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финансовая аналитика
УДК 332.8
The Application of Differential cost Technique for Pricing Decisions
CHRISTIAN CAVAZZONI
Doctor, Professor, University of Perugia, Italy E-mail: [email protected]
abstract. This study was conducted to investigate whether the use of differential cost technique can positively contribute to improved decision making concerning different processing methods, to take additional orders, to determine the degree of efficiency of an organization, but also to orient the corporate governance in solving management problems related to the production and distribution of goods (Arcangioli, 1964; Salzano, 1970). This study focuses on main considerations of recent circumstance, since in the current economic situation coupled with the productive potential of a business definitely require that the dynamics of an inelastic demand have to be taken into account. Keywords: differential cost; management accounting; cost-volume-profit graph; cost accounting.
использование стоимостных методик в процессе принятия решений по ценообразованию
КАВАЦЦОНИ ХРИСТИАН
доктор, профессор, Университет Перуджи, Италия E-mail: [email protected]
Аннотация. Это исследование было проведено с целью изучения, как применение дифференциального метода стоимости может положительно способствовать принятию решений, касающихся различных методик, для того чтобы получить дополнительные заказы, определить степень эффективности организации, а также ориентировать корпоративное управление на решении проблем, связанных с производством и распределением товаров (Arcangioli, 1964; Salzano, 1970). В текущей экономической ситуации сочетание производственного потенциала бизнеса и динамика неэластичного спроса должны быть приняты во внимание - вот основные положения данного исследования. ключевые слова: дифференциал стоимости; управленческий учет; объем затрат; прибыль; учет затрат.
1. The management accounting
Human capital and tangible assets are company tangible elements and their close relationship, both in terms of qualitative and quantitative level of interdependence, represents a company's life conditions.
Depending on its behaviour in the economic environment, an enterprise can be defined as (Ferrero, 1987): i) a social system: as its activities are mainly based on human labour/contributions/input; ii) a teleological system: as it is a not-spontaneous phenomenon; iii) an open system, as its operations are conditioned by a number of the different factors, constraints and opportunities existing in the
context in which it operates; iv) a dynamic system, as active in environment characterized by continuous instability.
The objectives that a company may aim to achieve can be numerous and diverse. However, it is generally recognised that its ultimate goals be, on one hand, the production of goods or services for the satisfaction of human needs, and, at the same time, the creation of wealth for its relevant stakeholders. To this end, it is necessary that continuous management control be exerted, so as to ensure the maintenance of the equilibrium conditions (Donna and Riccaboni, 2003; Giovannoni, 2004).
The correlation between business operations, over time can engender:
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i) exchange phenomena with other economies, resulting, on one hand, in the supply of services by factors of production and on the other, in the sale of goods on the market; and ii) internal management phenomena, relating to the use of the utility coming from those factors, whose availability is assured through their material transformation.
The first phenomenon is accounted by the financial accounting system aimed at the formation of the value system of the financial statement. Such statement is designed to measure the results of operations assigned to a closed accounting period, as well as the qualitative and quantitative composition of the working capital; the second phenomenon is monitored by the analytical accounting system that aims at determining different cost configurations, which are considered as a source of useful and reliable information (Cinquini, 2003; Marchi, 2003).
Management control required that tools be used by managers so as to take appropriate decisions for a company's activities; such tools, which relate to cost formation, and include its temporal and spatial dimension, play a key role (Branciari, 1996; Frank, 2004).
2. The Differential Cost
This study was conducted to investigate where the use of differential cost technique can positively contribute to improved decision making concerning different processing methods, to take additional orders, to determine the degree of efficiency of an organization, but also to orient the corporate governance in solving management problems relating to the production and distribution of goods (Arcan-gioli, 1964; Salzano, 1970).
This study focuses its main considerations on the latter circumstance, since in the current economic situation coupled with the productive potential of a business definitely require that the dynamics of an inelastic demand be taken into account. Many companies are compelled to implement policies aimed at increasing their level of production so as to reach a lower total cost per unit, or else at dealing with issues related to their excessive production capacity, generally through special offers and promotional discounts to increase sales (Kinney and Raiborn, 2011; Bragg, 2012).
In both assumptions, a firm's management can base its decisions on a differential cost analysis (Coda, 1968), requiring an increase in asset
production until a given amount, whose level is a function, both of the starting amount and of the amount to be added.
In general terms, the first assumption indicates the level of output where total revenues equate total costs (breakeven point, BEP), or the level of output that generates an adequate income (dimension of normal operating income, NI). The quantity to be added indicates an amount classified as «significant technical minimum», which relates to the type of product under consideration.
As enterprises co-ordinate various factors based on different proportionality ratios, more or less proportional, with the variations of the production, it follows that the best economic result related to a single product can also be found at a production level where those elements are not fully exploited (Hornen et al., 2011; Leslie and Wol-cott, 2010).
To this end, one needs to identify the most convenient production size within the maximum allowed, given the plants maximum dimension (maximum dimension, MD), linking the differential cost technique to the study of the diagram of profitability, where variable costs increase more than proportionally. Assuming that: x = output sold; a = variable cost per unit; b = growth rate of the variable cost per unit; c = TFC = total fixed costs; p = selling price for units price per unit sold?; TR = total revenues = p * x; TC = total costs = ax + bx2 + TFC; BEP = quantity of output sold at which total revenues equal total costs;
Ed = quantity of output sold at which the operating income reaches its highest point (economic dimension).
Pd = quantity of output sold at which is the highest productivity (productivity dimension). MD = maximum quantity of marketable output. In particular, equating the total revenue function to the total costs, it is possible to identify the level of production (x) corresponding to the equilibrium point (break even point): TR = ax + bx2 + c thus:
BEp, _ (p - a) -V(p - a)2 - 4bc 2b
m
output
Cost-Volume-Profit Graph in the case of more than proportional variable costs
BEP' =
(p - a) + yl(p - a)2 - 4bc
2b
At a closer glance, data analysis reveals two minimum sizes for cost amortization, in which one can place the area of profit, while the two loss areas are placed, respectively, to the left of the first break-even point and to the right of the second break-even point.
In the profit area a point of maximum profitability (MI) can be found, the distance between total revenue and total cost is the greatest, as well as a point of maximum productivity, which is characterized by the lowest cost per unit of the good under consideration (Guatri, 1954). The first (MI), is reached at the maximum distance between Rt and Ct:
TR — TC = px — (ax + bx2 +c) = max It is therefore necessary to derive the equation and set it equal to 0
d [px — (ax + bx2 + c] = p — a — 2bx = 0 da cui Ed = (p - a) /2b
The maximum productivity is obtained at the minimum point of the total cost per unit (TC, u): [TC, u] = (ax + bx2 +c) /x = a + bx + c/x = min In this case, it is necessary to derive the equation of [TC, u] and set it equal to 0. Hence:
d [a + bx + c/x] = b — c/x2 = 0 M
Different levels of production can be easily represented in a system of cartesian axes, placing the first axis (X) equal to the working volume and the
second (Y) equal to costs and revenues, namely variable, fixed and total:
The study of the proposed chart can help choose a level of production corrisponding to the best economic results for the goods, as well as to inquire why the maximum profitability does not coincide with the maximum productivity, due to the presence of more than proportional variable costs.
To this purpose, a comparison is made between total additional costs and total additional revenues related to the goods, in relation to an additional amount of production, to determine the total differential cost and the differential cost per unit. In fact, assuming that: x = output sold: a = incremental output, x + a = new output; TC (x) = x Total cost; TC (x + a) = Total cost x + a; Thus:
Total differential cost = TDC
TC (+ ) - TC ()
(x +a) (x)
DC, u (differential cost for unit) = CT (x+a)-CT (x) a
The total differential cost measures the cost that a company has to pay in order to increase the production of a «significant technical minimum,» while the differential cost per unit indicates the ratio between the total differential cost and the changes in the volume of production.
Accordingly, if a company needs to increase in production levels, the total costs to be incurred can have a more or less than proportional increase. For
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further clarification, three different scenarios in which total costs of the company Alfa in the transition from a production volume x (1.000) to a volume x + a (1.200) can be considered.
In this regard, please note that: i) the total fixed costs amounted to € 100,000, the original total cost, which amounted to 500,000 euro, switched to € 600,000 € 660,000 and € 564,000; ii) the unit sale price viable on the market for the initial amount is 510 euro; iii) the company intends to maintain its profit constant.
first hypothesis
unit can take. So as to maintain a constant profit, the company must in fact sell the amount a at a price equalling that value. Thus, with respect to the first 1.000 units, the total revenue (TR) amounted to 510.000 (510x1.000) whilst, as to the 200 additional units, the total revenues amounted to 100.000 (500x200), leaving the result unchanged.
TC TFC TVC
X=1.000 500.000 100.000 400.000
X=1.200 600.000 100.000 500.000
x=1.000 € x=1.200 €
PP, u 510 PP, u (1.000 units) PP, u (200 units) 510 500
TR 510.000 TR (1.000 units) TR (200 units) TR 510.000 100.000 610.000
TC 500.000 TC 600.000
PROFIT 10.000 PROFIT 10.000
TC, «(1000) = 500.000/1.000 = 500 TC, «(1.200) = 600.000/1.200 = 500
600.000 - 500.000 100.000 cnn DC,u --=-= 500
second hypothesis
1.200 -1.000
200
TC TFC TVC
X=1.000 500.000 100.000 400.000
X=1.200 660.000 100.000 560.000
Turning to the volume of production x + a the total cost increases proportionally, resulting in a differential cost per unit (DC, u) which equals the total cost per unit (TC, u), so that the variable cost is to be considered more than proportional to the same volume. The impact of the fixed cost per unit on the total cost per unit decreases (from 100 to 83, generating an economy of 17), while the variable cost per unit increases to the same extent (diseconomies of 17):
tc, «(1.000) -+i°00»0 -1.000 1.000
-100( FC, u)+400(VC, u) - 500
TC, «(1.200) - +5°°:°°^ -
1.200 1.200
- 83(FC, u) + 417(VC,u) - 500 FC,u - 83 -100 - -17 VC,u = 417 - 400 = +17
The differential cost per unit is the lower limit of the value, unless there are other particular strategies that the sale price of additional quantities per
When the total cost increases more than proportionally, the differential cost per unit is greater than the total cost per unit, both before and after an increase in the production. The impact of the fixed cost per unit decreases (-17) while the variable cost per unit increases (+67) generating a diseconomy of 50.
TC, u(1000) = 500.000/1.000 = 500
TC,u(1.200) = 660.000/1.200 = 550
DC,u -
660.000 - 500.000 160.000
1.200-1.000
200
- 800
100.000 400.000
TC,u(1.000) --+--
1.000 1.000
- 100(FC,u) + 400(VC,u) - 500
tc,u(1.200) - 100M+-1.200 1.200
- 83(FC, u) + 467(VC, u) - 550
FC, u - 83 -100 - -17 VC, u = 467 - 400 = +67
H
As far as the formation of the unit price of sales is concerned, it is to be considered that in order to achieve the same level of profit, the firm must sell the additional quantity at price per unit of 800, equal to the differential cost per unit. In this case, referring to the first 1.000 units, total revenue (TR) amounted to 510.000 (510x1.000) while for the 200 additional units, total revenues amounted to 160.000 (800x200).
FC,u = 83 -100 = -17 VC,u = 387 - 400 = -13
In this last case, in order to achieve the same level of profit, the company can sell the additional quantity at a unit price of 320, equal to the differential cost per unit. In reference to the first 1,000 units, total revenue (TR) amounted to 510,000 (510x1.000) while for the 200 additional units, total revenues amounted to 64.000 (320x200).
x=1.000 € x=1.200 €
PP, u 510 PP, u (1.000 units) PP, u (200 units) 510 800
TR 510.000 TR (1.000 units) TR (200 units) TR 510.000 160.000 670.000
TC 500.000 TC 660.000
PROFIT 10.000 PROFIT 10.000
x=1.000 € x=1.200 €
PP, u 510 PP, u (1.000 units) PP, u (200 units) 510 320
TR 510.000 TR (1.000 units) TR (200 units) TR 510.000 64.000 574.000
TC 500.000 TC 564.000
PROFIT 10.000 PROFIT 10.000
third hypothesis
TC TFC TVC
X=1.000 500.000 100.000 400.000
X=1.200 564.000 100.000 464.000
When the total cost increases less than proportionally, the differential cost per unit will be less than the total cost unit, both before and after an increase in the production, as a consequence. The impact of the fixed cost per unit decreases (-17), together with that of the unit variable cost (-13), which generates an economy of 30.
TC, u(1000) = 500.000/1.000 = 500 TC,u(1.200) = 564.000/1.200 = 470
DC, u =
564.000 - 500.000 64.000
1.200-1.000
200
= 320
тс, U(1.000) -+
1.000 1.000
-100( FC, u)+400(VC,u) - 500
TC, u(1.200) -100.000+i64^ 1.200 1.200
- 83(FC, u) + 387( VC,u) - 470
3. Concluding remarks
This study emphasizes that management accounting can rely on special tools of cost analysis offering a special perspective of the phenomena under investigation which is useful for taking informed operational decisions (Blocher et al., 2009; Lanen et al., 2010).
One of these tools is the differential cost analysis. Such tool together with the study of the diagram of profitability, where variable costs increase more than proportionally, can engender that knowledge useful to the management in solving various management problems relating to the production and distribution of goods.
From an operational point of view, the application of differential cost has been linked to the comparison between costs and additional total revenues of a product, with respect to variation in levels of production. The latter allows to determine the total differential cost, which measures the additional cost needed to increase the production of a «significant technical minimum», as well as the differential cost for unit, resulting by the ratio between the total differential cost and the variation in the production quantity. It also indicates the price limit within which the incremental amount can be sold on the market to increase profit or limit loss.
The concept of this particular tool of cost analysis allows a firm's management to assess the
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convenience to sell the additional quantity of a 7. good at a lower price than the overall unit cost and, at the same time, maintaining a degree of reasonably profitable activity.
Thus, the relevant corporate governance bod- 8. ies can address issues related to an increase or a surplus of production, through special offers and 9. promotional sales of products at different prices per unit.
To conclude, when there is a switch to an increase in production, there are no certain or de- 10. fined solutions, as data are often representative of estimated values and speculation (Zappa, 1957). It 11. is believed, however, that this study demonstrated that the cost differential technique is extremely useful for managers, especially with regard to their ability to co-ordinate inputs with marketing poli- 12. cies, so as to obtain the best possible economic results.
13.
References
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4. Branciari S., I sistemi di controllo nella pic-cola impresa, Giappichelli, Torino, 1996
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Olivotto L., Valore e sistemi di controllo. Strumenti per la gestione della complessita, McGraw-Hill, Milano, 2000 Salzano A., La rilevazione ed il controllo dei costi per le decisioni operative aziendali, Roma, 1970
Zappa G., Le produzioni nell'economia delle imprese, Giuffre, Milano, 1957
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