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1. the Efficiency of the Scientific Approach in Analysing the Break THE EFFICIENCY OF THE SCIENTIFIC APPROACH IN ANALYSING THE BREAK- POINT IN A MULTI-PRODUCT FIRM Sunday A. Effiong, (Ph.D); Akabom I. Asuquo, (Ph.D) and Chimaobi Okere (Esq) Abstract A major challenge in break-even analysis for multi-product firms is the problem of obtaining a single per unit contribution, single unit selling price and contribution margin ratio (CMR) that is representative of all the products in the firms’ sales mix structure. This paper introduces a scientific approach, using weighted average, as against the simple average used in the traditional approach. Using the Weighted Average Unit Contribution Margin (WAUCM) as a stepping stone, the paper covers up with the Weighted Average Unit Selling Price (WAUSP) and the Weighted Average Contribution Margin Ratio (WACMR). These three averages presented scientific solutions to the multi-product breakeven analysis problems. In comparing the traditional approach with the scientific approach, the paper adopts “contribution by sales mix analysis” to ascertain the approach that gives the optimal sales mix. It was observed that the scientific approach achieved lower break- even point in units and sales value than the traditional approach. The success was attributed to the optimal sales mix achieved by the scientific method. Therefore the scientific approach is recommended for use by companies involved in the multi-product break-even analysis and problems relating to multi-product break-even computations. Introduction The Break-Even Analysis technically known as the Cost – Volume – Profit (CVP) analysis, represents the application of marginal costing principles that seeks to show the relationship between cost, volume and profit at different activity levels which could be relied upon for short-term planning and decision making. Owing to the centrality of the break-even point (BEP) on C-V-P analysis, break-even analysis is often used in place of CVP analysis. Break-even analysis is one of the most important tools for management decision. It takes into consideration the nature of variable costs and the capacity of fixed costs. The turning point in break-even analysis is the break-even point. The break-even point is the sales volume (activity level) in units or in sales value, where total sales revenue equals total cost. It represents the point at which the firm makes no profit and makes no loss. It depicts the point where the firm earns enough contribution to pay for fixed costs only. At the break-even point, all expenses of the company are effectively paid for. The essence of this analysis is to help in assessing the profit potentials of the firm beyond the break-even point. It is an analytical model for achieving targeted results. The Nigerian Journal of Research and Production Volume 18 No 1, April, 2011 1 Sunday A. Effiong, (Ph.D); Akabom I. Asuquo, (Ph.D) and Chimaobi Okere (Esq) Some of the assumptions of break-even analysis according to Lucey (2002) include: 1. All costs must be resolved into fixed and variable elements. 2. Fixed cost must remain constant and variable costs vary proportionately with activity level. 3. Over the activity range being considered, cost and revenue behave in a linear relationship. 4. The only thing affecting costs and revenues is volume. 5. Stocks are valued at marginal costs only. Break-even point in volume is given as: Total fixed-cost divided by contribution per unit; break-even point in sales value is given as Total fixed cost divided by the contribution margin ratio (CMR). The contribution margin ratio is obtained by dividing contribution per unit (or total contribution) by the selling price per unit (or total sales revenue), respectively. For a mono-product firm, break-even analysis is simple to apply. A major challenge arises in the case of a multi-product firm. While it is easier to compute contribution per unit and the contribution margin ratio in a mono-product situation, it becomes more tasking in a multi-product environment, owing to the fact that there are more than one product, each with a different variable cost, different price and different contribution margin. Considering the usefulness of the break-even analysis as a short-run decision model, the purpose of the paper is to show the deficiencies inherent in the traditional approach when applied in a multi-product environment and to present a scientific approach which is not only useful in a multi-product break- even analysis but also applied in selecting optimal sales mix. Adeniji (2007) noted that the break-even analysis can be useful in short- run decisions such as choice of sales mix. In multi-product break-even analysis, firms seek to establish a sales mix at which the sum of the individual contributions from all the products in the sales mix structure is enough to pay for the fixed costs. In attempting a solution, the traditional approach adopts the use of simple average, where unit contribution is divided by unit sales revenue to arrive at the contribution margin ratio, which is applied as a divisor to the total fixed cost to produce the assumed break-even point in sales value. Break-even point in volume is then arrived at by first apportioning the total sales value (at break-even point) to individual products using the sales proportion (or mix). Thereafter, the individual contributions are divided by the corresponding unit selling prices to arrive at the break-even point in unit for each product, which adds-up to the break-even point in unit for all the products. In laying credence to the scientific approach, Hanson (2007) stated as follows: ‘‘to perform break-even analysis in a multi-product organisation, a constant sales mix must be assumed, or all products must have the same contribution margin ratio’’. According to his argument, this assumption 2 The Efficiency of the Scientific Approach in Analysing the Break- Point in a Multi- Product Firm facilitates the calculation of the weighted average contribution per mix. Continuing in this line of thought, Effiong (2004) presented the Weighted Average Unit Contribution Margin (WAUCM), which is applied in calculating the break-even point in unit, for a multi-product firm. In presenting the Weighted Average Unit Contribution Margin (WAUCM), Effiong (2004) further explained that the sales mix, in the sense of break-even analysis is the proportion of each of the products required for combination in the company’s sales structure in order to break-even. Hence, the sales mix is used in computing the WAUCM. The Weighted Average Unit Contribution Margin (WAUCM) is defined as the average of the several products unit contribution margins, weighted by the relative sales proportion of each product. The WAUCM can be computed using the formular: WAUCM = CMI x PS1 + CM2 x PS2 + CM3 x PS3 + … CMn x PSn TSM TSM TSM TSM Where: WAUCM: = Weighted Average Unit Contribution Margin CMI, CM2, … CMn = Unit Contribution Margin for Products 1 to n in the sales mix structure PS1, PS2 … PSn = Proportion of sales for products 1 to n in the sales mix structure TSM = Total sales from the combined proportion of all the products, (Effiong 2004). Analysis of the formular reveals that in arriving at a composite unit contribution margin, which represents a single contribution per unit for all the products in the sales mix, here referred to as the WAUCM, emphasis is not laid on the individual contributions only, rather the corresponding sales proportion is attached as a weight. This is an improvement on the simple average method which considers only the contribution made by individual products. The essence of this weighting is to match profitability with acceptability. While contribution per unit defines profitability, sales proportion represents market (consumer) acceptability. 3 Sunday A. Effiong, (Ph.D); Akabom I. Asuquo, (Ph.D) and Chimaobi Okere (Esq) The WAUCM thus calculated represents a single contribution per unit for all the products in the firm’s sales mix structure which is equivalent to the contribution per unit in the case of a mono-product firm. With this, the break- even point for a multi-product firm can be calculated as: Total Fixed Cost WAUCM In order to calculate the break-even point in sales value for a multi- product firm, there is need to obtain a contribution margin ratio that represents a single CMR for all the products in the firm’s sales mix structure. The traditional approach of dividing the total contribution by the total sales revenue (to arrive at the CMR), amounts to the use of simple average, with its short-coming. The effect is that the CMR so calculated is determined by contribution only. Again, the final quantity selected for the purpose of the break- even point reveals a situation where a product is allotted the highest quantity simply because it has the highest sales proportion and a relatively lower selling price. The effect of this is that the firm will need a larger quantity to break-even and higher sales revenue that is not proportionate to the large quantity. All that is required is a unit selling price that represents the selling prices of the individual products in the sales mix structure, which will divide the WAUCM to produce a Weighted Average Contribution Margin Ratio ((WACMR). This requirement is met by the Weighted Average Unit Selling Price (WAUSP). The Weighted Average Unit Selling Price (WAUSP), owes its origin to the secret of weights found in the Weighted Average Unit Contribution Margin (WAUCM). The idea here is to match “desirability” with “acceptability.” Price is one of the bundles of satisfaction which the customer buys (Esu, 2005:72). Hence, the effectiveness of price in the market place is determined by market acceptance.
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