Chapter 4- Cost-Volume-Profit Relationship PDF

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Chapter 4- Cost-Volume-Profit Relationship
Taught by Glenn Leonard ...

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Chapter 4: Cost-Volume-Profit Relationship Chapter 4 builds on the concept of cost behaviour and incorporates revenues to provide commonly used tools for analysis and short-term decision-making, including cost-volume-profit analysis and break-even analysis with and without corporate income taxes Cost-Volume-Profit (CVP) analysis is a powerful tool that helps managers understand the relationship among cost, volume, and profit. CVP focuses on how profits are affected by the following five elements: 1. 2. 3. 4. 5.

Prices of products Volume or level of activity Per unit variable costs Total fixed costs Mix of products sold for multi-product companies

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Because CVP analysis helps managers understand how profits are affected by these key factors, it is a vital tool in many business decisions These decisions include what products to manufacture and services to offer, what prices to charge, what marketing strategy to adopt, and what cost structures to implement Careful study of the elements and assumptions, however, is needed to avoid mistakes and to know when to extend the ideas presented in this chapter to more complex situations

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Learning Objectives (9) 1. Explain how changes in activity affect contribution margin and operating income. The Basics of Cost-Volume-Profit Analysis  One of the most common applications of CVP analysis is to examine how changes in activity levels, selling prices, variable costs per unit, or fixed costs will impact profits.  Preparing a contribution income statement is a useful first step for this type of analysis  The contribution income statement emphasizes the behaviour of costs and therefore is extremely helpful to a manager in judging the impact on profits of changes in selling price, cost, or volume

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The contribution format income statement is typically prepared for management’s use and would not ordinarily be made available to external stakeholders such as creditors, shareholders, or tax authorities

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Note that we use operating income as our measure of profit, we ignore income taxes throughout most of this chapter so that we can more easily focus on the central issues of CVP analysis

Contribution Margin  Contribution margin (CM) 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 – CM is used first to cover the fixed expenses, and then whatever remains goes toward profits  If the CM is not sufficient to cover the fixed expenses, then a loss occurs for the period

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If enough speakers are sold to generate $35,000 in CM, then all of the fixed costs will be covered and the company will have managed to a least break even for the month – that is, to show neither profit nor loss but just cover all of its expenses o To break-even point, the company needs to sell 350 speakers in a month, since each speaker sold yields $100 in CM o The break-even point is the level of sales at which profit is zero

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Once the break-even point is reached, operating income will increase by the CM per unit for each additional unit sold. If 351 speakers are sold in a month, for example, then we can expect the operating income for the month to be $100, since the company will have sold one speaker more than the number required to break even:

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To estimate profit at any sales level above the break-even point, simply multiply the number of units sold in excess of the break-even point by the unit CM

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The results represent the anticipated operating income for the period. Or, to estimate the effect of an increase in sales on profits, the manager can simply multiply the increase in units sold by the unit CM. The result will be the expected increase in operating income If Acoustic Concepts is currently selling 400 speakers per month and hopes to increase sales to 425 speakers per month, the anticipated effect on operating profits can be computed as follows:

Quick Check: Calculate the decrease in operating income if Acoustics Concepts sells 300 speakers per month instead of 400  Decrease number of speakers to be sold 100 x $100 per speaker = -$10,000 decrease in operating income 2. Prepare and interpret a cost-volume-profit (CVP) graph. Cost-Volume-Profit Relationship in Graphic Form Relationships among revenue, cost, profit, and volume can be expressed graphically by preparing a costvolume-profit (CVP) graph. A CVP graph highlights CVP relationships over wide ranges of activity Preparing the Cost-Volume-Profit Graph  In a CVP graph (sometimes called a break-even chart), unit volume is commonly represented on the horizontal x-axis.  Preparing a CVP graph involves three steps, as depicted in Exhibit 4-1, and can easily be accomplished using software such as Excel 1. Plot the line parallel to the volume axis that represents total fixed expenses  For acoustic concepts, total fixed expenses are $35,000 2. Plot the line representing total expenses (fixed plus variable) at various activity levels, for example, in exhibit 4-1, total expenses at an activity level 600 speakers are calculated as follows:

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Total expenses at other activity levels are calculated using this approach

3. Plot the line representing totals sales dollars at various activity levels. For example, in exhibit 4-1, sales at an activity level 600 speakers are $150,000 (600 speakers x $250 per speaker). Total sales at other activity levels are calculated using this approach

Quick Check:

Using the profit equation, verify that Acoustic Concepts will have a loss of $25,000, as shown in exhibit 43, if sales volume is 100 speakers  Profit = Unit CM x Q – Fixed expenses or profit = $100 x Q - $35,000  Profit = (100 x 100) – $35,000  Loss = $25,000

3. Use contribution margin (CM) ratio to compute changes in contribution margin and operating income resulting from changes in sales volume.  In this section, we show how the CM ratio can be used in CVP calculations.  As the first step, we have added a column to Acoustic Concepts’ contribution income statement, in which sales revenues, variable expenses, and CM are expressed as a percentage of sales

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The CM expressed as a percentage of total sales is referred to as the contribution margin (CM) ratio. This ratio is computed as follows:

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Some managers prefer to work with the CM ratio rather than the unit CM. The CM ratio is particularly valuable when trade-offs must be made between more dollar sales of one product and more dollar sales of another. Generally speaking, when trying to increase sales, products that yield the greatest amount of CM per dollar of sales should be emphasized

Quick Check: Calculate the effect on operating income if Acoustic Concepts has a $10,000 decrease in sales, assuming fixed costs do not increase  Change in CM = CM ratio x Change in sales  Change in CM = 40% x -$10,000  Change in CM = -$4,000

4. Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume. Some Applications of Cost-Volume-Profit Concepts  Now that we have covered the basics of CVP analysis we can turn to examining how changes to costs, prices, and volume will impact profits.  However, we first need to introduce another concept – the variable expense ratio o The variable expense ratio is the ratio of variable expenses to sales o It is computed by dividing total variable expenses by the total sales, or, in a singleproduct analysis, it is computed by dividing the variable expense per unit by the unit selling price o In this case, Acoustic Concepts, the variable expense ratio is 0.60; that is, variable expense is 60% of sales. Expressed as an equation the variable express ratio is

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The Learning Aid below summarizes the key concepts and formula that we will use in the analysis that follows:

Change in Fixed Cost and Sales Volume  Acoustic Concepts is currently selling 400 speakers per month at $250 per speaker, for total monthly sales of $100,000. The sales manager feels that a $10,000 increase in the monthly advertising budget would increase monthly sales by $30,000. Should the advertising budget be increase? The following table shows the effect of the proposed change in monthly advertising budget:

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Assuming no other factors need to be considered, the increase in the advertising budget should be approved since it would lead to an increase in operating income of $2,000. There are two shorter ways to present this solution. The first alternative solution follows:

Since in this case only the fixed costs and the sales volume change, the solution can be presented in an even shorter format, as follows:

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Notice that this approach does not require a knowledge of previous sales. Also notice that it is unnecessary under either alternative approach to prepare an income statement Both approaches involve an incremental analysis – they consider only those items of revenue, cost, and volume that will change if the new program is implemented Although in each case a new income statement could have been prepared, the incremental approach is simpler and focuses attention on the specific items involved in the decision

Change in Variable Costs and Sales Volume  Refer to the original data. Recall that Acoustic Concepts is currently selling 400 speakers per month. Management is contemplating the use of higher-quality components, which would increase variable costs (and thereby reduce the CM) by $10 per speaker. However, the sales manager predicts that the higher overall quality would increase sales to 480 speakers per month. Should the higher-quality components be used? The $10 increase in variable costs will decrease the unit CM by $10 – from $100 to $90

Change in Fixed Costs, Selling Price, and Sales Volume  The company is currently selling 400 speakers per month. To increase sales, the sales manager would like to reduce the selling price by $20 per speaker and increase the advertising budget by $15,000 per month. The sales manager argues that if these two actions are taken, unit sales will increase by 50% to 600 speakers per month. Should the changes be made? A decrease of $20 per speaker in the selling price will cause the unit CM to decrease from $100 to $80

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According to this incremental analysis, the changes should not be made. The $7,000 reduction in operating income that is shown above can be verified by preparing comparative income statements as follows:

Change in Variable Cost, Fixed Cost, and Selling Volume  The company is selling 400 speakers per month. The sales manager would like to pay the salesperson a 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 will increase monthly sales by 15% to 460 speakers per month. Should the change be made?

Importance of the Contribution Margin  CVP analysis seeks the most profitable combination of variable costs, fixed costs, selling price, and sales volume.

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The above examples show that the effect on the CM is a major consideration in deciding on the most profitable combination of these factors We have seen that profits can sometimes be improved by reducing the CM if fixed costs van be reduced by a greater amount. More commonly, we have seen that the way to improve profits is to increase the total CM o Sometimes this can be done by reducing the selling price and thereby increasing the volume, sometimes it can be done by increasing the fixed costs (such as advertising) and thereby increasing the volume, and sometimes it can be done by trading off variable and fixed costs with appropriate changes in volume The amount of the unit CM figure (and the size of the CM ratio) has significant influence on the actions a company is willing to take to improve profits The effect on the CM is critical to many operating decisions

5. Compute the break-even point in unit sales and sales dollars. Break-Even Analysis Break-Even Computation  Break-even analysis is an aspect of CVP analysis that is designed to answer questions such as how far sales could drop before the company begins to lose money  Earlier we defined the break-even point to be the level of sales at which the company’s profit (operating income) is zero  The contribution format income statement illustrated earlier in this chapter can be stated in equation form as follows:

The equation method

The formula method

Quick Check: Calculate the break-even point in units and sales dollars assuming Acoustic Concepts’ fixed costs are $40,000 and the CM remains the same at $100 per unit 

6. Determine the level of sales needed to achieve a desired target profit. Target Operating Profit Analysis  CVP formulas can also be used to determine the sales volume needed to achieve a target operating profit o Suppose that Acoustic Concepts would like to earn a target operating profit of $40,000 per month. o How many speakers would have to be sold?  The key to target profit analysis is recognizing that instead of solving for the unit sales where operating profits are zero, you instead solve for the unit sales where operating profits are $40,000. As such the simplified profit equation introduced in the previous section is again relevant:

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However, instead of solving the equation with $0 profits we include the target profit amount. This results in the slightly modified formula shown below that adds the target operating profit to the numerator in the expression on the right-hand side of the equation:

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Using this formula for Acoustic Concepts Inc. shows they must sell 750 speakers to generate $40,000 operating profit

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The following check shows selling 750 speakers will indeed lead to $40,000 in operating profit:

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If instead we want to calculate the dollar sales level required to achieve a target operating profit, a similar modification to the formula introduced in the previous section is required. The revised formula is as follows:

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Alternatively, we could simply multiply the number of speakers required to achieve $40,000 in operating profit by selling price of $250 to get the same result:

Quick Check: Calculate the sales units and sales dollars required if Acoustic Concepts has a target profit of $74,000. Assume fixed costs are $45,000, the sales price per unit is $250, and variable costs per unit are $150  Unit sold to attain the target profit = fixed expenses + target operating profit / unit CM  = $45,000 + $74,000 / $100 = 1,200  Dollar sales to attain target profit = fixed expenses + target operating profit / Cm ratio  = $45,000 + $74,000 / 40% = $300,000

After-Tax Analysis  Operating profit in the preceding analysis has ignored income taxes, but for-profit organizations are required to pay corporate income taxes  In general, operating profit after taxes can be computed as a fixed percentage of income before taxes  To calculate income taxes, we multiply the tax rate (t) by the operating profit before taxes (B). therefore, after-tax profit is equal to profit before taxes X (1 -t) and derived as follows:

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Dividing both sides by (1-t), income before taxes is equal to profit after taxes divided by 1 minus the tax rate (1 – t):

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Using the previous example, assume that the tax rate is 30% and the target operating profit is $49,000 after taxes. The target profit can be achieved by selling 1,050 speakers. The appropriate formula to us is:

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The Learning Aid below summarizes the key formulas used in break-even and target profit

7. Compute the margin of safety and explain its significance. The Margin of Safety  The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales  It states the amount by which sales can drop before losses begin to occur  The higher the margin of safety, the lower the risk of not breaking even  The formula calculating the margin of safety is a s follows:

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The margin of safety means that with the company’s current prices and costs, a reduction in sales of $12,500, or 12.5% from the current level, would result in just breaking even In a single-product firm 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 selling price per unit. o In this case, the margin of safety is 50 speakers ($12,500 / $250 per speaker = 50 speakers)

8. Explain cost structure and compute the degree of operating leverage at a particular level of sales, and explain how it can be used to predict changes in operating income. Cost-Volume-Profit Considerations in Choosing a Cost Structure  Cost structure refers to the relative proportion of fixed and variable costs incurred by an organization  An organization often has some latitude in trading off between fixed and variable costs o For example, fixed investments in automated equipment can reduce variable labour costs  In this section, we discuss the choice of a cost structure, focusing on the effect of cost structure on profit stability, in which operating leverage plays a key role Cost Structure and Profit Stability  Which cost structure is better – high variable costs and low fixed costs, or the opposite?  No single answer to this question is possible: either structure has its advantages  To summarize, without knowing future sales increases or decreases, it is not obvious which cost structure is better o Sterling Farm, with its higher fixed costs and lower variable costs, will experience wider swings in operating income as sales change, with greater profits in good years and greater losses in bad years o Bogside Farm, with its lower fixed costs and higher variable costs, will enjoy greater operating income stability and will be more protected from losses during bad years, but at a cost of lower operating income in good years Operating Leverage  Operating leverage is a measure of how sensitive operating income is to percentage changes in sales.  Operating leverage acts as a multiplier. If operating leverage is high, a small percentage increase in sales can produce much larger percentage increase in operating income

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The degree of operating leverage is a measure, at a given level of sales, of how a percentage change in sales volume will affect profits. It is computed by the following formula

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To illustrate, the degree of operating leverage for the two farms at a $100,00 sales level is as follows:

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Since the operating leverage for Bogside Farm is 4, the farm’s operating income grows four times as fast as its sales Similarly, Sterling Farm’s operating income grows seven times as fast as its sales. Thus, if sales increase by 10%, then we can expect the operating income of Bogside Farm to increase by 40%, and the operating income of Sterling Farm to increase by 70%. In general, this relation between the percentage change in operating income is given by the following formula:

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The degree of operating leverage is greatest at sales levels near the break-even point and decreases as sales and profits rise The following table shows the degree of operating leverage for Bogside Farm at the various sales levels. (data used earlier for Bogside Farm are shown in colour)

Indifference Analysis  CVP analysis is also useful for aiding decisions about the comparative pr...