Altimus, Cyrus A., Jr.

Tersine, Richard J.

English

eGrove (Univ. of Mississippi)

Management Adviser Volume 11 Number 3 Article 7 5-1974 Probabilistic Profit Planning: A Feasible Approach Richard J. Tersine Cyrus A. Altimus Jr. Follow this and additional works at: https://egrove.olemiss.edu/mgmtadviser  Part of the Accounting Commons, Business Administration, Management, and Operations Commons, and the Management Sciences and Quantitative Methods Commons Recommended Citation Tersine, Richard J. and Altimus, Cyrus A. Jr. (1974) "Probabilistic Profit Planning: A Feasible Approach," Management Adviser: Vol. 11: No. 3, Article 7. Available at: https://egrove.olemiss.edu/mgmtadviser/vol11/iss3/7 This Article is brought to you for free and open access by the Archival Digital Accounting Collection at eGrove. It has been accepted for inclusion in Management Adviser by an authorized editor of eGrove. For more information, please contact egrove@olemiss.edu. The recent SEC announcement that corporate esti­mates of future earnings could be publicly announced strongly implies that the next step could be that they are required to be. This will lead to a much more rigidly determined earnings forecast —PROBABILISTIC PROFIT PLANNING:A FEASIBLE APPROACHby Richard J. Tersine and Cyrus A. Altimus, Jr.Old Dominion UniversityCorporations have always been interested in profit planning.The usual approach has been through deterministic budgets by both formal and informal proc­esses. Profit-planning information is vital for internal decision mak­ing. Decisions concerning the se­lection, procurement, and utiliza­tion of resources are highly de­pendent on the accuracy of profit projections. Profit planning in the form of released estimates of fu­ture performance to financial in­stitutions has an important impact on the stock market vis-a-vis secu­rity prices.A future requirement?Historically, corporations have revealed future economic perform­ance informally with less than full public disclosure. This situation has dismayed many regulatory agencies. The Securities and Ex­change Commission now permits and may someday require corpo­rations to publish forecasts of their earnings.1 Proponents argue that simple fairness, not to mention legal requirements, dictates that forecasts be made public. Oppo­nents argue that forecasts could re­sult in a flood of lawsuits against management for any losses.As long as profit planning was only for internal management use, there was no necessity for formal control procedures. A requirement for public disclosure mandates the need for common formal proced­ures. Although full disclosure of profit forecasts is not required at this time, it may not be very far off on the time horizon. This ar­ticle will develop a probabilistic profit model that the authors be­lieve could meet this impending future need.The typical profit budget for a1—Securities Act Release 5362 and Ex­change Act Release 9984, February 2, 1973, “Statement by the Commission on Disclosure of Projections of Future Eco­nomic Performance.” single-product company is shown in Exhibit 1, page 47. This direct- costing format permits the use of breakeven and cost-volume-profit analysis. Fixed costs have been segmented into managed and com­mitted costs. Managed fixed costs are costs that can be modified in the short run, while committed fixed costs are both useful and ap­propriate in the preparation of probabilistic budgets.The segmentation of fixed costs into managed and committed costs allows a more detailed examination of the figures used to develop the profit budget. However, the bud­get in Exhibit 1 and others like it allow for no indication of poten­tial variability of the various esti­mates. The specific items in the budget are subjective estimates of the most likely values to occur. The neglect of variability is the most outstanding weakness in the typical deterministic profit budget. The uncertainties and dynamic fea­46 Management Advisertures surrounding an organization create a difficult atmosphere for the single most likely estimates used for profit planning. Precise definitions of such potentially vola­tile variables as revenue, selling price, sales mix, labor cost, and material cost are difficult—if even possible. When single estimates, rather than a range of possible outcomes, are used, the signifi­cance of dispersion is ignored.Budgets can be considered plans for the future which incorporate forecasted performance levels. Since the future is uncertain, no­body can forecast the future per­fectly. A useful approach is to treat uncertainty in terms of risk. Risk requires the gathering of ad­ditional information, insights, judg­ments, experience, hunches, and intuition to be able to make some kind of probability estimate about the relative likelihoods of perform­ance levels. Futuristic probability estimates frequently require both objective and subjective probabili­ties. Probabilities are objective if nearly everybody would arrive at the same values. Probabilities are subjective if they are determined by judgment, intuition, and ex­perience.With subjective probabilities, not all decision makers from different backgrounds would establish the same probability distribution for events. While this fact can be dis­couraging, there are benefits from such a process of subjective assimi­lation. It permits an analysis of one-of-a-kind problems that manag­ers previously had to handle with­out assistance. It encourages mean­ingful communication among mem­bers of the organization by pro­viding a common language in which to discuss problems. Ex­plicit consideration of performance risk sharpens thinking because it makes disagreements between managers explicit and puts the im­portance of various factors into perspective. The preparation of the model could be the greatest benefit from risk analysis.While a stochastic approach to profit planning may be advantag-Profit Budget for the Year Ending 197XEXHIBIT ISales 100,000 units @ $5Variable CostsManufacturing $2 per unitMarketing $1 per unit$200,000 100,000$500,000300,000Marginal Contribution Managed Fixed Costs Manufacturing Marketing Administration$ 10,000 5,000 20,000$200,00035,000Short-Run MarginCommitted Fixed CostsManufacturing Marketing Administration$ 80,00015,00020,000$165,000115,000Net Income Before Taxes Taxes—50%$ 50,00025,000Net Income After Taxes $ 25,000eous, the difficult task is to model realistic performance in a prob­abilistic framework. The account­ing profession has not specified how stochastic profit budgets should be constructed. As early as 1966, the American Accounting As­sociation encouraged the adoption of probabilistic financial state­ments, but did not offer any guide­lines.2 Numerous authors have ad­dressed the problems of risk and uncertainty.Variety of approachesJaedicke and Robichek3 used the normal probability distribution to consider risk in cost-volume-profit analysis. Magee4 developed deci­sion trees to determine expected net present value of alternative in­vestments. Hertz5 applied compu­ter simulation with specified dis-2—American Accounting Association, A Statement of Basic Accounting Theory, 1966, pp. 38, 59, and 65.3—Jaedicke, R. K., and A. A. Robichek, “Cost-Volume-Profit Analysis Under Con­ditions of Uncertainty,” The Accounting Review, October, 1964, pp. 914-26.4—Magee, John F., “How to Use Deci­sion Trees in Capital Investments,” Har­vard Business Review, September-Octo­ber, 1964, pp. 79-96.5—Hertz, David B., “Risk Analysis in Capital Investment,” Harvard Business Review, January-February, 1964, pp. 95- 106, and “Investment Policies that Pay Off,” Harvard Business Review, Janu­ary-February, 1968, pp. 96-108. tributions to obtain the expected return on investment. Hillier6 in­corporated risk into capital invest­ment decisions by assuming a nor­mal distribution. Byrne et al.7 rec­ommended decision trees and net­work concepts in financial state­ments. Tersine and Rudko8 ad­vocated bivariate risk treatment in capital investments with uncertain lifetimes. Coughlan9, Hespos and Strassman10, and Springer et al.11, provided procedures for develop­ing stochastic financial statements. Greer12 developed procedures for6—Hillier, Frederick S., “The Derivation of Probabilistic Information for the Eval­uation of Risky Investments,” Manage­ment Science, Volume 9, 1963, pp. 443- 57.7—Byrne, R., et al., “Some New Ap­proaches to Risk,” The Accounting Re­view, January, 1968, p. 33.8—Tersine, Richard J., and William Rud­ko, “A Bivariate Stochastic Approach to Capital Investment Decisions,” The En­gineering Economist, May, 1972, pp. 157-76.9—Coughlan, John W., “Profit and Proba­bility,” Advanced Management Journal, April, 1968.10—Hespos, R. F., and P. A. Strassman, “Stochastic Decision Trees for Analysis of Investment Decisions,” Management Science, August, 1965, pp. 244-59.11—Springer, Clifford H., et al., Proba­bilistic Models, Irwin, 1968, chapts. 4 & 5.12—Greer, Willis R., “Capital Budgeting Analysis with the Timing of Events Un­certain,” Accounting Review, January, 1970, pp. 103-114.May-June, 1974 47EXHIBIT 2Pessimistic Most Likely OptimisticSales ($5 per unit) $400,000 $500,000 $585,000Variable CostManufacturingMarketing ($1 per unit)150,00080,000200,000100,000240,000 125,000Marginal Contribution $170,000 $200,000 $220,000Managed Fixed Cost Manufacturing Marketing Administration$ 5,0004,00015,000$ 10,000 5,000 20,000$ 15,0008,00022,000Short-Run Margin $146,000 $165,000 $175,000Committed Fixed Costs Manufacturing Marketing Administration$ 80,00015,00020,000$ 80,00015,00020,000$ 80,00015,00020,000Net Income Before TaxesTaxes—50%Net Income After Taxes$ 31,00015,500$ 15,500$ 50,00025,000$ 25,000$ 60,00030,000$ 30,000handling investments with uncer­tain lifetimes. Furst and Mark- land13 applied probabilistic tech­niques to franchising opportunities. Many authors have described de­tailed approaches to probabilistic financial analysis.MethodologyThe beta distribution is a gen­eral distribution which can acquire a wide variety of shapes between any two finite values an analyst cares to choose. The beta distribu­tion can be made symmetrical, skewed, peaked, or flat which adds the variety that describes many en­vironmental phenomena. This flex­ibility of form renders the beta a useful distribution when no theo­retical justification for another dis­tribution can be found. The beta distribution currently in use in PERT fits the requirements for probabilistic profit planning. Be­cause of its current use in plan­ning, management should be fa­miliar with its uses and the re­quirements of the needed infor­mation.The beta asks for three esti­mates, i.e., a pessimistic, most13—Furst, Richard, and E. Markland, “Franchising Opportunities: A Probabil­istic Approach," Financial Executive, February, 1970, pp. 20-25.likely, and an optimistic, reveal­ing the discrete nature of the in­puts. The criteria for selecting the inputs are well outlined in most texts concerning PERT. They in­clude the statement that the pes­simistic and optimistic estimate have at most a one per cent chance of being outside their stipulations barring any extreme “act of God.”14Three-level budgetA three-level profit budget is shown in Exhibit 2, above. The three levels are the pessimistic, most likely, and optimistic esti­mate respectively. As can be seen, the three-level estimates (Exhibit 2) are more informative than the most likely values (Exhibit 1). Ex­hibit 2 estimates show that profit after taxes can be as low as $15,500 or as high as $30,000. The use of the most likely estimate of $25,000 can, therefore, be misleading.A range of possible profit is more meaningful than a point estimate, but it is still not adequate. A deci­sion maker needs to know the prob­abilities associated with different profit levels. The beta distribution is a very efficient distribution that14—Hough, Louis, Modern Research for Administrative Decisions, Prentice Hall Inc., 1970, p. 361. permits a user to obtain a tre­mendous amount of information from only three inputs. Ferrara and Hayya15 advocated the beta distri­bution for profit planning, but they did not develop the technique to its fullest potential. They simply reverted to the assumptions of normality.Fortunately, it is not necessary to work directly with the formula­tion of the beta distribution. Stand­ard charts have been developed which allow a quick and easy solu­tion. The first step is to standardize the mode or the value of the vari­able at which the frequency is at a maximum. The most likely esti­mate for the beta distribution is defined as the mode. The mode is standardized by the following for­mula :m-p  r =---- — = standardized modeo-pwhere m is the mode or most likely estimate, p is the pessimistic esti­mate, and o is the optimistic esti­mate.15—Ferrara, William L., and Jack C. Hayya, “Toward Probabilistic Profit Budgets,” Management Accounting, Oc­tober, 1970, pp. 23-28.RICHARD J. TERSINE is associate professor of business management at Old Dominion University, Norfolk, Va. He has held positions in man­agement and engineer­ing with several aero­space firms, including the Boeing Company,Pan American World Airways, Inc., and the Martin Company. Dr. Tersine received his D.B.A. from Florida State University, Talla­hassee. He is the author of many technical articles and has coauthored Models and Problems in Operations Management, Grid Inc., Columbus, Ohio, 1974, with Dr. AltimusCYRUS A. ALTIMUS, Jr., is associate professor of business management at Old Dominion University. He was an instructor of management at the Pennsylvania State Uni­versity, where he re­ceived his Ph.D. in business administration.Among his consulting engagements, Dr. Alti­mus has served as an education adviser to the Xerox Corporation and has researched shoplifting in the Tidewater, Va., area for the Tidewater Retail Merchants Association.48 Management AdviserThe next step is to substitute any given profit level t for which you want to determine the probability of earning less than this amount into the formula:Xt = t-p = standardized profit o-p level for tThe standardizing formulas are necessary so that Chart 1, below, can be used in establishing profit level probabilities.By using Chart 1, the probability of earning less than a given amount can be determined.16 Chart 1 is16—Chart 1 was taken from Willis R. Greer, Jr., “Capital Budgeting Analysis with the Timing of Events Uncertain,” Accounting Review, January, 1970, p. 112. The chart is developed for values of the standardized mode r up to .5. For values of r in excess of .5 (r > .5), it is necessary to work with the complements of both r and Xt. The probability read from the chart represents the probability that the investment will earn more than t.used in the following manner. Cal­culate the standardized mode (r) for the investment and the desired value(s) of Xt. Enter Chart 1 at r on the vertical axis and consult the scale at the top of the Chart to locate the curve that represents Xt. From the intersection of r and Xt, drop to the bottom scale of the chart to obtain the percentage value. The percentage value indi­cates the probability that the in­vestment will earn less than the given amount Xt.Example 1: From the informa­tion in Exhibit 2, what is the prob­ability of earning less than $25,000?m-p 25,000-15,500r = ____                   =.65o-p 30,000-15,500t-p 20,000-15,500x ___  = .31 o-p 30,000-15,500Note that r is greater than .5, so we enter Chart 1 with the comple­ments of r and Xt (.35 and .69). The resultant probability read from the bottom of Chart 1 is approx­imately .95. Since we used the complements, the probability that profit will be less than $20,000 is .05. The probability that profit will exceed $20,000 is .95.By defining the confidence level as the probability that profit will exceed a given size, we can obtain the probabilistic information shown in Exhibit 3, page 50, about the data in Exhibit 2.The profit level (t) for a given confidence level in Exhibit 3 is determined in the following man­ner. The first step is to determine Xt from Chart 1. The Xt value is obtained by finding the intersec­tion of the standardized mode (r) and the given confidence level on the lower horizontal axis and pro­ceeding up the curve lines to the approximate Xt value on the top horizontal scale. The profit level (t)CHART 1BETA CURVE AREA CHARTPERCENTAGE OF THE TOTAL AREA WHICH LIES BETWEEN THE EXTREMELOW END OF THE BETA DISTRIBUTION AND SELECTED VALUES OF XMay-June, 1974 49EXHIBIT 3ConfidenceLevelXTFormula* Profit(T)95% .31 .31 (30,000 — 15,500) +15,500 — $20,00075% .49 .49(30,000 — 15,500) + 15,500 — 22,60050% .62 .62(30,000 - 15,500) + 15,500 = 24,49025% .73 .73(30,000 — 15,500) + 15,500 = 26,08515% .79 .79(30,000 - 15,500) + 15,500 26,955*Profit = t = xt(o —p)+p Probability profit planning requires an estimate based largely on guesswork. But the beta distribution, familiar from PERT, does provide a flexible tool that can incorporate any degree of complexity or realism desired . . .is then obtained from the follow­ing formula:t = Xt (o-p) +pSteps in the procedureThe following is a recap of the steps in the procedure:Step 1. Determine the optimis­tic (o), most likely (m), and pessimistic (p) bud­gets.Step 2. Standardize the mode (r) m - p use formula r =--------  o -p (Note: if r greater than .50 use reciprocal)Step 3. Determine xt value(s) corresponding to the confidence levels re­quired.Enter Chart at r level on the vertical line. Fol­low this line over to the confidence level re­quired and then follow the curve up to the top axis to read the xt value. (Note: if reciprocals were used to find r, the reciprocal of xt must also be used.)Step 4. Find the profit corre­sponding to the confi­dence level by using for­mula: profit = t = x (o-p) + pThere are many situations where a business might require a mini­mum level of profit. This could oc­cur when a firm has had a history of dividend payments that manage­ment feels constrained to main­tain but existing or proposed fi­nancing requires that no dividends be disbursed unless a minimum profit level is attained. By using the outlined procedure a manager can find the probability of gen­erating some desired level of profit.Example 2: From the informa­tion in Exhibit 2, what is the prob­ability of earning at least $23,000 profit?Profit = t = xt (o-p) + p 23,000 = xt (30,000-15,500)+ 15,500xt = .52The probability can now be read from Chart 1 by entering at the .48 level on the top scale and follow­ing the curve down to the intersec­tion with the standardized mode (.35). The probability is then read from the bottom of the chart. In this case, there is a .71 probability that the firm will earn at least $23,000.ConclusionProbability profit planning neces­sitates a stochastic interpretation. The beta distribution permits man­agement to incorporate their abili­ties in the estimation process. The changing states of nature (econ­omy, competition, legal environ­ment) can be reflected in man­agement estimates and revealed through the beta approximation. It could be integrated into corporate profit planning with little difficulty.The basic characteristics of the beta model can be extended to in­clude any degree of complexity and realism desired. The beta dis­tribution does not provide a pa­nacea for probabilistic profit fore­casting, but it does provide a flex­ible tool. The data inputs are very simple and the tri-level budget in­puts are within the realm of exist­ing practice. It could provide the consistency and flexibility needed for external reporting on future economic performance.50 Management Adviser

Probabilistic Profit Planning: A Feasible Approach

https://egrove.olemiss.edu/cgi/viewcontent.cgi?article=1189&context=mgmtadviser

Probabilistic Profit Planning: A Feasible Approach

Abstract

Similar works

Full text

Available Versions

eGrove (Univ. of Mississippi)