Digital Commons@ Loyola Marymount University Loyola Law School Fince & CIS Faculty Works Fince & Computer Information Systems 1-1-1984 A Markovi Model for Valuation of Hum Assets Acquired Orgizational Purchase Eric G. Flamholtz University of California - Los Angeles George T. Geis University of California - Los Angeles Richard J. Perle Loyola Marymount University, rperle@lmu.edu Repository Citation Flamholtz, Eric G.; Geis, George T.; Perle, Richard J., "A Markovi Model for Valuation of Hum Assets Acquired Orgizational Purchase" (1984). Fince & CIS Faculty Works. 3. http://digitalcommons.lmu.edu/fina_fac/3 Recommended Citation Flamholtz, E.G., Geis, G.T., Perle, Richard J. "A Markovi Model for Valuation of Hum Assets Acquired Orgizational Purchase." Interfaces 14 (1984): 11-15. This Article is brought to you for free open access Fince & Computer Information Systems at Digital Commons @ Loyola Marymount University Loyola Law School. It has been accepted for inclusion in Fince & CIS Faculty Works authorized administrator of Digital Commons@Loyola Marymount University Loyola Law School. For more information, please contact digitalcommons@lmu.edu.
A Markovi Model for Valuation of Hum Assets Acquired Orgizational Purchase Eric G. Flamholtz Graduate School of Magement, Hum Resource Magement Institute of Industrial Relations University of California, Los Angeles Los Angeles, California 90024 Center for George Richard T. Geis J. Perle Center for Hum Resource Magement Institute of Industrial Relations University College of Business of California, Los Angeles Loyola Marymount University Los Angeles, California 90045 A corporation acquires assets liabilities of a securities brokerage firm for a price in excess of net book value. A Mar kov alysis is used in conjunction with hum resource accounting to value a pool of account executives employed brokerage firm. The tax implications of imputing a portion of purchase price premium to pool of hum assets (as opposed to goodwill) are discussed. It is increasingly recognized that United States is experiencing a qualita tive trsformation from industrial, goods-producing economy to a service based economy. In addition, services being provided in newly emerging economy often a require considerable amount of training experience. Ac cordingly, a distinctive feature of emerging economy is increasing em phasis on importce of hum capi tal ( knowledge, skills, experience of people) as opposed to physical capital. One outgrowth of this economic metamorphosis has been development of a field known as "hum resource ac counting" (HRA). HRA is concerned with identifying, measuring, reporting (to magement investors) data relating to hum resources in orgization. It involves measuring accounting for economic value of people as orgiza tional resources [Flamholtz 1974]. A Markov alysis c be used in con junction with hum resource accounting to assign value to a pool of hum assets. The Problem A corporation purchases assets liabilities of a securities brokerage firm for a price in excess of net book value. A por Copyright? 1984, The Institute of Magement Sciences 0092-2102/84/1406/0011$01.25 This paper was refereed. DYNAMIC PROGRAMMING? MARKOV, FINITE STATE FINANCIAL rnstttutions? BROKERAGE AND TRADING INTERFACES 14: 6 November-December 1984 (pp. 11-15)
FLAMHOLTZ, GEIS, PERLE tion of purchase price premium was attributable to (unmeasured) value of intgible asset acquired pur chaser, that is, hum capital or hum assets represented acquired pool of account executives (registered rep resentatives) employed brokerage firm. If asset c be depreciated for tax purposes, a corporation c generate a cash flow savings which represents a sig nifict economic benefit. In order for intgible asset to qualify for a deprecia tion allowce for tax purposes, it must be established that (1) asset has a lim ited useful life which c be ascertained with reasonable accuracy, (2) asset has a value separate distinct from goodwill (Revenue Ruling 64-465, 1974-2 CB 65). Consequently, we designed this study to determine what portion (if y) of purchase price premium represents pay ment for hum assets as opposed to goodwill. Specifically, tions were swered: following ques (1) What is fair market value of asset associated with acquired pool of account executives? (2) What is useful life of this asset? (3) What is appropriate schedule to use in amortization of asset? Model Formulation Our approach to this problem involved applying HRA concepts toger with a Markov alysis. A finite stationary Mar kov process is assumed to describe movement in sales commis year-to-year sions generated individual account executives (AEs). The necessary condi tions specifications for applying model to evaluation of AEs are (1) Each AE is in exactly one of four pos sible states during each year. Three of states are trsient are de fined relative amount of nual sales commissions produced. They are titled high, medium, low produc ers. The fourth state is absorbing state into which AE enters when he leaves firm. This fourth state is ti tled termination, it is assumed that once AE is terminated, he will never return to firm. (2) At end of each year, each AE may remain in his" present state or move to y of or states. If his present state is that of termination, he must, of course, remain in that state. (3) The trsient state occupied AE during current year depends only on state he occupied during immediately preceding year. If we as sume that AE generates sales be cause of his selling techniques, this specification n also requires us to assume that sales techniques not used or reinforced during past year will not be helpful in generating sales dur ing current year. (4) The trsition probabilities of moving between states remain constt over time. (5) The trsition probabilities are same for each individual AE. Hum Resource Valuations Generated The most importt output of model is cumulative (over time) dis counted expected value of future profits attributable to group of AEs with firm at time of acquisition. The sum of this discounted stream of future earnings INTERFACES 14:6 12
HUMAN ASSETS may n be considered as estimation of total depreciable value of hum asset, DT, at time of acquisi tion is represented equation (1) in appendix. In order to calculate DT, it is first neces sary to determine schedule which that value will be amortized. Any accept able method (straight line, double declin ing balce, so forth) might be used over N year life of asset; however, a more rational method would be to amor tize in each future year discounted profit expected to be generated hum asset in that year. This value for y year n, Dn, is calculated equation (2) in appendix. Estimation of Model's Parameters The generation of a realistic amortiza tion schedule requires empirical esti mation of behavioral characteristics of assumed Markov process. We must estimate initial state probabilities (tt?0 values) one-step trsition matrix probabilit?s (Pi?1} values). For purpose of estimating trsition probabilities, we defined four mutually exclusive exhaustive "service states": (1) high, (2) medium, (3) low sales performce (as measured nual sales commis sions), (4) exit state (termination). The high, medium, low states were defined upper, middle, lower third of nual sales commissions during each year. Next we tracked each AE examining personnel records to determine which state individual occupied for a period of six years prior to firm's ac quisition date. Thus, each AE was ob served making five trsitions between within four states of process. State During Year n + 1 State During Yearn High Medium Low Terminated High 0.7431 0.1927 0.0000 0.0643 Medium 0.0786 0.6900 0.1921 0.0343 Low 0.0042 0.1081 0.7500 0.1377 Terminated 0.0000 0.0000 0.0000 1.0000 Table 1: State-to-state rate based chgeover on nual account executive performce over chges averaged six-year study period (estimate of one-step Markovi tr sition probabilities). The one step trsition matrix shown in Table 1 was generated aggregating year-to-year trsitions for all AEs for all years. If acquisition occurred exactly at year-end, values could be estimated measuring proportions of firm's AEs in each of four states at that point in time. However, it is difficult to measure se proportions when acquisition occurs at or times of If asset c be depreciated for tax purposes, a corpora tion c generate a cash flow... savings year because accounting records of AE sales performce are normally kept on a calendar year basis. Thus, measurement of proportions associated flows would not be synchronous. In this problem it is assumed that acquisition occurred two months prior to year-end so to achieve synchronization we ad justed proportions or forecast what ir year-end values would be two months after acquisition. The adjustment is made starting process allow ing it to run only two-twelfths of a year November-December 13 1984
FLAMHOLTZ, GEIS, PERLE under assumption that, collectively, AEs gradually chge from one state to or. The process is n restarted at beginning of first whole year with initial state probability (7^) values in Table 2. Successive values of ir^ are n generated applying appendix equation (2). Proportion State, i at Acquisition Time 7rto 1. High 0.1163 0.1149 2. Medium 0.2425 0.2425 3. Low 0.6412 0.6222 4. Terminated 0.0000 0.0176 Table 2: Initial state proportions prob abilities. This shows that during two months from acquisition to year-end, ex pected number of high low producers de clines while expected number of medium producers increases. It is also expected that 1.76 percent of all AEs will terminate during this time period. Results The hum asset value acquired related schedule for amortization of asset associated with account execu tives, calculated as Dn, n=l, 2,... N, is shown in Table 3. The reported data is disguised unstated multiple hence does not reflect actual amounts. Amortization in first year reflects a partial year income stream reflecting acquisition date. Note that total value of asset pool, as calculated from ap pendix equation (1) is simply sum of yearly amortizations or $8,208,254. The oretical maximum life of asset was determined to be 40 years. (From accounting viewpoint, use ful life of asset for amortization pur poses was determined to be 17 years. Ninety-five percent of value of hum assets will be realized end of sixteenth year after date of acquisi tion. Since less th five percent of original asset's value will remain after sixteenth year, this amount in aggre gate is not considered to be material, it should be "written off" in seven teenth year.) This 40-year life was selected for fin cial as well as practical reasons. From a fi ncial point of view, amount of amortization after year 40 was considered to be immaterial. From a practical point of view, 40 years is viewed as reasonable for expected maximum tenure of ac count executive. Although dollar amounts given in Table 3 are disguised, acquiring cor poration did use method for hum asset valuation described in this study for tax reporting purposes. (It should be noted that actual amortization schedule used corporation for tax purposes involved a "switch over" to straight line amortization, details of which are not reported here.) The Study's Implications The attribution of value to a pool of hum assets obtained through acqui sition has obvious tax implications. Speci fically, if acquiring firm c depreciate hum assets acquired, it will gener ate significt cash savings. The amortization allowce obtained a determining value for asset c be importt consideration in Ex Ante acquisition alysis valuation, for if hum capital c be depreciated, ef fective cost of acquisition is decreased. The use of a Markov process in forecast ing future number of account execu tives in service states would seem to be a INTERFACES 14:6 14
HUMAN ASSETS Amort. Amort. Amort. Amort. Year Per Yr. Year Per Yr. Year Per Yr. Year Per. Yr. 1 $ 228,348 11 $268,286 21 $35,635 31 $4,607 2 1,255,077 12 220,066 22 29,067 32 3,754 3 1,088,822 13 180,275 23 23,696 33 3,058 4 934,649 14 147,522 24 19,314 34 2,492 5 795,707 15 120,616 25 15,741 35 2,030 6 673,048 16 98,550 26 12,828 36 1,654 7 566,400 17 80,475 27 10,454 37 1,347 8 474,730 18 65,686 28 8,518 38 1,098 9 396,622 19 53,595 29 6,941 39 894 10 326,536 20 43,717 30 5,655 40 728 Total value of account executive pool $8,208,254 Table 3: Hum asset value related amortization schedule for stockbrokers acquired in acquisition. major factor in meeting Internal Reve nue Service's criteria for depreciation al lowce; that is, limited useful asset life that c be determined with reasonable accuracy asset value separate dis tinct from goodwill. Given growing appreciation of importce of hum assets in orgizar tions, valuation of se assets seems not only reasonable, but necessary. In a hum capital intensive economy much of value of firm is comprised of hum, rar th assets. References physical or fincial, Flamholtz, Eric G. 1974, Hum Resource Ac counting, Dickenson Publishing, Encino, California. Hillier, Frederick S. Lieberm, Gerald G. 1980, Introduction to Operations Research, Hol den Day, S Frcisco, California. APPENDIX The total depreciable value of hum asset is discounted sum of future earnings, *>T - t Dn (1) The nual depreciable timated to be value is n es D S^T^nVin (1 + d)n where 7Tin = probability of AE being in state ; during year n, Vjn = undiscounted value of profit attributable to sales ef fort of AE who is in state ; during year n, d = discount rate, S = number of AEs with firm at time of acquisition, N = a practical upper limit on number of years AE might spend with firm after acquisition, M = number of states. The value of 7rjn are found em ploying one-step trsition prob abilities Chapm-Kolmogorov equations which may be found in Hillier Lieberm [1980]; m *jnr??ioty for; = 1, 2,..., m (3) where 7ri0 = probability of AE being in state i at beginning of first year,? Pifn) The w-step trsition probability which is conditional probability that AE, starting in state i in first year, will be in state ; after n years. November-December 15 1984