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Chapter 7 Cost-Volume-Profit Analysis

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Chapter 7 Cost-Volume-Profit Analysis Part II Management Accounting Decision-Making Tools Chapter 7 • Cost-Volume-Profit Analysis Chapter 8 • Comprehensive Business Budgeting Chapter 9 • Incremental Analysis and Decision-making Costs Chapter 10 • Incremental Analysis and Cost-Volume-profit Analysis: Special Applications Chapter 11 • Economic Order Quantity Models Chapter 12 • Capital Budgeting Decisions Tools Chapter 13 • Pricing Decision Analysis Management Accounting | 113 Cost-Volume-Profit Analysis The success of a business as measured in terms of profit depends upon adequate sales; that is; the volume of sales must be sufficient to cover all costs and allow a satisfactory margin for net income. When the proportion of fixed costs in a business becomes large in relation to total costs, then volume becomes an extremely important factor in achieving profitability. For example, a business with only variable costs would be able to report net income at any level of sales as long as price exceeds the variable cost rate. However, a business with only fixed costs cannot show a profit until the contribution from sales is equal to the amount of fixed expenses. Therefore, a minimum level of sales is absolutely essential in a business that incurs fixed expenses. Because changes in volume can have a profound impact on the profits of a business, cost-volume-profit analysis has been developed as a management tool to enable analysis of the following variables: 1. Price 2. Quantity 3. Variable costs 4. Fixed costs The focal point of cost-volume-profit analysis is on the effect that changes in volume have on fixed and variable costs. Volume may be regarded as either units sold or the dollar amount of sales. Typically, the theory of cost-volume-profit analysis is explained in terms of units. However, using units as the measure of volume for computing break even point or target income point requires that the business sell 114 | CHAPTER SEVEN • Cost-Volume-Profit Analysis only a single product. Since all businesses from a practical viewpoint sell multiple products, the real world use of cost-volume-profit analysis requires that volume be measured in terms of sales dollars. Cost-volume-profit analysis may be used as (1) a tool for profit planning and decision-making and (2) as a tool for evaluating the profitability of proposed business ventures. In this chapter, the discussion of profit analysis shall be limited to its use as a current period profit and decision-making tool. Nature of Cost-Volume-Profit Analysis In chapter 5, the subject of cost behavior was discussed. The point was made that the costs of a business could be classified as either fixed or variable. Mathematically, it was stated: TC = V(Q) + F (1) TC - total costs V - variable cost rate Q - quantity Revenue or sales may be defined as: S = P(Q) (2) S - sales P - price Income may be defined as: I = R - E (3) R - revenue E - expense I - income When equations (1) and (2) are substituted into equation (3), equation (3) becomes I = P(Q) - V(Q) - F (4) Equation (4) is recognized in this chapter as the foundation of cost-volume- profit analysis. Quantity (Q) is generally treated as the independent variable; that is, income is regarded as a function of quantity (Q). The variable cost rate (V) and fixed expenses (F) are assumed to be constants. However, for certain analytical purposes, the values of V and F may be assigned different values in order to determine the effect of the changes in these values on net income. Equation 4, it should be noted, may be used as a tool of analysis only for a single product business. For firms that have more than one product, another equation which emphasizes sales as volume in dollars must be used: I = S - v(S) - F (5) S - sales in dollars v - variable cost percentage In a multiple product business, it is necessary to express variable cost as a percentage of sales. This percentage will be discussed in detail in a later section of this chapter. Management Accounting | 115 Cost-volume-profit Analysis for a Single Product Business Frequently, it is necessary to ask the question: how many units must be sold in order to attain a given level of net income? Equation (4) may be used to answer this question; however, in order to do so it is necessary to solve for quantity, Q. I = Q(P - V) - F I + F = Q(P - V ) I + F Q = ––––– (6) P - V Equation (6) may be used to determine the quantity of sales required to attain any desired level of income. For example, assume that the Acme Company’s selling price is $10 and its variable cost rate is $8. Also, assume that it has fixed expenses of $5,000. Suppose that management desires to earn $8,000 for the period. How many units must the company sell in order to attain the desired net income? Answer: This question may be answered simply by substituting these given rev- enue and cost values into equation 6: I + F $8,000 + $5,000 $13,000 Q = –––– = ––––––––––––– = ––––––– = 6,500 units P - V $10 - $8 2 Therefore, the Acme Company must sell 6,500 units to earn $8,000. The validity of this answer can be demonstrated as follows: Sales (6,500 x $10) $65,000 Expenses: Variable (6,500 x $8) $52,000 Fixed 5,000 _______ Total expenses $57,000 _______ Net income $ 8,000 ––––––– In management accounting literature, considerable emphasis is given to the concept of a break even point. While it is an interesting academic exercise to compute break even point, it should be stressed that a company does not set a goal to break even. The primary object of management in using cost-volume-profit analysis is to determine target income point and not break even point. Nevertheless, assuming for some reason that it is considered desirable to know the break even point of a business, the break even point is calculated exactly in the same way as target income point. Equation (6) may be used to compute break even point. Break even point is simply the quantity of sales that achieves zero net income. It is that level of sales where total sales equals total expenses. Using the same data from the example above, break even point may be computed as follows: 116 | CHAPTER SEVEN • Cost-Volume-Profit Analysis I + F 0 + 5,000 5,000 Q = ––––– = –––––––– = ––––– = 2,500 units P - V 10 - 8 2 The correctness of this answer may be demonstrated as follows: Sales (2,500 x $10) $25,000 Expenses: Variable (8 x 2,500) $20,000 Fixed 5,000 –––––– 25,000 ––––––– Net income $ 0 ––––––– Cost-volume-profit Analysis for a Multiple Product Business A company with more than one product cannot use equations (4) or (6) as illustrated and discussed above. It is not possible to logically add different quantities of product. The saying that “you can’t add apples and oranges” applies here. However, it is possible to meaningfully add the dollar value of oranges to the dollar value of apples. In a multiple product business, it is necessary to use the dollar value of sales as the measure of volume. Equation 5, as previously indicated, is the basis of cost-volume-profit analysis for a multiple product business. I = S - v(S) - F S - sales in dollars v - variable cost percentage The expression v(S) represents total variable expenses. It may be calculated by simply dividing total variable expenses or cost by total sales: TVE v = –––– (7) S Where: v - variable cost percentage TVE - total variable expenses S - sales ($) The variable, v, requires an explanation. As used in the above equation, it is the variable cost percentage; that is, it represents the percentage that total variable cost bears to total sales. The variable cost percentage is assumed to be constant at all levels of activity. For example, assume that v = 70%. Total variable costs would vary with sales as illustrated: Q v TVC ––––––– – ––––––– $ 10,000 .7 $ 7,000 $100,000 .7 $ 70,000 $200,000 .7 $140,000 $400,000 .7 $280,000 Management Accounting | 117 In order for the variable cost percentage to hold constant in a multiple product business, it is necessary for the sales mix ratio to remain the same. The sales mix ratio is discussed later in this chapter. As in the case of a single product firm, it is desirable to ask the question: how many units must be sold in order to attain a desired income level? Equation 5 may be used to answer this question; however, it is first necessary to solve for S (sales) as follows: I = S - v(S) - F S(1 - v) - F = I S(1 - v) = I + F I + F S = –––––– (8) 1 - v This equation may be used to compute the dollar level of sales required to attain a desired level of income. For example, assume that the Barton Company’s variable cost percentage is 80% and its fixed cost is $10,000. Furthermore, assume that management has set a profit goal of $50,000. What must the dollar volume of sales be in order to attain the $50,000 income objective? Answer: I + F 50,000 + 10,000 60,000 S = –––––– = –––––––––––––– = –––––– = $300,000 1 - v 1 - .8 .2 The correctness of this answer can be demonstrated as follows: Sales $300,000 Expenses: Variable ($300,000 x .8) $240,000 Fixed 10,000 250,000 ––––––– ––––––– Net income $ 50,000 ––––––– The Contribution Margin Concept The study and use of cost-volume-profit analysis requires understanding the concept of contribution margin. The study of this unique concept contributes greatly to an understanding of the importance of changes in volume.
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