Developing a Cost-Volume-Profit Model in Production Decision System Based on MAD Real Options Model

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Procedia Economics and Finance 3 (2012) 350 – 354

Emerging Markets Queries in Finance and Business

Developing a cost - volume - profit model in production decision system based on MAD real options model Stefan Daniela,* a

1, 540 080, Romania

Abstract Although that is true, CVP analysis helps to bridge the gap that widened lately between accounting and budgetary control literature on one side and financial economics models evaluating flexibility in economic decision, in particular real options literature, on the other. The main objective of this paper is to explain how to cam we use real options modeling in decisions related to the production process.

2012 Published Elsevier © 2012 The©Authors. Published byby Elsevier Ltd. Ltd. Selection and peer-review under responsibility of the Selection and peer review under responsibility of Emerging Markets in Finance and Business local organization. Markets Queries in Finance and Business localQueries organization.

Emerging

Keywords: Real Options, Risk, CVP Model, Marketed Asset Disclaimer;

1. Introduction The original model CVP Model, presented by Hess, 1903 and Mann, 1903-07, has progressed from the basic one product model and no uncertainty, with fix costs and variable costs, to a more diversified and complex design with multiproduct situations and uncertainty. Initially, new development in the model has been brought by Williams, 1922 who proposes a new distinction among costs type introducing a new category of semi variable costs which include costs that are not directly related to variable or fixed costs and the idea was developed by all the authors interested in the costs issue Spranzi, 1964, Dean, 1936, De Bodt, 1964, etc. An

* Corresponding author. Tel. 0040744-345-564 E-mail address:[email protected]

2212-6716 © 2012 The Authors. Published by Elsevier Ltd. Selection and peer review under responsibility of Emerging Markets Queries in Finance and Business local organization. doi:10.1016/S2212-5671(12)00163-3

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Stefan Daniel / Procedia Economics and Finance 3 (2012) 350 – 354

important contribution to this model was brought by Jaedicke & Robichek, 1964, whom, for the first time, introduced in this model the problem of uncertainty. His ideas has been developed further by Jarrett, 1973, who has extended the use of this model with the aid of Bayesian Decision Theory in the propose of identifying the optimal action and by Barry, Velez-Arocho, & Welch, 1984. Additional links between CVP model and decision-making theory were outlined by Yunker, 2001, offering a perspective of the link between the CVP model and the demand curve and connecting the volatility of the profit not only on price, like Jaedicke & Robichek, 1964, but also on quantity. Developments of joint CVP model and real options model has been made by Aleessi, 2001, who reinterpreted Cost Volume Profit CVP analysis as a real options dynamic programming DP. Currently CVP model represents a well-ordered model with known capabilities and limits based on a extended literature developed in this area Demski & Kreps, 1982, Tsai & Lin, 1990, Kaplan & Atkinson, 1998, González, 2001, Horngren, Datar, & Foster, 2003. One of the limits of the model is related to its poor capacity to work with a multiproduct situation. Following this direction we proposed Stefan D, Stefan B, Savu, Sumandea, & Comes, 2008 a model of CVP function based on independent variables with value restrictions. We proved this model problem. Combining the results of previous researchers regarding the implication of uncertainty on the CVP model and the function based on independent variables this could generate the further development of the CVP Model in mix with Real options theory. 2. CVP approach The equation of the deterministic CVP model in the traditional approach is the following :

Pr(x)

px (bx a) ( p b)x a

(1)

where: Pr(x) = profits p = price x = quantity sold b = unit (average) variable cost a = fixed cost The major application of this model is to identify the breakeven quantity which is defined as the amount of sales adequate to realize revenue equal with costs, given specified values for price p, unit variable cost b, and fixed cost a. Profits are equated to zero and the equation is solved algebraically for the breakeven quantity x in terms of the parameters p, b and a. The manager then considers whether the firm is liable to sell this quantity and if the answer is yes, then decision of goods production is undertaken. Further deterministic development of the model extended the issue to a multiproduct situation and the conclusions are that in this type of situation the validity of the model is restricted by the structure of the sales. From this perspective the model is applicable only if the sales structure remains unchanged when the total sold quantity grows or decreases. The multiproduct equation (n type of products) for the breakeven quantity becomes:

Pr ( x1 , x2 ,..,xn )

n i 1

pi xi

n i 1

(bi xi

ai )

n i 1

( pi

bi ) xi

a (2)

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Stefan Daniel / Procedia Economics and Finance 3 (2012) 350 – 354

Initially, we have to say that the CVP model uses the production costs grouped on behaviour criteria: variable costs and fixed costs. But from the practical perspective of how the unit (average) cost can be determined, the classification of costs must be done according to the possibility of identifying the costs on the product, so in practice it is used the distinction between indirect or common costs and direct costs is used. So, to calculate a cost per unit of product, first it is necessary to identify the direct and indirect costs and only after the cost per unit of product has been calculated, the variable component and the fix component can be determined. Variable costs + Fixed costs = Direct costs + Indirect costs

(3)

Secondly the assumption that the sales structure remains unchanged is not a practical one; it is hard to find nowadays a company that can maintain this constraint. In these circumstances, the model needs to be restated given the practical reality. Both the direct costs and indirect costs have two components: a fixed one and a variable one. So for the cost of each product we have the following relations between variable and fixed costs at one hand and direct and indirect costs on the other hand: bi = bdirect i + bindirect i and a = adirect + aindirect

(4)

where: bi = represents the unit (average) variable cost for product i; bdirect i = represents the part of unit variable cost for product i that is generated by the direct costs; bindirect i = represents the part of unit variable cost for product i that is generated by the indirect costs; a - represents the fixed costs;, adirect - represents the part of fixed cost generated by the direct costs;, aindirect represents the part of fixed cost generated by the indirect costs Thanking account of these remarks we have proven in one of our paper that the cost volume profit model can be written as follows:

Pr ( x1 , x2 ,.., xn )

n

pi xi

i 1

xi

n

h

i 1 j 1

xi kmij cm j

n

CFi g ( f ( x1 , x2 ,...,xn )) Cindirect

fixed

max

i 1

X i min , X i max , i 1, n (5)

where: xi represents the quantity of product i; k mij - represents the quantity of material j used to produce one unit of product i;

cm j - represents the cost per unit for the material j. CFi = represents the fixed costs directly linked to the product i; Xi min, Xi max - represents the lower and the upper quantity limit that can be created by the given level on direct fixed costs (CFi) generated by the product i;

Stefan Daniel / Procedia Economics and Finance 3 (2012) 350 – 354

3. Real options approach Since the first development of Jaedicke and Robichek, 1964, an extensive literature has developed on costvolume-profit analysis under uncertainty, several stochastic CVP models have been developed: single-product versus multi-product, single production technology versus multiple technologies, single uncertainty source versus multiple uncertainty sources, uncertainty with respect to price versus uncertainty with respect to sales quantity, the assumption that production equals sales versus differentiation of the production quantity from the sales quantity, specification of the decision question simply as produce-not produce versus determination of a quantity to produce and/or a price to set, use of the fundamental CVP equation alone versus the addition of an sold to price charged, and so on. Recognizing the uncertainty represents a big step forward but does not solve the decision problem, all models still remain at the traditional use of the CVP model. In traditional CVP model decisions can be taken according to a passive management framework. The shortcomings of this approach are that it cannot take account of future decisions, for extending the production or abandonment, for switching to the best production. So is not using an active management flexibility Although that is true, CVP analysis helps to bridge the gap that widened lately between accounting and budgetary control literature on one side and financial economics models evaluating flexibility in economic decision, in particular real options literature, on the other. As a matter of fact, in our opinion, CVP analysis can be considered a useful tool to specify correctly the interactions among the various profitability drivers and design accordingly the real option valuation framework. On the other hand, budgetary control procedures should take the necessary feedback from financial modelling of decision flexibility, focusing their attention on the variables considered most important in determining profitability. Because the CVP model is a decision model were the condition is linked to the value of the result function, with strict positive value, this value can be considered as an exercise price for an abandonment option and the production can be seen as a long term project. Because in this case is virtually impossible to identify a portfolio of traded assets that exactly imitate risks and returns of companies profit, we can use Copeland and Antikarov, 2001, Marketed Asset Disclaimer model MAD. They proposed a simpler approach free from any market-traded asset. This new simpler approach is based on the marketed asset disclaimer MAD assumption. MAD technique uses the present value of a project without options as the best-unbiased estimate for the market value of the project. The MAD assumption eliminates the difficulty of identifying a twin portfolio of linearly independent securities that can generate the same risk and cash flow as the project. In our approach we can use the present value of the futures profits; determined using the profit function presented earlier. If we take into consideration the fact that the volatility of the price, demand, costs are sources of uncertainty for the final result we can use the compound volatility of profit function as the volatility of the asset used in the real options model. The exercise price is equal to the breakeven point of the model, equal to zero. The forecast period can be identified with the real options maturity. Table 1. Analogy between real options methodology and CVP model

Parameters of the real options model

3. Future risk-free interest rate 4. Real option maturity

Parameters for CVP with real options methodology 1. Current value of discounted profits 2. Strike price, the breakeven point of the model 3. Future risk-free interest rate 4. Forecast period 5. Volatility of the profits

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4. Conclusion

The purpose of this paper is to investigate few new methods and the results are offered under new hypothesis. The main purpose is to explain how to cam we use real options modeling in decisions related to the production process. This is performed drawing a parallelism between traditional CVP analysis and the real options approach to investment evaluation. Moreover, this approach can be adapted to others real options evaluation methods. Acknowledgements This paper was supported by the Sectorial Operational Programme Human Resources Development SOP HRD, financed from the European Social Fund and by the Romanian Government under the contract number SOP HRD/89/1.5/S/62988.

References Alesii, Giuseppe, Kulatilaka 88 as a CVP Analysis in a Real Option Framework: A Review, Gauss Codes and Numerical Examples (February 3, 2001). Universita degli Studi - L'Aquila, Facolta di Economia, Dip. di Sistemi ed Istituzioni per l'Economia Serie Working Papers di Economia Aziendale. Available at SSRN: http://ssrn.com/abstract=258694 or http://dx.doi.org/10.2139/ssrn.258694 Barry, C. B., J. I. VelezQuarterly Review of Economics and Business 24(2), 71 90, (1984). De Bodt, G. 1964. Direct costing et programmation économique de l'entreprise à produits multiples, Paris: Dunod. Dean, J. 1936. Statistical Determination of Costs. Studies in Business Administations VII: 13 23. Demski, J. S., & Kreps, D. M. 1982. Models in Managerial Accounting, Journal of Accounting Research 20, Supplement: Studies on Current Research Methodologies in Accounting: A Critical Evaluation, 117 142. González, L. 2001. Multiproduct CVP analysis based on contribution rules, International Journal of Production Economics 73(3): 273 284. Hess, H. 1903. Manufacturing: Capital, Cost, Profit and Dividends, Engineering Magazine , 892 898. Horngren, C. T.; Datar, S. M., & Foster, G. 2003. Cost Accounting: A Managerial Emphasis, 11th Edition. Person Education, New Jersey. Jaedicke, R. K., & Robichek, A. A. 1964. Cost-Volume-Profit Analysis under Conditions of Uncertainty, Accounting Review 39(4): 917 926. Kaplan, R. S., & Atkinson, A. A. 1998. Advanced Management Accounting. Prentice Hall, New Jersey. Mann, J. 1903-07. On cost or expenses, vol. 5, in G. Lisle, Encyclopedia of accounting 8 vols.: 199 225. William Green & Sons, Edinburgh. Spranzi, A. 1964. Introduzione allo studio della variabilità dei costi di produzione. A. Giuffre. Milano. Tsai, W.-H., & Lin, T.-M. 1990. Nonlinear multiproduct CVP analysis with 0 1 mixed integer programming, Engineering Costs and Production Economics 20(1): 81 91. Williams, J. 1922. Technique for The Chief Executive, Bulletin of The Taylor Society VII: 47 68. Copeland, T., Antikarov, V., 2001. Real Options Texere LLC Publishing, New York