,952Less (nonmortgage) liabilities              172,665                            _______Partnership value                    187,287Value of 50% interest                   93,643Less 20% marketability discount              18,729                            _______Correct value                       74,914CLINTONReal estate value (per Keith appraisal)           $ 665,000Less outstanding mortgage balance       587,500                      ________Real estate equity                   $ 77,500Plus cash and accounts receivable            113,709Less (nonmortgage) liabilities              32,818          *345                    _______Partnership value                    158,391Value of 50% interest                   79,196Less 20% marketability discount              15,839                            _______Correct value                       63,357GMAThe fifth partnership at issue is GMA, which is different from the housing partnerships. Decedent and Fred Jr. formed GMA because HUD required a separate partnership to manage the housing partnerships. GMA received a management fee from each of the housing partnerships equal to 10 percent of rental income. GMA held no fixed assets, and its only significant expense was salary it paid to decedent and Fred Jr.In valuing GMA, respondent introduced the report of Kaye, who valued GMA for Fred Jr.'s former spouse in the equitable distribution proceedings. Petitioner introduced the report of Beck, who valued GMA for Fred Jr. in the earlier proceedings. Kaye used an income approach, under which he capitalized an after-tax*346  income figure using a capitalization rate derived from comparisons with large, publicly traded real estate management companies. He found the value of GMA as a whole to be $ 450,000.  15 Beck, on the other hand, believed that the value of GMA was intrinsically tied to the value of the four housing partnerships. Further, he argued that because GMA had no fixed assets and its only assets were accounts receivable from the housing partnerships, its value was simply equal to the net realizable accounts receivable as of December 1989 (the time closest to the valuation date for which figures were available).We agree with Beck's assertion that the value of GMA was tied to the value of the housing partnerships,*347  but we disagree with his conclusions as to the value of GMA. He failed to recognize that the hypothetical buyer investing in GMA would not merely be buying the accounts receivable on a particular date, but instead would be buying the income stream attributable to 10 percent of the rental income of each of the four housing partnerships, minus expenses associated with managing the housing partnerships. Thus, we reject Beck's approach altogether.Petitioner makes no specific challenges to the income approach used by Kaye. Rather, petitioner makes two arguments: (i) That Kaye valued the partnership as a whole, rather than decedent's interest, and that discounts for lack of control and lack of marketability apply; and (ii) that the fact that GMA's value depended on the value of the housing partnerships should be taken into consideration. With respect to discounts, we apply the same discounts, and for the same reasons, that we applied in the case of the housing partnerships. Respondent concedes a lack of marketability discount of 15 to 20 percent with respect to GMA, petitioner has not demonstrated that a greater discount applies, and we accordingly apply a discount of 20 percent for lack*348  of marketability. Further, petitioner has not demonstrated that a minority interest discount applies, given that Fred Jr. and decedent each held 50-percent partnership interests, and there is no evidence that Fred Jr. controlled GMA to a greater extent than the housing partnerships. 16With respect to whether Kaye's valuation approach took into account the relationships between GMA and the housing partnerships, we believe it did. Kaye was aware of the relationship, and he knew that GMA's income consisted of accounts receivable generated by the management fees, equal to 10 percent of rental income, paid by the housing partnerships. Moreover, Kaye's approach used actual income figures of GMA. We believe Kaye sufficiently considered the value of GMA in relation to the housing partnerships.Using Kaye's value of $ 450,000, and applying a discount of 20 percent for lack of marketability, we find that decedent's 50- percent interest in GMA was worth $ 180,000. *349  To reflect the foregoing,Decision will be entered under Rule 155.  Footnotes1. Sec. 5.02 of each partnership agreement provides:     Notwithstanding any of the foregoing, Fred D. Godley, or   his personal representative, heirs or assigns, shall have the   option to purchase the Partnership interest of F.O. Godley from   either F.O. Godley or his personal representative, heirs or   assigns, for the sum of Ten Thousand $ 10,000. This option may be   exercised at any time during the existence of the Partnership.   Fred D. Godley shall notify all other Partners in writing of his   intention to exercise this option to purchase.↩2. Petitioner was unable to produce a copy of the partnership agreement for GMA, but the testimony supports, and we have found, that a similar option agreement existed in the case of GMA.↩3. No lack of marketability discount was applied to the net asset value of GMA.↩4. In his trial testimony, Beck clarified that the compounding of these two discounts would produce a total discount of 36.25 percent.↩5. The parties have stipulated that these values are correct.↩1. The 1990 audited financial statements for Monroe identifythe current trust funds as consisting of the Principal and InterestFund, the Investment Interest Fund, and the Revenue Fund.↩2. The 1990 financial statement for Charlotte identifies thecurrent trust funds as the Principal and Interest Fund, the Tax &Insurance Escrow, and the Depository Fund.↩3. The 1990 financial statement for Rocky Mount identifies thecurrent trust funds as the Principal and Interest Fund, the Insuranceand Tax Escrow Fund, and the Surplus Fund.↩6. Sec. 2703, relating to the valuation of property subject to options, is not applicable to an agreement entered into before Oct. 9, 1990, unless there has been substantial modification since Oct. 8, 1990. See Omnibus Budget Reconciliation Act of 1990, Pub. L. 101-508, sec. 11602(e)(1)(A)(ii)(I), 104 Stat. 1388-500. The options in issue were executed before Oct. 9, 1990, and were not substantially modified thereafter.↩7. Petitioner also called as a witness a HUD official who corroborated Fred Jr.'s assertion that he was primarily responsible for the partnership's dealings with HUD. However, we note that, in contrast to Fred Jr.'s emphasis in his testimony at trial in this case that the idea of developing HUD-assisted housing projects was entirely his own, when asked under oath 6 years earlier in connection with the equitable distribution proceedings whose idea it had been, Fred Jr. testified that he could not recall. The subsequent improvement in Fred Jr.'s recollection on this point in the instant proceeding -- in a manner which serves his financial interests--casts doubt on the credibility of his other testimony in this proceeding.↩1. The determinations under the market approach represent theaverage of a range estimated by Dvorak. The estimated range forCharlotte was from $ 1,050,000 to $ 1,225,000 and the estimated rangefor Monroe was from $ 1,275,000 to $ 1,400,000.↩8. Indeed, the owner could apply for additional payments beyond the first 2 months.↩9. Dvorak actually used discount and capitalization rates. A capitalization rate is the reciprocal of a net income multiplier.↩10. Dvorak was valuing the subject property as of two dates, 1985 and 1989, for purposes of the equitable distribution proceedings.↩11. Even the lower of Dvorak's two capitalization rates is arguably too high, since it takes no account of the HUD subsidies (which tended to REDUCE the risk perceived by an investor, in our view). Nevertheless, in the absence of an evidentiary basis on which to compute the extent to which the capitalization rate should be adjusted downward, we adopt the lower of the two computed by Dvorak. Sum of present values: $ 1,478,407 Estimated value: $ 1,480,000↩1. This figure equals the reversionary value of $ 1,616,196 plusthe net operating income from year 4 of $ 199,039. The reversionaryvalue equals the net operating income from year 5, $ 202,024, dividedby Dvorak's terminal capitalization rate of 12 percent, minus costsof sale of $ 67,341.↩2. Dvorak discounted to present value using a 15-percentdiscount rate.↩1. These figures include the adjustment to the vacancy ratethat we have concluded is appropriate, from 3 percent down to 1percent. This caused an increase of $ 5,202 (2 percent of the rentalincome figure of $ 259,200) each year in 1985 dollars. The figures inthe table are inflated to 1989 dollars using Dvorak's inflation rateof 1.5 percent per year.↩2. This figure equals the reversionary value of $ 1,823,313 plusthe net operating income from year 4 of $ 204,899. The reversionaryvalue equals the net operating income from year 5, $ 207,972, dividedby our adjusted terminal capitalization rate of 11 percent, minuscosts of sale of $ 67,341.↩3. We discount to present value using our adjusted 13-percentdiscount rate.↩1. In contrast to his computations for Charlotte, Dvorak didnot inflate the net operating income figures for Monroe by 1.5percent from year to year, nor did he adjust the starting netoperating income figure for inflation to state it in 1989 dollars.Dvorak gives no reason for failing to make these adjustments, and forconsistency we make them in the table that follows.↩2. This figure equals the reversionary value of $ 1,440,815 plusthe net operating income from year 4 of $ 176,350. The reversionaryvalue equals the net operating income from year 5, $ 176,350, dividedby Dvorak's terminal capitalization rate of 11.75 percent, minuscosts of sale of $ 60,034.↩3. Dvorak discounted to present value using a 14-percentdiscount rate.↩1. These figures include an adjustment to the vacancy rate thatwe have concluded is appropriate, from 3 percent down to 1 percent.This caused an increase of $ 5,019 (2 percent of the rental incomefigure of $ 250,080) each year in 1985 dollars. The figures in thetable are inflated to 1989 dollars using Dvorak's inflation rate of1.5 percent per year and inflated at the same rate year by year.↩2. This figure equals the reversionary value of $ 1,783,308 plusthe net operating income from year 4 of $ 204,311. The reversionaryvalue equals the net operating income from year 5, $ 207,376, dividedby our adjusted terminal capitalization rate of 11.25 percent, minuscosts of sale of $ 60,034.↩3. We discount to present value using our adjusted 13-percentdiscount rate.↩12. The valuations of the accounts receivable and accrued liabilities were based on audited financial statements dated Dec. 31, 1988. The 1989 financial statements were not yet prepared as of the performance of the appraisals, and thus the reconstructed market income statements for 1989 were used for both the market analysis and the operational analysis.↩13. Petitioner also argues with respect to Godley Realty that its accounts receivable were not actually accounts receivable; that is, petitioner argues that they were not amounts owed by Godley Realty to each housing partnership but rather were distributions from Godley Realty, before it was incorporated, to decedent and Fred Jr. and were incorrectly recorded as receivables held by the housing partnerships. We reject this argument for a number of reasons. First, the supporting evidence is at best vague and imprecise. Second, in contradiction to this position, petitioner submitted an expert report that treated these amounts as accounts receivable. Finally, petitioner allowed respondent to treat the corresponding amounts as accounts payable in the hands of Godley Realty, which resulted in their treatment as liabilities at face value when respondent and petitioner reached agreement on the valuation of Godley Realty.↩14. We have considered whether a similar adjustment to take into account the trust funds is warranted in the case of Keith's appraisals of the Clinton and Rocky Mount properties and conclude that it is not. First, in the case of Clinton, that partnership held only a maintenance reserve of $ 8,920, which we believe would not have been a material consideration in a hypothetical sale. The Rocky Mount partnership, however, did not hold trust funds of a magnitude similar to those of Charlotte and Monroe. Nonetheless, we note that Keith ultimately relied on his market-based value rather than his income- based value in reaching his conclusion regarding Rocky Mount. Keith's market-based value for Rocky Mount was $ 1,400,000, while his income- based value was $ 1,325,000. In calculating his income-based value Keith used a discount rate of 15 percent. If we adjust this rate to 13 percent, as we did in the case of Dvorak's Charlotte report, the value under Keith's income approach would be $ 1,400,901, rounded to $ 1,400,000, equal to the value under Keith's market-based approach and to Keith's final value. We note again that respondent has accepted this value and find that any adjustment to Keith's discount rate to reflect the existence of the trust funds would not alter the final value of Keith's Rocky Mount appraisal.↩15. We note that in the notice of deficiency respondent determined the value of decedent's 50-percent interest in GMA to be $ 330,688. By proffering Kaye's report, respondent has apparently abandoned the position that decedent's interest in GMA has a value any greater than $ 225,000 (50 percent of $ 450,000).↩16. The partnership agreement of GMA is not in the record.↩