BUS 215; Banfield, Ch 5 Week 3 Notes
BUS 215; Banfield, Ch 5 Week 3 Notes BUS 215
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BUS 215 CH 5; ostVolumeProfit Relationships I. Costvolumeprofit (CVP) analysis helps managers make many important decisions such as what products and services to offer, what prices to charge, what marketing strategy to use, and what cost structure to maintain. Its primary purpose is to estimate how profits are affected by the following five factors: 1. Selling prices. 2. Sales volume. 3. Unit variable costs. 4. Total fixed costs. 5. Mix of products sold. ● To simplify CVP calculations, managers typically adopt the following assumptions with respect to these factors ○ Selling price is constant. The price of a product or service will not change as volume changes. ○ Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit. The fixed element is constant in total over the entire relevant range. ○ In multiproduct companies, the mix of products sold remains constant. ● While these assumptions may be violated in practice, the results of CVP analysis are often “good enough” to be quite useful. ○ Perhaps the greatest danger lies in relying on simple CVP analysis when a manager is contemplating a large change in sales volume that lies outside the relevant range. ○ However, even in these situations the CVP model can be adjusted to take into account anticipated changes in selling prices, variable costs per unit, total fixed costs, and the sales mix that arise when the estimated sales volume falls outside the relevant range. A. The Basics of CostVolumeProfit (CVP) AnalysiS ● The contribution income statement emphasizes the behavior of costs and therefore is extremely helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. ● ● Note that this contribution income statement has been prepared for management’s use inside the company and would not ordinarily be made available to those outside the company. ● ontribution Margin ○ Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. ○ Thus, it is the amount available to cover fixed expenses and then to provide profits for the period. ○ Notice the sequence here—contribution margin is usfirs to cover the fixed expenses, and then whatever remains goes toward profits. If the contribution margin is not sufficient to cover the fixed expenses, then a loss occurs for the period. ○ To illustrate with an extreme example, assume that Acoustic Concepts sells only one speaker during a particular month. The company’s income statement would appear as follows: ■ ○ For each additional speaker the company sells during the month, $100 more in contribution margin becomes available to help cover the fixed expenses. ■ ○ If enough speakers can be sold to generate $35,000 in contribution margin, then all of the fixed expenses will be covered and the company willbreak even for the month— neither profit nor loss; just cover all of its costs. To reach the breakeven point, the company will have to sell 350 speakers in a month because each speaker sold yields $100 in contribution margin: ■ ○ Computation of the breakeven point is discussed in detail later in the chapter; for the moment, note that the breakeven point is the level of sales at which profit is zero. ○ Once the breakeven point has been reached, net operating income will increase by the amount of the unit contribution margin for each additional unit sold. ○ if 351 speakers are sold in a month, then the net operating income for the month will be $100 because the company will have sold 1 speaker more than the number needed to break even: ■ ○ To estimate the profit at any sales volume above the breakeven point, multiply the number of units sold in excess of the breakeven point by the unit contribution margin. The result represents the anticipated profits for the period. ○ to estimate the effect of a planned increase in sales on profits, simply multiply the increase in units sold by the unit contribution margin. The result will be the expected increase in profits. → result will be the expected increase in profits. ○ if Acoustic Concepts is currently selling 400 speakers per month and plans to increase sales to 425 speakers per month, the anticipated impact on profits can be computed as follows: ■ ■ ■ if sales are zero, the company’s loss would equal its fixed expenses. Each unit that is sold reduces the loss by the amount of the unit contribution margin. Once the breakeven point has been reached, each additional unit sold increases the company’s profit by the amount of the unit contribution margin. ● CVP Relationships in Equation Form ○ contribution format income statement can be expressed in equation: ■ profi stands for net operating income in equations. ○ When a company has only a single product, we can further refine the equation as follows: ○ It is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows: ● CVP Relationships in Graphic Form ○ The relationships among revenue, cost, profit, and volume are illustrated ocostvolumeprofit (CVP) graph. A CVP graph highlights CVP relationships over wide ranges of activity. ○ Preparing the CVP Graph ■ In a CVP graph (sometimes called a breakeven chart), unit volume is represented on the horizontal X) axis and dollars on the verticY) axis. Preparing a CVP graph involves the three steps depicted inExhibit 51: ■ ● 1. Draw a line parallel to the volume axis to represent total fixed expense. For Acoustic Concepts, total fixed expenses are $35,000. ● 2. Choose some volume of unit sales and plot the point representing total expense (fixed and variable) at the sales volume you have selected. IExhibit 51, Bob Luchinni chose a volume of 600 speakers. Total expense at that sales volume is: After the point has been plotted, draw a line through it back to the point where the fixed expense line intersects the dollars axis. ● 3. Again choose some sales volume and plot the point representing total sales dollars at the activity level you have selected. Exhibit 51, Bob Luchinni again chose a volume of 600 speakers. Sales at that volume total $150,000 (600 speakers × $250 per speaker). Draw a line through this point back to the origin. ■ The interpretation of the completed CVP graph is given Exhibit 52. The anticipated profit or loss at any given level of sales is measured by the vertical distance between the total revenue line (sales) and the total expense line (variable expense plus fixed expense) ■ ● The breakeven point is where the total revenue and total expense lines cross ■ As discussed earlier, when sales are below the breakeven point—in this case, 350 units—the company suffers a loss. ● Note that the loss (represented by the vertical distance between the total expense and total revenue lines) gets bigger as sales decline. ● When sales are above the breakeven point, the company earns a profit and the size of the profit (represented by the vertical distance between the total revenue and total expense lines) increases as sales increase. ■ An even simpler form of the CVP graph, which we call a profit graph, is presenteExhibit 53. That graph is based on the following equation: ● ■ Because this is a linear equation, it plots as a single straight line. To plot the line, compute the profit at two different sales volumes, plot the points, and then connect them with a straight line. ● For example, when the sales volume is zero (i.eQ = 0), the profit is − $35,000 (= $100 × 0 − $35,000). When Q is 600, the profit is $25,000 (= $100 × 600 − $35,000). ● These two points are plotted Exhibit 53 and a straight line has been drawn through them. ■ The breakeven point on the profit graph is the volume of sales at which profit is zero and is indicated by the dashed line on the graph. ● Note that the profit steadily increases to the right of the breakeven point as the sales volume increases and that the loss becomes steadily worse to the left of the breakeven point as the sales volume decreases. ● Contribution Margin Ratio (CM Ratio) ○ The contribution margin as a percentage of sales is referred to ascontribution margin ratio (CM ratio. This ratio is computed as follows: ○ For Acoustic Concepts, the computations are: ■ ○ In a company such as Acoustic Concepts that has only one product, the CM ratio can also be computed on a per unit basis as follows: ■ ○ The CM ratio shows how the contribution margin will be affected by a change in total sales. Acoustic Concepts’ CM ratio of 40% means that for each dollar increase in sales, total contribution margin will increase by 40 cents ($1 sales × CM ratio of 40%). Net operating income will also increase by 40 cents, assuming that fixed costs are not affected by the increase in sales. Generally, the effect of a change in sales on the contribution margin is expressed in equation form as: ■ ○ As this illustration suggestthe impact on net operating income of any given dollar change in total sales can be computed by applying the CM ratio to the dollar change. For example, if Acoustic Concepts plans a $30,000 increase in sales during the coming month, the contribution margin should increase by $12,000 ($30,000 increase in sales × CM ratio of 40%). As we noted above, net operating income will also increase by $12,000 if fixed costs do not change. ■ ○ The relation between profit and the CM ratio can also be expressed using the following equations: or, in terms of changes, ● Some Applications of CVP Concepts ○ The variable expense ratio is the ratio of variable expenses to sales. It can be computed by dividing the total variable expenses by the total sales, or in a single product analysis, it can be computed by dividing the variable expenses per unit by the unit selling price. ○ This leads to a useful equation that relates the CM ratio to the variable expense ratio as follows: ○ ○ Change in Fixed Cost and Sales Volume ■ ■ Assuming no other factors need to be considered, the increase in the advertising budget should be approved because it would increase net operating income by $2,000. There are two shorter ways to arrive at this solution. The first alternative solution follows: ● Alternative Solution 1 ○ ○ Because in this case only the fixed costs and the sales volume change, the solution can also be quickly derived as follows: ● Alternative Solution 2 ○ ○ Notice that this approach does not depend on knowledge of previous sales. ○ Also note that it is unnecessary under either shorter approach to prepare an income statement. Both of the alternative solutions invoincremental analysis—they consider only the costs and revenues that will change if the new program is implemented. ○ Change in Variable Costs and Sales Volume ■ Recall that Acoustic Concepts is currently selling 400 speakers per month. Prem is considering the use of higherquality components, which would increase variable costs (and thereby reduce the contribution margin) by $10 per speaker. However, the sales manager predicts that using higherquality components would increase sales to 480 speakers per month. Should the higherquality components be used? ■ The $10 increase in variable costs would decrease the unit contribution margin by $10—from $100 down to $90. ■ Solution ■ According to this analysis, the higherquality components should be used. Because fixed costs would not change, the $3,200 increase in contribution margin shown above should result in a $3,200 increase in net operating income. ○ Change in Fixed Cost, Selling Price, and Sales Volume ■ Concepts is currently selling 400 speakers per month. To increase sales, the sales manager would like to cut the selling price by $20 per speaker and increase the advertising budget by $15,000 per month. The sales manager believes that if these two steps are taken, unit sales will increase by 50% to 600 speakers per month. Should the changes be made? ■ A decrease in the selling price of $20 per speaker would decrease the unit contribution margin by $20 down to $80. ■ Solution ■ According to this analysis, the changes should not be made. The $7,000 reduction in net operating income that is shown above can be verified by preparing comparative income statements as shown on the next page. ■ ○ Change in Variable Cost, Fixed Cost, and Sales Volume ■ company is currently selling 400 speakers per month. The sales manager would like to pay salespersons a sales commission of $15 per speaker sold, rather than the flat salaries that now total $6,000 per month. The sales manager is confident that the change would increase monthly sales by 15% to 460 speakers per month. Should the change be made? ■ Solution Changing the sales staff’s compensation from salaries to commissions would affect both fixed and variable expenses. Fixed expenses would decrease by $6,000, from $35,000 to $29,000. Variable expenses per unit would increase by $15, from $150 to $165, and the unit contribution margin would decrease from $100 to $85. ■ ■ ○ Change in Selling Price ■ Concepts is currently selling 400 speakers per month. The company has an opportunity to make a bulk sale of 150 speakers to a wholesaler if an acceptable price can be negotiated. This sale would not disturb the company’s regular sales and would not affect the company’s total fixed expenses. What price per speaker should be quoted to the wholesaler if Acoustic Concepts is seeking a profit of $3,000 on the bulk sale? ■ Solution ■ ■ Notice that fixed expenses are not included in the computation. This is because fixed expenses are not affected by the bulk sale, so all of the additional contribution margin increases the company’s profits. II. BreakEven and Target Profit Analysis A. BreakEven Analysis ■ Managers use breakeven and target profit analysis to answer questions such as how much would we have to sell to avoid incurring a loss or how much would we have to sell to make a profit of $10,000 per month? ■ the breakeven point as the level of sales at which the company’s profit is z To calculate the breakeven point (in unit sales and dollar sales), managers can use either of two approaches, the equation method or the formula method. ● The Equation Method ○ ○ Acoustic Concepts will break even (or earn zero profit) at a sales volume of 350 speakers per month. ● The Formula Method ○ The formula method is a shortcut version of the equation method. ○ centers on the idea discussed earlier in the chapter that each unit sold provides a certain amount of contribution margin that goes toward covering fixed expenses. In a single product situation, the formula for computing the unit sales to break even is: ○ ○ In the case of Acoustic Concepts, the unit sales needed to break even is computed as follows: ■ BreakEven in Dollar Sales ● In addition to finding the breakeven point in unit sales, we can also find the breakeven point in dollar sales using three methods. ○ First, we could solve for the breakeven pointunitsales using the equation method or formula method and then simply multiply the result by the selling price. In the case of Acoustic Concepts, the breakeven point in dollar sales using this approach would be computed as 350 speakers × $250 per speaker, or $87,500 in total sales. ○ Second, we can use the equation method to compute the breakeven point in dollar sales. Remembering that Acoustic Concepts’ contribution margin ratio is 40% and its fixed expenses are $35,000, the equation method calculates the breakeven point in dollar sales as follows ○ Third, we can use the formula method to compute the dollar sales needed to break even as shown below: (a) (b) ○ you’ll notice that the breakeven point in dollar sales ($87,500) is the same under all three methods. This will always be the case because these methods are mathematically equivalent. B. Target Profit Analysis ■ In target profit analysis, we estimate what sales volume is needed to achieve a specific target profit. ■ For example, suppose Prem Narayan of Acoustic Concepts would like to estimate the sales needed to attain a target profit of $40,000 per month. To determine the unit sales and dollar sales needed to achieve a target profit, we can rely on the same two approaches that we have been discussing thus far, the equation method or the formula method. ● The Equation Method ○ To compute the unit sales required to achieve a target profit of $40,000 per month, Acoustic Concepts can use the same profit equation that was used for its breakeven analysis. ○ ○ Thus, the target profit can be achieved by selling 750 speakers per month. Notice that the only difference between this equation and the equation used for Acoustic Concepts’ breakeven calculation is the profit figure. In the breakeven scenario, the profit is $0, whereas in the target profit scenario the profit is $40,000. ● The Formula Method ○ in a single product situation, we can compute the sales volume required to attain a specific target profit using the following formula: ○ ○ ● Target Profit Analysis in Terms of Dollar Sales ○ First, we can solve for thuni sales needed to attain the target profit using the equation method or formula method and then simply multiply the result by the selling price. In the case of Acoustic Concepts, the dollar sales to attain its target profit would be computed as 750 speakers × $250 per speaker, or $187,500 in total sales. ○ Second, we can use the equation method to compute the dollar sales needed to attain the target profit. Remembering that Acoustic Concepts’ target profit is $40,000, its contribution margin ratio is 40%, and its fixed expenses are $35,000, the equation method calculates the answer as follows: (a) ○ Third, we can use the formula method to compute the dollar sales needed to attain the target profit as shown below: (a) (b) In the case of Acoustic Concepts, the computations would be: (c) (d) Again, you’ll notice that the answers are the same regardless of which method we use. This is because all of the methods discussed are simply different roads to the same destination. C. The Margin of Safety ■ The margin of safety is the excess of budgeted or actual sales dollars over the breakeven volume of sales dollars. ● It is the amount by which sales can drop before losses are incurred. The higher the margin of safety, the lower the risk of not breaking even and incurring a loss. ● The formula for the margin of safety is: ● ● The calculation of the margin of safety for Acoustic Concepts is: ● ● This margin of safety means that at the current level of sales and with the company’s current prices and cost structure, a reduction in sales of $12,500, or 12.5%, would result in just breaking even. ○ In a singleproduct company like Acoustic Concepts, the margin of safety can also be expressed in terms of the number of units sold by dividing the margin of safety in dollars by the selling price per unit. In this case, the margin of safety is 50 speakers ($12,500 ÷ $250 per speaker = 50 speakers). III. CVP Considerations in Choosing a Cost structure A. Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in trading off between these two types of costs. For example, fixed investments in automated equipment can reduce variable labor costs. In this section, we discuss the choice of a cost structure. We also introduce the concept ofoperating leverage. B. Cost Structure and Profit Stability ■ To summarize, without knowing the future, it is not obvious which cost structure is better. Both have advantages and disadvantages. ● Sterling Farm, with its higher fixed costs and lower variable costs, will experience wider swings in net operating income as sales fluctuate, with greater profits in good years and greater losses in bad years. ● Bogside Farm, with its lower fixed costs and higher variable costs, will enjoy greater profit stability and will be more protected from losses during bad years, but at the cost of lower net operating income in good years. C. Operating Leverage ■ Using a lever, a massive object can be moved with only a modest amount of force. In businesoperating leverage erves a similar purpose. ■ Operating leverage is a measure of how sensitive net operating income is to a given percentage change in dollar sales. ● Operating leverage acts as a multiplier. If operating leverage is high, a small percentage increase in sales can produce a much larger percentage increase in net operating income. ■ Operating leverage can be illustrated by returning to the data for the two blueberry farms. ● We previously showed that a 10% increase in sales (from $100,000 to $110,000 in each farm) results in a 70% increase in the net operating income of Sterling Farm (from $10,000 to $17,000) and only a 40% increase in the net operating income of Bogside Farm (from $10,000 to $14,000). ● Thus, for a 10% increase in sales, Sterling Farm experiences a much greater percentage increase in profits than does Bogside Farm. Therefore, Sterling Farm has greater operating leverage than Bogside Farm. ■ The degree of operating leverage at a given level of sales is computed by the following formula: ● ● The degree of operating leverage is a measure, at a given level of s of how a percentage change in sales volume will affect profits. ● If two companies have the same total revenue and same total expense but different cost structures, then the company with the higher proportion of fixed costs in its cost structure will have higher operating leverage. ● The degree of operating leverage is not a constant; it is greatest at sales levels near the breakeven point and decreases as sales and profits rise. The following table shows the degree of operating leverage for Bogside Farm at various sales levels. (Data used earlier for Bogside Farm are shown in color.) ● ○ Thus, a 10% increase in sales would increase profits by only 15% (10% × 1.5) if sales were previously $225,000, as compared to the 40% increase we computed earlier at the $100,000 sales level. The degree of operating leverage will continue to decrease the farther the company moves from its breakeven point. At the breakeven point, the degree of operating leverage is infinitely large ($30,000 contribution margin ÷ $0 net operating income = ∞). ○ The degree of operating leverage can be used to quickly estimate what impact various percentage changes in sales will have on profits, without the necessity of preparing detailed income statements. ○ As shown by our examples, the effects of operating leverage can be dramatic. If a company is near its breakeven point, then even small percentage increases in sales can yield large percentage increases in profiThis explains why management will often work very hard for only a small increase in sales volu If the degree of operating leverage is 5, then a 6% increase in sales would translate into a 30% increase in profits. IV. Structuring Sales Commissions A. Commissions based on sales dollars can lead to lower profits. B. C. Which model will salespeople push hardest if they are paid a commission of 10% of sales revenue? The answer is the Turbo because it has the higher selling price and hence the larger commission. On the other hand, from the standpoint of the company, profits will be greater if salespeople steer customers toward the XR7 model because it has the higher contribution margin. ■ To eliminate such conflicts, commissions can be based on contribution margin rather than on selling price ■ If this is done, the salespersons will want to sell the mix of products that maximizes contribution margin. Providing that fixed costs are not affected by the sales mix, maximizing the contribution margin will also maximize the company’s profit ■ In effect, by maximizing their own compensation, salespersons will also maximize the company’s profit. V. Sales Mix A. The Definition of Sales Mix ■ The term sales mix refers to the relative proportions in which a company’s products are sold. ● The idea is to achieve the combination, or mix, that will yield the greatest profits. Most companies have many products, and often these products are not equally profitable. ● Hence, profits will depend to some extent on the company’s sales mix. Profits will be greater if highmargin rather than lowmargin items make up a relatively large proportion of total sales. ■ Changes in the sales mix can cause perplexing variations in a company’s profits. A shift in the sales mix from highmargin items to lowmargin items can cause total profits to decrease even though total sales may increase. ● Conversely, a shift in the sales mix from lowmargin items to highmargin items can cause the reverse effect—total profits may increase even though total sales decrease. ● It is one thing to achieve a particular sales volume; it is quite another to sell the most profitable mix of products. B. Sales Mix and BreakEven Analysis ■ If a company sells more than one product, breakeven analysis is more complex than discussed to this point. ● The reason is that different products will have different selling prices, different costs, and different contribution margins. ● Consequently, the breakeven point depends on the mix in which the various products are sold. ■ 54 Exhibit ● As shown in the exhibit, the breakeven point is $60,000 in sales, which was computed by dividing the company’s fixed expenses of $27,000 by its overall CM ratio of 45%. However, this is the breakeven only if the company’s sales mix does not change. Currently, the Monuments DVD is responsible for 20% and the Parks DVD for 80% of the company’s dollar sales. Assuming this sales mix does not change, if total sales are $60,000, the sales of the Monuments DVD would be $12,000 (20% of $60,000) and the sales of the Parks DVD would be $48,000 (80% of $60,000).As shown in Exhibit 54, at these levels of sales, the company would indeed break even. ● But $60,000 in sales represents the breakeven point for the company only if the sales mix does not change. If the sales mix changes, then the breakeven point will also usually change. ■ This is illustrated by the results for October in which the sales mix shifted away from the more profitable Parks DVD (which has a 50% CM ratio) toward the less profitable Monuments CD (which has a 25% CM ratio). These results appear ixhibit 55. ● ● the sales mix is exactly the reverse of what it was Exhibit 54, with the bulk of the sales now coming from the less profitable Monuments DVD. ● Shift in sales mix causes both the overall CM ratio and total profits to drop sharply from the prior month even though total sales are the same. ○ The overall CM ratio has dropped 45% in sept to only 30% in oct, and net operating income has dropped from $18,000 to only $3k. Additionally, with the drop in the overall CM ratio, the company’s breakeven point is no longer $60,000 in sales. ○ Because the company is now realizing less average contribution margin per dollar of sales, it takes more sales to cover the same amount of fixed costs. Thus, the breakeven point has increased from $60,000 to $90,000 in sales per year. ● In preparing a breakeven analysis, an assumption must be made concerning the sales mix. Usually the assumption is that it will not change. However, if the sales mix is expected to change, then this must be explicitly considered in any CVP computations. VI. Glossary
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