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Sales forecasts are uncertain at best. For this reason, it is important for management to know approximately what cost changes can be expected to go along with volume changes. It must know what levels of production and sales volume are necessary for profitable operation. It must know how much effort and cost are justified to keep volume at a high level. Break-even analysis provides this sort of information. Break-even analysis is so called because the focal point of the analysis is the break-even point the level of sales volume at which revenues and costs are just equal. At this level, there is neither profit nor loss.
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A break-even chart is illustrated in Fig. 11.1. A break-even chart can be prepared from budget figures and knowledge of capacity levels.
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FIGURE 11.1 A break-even chart.
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In Fig. 11.1, it is assumed that fixed costs for production are $20,000 and for selling and administrative activities, $10,000. Variable production costs are $12.50 per unit, or a total of $50,000 at the maximum capacity of 4000 units. Variable selling and administrative costs are $5.00 per unit, or $20,000 at the 4000 level. This gives minimum costs of $30,000 (the total fixed costs) at zero production and maximum total costs of $100,000 at 4000 units. The selling price is $35 per unit. A total cost line is drawn from the $30,000 cost level for no production to the $100,000 level for maximum production and sales. A total revenue line is drawn from the zero line for no revenues to $140,000 for the maximum sales of 4000 units. The point where these two lines cross is the break-even point the level of operation at which there will be neither profit nor loss. The area enclosed by the two lines below the break-even point represents loss, and the enclosed area above the break-even point represents profit, Fig. 11.1. Figure 11.1 shows that the volume at which the business can be expected to break even is slightly below one-half the maximum point, or between 1500 and 2000 product units. The exact level can be calculated as follows: Fixed costs 3 $3 0, 000 = = 1714 . 29 units Selling price variable costs/units $ 17 . 50
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Verification Gross revenue (1714.29 units at $35) Less: variable costs (1714.29 units at $17.5) Contribution margin Less: fixed costs Net profit or loss $60,000 30,000 30,000 30,000 $0
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A break-even chart can give approximate answers to many questions. For example, if the variable production costs are expected to increase 10 percent in the coming year without any change in the selling price of the product, the total cost line will be drawn steeper, and a new higher break-even point will result. This will show what increase in sales volume is needed to offset the increased costs. Or suppose a change in selling price of the finished product is being considered. The total revenue line will now be steeper for an increase or less steep for a decrease in selling price. The chart will then show the effect on profit if the sales volume remains the same or if, for example, it drops as it might if the price is increased. Suppose the manufacturing firm whose figures are used in Fig. 11.1 is producing and selling 2000 units, thus making a profit of $5000. Now suppose it wants to give its employees a general wage increase. As planned, the increase has the effect of adding $1 to the variable costs of each unit (thereby decreasing the contribution by the same amount) and $3000 to fixed costs. The owner wants answers to these questions: How many units must the owner produce and sell at $35 each to realize the same profit $5000 Can the owner produce this volume without investing any more in the plant and equipment The required units are calculated by using the following formula. (The calculation can be verified as described in the preceding formula.) Fixed costs + decreased profit $ 33, 000 + $ 5000 = = 2303 units Selling price va riable costs/unit $ 16 . 50 Thus, the manufacturing firm will have to produce and sell 2303 product units instead of 2000 in order to realize the same $5000 profit. Since the plant capacity is 4000 units, management can increase production to 2303 units without any further investment in plant and equipment. Break-even charts give quick approximate answers. They should not take the place of detailed calculations of the results of anticipated changes, but they do encourage careful consideration of the effects of any increases in either fixed or variable costs. They can also be a constant reminder of the importance of maintaining a high sales volume.
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