COMMONWEALTH OF KENTUCKY, JEFFERSON COUNTY PROPERTY VALUATION ADMINISTRATOR v. LHR PARTNERS, LTD.; COMMONWEALTH OF KENTUCKY, KENTUCKY STATE FAIR BOARD; KENTUCKY FAIR EXPOSITION CENTER; AND KENTUCKY BOARD OF TAX APPEALS

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RENDERED: May 24, 2002; 10:00 a.m. NOT TO BE PUBLISHED C ommonwealth O f K entucky C ourt O f A ppeals NO. 2001-CA-001229-MR COMMONWEALTH OF KENTUCKY, JEFFERSON COUNTY PROPERTY VALUATION ADMINISTRATOR v. APPELLANT APPEAL FROM JEFFERSON CIRCUIT COURT HONORABLE JUDITH MCDONALD-BURKMAN, JUDGE ACTION NO. 00-CI-003010 LHR PARTNERS, LTD.; COMMONWEALTH OF KENTUCKY, KENTUCKY STATE FAIR BOARD; KENTUCKY FAIR EXPOSITION CENTER; AND KENTUCKY BOARD OF TAX APPEALS APPELLEES OPINION REVERSING ** ** ** ** ** BEFORE: GUDGEL, CHIEF JUDGE; JOHNSON AND TACKETT, JUDGES. JOHNSON, JUDGE: The Commonwealth of Kentucky and the Jefferson County Property Valuation Administrator have appealed from an opinion and order entered by the Jefferson Circuit Court on May 23, 2001, which affirmed an order of the Kentucky Board of Tax Appeals, reducing the tax liability of LHR Partners, Ltd., for the tax years 1994-1998. Having concluded that the Board’s decision was not supported by substantial evidence, since it failed twice to follow required mathematical formulas, we reverse. LHR is the owner of a leasehold interest in the Hyatt Regency Hotel in Louisville, Jefferson County, Kentucky. This first-class, 380-room hotel includes numerous meeting rooms, a health club, a swimming pool, and two restaurants. The hotel facility is situated on a two-acre parcel of land owned by the Kentucky State Fair Board. LHR leases the property from the Commonwealth of Kentucky for the sum of $270,000.00 per year, plus a percentage of the hotel’s annual gross receipts.1 The lease will expire at the end of 2007 unless LHR exercises its option to renew the lease. It has the right to renew the lease for two, 10-year periods at a cost of $2,500.00 per renewal. If both lease renewal options are exercised, the lease would extend through 2027.2 Since the Commonwealth of Kentucky owns the land upon which the hotel is situated, the real property, and all improvements to the real property, are exempt from taxation.3 However, LHR’s leasehold interest in the hotel is subject to ad valorem property taxes based on the fair cash value of the 1 LHR has never paid additional rent based on a percentage of annual gross receipts. 2 At the conclusion of the lease, LHR is required to deliver the physical structure of the hotel, including all its fixtures and furnishings, to the Commonwealth in good condition and free and clear of any liens and encumbrances. 3 See Kentucky Constitution, § 170. -2- leasehold.4 The responsibility of assessing the fair cash value of LHR’s leasehold lies with the Jefferson County PVA. In 1994, the Jefferson County PVA dramatically increased the assessed value of LHR’s leasehold interest in the hotel. Following standard administrative procedures, LHR appealed this new assessment to the Jefferson County Board of Assessment Appeals. After the Board of Assessment Appeals affirmed the PVA’s assessment, LHR appealed to the Kentucky Board of Tax Appeals. On May 11, 1999, an evidentiary hearing was held before the Board of Tax Appeals. The Board heard conflicting testimony in support of differing assessments from each party’s expert witness. LHR’s expert, Lin Bell, applied the income approach evaluating the leasehold interest. in First, Bell totaled the income generated by the hotel’s various components, including real property, furniture, fixtures, equipment, and goodwill. Second, in order to arrive at the fair cash value of LHR’s leasehold interest, Bell used a 14% discount rate5 to estimate the present value of this income stream for the remaining years of the leasehold. While acknowledging the favorable terms of the option to renew the lease, Bell testified that it would be 4 See Kentucky Constitution, § 172; Kentucky Revised Statutes (KRS) 132.195(1). 5 The discount rate was calculated by assuming an 11% expected rate of return for a potential buyer’s investment, a 1.6% tax base component, and a 1.4% component to reflect expected increases in income over the remaining term of the lease. -3- improper to include in the evaluation a renewal of the lease which might not occur. The PVA’s expert, Ron Galloway, used a combination of three valuation approaches: the cost approach, Bell’s income approach, and the sales comparison approach. In light of the favorable terms of the lease, Galloway assumed that the options to extend the lease for two, 10-year periods would be exercised. Additionally, he included the hotel’s income from off-site catering fees. The Board of Tax Appeals chose to use Bell’s income method in setting the fair cash value of the leasehold. However, the Board rejected Bell’s 14% discount rate, replacing it with a 12.5% discount rate; and the Board assumed a 20-year extension of the lease in calculating the value of the leasehold. The Commonwealth appealed the Board’s order to the Jefferson Circuit Court. The Commonwealth claimed the Board committed two computation errors in calculating the present value of the hotel’s future income stream. In support of its claim, the Commonwealth sought to introduce before the circuit court a discount rate table from a treatise entitled Capitalization Theory and Techniques.6 The Commonwealth argued that the table demonstrates that beginning with the year 1994 the Board mistakenly applied the second-year discount factor to the hotel’s first year’s income stream, and that this mistake in turn caused 6 Akerman, Charles B., Capitalization Theory and Techniques (Appraisal Institute). -4- all the succeeding years of the term of the leasehold to be computed with the wrong discount factor. Similarly, the Commonwealth argued that the Board miscalculated the fair cash value for the years 1995, 1996, 1997 and 1998 by using incorrect discount factors. These computation errors for 1995 through 1998 occurred when the Board shortened the length of the leasehold term by eliminating one year from the leasehold term for each successive tax year. Instead of applying the same discount factor for the first year of each new leasehold term and decreasing the discount factor each successive year of the leasehold term, the Board took the highest discount factor off of the leasehold term for each subsequent tax year. Instead, the discount factors should have been the same for each leasehold term with the exception of the discount factor for the final year of the previous leasehold term, which would be eliminated. In other words, the discount factor used to compute the value of the leasehold in the second year of the leasehold term for year 1994 was mistakenly used as the discount factor for the first year of the tax year 1995; the discount factor used in the third year of the leasehold term for year 1994 was mistakenly used as the discount factor for the first year of the tax year 1996; the discount factor used in the fourth year of the leasehold term for year 1994 was mistakenly used as the discount factor for the first year of the tax year 1997; and the discount factor used in the fifth year of the leasehold term for year 1994 was mistakenly used as the discount factor for the first year of the tax year -5- 1998. These alleged errors can best be demonstrated by referring to the computation table used by the Board: YEAR ADJUSTED NET INCOME 7 12.5% DISCOUNT FACTOR 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2489 2215 3050 3455 3541 3630 3721 3971 4223 4478 4736 4996 5258 5523 5633 5746 5861 5978 6098 6220 6344 6471 6600 6733 6867 7004 7145 7287 7433 7582 7734 7888 8046 8207 0.790123 0.702332 0.624295 0.554929 0.493270 0.438462 0.389744 0.346439 0.307946 0.273730 0.243315 0.216280 0.192249 0.170888 0.151901 0.135023 0.120020 0.106685 0.094831 0.084294 0.074926 0.066603 0.059202 0.052624 0.046777 0.041580 0.036960 0.032853 0.029203 0.025958 0.023074 0.020510 0.018231 0.016205 INDICATED VALUE NPV 8 $1,966,616 $1,556,665 $1,904,100 $1,917,280 $1,746,669 $1,591,617 $1,450,237 $1,375,709 $1,300,456 $1,225,763 $1,152,340 $1,080,535 $1,010,845 $ 943,814 $ 855,728 $ 755,860 $ 703,443 $ 637,792 $ 578,264 $ 524,291 $ 475,358 $ 430,993 $ 390,763 $ 354,291 $ 321,225 $ 291,247 $ 264,064 $ 239,416 $ 217,073 $ 196,811 $ 178,444 $ 161,787 $ 146,886 $ 132,993 LESS GOODWILL INDICATED VALUE OF INCOME $28,098,175 $26,131,559 $24,575,893 $22,671,794 $20,754,514 $19,007,845 $17,416,228 $15,965,990 $14,590,281 $13,289,825 $12,064,062 $10,911,722 $ 9,831,187 $ 8,820,342 $ 7,876,528 $ 7,020,800 $ 6,244,940 $ 5,541,497 $ 4,903,704 $ 4,325,440 $ 3,801,149 $ 3,325,791 $ 2,894,798 $ 2,504,036 $ 2,149,744 $ 1,828,519 $ 1,537,272 $ 1,273,208 $ 1,033,793 $ 816,720 $ 619,909 $ 441,466 $ 279,679 $ 132,993 $4,200,000 $4,200,000 $4,200,000 $4,200,000 $4,200,000 $23,898,175 $21,931,559 $20,375,893 $18,471,794 $16,554,514 The Commonwealth’s first claim is that the correct discount factor for the first year of the leasehold based on a 7 Amounts are in thousands. 8 Net present value. -6- 12.5% discount rate should be 0.88889 and not 0.790123. The Commonwealth’s second claim is that the discount rate of 0.88889 must be used for the first year of each succeeding tax year. The Jefferson Circuit Court rejected the Commonwealth’s arguments. The circuit court stated that it could not take judicial notice of the discount rate table, and affirmed the order of the Board. This appeal followed. When a reviewing court examines the decision of an administrative agency, the court must determine whether the agency’s decision is arbitrary.9 “In determining whether an agency’s action was arbitrary, the reviewing court should look at three primary factors. The court should first determine whether the agency acted within the constraints of its statutory powers or whether it exceeded them. Second, the court should examine the agency’s procedures to see if a party to be affected by an administrative order was afforded [her] procedural due process. The individual must have been given an opportunity to be heard. Finally, the reviewing court must determine whether the agency’s action is supported by substantial evidence. If any of these three tests are failed, the reviewing court may find that the agency’s action was arbitrary” [citations omitted].10 The Commonwealth does not claim that the Board either exceeded its statutory authority or denied it procedural due process, but the Commonwealth does claim that the Board’s 9 Commonwealth, Transportation Cabinet v. Cornell, Ky.App., 796 S.W.2d 591, 594 (1990). 10 Bowling v. Natural Resources & Environmental Protection Cabinet, Ky.App., 891 S.W.2d 406, 409 (1994)(quoting Cornell, supra). -7- assessments were arbitrary and capricious because they were not supported by substantial evidence. The Commonwealth states in its brief that the Board’s mathematical computations are “empirically wrong.” The Commonwealth points out that “there is absolutely no evidence in the record for the proper mathematical conversion for a 12.5% discount factor” [emphasis original]. The Commonwealth also argues that “the failure of the Board to acknowledge that each successive tax year should be treated as its own year, . . . is clearly erroneous.” The Commonwealth observes that if the year 1995 is viewed separate and apart from the other years, then it becomes clear that the 1995 year would be valued by taking “the value of the income stream beginning January 1, 1995, through 2027. relevance to this computation.” The year 1994 would be of no We agree with the Commonwealth on both issues. Substantial evidence has been defined as evidence “which, when taken alone or in light of all the evidence, has sufficient probative value to induce conviction in the mind of a reasonable person.”11 When analyzing whether an administrative agency decision is supported by substantial evidence, it should also be noted that the agency is afforded great latitude in evaluating evidence and in determining the credibility of witnesses, and although a reviewing court might have come to a different conclusion had it heard the case de novo, such a 11 Id. (citing Kentucky State Racing Commission v. Fuller, Ky., 481 S.W.2d 298, 308 (1972); and Blankenship v. Lloyd Blankenship Coal Co., Inc., Ky., 463 S.W.2d 62 (1970)). -8- disagreement does not deprive the agency’s decision of support by substantial evidence.12 “[T]he possibility of drawing two inconsistent conclusions from the evidence does not prevent an administrative agency’s finding from being supported by substantial evidence.”13 Indeed, an administrative agency’s trier of facts may hear all the evidence and choose the evidence that he believes.14 However, when an administrative agency’s finding involves a mathematical error in calculating the discount factor and an error in applying the discount factor to the term of the leasehold, that finding is not supported by substantial evidence and is arbitrary and capricious. While we decline to take judicial notice of the specific present value table sought to be introduced by the Commonwealth, we will take notice of common mathematical formulas,15 and we will correct obvious mathematical errors when they are evident.16 The Board applied a discount factor of 0.790123 in calculating the present value of the hotel’s projected income stream for the first year of the 12 Id. at 410. 13 Fuller, supra at 307. 14 Bowling, supra at 410 (citing Cornell, supra at 594). 15 See Pattie A. Clay Infirmary Association v. First Presbyterian Church of Richmond, Ky., 551 S.W.2d 572, 574 (1977)(holding that courts may take judicial notice of facts which are susceptible to immediate and accurate determination by resort to readily accessible and indisputable sources). 16 See Penrod v. Penrod, Ky., 489 S.W.2d 524 (1972)(holding that reviewing court will correct obvious mathematical errors committed by a trial court). -9- leasehold based on a 12.5% discount rate. Given the 12.5% discount rate as found by the Board in its ruling, the correct discount factor for the first year is 0.888889. Such a fact is easily verified by consulting any standard present value chart or by mathematical calculation.17 The discount factor of 0.790123, 17 Assuming a discount factor of 12.5%, the mathematical calculation for the first year is as follows: Discount factor = 1 (1 + R)n R = The discount rate n = The number of years DF = 1 (1 + R)n DF = 1 (1 + 12.5%)1 DF = 1 (1 + .125)1 DF = 1 1.1251 DF = 1 1.125 DF = 0. 888889 SECOND YEAR: DF = 1 (1 + 1.25)2 DF = 1 1.1252 DF = 1 1.265625 DF = 0.790123 -10- which was erroneously used by the Board for the first year, is actually the discount factor to be applied to the income stream in the second year. The Board’s error becomes even more obvious when one considers that LHR’s suggested discount factor for year one, which employed a more generous 14% discount rate, was 0.877193. Obviously, since the Board chose a discount rate of 12.5%, a rate less favorable to LHR than the 14% discount rate it suggested, the discount factor for the first year would have to be greater than 0.877193, not less. Furthermore, the same discount factor for year one of the leasehold term that is used for tax year 1994, must be used for year one of the remaining leasehold terms of each additional tax year. The tax year of 1994 will include the leasehold discounted values for a 34-year period; 1995, a 33-year period; 1996, a 32-year period; 1997, a 31-year period; and 1998, a 30-year period, respectively. While each succeeding year will have one less year included in the term of the leasehold, the decrease in the length of the term of the leasehold does not change the starting point of the computation for each tax year. The discount rate of 12.5% is the same for each tax year, and accordingly, the discount factor of 0.88889 must be the same for the first year of each leasehold term for each tax year. The one year decrease in the term of the leasehold is taken off at the end of the present value factor column, not at the beginning. The correct computations for the five tax years are as follows: -11- Year Adjusted Net Income 12.5% Discount Factor Indicated Value NPV 1994 $2,489,000 0.888889 $2,212,445 1995 $2,215,000 0.790123 0.702332 0.624295 0.554929 $1,965,004 1999 $3,630,000 0.493270 $1,790,570 2000 $3,721,000 0.438462 $1,631,517 2001 $3,971,000 0.389744 $1,547,673 2002 $4,223,000 0.346439 $1,463,012 2003 $4,478,000 0.307946 $1,378,982 2004 $4,736,000 0.273730 $1,296,385 2005 $4,996,000 0.243315 $1,215,602 2006 $5,258,000 0.216280 $1,137,200 2007 $5,523,000 0.192249 $1,061,791 2008 $5,633,000 0.170888 $962,612 2009 $5,746,000 0.151901 $872,823 2010 $5,861,000 0.135023 $791,370 2011 $5,978,000 0.120020 $717,480 2012 $6,098,000 0.106685 $650,565 2013 $6,220,000 0.094831 $589,849 2014 $6,344,000 0.084294 $534,761 2015 $6,471,000 0.074926 $484,846 2016 $6,600,000 0.066603 $439,580 2017 $6,733,000 0.059202 $398,607 2018 $6,867,000 0.052624 $361,369 2019 $7,004,000 0.046777 $327,626 2020 $7,145,000 0.041580 $297,089 2021 $7,287,000 0.036960 $269,328 2022 $7,433,000 0.032853 $244,196 2023 $7,582,000 0.029203 $221,417 2024 $7,734,000 0.025958 $200,759 2025 $7,888,000 0.023074 $182,008 2026 $8,046,000 0.020510 $165,023 2027 $8,207,000 0.018231 $27,410,286 $2,156,939 1998 $3,541,000 $4,200,000 $2,142,113 1997 $3,455,000 Indicated Value of Income $1,750,122 1996 $3,050,000 $149,622 Year Adjusted Net Income 12.5% Discount Factor NPV $31,610,286 Less Goodwill Indicated Value -12- Less Goodwill Indicated Value of Income 1995 $2,215,000 0.888889 $1,968,889 1996 $3,050,000 0.790123 $2,409,875 1997 $3,455,000 0.702332 $2,426,557 1998 $3,541,000 0.624295 $2,210,629 1999 $3,630,000 0.554929 $1,965,004 2000 $3,721,000 0.493270 $1,835,458 2001 $3,971,000 0.438462 $1,741,133 2002 $4,223,000 0.389744 $1,645,889 2003 $4,478,000 0.346439 $1,551,354 2004 $4,736,000 0.307946 $1,458,432 2005 $4,996,000 0.273730 $1,367,555 2006 $5,258,000 0.243315 $1,279,350 2007 $5,523,000 0.216280 $1,194,514 2008 $5,633,000 0.192249 $1,082,939 2009 $5,746,000 0.170888 $981,922 2010 $5,861,000 0.151901 $890,292 2011 $5,978,000 0.135023 $807,167 2012 $6,098,000 0.120020 $731,882 2013 $6,220,000 0.106685 $663,581 2014 $6,344,000 0.094831 $601,608 2015 $6,471,000 0.084294 $545,466 2016 $6,600,000 0.074926 $494,512 2017 $6,733,000 0.066603 $448,438 2018 $6,867,000 0.059202 $406,540 2019 $7,004,000 0.052624 $368,578 2020 $7,145,000 0.046777 $334,222 2021 $7,287,000 0.041580 $302,993 2022 $7,433,000 0.036960 $274,724 2023 $7,582,000 0.032853 $249,091 2024 $7,734,000 0.029203 $225,856 2025 $7,888,000 0.025958 $204,757 2026 $8,046,000 0.023074 $185,653 2027 $8,207,000 0.020510 $168,326 Year Adjusted Net Income 12.5% Discount Factor $33,023,186 Indicated Value NPV 1996 $3,050,000 0.888889 $2,711,111 1997 $3,455,000 0.790123 $2,729,875 1998 $3,541,000 0.702332 $2,486,958 1999 $3,630,000 0.624295 $34,941,151 $2,266,191 -13- $4,200,000 $28,823,186 Less Goodwill Indicated Value of Income $4,200,000 $30,741,151 2000 $3,721,000 0.554929 $2,014,392 2001 $3,971,000 0.493270 $1,958,775 2002 $4,223,000 0.438462 $1,851,625 2003 $4,478,000 0.389744 $1,745,274 2004 $4,736,000 0.346439 $1,640,735 2005 $4,996,000 0.307946 $1,538,498 2006 $5,258,000 0.273730 $1,439,272 2007 $5,523,000 0.243315 $1,343,829 2008 $5,633,000 0.216280 $1,218,305 2009 $5,746,000 0.192249 $1,104,663 2010 $5,861,000 0.170888 $1,001,575 2011 $5,978,000 0.151901 $908,064 2012 $6,098,000 0.135023 $823,370 2013 $6,220,000 0.120020 $746,524 2014 $6,344,000 0.106685 $676,810 2015 $6,471,000 0.094831 $613,651 2016 $6,600,000 0.084294 $556,340 2017 $6,733,000 0.074926 $504,477 2018 $6,867,000 0.066603 $457,363 2019 $7,004,000 0.059202 $414,651 2020 $7,145,000 0.052624 $375,998 2021 $7,287,000 0.046777 $340,864 2022 $7,433,000 0.041580 $309,064 2023 $7,582,000 0.036960 $280,231 2024 $7,734,000 0.032853 $254,085 2025 $7,888,000 0.029203 $230,353 2026 $8,046,000 0.025958 $208,858 2027 $8,207,000 0.023074 $189,368 Year Adjusted Net Income 12.5% Discount Factor 1997 $3,455,000 0.888889 $3,071,111 1998 $3,541,000 0.790123 $2,797,826 1999 $3,630,000 0.702332 $2,549,465 2000 $3,721,000 0.624295 $2,323,002 2001 $3,971,000 0.554929 $2,203,623 2002 $4,223,000 0.493270 $2,083,079 2003 $4,478,000 0.438462 $1,963,433 2004 $4,736,000 0.389744 $1,845,828 2005 $4,996,000 0.346439 $1,730,809 2006 $5,258,000 0.307946 $1,619,180 Indicated Value NPV $36,315,606 -14- Less Goodwill $4,200,000 Indicated Value of Income $32,115,606 2007 $5,523,000 0.273730 $1,511,811 2008 $5,633,000 0.243315 $1,370,593 2009 $5,746,000 0.216280 $1,242,745 2010 $5,861,000 0.192249 $1,126,771 2011 $5,978,000 0.170888 $1,021,568 2012 $6,098,000 0.151901 $926,292 2013 $6,220,000 0.135023 $839,843 2014 $6,344,000 0.120020 $761,407 2015 $6,471,000 0.106685 $690,359 2016 $6,600,000 0.094831 $625,885 2017 $6,733,000 0.084294 $567,552 2018 $6,867,000 0.074926 $514,517 2019 $7,004,000 0.066603 $466,487 2020 $7,145,000 0.059202 $422,998 2021 $7,287,000 0.052624 $383,471 2022 $7,433,000 0.046777 $347,693 2023 $7,582,000 0.041580 $315,260 2024 $7,734,000 0.036960 $285,849 2025 $7,888,000 0.032853 $259,144 2026 $8,046,000 0.029203 $234,967 2027 $8,207,000 0.025958 $213,037 Year Adjusted Net Income 12.5% Discount Factor Indicated Value NPV 1998 $3,541,000 0.888889 $3,147,556 1999 $3,630,000 0.790123 $2,868,146 2000 $3,721,000 0.702332 $2,613,377 2001 $3,971,000 0.624295 $2,479,075 2002 $4,223,000 0.554929 $2,343,465 2003 $4,478,000 0.493270 $2,208,863 2004 $4,736,000 0.438462 $2,076,556 2005 $4,996,000 0.389744 $1,947,161 2006 $5,258,000 0.346439 $1,821,576 2007 $5,523,000 0.307946 $1,700,786 2008 $5,633,000 0.273730 $1,541,921 2009 $5,746,000 0.243315 $1,398,088 2010 $5,861,000 0.216280 $1,267,617 2011 $5,978,000 0.192249 $37,400,060 $1,149,265 -15- Less Goodwill $4,200,000 Indicated Value of Income $33,200,060 2012 $6,098,000 0.170888 $1,042,075 2013 $6,220,000 0.151901 $944,824 2014 $6,344,000 0.135023 $856,586 2015 $6,471,000 0.120020 $776,649 2016 $6,600,000 0.106685 $704,121 2017 $6,733,000 0.094831 $638,497 2018 $6,867,000 0.084294 $578,847 2019 $7,004,000 0.074926 $524,782 2020 $7,145,000 0.066603 $475,878 2021 $7,287,000 0.059202 $431,405 2022 $7,433,000 0.052624 $391,154 2023 $7,582,000 0.046777 $354,663 2024 $7,734,000 0.041580 $321,580 2025 $7,888,000 0.036960 $291,540 2026 $8,046,000 0.032853 $264,335 2027 $8,207,000 0.029203 $239,669 For the foregoing reasons, the opinion and order of the Jefferson Circuit Court, which affirmed the order of the Kentucky Board of Tax Appeals, is reversed. ALL CONCUR. BRIEF AND ORAL ARGUMENT FOR APPELLANT: BRIEF AND ORAL ARGUMENT FOR APPELLEE: Lawrence E. Osterhage Louisville, Kentucky Robert L. Ackerson Louisville, Kentucky -16-

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