John J. Bernardo is an Associate Professor of Management in the College of Business and Economics at the University of Kentucky Alan Reinstein is an Associate Professor of Accounting at Oakland University in Rochester, Michigan

Bernardo, John J.

Reinstein, Alan

English

Georgia Southern University: Digital Commons@Georgia Southern

Southern Business Review Volume 13 Issue 1 Article 6 April 1987 A Budgeting Model for Analysis of Subsidized Programs John J. Bernardo University of Kentucky Alan Reinstein Oakland University Follow this and additional works at: https://digitalcommons.georgiasouthern.edu/sbr  Part of the Business Commons, and the Education Commons Recommended Citation Bernardo, John J. and Reinstein, Alan (1987) "A Budgeting Model for Analysis of Subsidized Programs," Southern Business Review: Vol. 13: Iss. 1, Article 6. Available at: https://digitalcommons.georgiasouthern.edu/sbr/vol13/iss1/6 This article is brought to you for free and open access by the Journals at Digital Commons@Georgia Southern. It has been accepted for inclusion in Southern Business Review by an authorized administrator of Digital Commons@Georgia Southern. For more information, please contact digitalcommons@georgiasouthern.edu. A BUDGETING MODEL FOR A AL YSIS OF SUBSIDIZED PROGRAMS 10h11 J. Bemardo a11d Ala11 Rei11.11ein Problem Definition The basic problem in budgeting a governmentally ~ubsidtzed service is that the total cost of the ~ervice usually remains unknown. leading to a discrepancy between the subsidy and the real COM of offering the service. Thts problem i, complicated by a difficulty common to all budgeting: the need to constantly revise budgets to reflect changing conditions conflict~ with the need to con~truct them for a lhed period of time. The purpose of this article is to develop a full-cost pricing scheme for a service whose fixed costs (those associated with making the service availahle) may change over time. but whme market price must include variable costs (those associated with offering the service). This is tantamount to determining the time path of future ,ubsidies for offering this service. The approach need, to be a . dynamic. ,o that II can determine the amount of ,ubsidy needed at each decision point in time. b. derived from an understanding of ,ub,idie, and economic theory. and c. compatible with standard accounting systems. Such a model would be generalizable to any service ,ubsid1zed in any fashion. including in-hou,e ,ervices (e.g .• consulting) that firms provide to other cost center, in the ,amc organi£ation and to sy,tem, where a ,ubsidy i, permanently needed such a, when ,ubsid1zcd ,ervices ,trc never expected to reach break-even volume. The Method Two co,t question, arc paramount: I . What portion of fixed coM, should the service-granting organization bear'! 2. What should the service cost be'! The am\\Cr, depend. first. on prinr dcc1st0n, that ma} be non-ct·onom1c A ,ervice exi,ts lo satbfy demand. and in th.: long run the u-.er commonly hear, pan of the total r.:0,1 of the service: but ho" much the u,cr bear, depend, upon the type of service. A health care facility for the indigent. for example. ma) he wb~id1zed complete!). while a technology tran~fer center will he expected to recoup it, service co~t eventually. A model. then. mu,t be flexible enough to provide for a range of payback assumption~. Wh1k: ignortng the subjective mea~urement of ~ocial benefit. our model alkm, the long-run percentage of fix-t:d co,ts ~ub\id1£ed (i.e .. 1he loading factor) to vary between O and 100 percent. A graphical linear breakeven model of a ,ubsidiLcd ~ervicc appear~ in Figure I, with: FC Fixed Co~t~ V Variable Co~t~ TR Total Revenue 33 -- TC = Total Cosh Q• = Long-Run Expected Activity The program was to be subsidized until volume reached the "break-even .. point. q1 Actual Usage R1 = Revenues Necessary to Breakeven at q1 R2 = " Expected .. Revenue~ Dunng "Initial" Subsidy Period MC = Marginal Cost of the Service p = Transfer Pnce of the Service (1.e .. slope of TR) R1 - R2 represents the required subsidy at u,agc level q 1. $ - - - - - -lit SUBSIDY t FC - - - - - -Rz I --, FIGURE I: A typical brcakcven graph for a service having a long-run expected ac11v1ty of Q* and an actual u,agc of q1. TR TC In developing a full cost pncing scheme for a ,ub,iJiied service. FC. o•. and MC are known or can be determmeu by the de,1gn of the unit offering the ..ervice. but P mu,t be determined In general. I) P = MC + LF(FC - S). where Sis the subsidy for the service, and LF is the per unit loading factor for the fixed costs. The subsidizing agent will often use inefficient trial and error approaches to solve Equauon ()), selectmg among three pos,iblc actions: I. Alter the user fees (i.e., P) 2. Alter the suhs1dy (i.e., S) 3. Alter the expected activity (1.e., FC) Many puhlic sector and non-profit organizations have expenenceJ significant problems because they used short-run buJgets and plans for subsidized services. For example. during the 1960s. the Ford Foundation spent $2 million to help 34 _J establish Monteith College at Wayne State University as an "honors college" for "non-honors, average students." The concept of unstructured education was innovative and expensive. When the subsidy expired, Monteith's demise wa5 not far behind [Riesman, Gusfield and Gamson, 1970). Budgeting's Role in Solving the Problem Horngren (1985. p. 123) defines a budget as a quantitative expression of an action plan with the usual planning and control period of one year. A good budget helps management plan. coordinate , implement, and evaluate operations. Our dynamic budgeting model has significant advantages over the three typc5 of budgets that the public sector generally uses: line-item veto, zero-based budgets (ZBB) and incremental budgets. Under a line-item veto. the executive can unilaterally delete expenditures unless the legislature overrides the decision (usually requiring a two-thirds majority). While the governors of 43 states and many other governmental executives e.g .. county commissioners have this power. other than applying incremental budgeting action5 e.g., veto any appropriation exceeding 2%. above the rate of inflation. the line-item veto method is seldom applied 5ystematically and is often subject to panisan pressure. ZBB b 5aid to have originated in I 924 when C. Hilton Young advocated reju5tifying budgets annually (Buck (1934. p. 172]). However. it was not until the early 1970s that ZBB became the watchword for effective control of the management proce5S. After "successfully " applying this i:onccpt as Governor of Georgia. President Carter asked each federal agency to develop its 1979 fiscal year-end budget using a ZBB system (Herzlinger [ 1979)). Many expens have criticized the ZBB concept of rejustifying all expenditures "from scratch" each year. Robert Anthony (19771 Mated that the concept was not workable. In general the concept proved impractical becau5e of the massive time required for implementation (e.g .. ranking and con~olidating programs). In 1981. President Reagan cancelled the ZBB requirements. While some private corporations and municipalities (e.g., ,cc Connel [ 19801). univcrsitie~ (e.g .. ~ee Bennett. O"'en and Warner [ 19801) and CPA firms (e.g., ,ee Brown [ 1981)) have experienced some success with the ZBB concept. implementation has remained a problem. Incremental or priority incremental budgets require the government agency to concentrate each year·s review on proposed increases while the "base" (current level of ~pending) receives little scrutiny. Again, however. the proce~s may be difficult to implement because immediate priorities often overrule long-term objectives, and the proce~s generally ignores long-term cons1dera11ons. The budgeting model reported here is superior to these three approaches m that it conMder~ the long-run effects of offering a ~ub,1dizcd service. and it can then alter the subsidy or price ba~cd upon changes in demand or other priorities. Model Development The following ca~e study demonstrates an application of the model summarized by Equation (I) for a full-cost pricing scheme for a ~ubsidized service. The model wa& implemented for a government-sponsored program whose goal was to transfer technology from its data bases to ~late and local government units and to private 35 • SMZFI industry. The initial pricing strategy was to charge users only the variable costs of the service, with the government subsidizing the fixed costs. Total costs were absorbed and fees were then raised to cover actual costs as demand changed, with the long-run goal of eliminating the subsidy. While the government never expected to recover this subsidy. subsequent additions to capacity were to be funded by other means. Thus. a short term marginal cost pricing scheme provided the necessary pricing and subsidy information. The marginal costs of primary interest are associated with the actual process of supplying customers with the requested information. In our application all search procedures consist of two stages: (I) identifying the problem and reviewing the abstracts, and (2) analyzing the relevant informa11on and reporting the results to the users. As outlined in Figure 2, four step5 are required to provide thi~ service: I. Develop the problem and design the search strategy. 2. Initiate the search process. conduct the initial data analysb. and prepare a report. 3. Supply documents. 4. Conduct ex-post analysis and add111onal report preparatlon. The costs of obtaining the above information generally varied by the type and complexity of question a~ked. TICLII.£ 2 A) tn,~try C) Ltxal Govt.• Md'•• etc. Semce lnforaatl.an Sourt.l!& (I) (2) Fl.O,I or suncn• hiit1.al leq\1-fi&t leV"lc"' lequeat for of Stwhu •M A.batracu ------+Oo<u.-.nt:)} 111 ,j Pul&aiqr, Anal)'&U J AMlysu ldantlfJ .... In.to Conulid.atioo, SoW'"CH of l Abltr&CU Conduct Searer,, .. Coeputer IDct\Ul"J'--,. hd Le,b Couoru.ia NASA lf:Harcb and Spact Ce-nu:u Colhae lrohuor, 1 l Clo<\allnU Ordered tradr M•oc1at1on• •staa1 r,\atlen 1 ttlroucb II art hi D•r•nthuu lnfor-ation7 Received ( )) leport Pre,.red And T''····· Doci.aaDtl Re cinved &D4 Pouibl,.-M.ril11:ed lequelt for rurtbll!r Ana lJt U C•) The goal of the pricing ~ystem wa~ to determine, for the three major categories of cuMomers. the minimum price that would include marginal co~t~ plus the "proper" portion of fixed co~ts. After identifying the costs, prices for services rendered could be based on either of two alternatives: I . Cost range~ can he used to ascertain minimum and maximum charges on the cos~ of the service, with the agency absorbing (or receiving) any costs exceedmg (less than) the quoted range. 36 a sr en szrmrnnr TSF ... , -EYMIJOII 2. A single, weighted average quoted price can be used, again with the service-granting agency absorbing the differences. Although we used the second alternative for pricing purposes. the model also may be calibrated using the first alternative. The objective of the analysis is to determine a price <Pj) for service j: (I -a) Pj = MCj + LFj(FC - S) where MCj is the marginal cost associated with service j. LFj is the fixed charge loading factor for allocating fixed cost~ among . . . 3 the three customer services J (1.e., E LFj = I). j= I FC is the fixed cost of offering the service. S is the subsidy (i.e., TCj - TRj). The pricing scheme represented by equation ( 1-a) is general in that I. if S =0. Pj is the breakeven price at Qj ; however. S = 0 only if designed capacity equals actual capacity; 2 . if S = FC, the subsidy equals the fixed cost of offering the service. and the user pays only the marginal cost a~sociated with 3 . its use; if O < S < FC. then the offering agent agrees to absorb a percentage. S/FC. of the cost of the service. which generally occurs under "normal'' initial s ituations. Defining Qj as the long-run expected activity of the service at the break-even point. 2) Qj = Dj where Dj is the demand for the service j. In general. Dj i~ a function of the price. Pj, and the utility of the service. Uj, as follows: 3) Dj = f(Pj. Uj) Smee the goal 1s to price a non-profit service (i.e., equation (2) hold~) by specifying Dj, Pj could be determined by ~ubMituting (3) into (I-a). In the problem investigated. as with mo~t new services, a lack of "history" of product demand prevented determining a functional form for equation (3). Instead. a marginal cost pricing scheme wa~ u~ed to determine MC and LF ·. Since marginal cost equals the average variahf e cost w~en the latter i~ at the minimum, estimating fixed cost~ and minimum variable costs in~ure~ that the result is a minimum price for the service that fully absorbs all costs minus the subsidy. To obtain a full-costing loading factor LFj, vcj LFj = -N~'--- for j = 1,2, ... N E VCi J=I where N is the number of services offered. Colantoni. Manes and Whinston [ 19691 provide the rationale for allocating fixed costs based solely upon variable costs, as used in this subsidized services model. Generally, fixed costs should be allocated based upon the "right" to use a service (i.e., the long-run capacity to provide the service). For example. fixe.d maintenance costs are allocated based upon relative square footage-regardless of actual 37 --maintenance used. However, in pricing decisions. their methodology yields the total minimum price which can still absorb all fixed costs . That is, it satisfies the least price criteria goal of the servicc5. Application The results of a work methods study helped estimate the long-run activity of Q* and the associated variable costs. Each technician accumulated the elapsed time to completion for each request and categorized the data according to the stage of the analysis. Following a 100% sampling for ~ix weeks. 179 inquiries helped form preliminary cost and time estimates. Table I shows the variable coM estimate that re~ults for each type of request-state and local government and industry. re5pectively. For example , the state government's reque5tS at Stage I averaged $8.13 and totaled $49.00. TABLE l AVERAGE VARIABLE COSTS AND FIXED COST LOADING FACTORS A enc State Local Bu& ines6 and Government Government Industry Average Variable Costs (for the Technology Transfer Service by the Requesting Agency) Stage I Stage 2 Total Fixed Costs Loading Factors 8.13 40.87 $49~0() Actual Variable Cost (as a ratio .28 of total variable costs) Full Utilization Load (Based Upon Actual Time Studies) 250 Loading Factor per Job .00112 8.44 45.90 354. 34 40 230 .00174 24.5D 45.35 $69.85 32 230 .OOIJ9 Total 1.00 710 .0014 Based upon a six-week pilot study of time estimates. computations and work Mudy information, it was estimated that the unit could handle 710 typical request5 per month-with the state governments, local governments and business and indu5try normal activity at 250. 230 and 230 monthly requests. respectively. However. during the start-up period. the unit operated at approximately 20 percent of capacity. with actual variable costs for the three service classes comprising 28, 40, and 32 percent, respectively. of all variable costs. A5 al so noted in Table I. the loading factor per job (LC·) equals the above quotient of costs divided by the expected long-run activity fo; each service class [i .e., (average variable cost as a ratio of total variable costs)/(long-run expected activity for that agency)] . 38 ---7 JP 77 rws lll:§61 S Combining the information from Table I yields the prices charged for the subsidized services, where P 1, P 2 and P 3 represent state government. local government and business/industry. respec1ively. P, = $49.00 + .OOl 12(FC-S) P, = $54.34 + .00174(FC-S) P3 = $69.85 + .00139(FC - S) By analyzing the variance of expected revenues over time, a time path of price and subsidy as a function of utilization can be determined. If the demand for the service grows as expected. the subsidy will reach zero, and the price equals the actual variable costs plus a portion of fixed costs. However, if the actual subsidy exceeds the planned subsidy. FC muM be decreased. or demand increased to meet long-run objectives. Conclusions This paper presents a method for planning subsidies over time for a not-for-profit service. In particular. we showed by actual case history how to eMimate a full cost pricing scheme. The relationship P) = MCj + LFj<FC-S) yields a price for ~ervice j given a subsidy. A, time 'progresses." the effect of changes m the subsidy can be analyzed. The objective is to reach a zero subsidy level. B) Figure I. we see that this is at the long-run expected capacity Q•. IfQ• is not attainable. the model can be used to forecast the required subsidy given q. or be used to determine the new price given actual utilization. In either case the model can predict the budget impact by utilizing the interrelationship between price and subsidy. Thus. the developed budgeting model is superior to conventional models m that it sets a long-run perspective. provides a method for continual change. and terminates with (a) a zero or mimmum subsidy. or (bl costs of maintaining the subsidy incorporated into the decision model. Bibliograph~ Anthony. Robert N .. "Zero-Base Budgeting: A Useful Fraud'.1" The Govern-ment Accountants Journal. (Summer 1977): 8-12. Bennet. Kenneth. L. Owen and T. Wagner, ··implementing ZBB at Stanford University." Business Officer (May I 980): 21-23. Brown. Ray L., "Beyond Zero-Ba,c Budget mg," Journal of Accountancy. (March 1981): 44-52. Buck. A.E .. The Budgets in Government Today. New York: MacMillan. 1973. Colantoni. C.S .. R.P. Manes and A. Whinston. "Programming Profile Rates and Pricing Decisions," Accounting Re,•iew (July 1969): 467-481. HerLlinger, Regina E., "Zero-Base Budgeting in the Federal Government: A Case Study ." Sloan Management Review. (Winter 1979): 3-14. Horngren, Charles T ., Cost Accounting: A Manageria l Emphasis, 6th ed. Englewood Cliffs, N .J.: Prentice-Hall , I 985. 39 77 .. Rei, man, D .. J . Gusfield and Z. Gam,on. Academic Values and Mass Education: The Earl) Years of Oakland and Monteith. Garden City. N.Y.: Doubleday. 1970. John J. Bernardo is an Associate Pmfe"or of Management in the College of Busine,, and Economics at the Universit) of Kentucky Alan RemMcm is an As~iate Profe\sor of Accounting at Oal..land Umvcr~ity m Rnchc\ter. Michigan. 40 

A Budgeting Model for Analysis of Subsidized Programs

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A Budgeting Model for Analysis of Subsidized Programs

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