1 Part II Management Accounting Decision-Making Tools Chapter 7 Chapter 8 Chapter 9 Cost-Volume-Profit Analysis Comprehensive Business Budgeting 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
3 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
4 114 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-volumeprofit 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.
5 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 revenue 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:
6 116 CHAPTER SEVEN Cost-Volume-Profit Analysis I + F 0 + 5,000 5,000 Q = = = = 2,500 units P - V 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: v = TVE S (7) 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
7 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 60,000 S = = = = $300, v The correctness of this answer can be demonstrated as follows: Sales $300,000 Expenses: Variable ($300,000 x.8) $240,000 Fixed 10, ,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. In an aggregate sense, contribution margin is simply total sales less total variable costs. From a decisionmaking tool perspective, it is also necessary to understand the concept mathematically. Variation of this concept include: Single product business: Total contribution margin - P(Q) - V(Q) or Q(P - V) Contribution margin rate (per unit of product) - ( P - V) Multiple product business Total contribution margin - S - v(s) or S(1 - v) Contribution margin percentage - ( 1 - v)
8 118 CHAPTER SEVEN Cost-Volume-Profit Analysis The contribution margin rate (per unit) and the contribution margin percentage are often called the contribution margin ratio. A ratio may be expressed on a unit basis or a percentage basis. The concept of contribution margin provides a rather unique way of interpreting the activity of a business. At the start of the operating period, a business with fixed expenses would show a loss. At zero sales, the loss would be equal to total fixed expenses. As each unit of product is sold, the loss is gradually reduced by the contribution margin of each unit sold. No profit can be reported until total contribution equals total fixed expenses. After break even point, each unit sold contributes to net income an amount equal to the contribution margin per unit of product. Total Contribution Margin - As previously defined, total contribution margin is total sales less total variable costs. Mathematically, in terms of the profit equation for a single product business, total contribution margin is equal to P(Q) - V(Q). It is important to understand that the term contribution means a contribution first to fixed expenses. As previously mentioned, there can be no profit in a business until total contribution equals total fixed expenses. When this occurs, the business has reached break even point. Break even point is that quantity of sales that causes total contribution margin to be exactly equal to total fixed expenses. Contribution Margin Per Unit of Product - The use of cost-volume-profit analysis as a decision-making tool also requires understanding of the concept of contribution margin per unit of product. The contribution margin rate is simply price less the variable cost rate. Mathematically, the contribution margin rate is P - V. The use of the contribution margin rate is obvious in equation 6: I + F Q = P - V The denominator in this equation, P - V, is the contribution margin rate and, I + F, is the total contribution desired. An important question is: how much contribution is required in any business? The answer is that the contribution required must be enough to pay fixed expenses and then be sufficient to allow the firm to attain the desired level of income. Consequently, I + F, represents the total required contribution. Illustration The Acme Company s accountant provided the following cost-volume-profit data: P - $10.00 V - $8.00 F - $5,000 I - $25,000 The company s contribution margin rate is $2 ($10 - $8). Each sale contributes $2. If the company sells 1,000 units, then the total contribution would be $2,000. The company obviously needs an additional $3,000 of contribution to reach break even point. When sales reach 2,500 the total contribution is $5,000 which is equal to fixed expenses. Break even point has been reached. Each additional units sold after break
9 Management Accounting 119 even point contributes $2 to income. If 2,600 units are sold, net income would be $200 ($2 x 100). Contribution Margin Percentage - In a multiple product firm, it is necessary to talk in terms of contribution as a percentage. Mathematically, the contribution margin percentage rate is 1 - v. The contribution margin percentage requires that the variable cost percentage be first computed. If the variable cost percentage is 70%, then the contribution margin percentage would be 30% (1 -.70). The importance of the contribution margin percentage is apparent from examining equation 8: S = I + F 1 - v The contribution margin percentage is the percentage that each dollar of sales contributions towards fixed expenses and desired net income. The total contribution required to attain the desire income goal can be computed by simply dividing total desired contribution by the contribution margin percentage. Contribution Margin Income Statement - Cost-volume-profit analysis may be made an integral part of financial reporting. Companies who do this generally prefer to prepare income statements in which fixed costs, variable cost, and contribution margin are explicitly shown. For example, assume that during the year the Acme Company had sales of $50,000 and fixed and variable costs as follows: Fixed Expenses Variable Expenses Selling Selling Advertising $5,000 Sales people commissions $ 5,000 Sales people salaries $3,000 Sales people travel $ 2,000 Supplies $ 500 Cost of goods sold $20,000 General & Admin. General & Admin. Utilities $ 500 Supplies $ 5,000 Supplies $ 500 Other $ 2,000 Executive salaries $2,000 Depreciation $1,000 Based on the above data, the following income statement may be prepared as shown in Figure 7.1. Graphical Illustration of Cost-volume-profit Analysis Because the fundamental relationships of cost-volume-profit analysis are basically mathematical in nature, the elements of cost-volume-profit analysis can be illustrated graphically. The general procedure is to plot the revenue and cost functions on the same graph. In order to illustrate the cost-volume-profit graphically, the following data has been assumed: Price $10 Variable cost rate $6 Fixed expenses $20,000 For purposes of preparing the graph, assume different levels of quantity starting with 1,000 units and increasing activity by increments of 1,000 units. The following calculations are helpful in plotting the graph.
10 120 CHAPTER SEVEN Cost-Volume-Profit Analysis Figure 7.1 Acme Manufacturing Company Income Statement, Contribution Basis For the Year Ended, Dec. 31, Sales $50,000 Variable costs: Selling: Cost of goods sold $20,000 Sales people commissions 5,000 Sales people travel 2,000 $27,000 General & Admin. Supplies $ 5,000 Other 2,000 7,000 $34,000 Contribution Margin $16,000 Fixed Expenses: Selling: Advertising $ 5,000 Sales people salaries 3,000 Supplies 500 $8,500 General & Admin. Executive salaries $ 2,000 Utilities 500 Supplies 500 Depreciation 1,000 4,000 $12,500 Net income $ 3,500 Revenue (sales) Total Variable Costs Q P Total Sales Q V Total Variable Costs 1,000 $10 $10,000 1,000 $6 $ 6,000 2,000 $10 $20,000 2,000 $6 $12,000 3,000 $10 $30,000 3,000 $6 $18,000 4,000 $10 $40,000 4,000 $6 $24,000 5,000 $10 $50,000 5,000 $6 $30,000 The procedure for preparing the cost-volume-chart is as follows: (1) Plot the data for total fixed costs (See Figure 7.2a) (2) Plot the data for total variable expenses (See Figure 7.2b) (3) Plot the data for total sales (See Figure 7.2c)
11 Management Accounting 121 Figure a 2b Fixed Cost Total Fixed and Variable Cost Cost $ Cost $ Volume Volume (Quantity) 2c Cost-Volume-Profit Chart Sales/Cost ($) Volume (Quantity) Figure 7.2c represents the completed cost-volume-profit graph. The graph represents an excellent visual means of presenting the basic concepts and cost behavior relationships inherent in cost-volume-profit analysis. An enlarged version of Figure 7.2c is presented is Figure 7.3. Notice that the Acme Company s break even point can easily be seen to be 5,000 units. Assume that the Acme Company desires to attain an income level of $7,000. The level of sales that will result in this amount of income is $67,500. The graph can be easily used to shown net income and net loss as has been done in Figure 7.3a. In addition, the concept of contribution margin can be visually represented in Figure 7.3. Notice that in Figure 7.3 that variable cost has been plotted before fixed cost. Note that in Figure 7.3B, the total contribution margin area is indicated by an arrow. By definition total contribution margin is simply total sales less total variable expenses, and this is exactly what is shown in Figure 7.3B. Also, notice that at break even point, the total contribution margin is equal to fixed costs, as illustrated by chart 7.3B. The break even point may be defined in several ways. One definition defines break even point as that level of sales where total contribution margin is equal to total fixed expenses as illustrated in 7.3B. Another definition defines break even point as that level of sales where sales = total expenses (Figure 7.3A). Obviously, in both definitions, net income is zero at break even point.
12 122 CHAPTER SEVEN Cost-Volume-Profit Analysis Figure 7.3 Graphical Illustration of Contribution Margin (000) (000) Net Income Contribution margin 40 Net Loss Contribution margin = fixed expenses 0 A 0 2,500 5,000 6,750 2,500 5,000 6,750 Volume (units) B Volume (units) Basic Assumptions of Cost-volume-profit Analysis In the next section, illustrations will be given on how cost-volume-profit analysis may be used as a profit planning and decision-making tool. However, effective use of cost-volume-profit analysis for planning purposes requires understanding of certain basic assumptions. Unless the following assumptions are substantially met, any attempt to use cost-volume-profit analysis in a real world situation may prove to be inaccurate and misleading. Cost-volume-profit analysis assumptions may be summarized as follows: 1. Within a relevant range of volume, the variables price, quantity, fixed costs, and variable costs are subject to managerial control. 2. Price and the variable cost rate are constant within the relevant range of activity. This assumption simply means that variable costs and revenues are assumed to vary linearly with changes in volume. State differently, changes in volume have no effect on price, the variable cost rate, and fixed costs. 3. In a multiple product company, the sales mix ratio remains constant with changes in total sales.
13 Management Accounting In a company that uses absorption costing, unless sales equals production, there exists no unique break even point. When direct costing is used, no problems arise when production varies from sales. In direct costing, fixed manufacturing overhead is treated as a period charge. Direct costing and absorption are discussed in some depth in chapter 6. Cost-Volume-Profit Analysis: A Decision-making Analysis Tool Previous discussion of C-V-P was based on the assumption that price, the variable cost rate, and fixed costs remain constant with increases or decreases in quantity. Changes in quantity do not cause changes in the other variables. However, price, the variable cost rate, and fixed costs can change for reasons other than changes in volume. Management can at any time decide to increase or decrease price. Suppliers at any time can increase or decrease the cost per unit of materials. Many, if not most, variable costs and expenses can be changed by management simply by making the decision to do so. Since price, variable costs, and fixed costs can be increased or decreased at the will of management, the cost-volume-profit equations can be used to perform whatif analysis. In broad terms, six basic questions may be asked regarding changes in revenues and costs: Price What is the effect on break even point and target income point of an increase in price? What is the effect on break even point and target income point of a decrease in price? Variable cost rate What is the effect on break even point and target income point of an increase in the variable cost rate? What is the effect on break even point and target income point of a decrease in the variable cost rate? Fixed Expenses What is the effect on break even point and target income point of an increase in fixed costs? What is the effect on break even point and target income point of a decrease in fixed costs? An effective way to answers these questions is to use a P/V graph. A P/V graph shows the relationship of net income to volume (sales dollars or units). A P/V graph is shown in Figure 7.4. In this graph, volume is the independent variable and net income the dependent variable. To illustrate how a P/V graph is constructed, assume the following:
14 124 CHAPTER SEVEN Cost-Volume-Profit Analysis Figure 7.4 Price (P) $10 Variable cost rate (V) $8 Fixed Costs (F) $5, P/V Chart Based on this data, the table below may be prepared. Q P(Q) V(Q) F NI 1,000 10,000 8,000 5,000 (3,000) 2,000 20,000 16,000 5,000 (1,000) 3,000 30,000 24,000 5,000 1,000 Net Income $ Q 4,000 40,000 32,000 5,000 3,000 Volume (units) 5,000 50,000 40,000 5,000 5,000 Net Income Figure 7.5 Changes in Net Income Line $ $ $ Net Income $ Net Income Increase in Price A Net Income Net Income Q Q Q $ Decrease in Price Increase in Variable Cost B C $ Q Q Q Net Income Net Income Decrease in Variable Cost D Increase in Fixed Cost E Decrease in Fixed Cost F In Figure 7.5 is illustrated the effect on break even point and net income of changes in price, variable cost, and fixed expenses. In chart A, an increase in price shifts the line upwards and to the left. The result is a decrease in break even point. In Chart B, a decrease in price has the opposite effect. Break even point has increased in chart C. The increase in variable expenses caused the income line to shift downwards and to the right. The opposite is true of a decrease in the variable expense rate. Break even point has decreased. An increase in fixed expenses will cause the income line to shift to the left and upwards. The result is a decease in break even point. The
15 Management Accounting 125 opposite is true for an increase in fixed expenses. Whether a given change is good or bad for fixed expenses such as advertising can not be stated. For example, an increase in advertising might cause an increase in sales with a resulting increase in net income. The P/V graph can effectively be used to illustrate changes in price, the variable cost rate, and fixed costs. A change in one of these variables will cause a shift or movement in the net income line. Changes in Price - An increase in price will most likely result in a decrease in sales. However, a decrease in sales does not necessarily mean a decrease in net income. Regarding the units that are sold, the contribution margin is greater. Consequently, less units of sales are required to attain a profit goal. Given an increase in price, management will probably want to ask the question: how many units of sales can be lost and the same net income earned? This question can be answered by using the following equation: I + F Q = Figure 7.6 P/V Chart P - V The procedure is simply to $ P/V Chart compute Q, or quantity, at the new P=$12.00 P=$10.00 price and then subtract this quantity from the quantity of sales before 7500 the price change. Illustration Last year, at a sales volume of 5,000 units, the Ace Manufacturing Company s income statement show the following: Sales (5,000 x $10) $50,000 Expenses Variable ($8 x 5000) 40,000 Fixed 5,000 45,000 Net income $ 5, Management is considering increasing price to $12 per unit. At the new price, the quantity necessary to earn the same income would be: 5, ,000 10,000 Q = = = 2, At the new price, only 2,500 units need to be sold to earn $5,000. The company can lose one half of its sales without suffering any loss in income. The effect of the change in price on break even point and net income at different levels of sales is shown in Figure 7.5A. Note that in Figure 7.6, the income function shifts upward and to the left. BEP point is now 1,250 units and the income previously earned at 5,000 units can now be earned at 2,500 units ,250 2,500 3,750 5,000 units
16 126 CHAPTER SEVEN Cost-Volume-Profit Analysis Multiple Product Business and Sales Mix The break even point and target income point for a multiple product business can be computed using equation 8. This equation requires that variable cost be expressed as a percentage of sales. A number of questions arise unique to multiple product business. One of these problems pertains to the fact that the sale of multiple products give rise to a sales mix ratio. The term sales mix refers to the ratio of the units sold for each product. If product A is sold at the rate of 10,000 units per year and product B at the rate of 20,000 per year, then the sales mix ratio is 1:2. There are two methods for computing the variable cost percentage in a multiple product business. The first method was previously discussed and presented as equation 7 TVE v = S The second method involves using the sales mix ratio and knowing the variable cost rates of each product: Mathematically, this method may be defined as follows: V i Q v = i (9) P i Q i i = 1, n Where: v - aggregate percentage variable cost V i - variable cost rate of product i Q i - quantity of product i P i - price of product i To illustrate, assume the following: Product A Product B Price $12.00 $ 8.00 Variable cost $ 8.00 $ 2.00 Quantity 1, Fixed cost $300 $1,000 Based on the above information, the variable cost percentage may be calculated as follows: P i Q i = 12(1,000) + 8(400) = 12, ,200 = 15,200 V i Q i ) = 8(1,000) + 2(400) = 8, = 8,800 Changes in the Sales Mix Ratio V i Q i 8,800 v = = =.5789 P i Q i 15,200 A number of questions arise concerning changes in the sales mix ratio: 1. Does a change in the sales mix ratio have an affect on the variable cost percentage? 2. Can a separate break even point be computed for each product?
17 Management Accounting Is the most profitable product the product with largest contribution margin? 4. Should the product that generates the highest volume of sales dollars also be the product that is promoted the most? 5. Is it possible for sales to increase and costs per unit to remain the same and yet for net income to decrease? Effect of a Change in the Sales Mix Ratio on the Variable Cost Percentage Computing a break even point in a multiple product business is based on the assumption that the sales mix remains the same. In the above example, the sales mix ratio was 2.5 to 1. Based on this ratio, the break even point is: 1,300 1,300 BEP = = = 3, Suppose, in fact, the ratio become the opposite; that is 1:2.5. The variable cost percentage then becomes. 8.00(400) (1000) 5,200 v = = = (400) (1000) 12,800 The break even point is now: 1,300 1,300 BEP = = = 2, If a significant change is the sale mix ratio occurs, then the previous computation of the break even point based on the original sales mix is unreliable. Computing Break even Point for each Product - It is still possible to compute a break even point for each product separately; however, now care must be taken to not include common fixed costs in the total fixed costs for each product. Common fixed costs are those costs that occur whether or not the particular product is sold. For example, salaries to top management are most likely to be common in nature. Assuming there are no common costs in the fixed costs of products A and B, then the individual product break even points may be computed as follows: Product A Product B ,000 1,000 BEP = = = 900 BEP = = = 1, Contribution Margin Rate Differences - It is highly unlikely that the contribution margin rate of each product will be the same. The question is: will the product with the largest contribution margin rate be the most profitable? The answer is no. Net income also depends on the quantity sold. Because the contribution rate is the greatest, this is no guarantee that this product will even be profitable. Using the same data as previously, net income for products A and B may be computed as shown in Figure 7.7: As can clearly be seen, product B which has a greater contribution margin rate
18 128 CHAPTER SEVEN Cost-Volume-Profit Analysis Figure 7.7 Effect of Different Contribution Margin Rates Product A Product B Income Statement Sales ($12 x 1,000) $12,000 Variable expenses ($8 x 1000) 8,000 Contribution margin 4,000 Fixed Expenses 1,000 Net income $ 3,000 Income Statement Sales ($8 x 400) $3,200 Variable expenses ($2 x 400) 800 Contribution margin 2,400 Fixed Expenses 300 Net income $2,100 ($6.00 versus $4.00 for product A) is not the most profitable product. While product A does have the greater sales volume in dollars this does not mean that the product with the highest sales volume will be the most profitable. Profitability also depends on the contribution margin rate and the amount of fixed expenses. Increasing Sales, Constant Costs, and Decreasing Net Income - One of the unusual phenomenons in a business is that sales can be increasing and costs can be constant yet the business is experiencing a decrease in net income. This situation can happen when there is a substantial shift in the sales mix from the product with the greatest contribution margin rate to the products with a lower contribution margin rate. To illustrate, assume that all costs remain the same in our example except that the sales mix becomes 1,100 to 300. Based on this mix, net income for each product may be computed as seen in Figure 7.8: Figure 7.8 Effect of a Change in Sales Mix Ratio Product A Income Statement Sales ($12 x 1,100) $13,200 Variable expenses ($8 x 1100) 8,800 Contribution margin 4,400 Fixed Expenses 1,000 Net income $ 3,400 Product B Income Statement Sales ($8 x 300) $2,400 Variable expenses ($2 x 300) 600 Contribution margin 1,800 Fixed Expenses 300 Net income $1,500
19 Management Accounting 129 Combined income then is: Income Statement Sales $15,600 Variable expenses 9,400 Contribution margin 6,200 Fixed Expenses 1,300 Net income $ 4,900 Previously, combined sales was $15,200 ($12,000 + $3,200). Now combined sales is $15,600 ($13,200 + $2,400); however net income is now $4,900 ($3,400 + $1,500) whereas it was previously $5,100 ($3,000 + $2,100). Even though sales increased by $400, net income has decreased by $200. This decrease in net income happened despite that fact that price, the variable cost rates, and fixed costs remained the same. A multiple product business requires close monitoring of the profitability of each product. General rules for managing and promoting each product based on price, variable cost rates and fixed cost are difficult to formulate. The computation of break even or target income point does not tell management which product will be become the most profitable. However, the effect of changes or shifts in the sales mix can easily be calculated. The best approach to evaluating multiple products is to prepare segmental income statements. This management accounting tool is discussed in depth in chapter 15. A product that is not making a significant contribution to fixed expenses should be a candidate for discontinuance. If after all attempts to increase the segmental contribution have failed, the only course of action is to discontinue the product. Adding and discontinuing products is a constant and ongoing process. The role of the management accounting and the use of the appropriate management accounting tools becomes extremely important in a multiple product business. Computing Target Income Point After Taxes In order to compute a target income point, it is necessary to specify the desired level of income. However, the concept of net income is somewhat ambiguous. Net income can be before taxes or after taxes. Up to this point in this chapter, it has been assumed that the desired level of net income is net income before taxes, although this assumption was never explicitly made. Net income after income taxes in many instances is more useful in making decisions. For example, a dividend policy is easier to formulate based on net income after taxes. Also, in planning cash flow, net income after taxes is more useful. However, net income before tax and after tax are obviously not independent of each other. In order to specify net income after tax as the goal in computing target income point, it is still necessary to know net income before tax. To illustrate, assume that the goal is
20 130 CHAPTER SEVEN Cost-Volume-Profit Analysis to earn $120,000 after tax and that the tax rate is 40%. The equation for converting after tax income to before tax income is: NI bt = NI at / (1 - T) Where: NI bt - net income before tax NI at - net income after tax T - tax rate If the desired net income after tax is $120,000 and the tax rate is 40%, then net income before tax is: Ni bt = $120,000 / ( 1 -.4) = $120,000 /.6 = $200,000 If price is $100, V is $70,00, and fixed expenses $400,000, then we can compute target income point using a slightly modified version of equation 6. I + F Q = (6) P - V NI AT / (1 - T) + F Q = P - V Based on this equation, then target income point maybe be computed as follows: 120,000 /( 1 -.4) + 400, , ,000 Q = = = ,000 = 20, The correctness of this computation can be demonstrated as follows: Sales $2,000,000 Variable expenses 1,400,000 Contribution margin $ 600,000 Fixed expenses $ 400,000 Net income before taxes $ 200,000 Tax expense 80,000 Net income after taxes $ 120,000
21 Management Accounting 131 Summary Cost-volume-profit analysis is a powerful analytical tool. It can be effectively used in many different kinds of decisions. Cost-volume-profit analysis is based on the theory of cost behavior and as such it is imperative that the management accounting and also management have a good understanding of cost behavior. Because cost-volume-profit analysis is based on a number of critical assumptions, it is also important to recognize when the use of this tool is valid and when it is not. If the data used in cost-volume-profit analysis extends too far beyond the relevant range, the results obtained can be inaccurate and misleading. Nevertheless, as long as the assumptions on which cost-volume-profit analysis is based hold true, then the tool can provide very useful information concerning decisions to be made and the evaluation of results already obtained. Q. 7.1 Define the following terms: a. Fixed cost i. Contribution margin rate b. Variable cost j. Variable cost rate c. Semi-variable cost k. Break even point d. Step cost l. Target income point e. Average fixed cost m. Contribution margin income f. Average variable cost statement g. Relevant range n. Sales mix h. Contribution margin o. Net income before tax Q. 7.2 Define the following mathematically. a. Sales b. Total variable cost c. Total fixed cost d. Net income Q. 7.3 What are the two basic equations from which formulas for break even point or target income point may be derived? Q. 7.4 Explain how cost-volume-profit analysis may be used as a tool for decision-making. (Give several examples.) Q. 7.5 What are the basic assumptions that underlie cost-volume-profit analysis? Q. 7.6 What equation may be used to answer the question: how many units must be sold in order to attain a desired level of net income? What equation may be used to answer the question: how many dollars of sales are required in order to attain a desired level of net income? Q. 7.7 Draw a graph illustrating break even point. On this chart, show total sales, total variable cost, and total fixed costs. Shade in the areas of net loss and net income.
22 132 CHAPTER SEVEN Cost-Volume-Profit Analysis Q. 7.8 Define the following mathematical expressions: a. P(Q) - V(Q) b. P - V c. 1 - v d. Q(P - V ) Q. 7.9 If total contribution margin is $100,000 and fixed expenses is $80,000, then the difference ($100,000- $80,000 = $20,000) is called? Q When total fixed expenses equals total contribution margin, then this point is called? Q What effect do the following changes have on break even point: a. Increase in price b. Decrease in price c. Increase in the variable cost rate d. Decrease in the variable cost rate e. Increase in fixed expenses f. Decrease in fixed expenses Q What assumption must be made in order to use cost-volume-profit analysis in a multiple product business? Q What effect does a change in the sales mix ratio have on the variable cost percentage? Q Assume a business has three products. What equation may be use to compute the variable cost percentage? Q Draw a chart that illustrates the use of this equation: I = P(Q) - V(Q) - F Note: ( use only one line to prepare this chart) Explain how this chart shows break even point. Q Given that price, the variable cost rates, and fixed costs have not changed, explain how net income can decrease even though total sales has increased.
23 Management Accounting 133 Exercise 7.1 Contribution Margin Income Statement The management accountant has done an analysis of costs and has arrived at the following cost-volume-profit analysis data based on general ledger information for the year ended December 31, 20xx. Sales $ 100,000 Variable expenses Selling $ 20,000 General and administrative $ 10,000 Cost of goods sold $ 50,000 Fixed Selling $ 5,000 General and administrative $ 2,000 Cost of goods sold $ 10,000 Units sold 1,000 Desired level of income $ 50,000 Required: 1. Prepare a contribution margin income statement. 2. Determine the units that must be sold to attain the desired level of net income. Exercise 7.2 Preparing a Break even Graph Based on the following information, prepare a break even chart. Price $ Variable cost rate $ Fixed expenses $ 50,000 Desired net income $ 80,000 Exercise 7.3 Contribution Margin Income Statement Income Statement (Sales - 10,000 units) Sales $200,000 Expenses $150,000 Net income $ 50,000
24 134 CHAPTER SEVEN Cost-Volume-Profit Analysis It has been determined that of the $150,000 of expenses, $100,000 were fixed. The desired company net income is $150,000. Required: 1. Based on the above information, prepare a contribution margin income statement. 2. Answer the following: a. Contribution margin per unit of product b. Variable cost rate c. Total desired contribution d. Break even point e. Target income point Exercise 7.4 Cost-Volume-Profit Relationships Cost-Volume-Profit Chart $ I K E J M C G L N A D B F H Q Based on the above cost-volume-profit chart, identify the following line segments: Line Segments 1 A - B 2 C - D 3 E - F 4 G - H 5 I - J 6 K - L 7 M - N
25 Management Accounting 135 Exercise 7.5 Computing New Target Income Point The owner of the Brown Retail Company believes that current sales volume is less than potential because of inadequate advertising. He has tentatively decided to increase his advertising budget by $2,000. Last year s income statement was as follows: Sales (1,000 $20.00) $20,000 Variable expenses $10,000 Contribution margin $10,000 Fixed expenses $ 6,000 Net income $ 4,000 Advertising, if increased, will change from $2,000 to $4,000. The maximum market potential is probably between 1,300 and 1,400 units of product. Required: Evaluate this proposed increase in advertising. To offset the increase in advertising, by how much must sales increase in units. Exercise 7.6 Computing Break even point and Target Income Point The following information from the records of the Ajax Manufacturing Company has been provided to you: Sales price: Product A $ Product B $ Product C $ Variable costs: Product A $ Product B $ Product C $ Units sold: Product A $ 1,000 Product B $ 2,000 Product C $ 3,000 Fixed costs for each product was determined as follows: Product A $ 40,000 Product B $ 30,000 Product C $ 80,000 Common fixed costs of the business are $200,000.
26 136 CHAPTER SEVEN Cost-Volume-Profit Analysis Required: 1. Compute the variable cost percentage for each product. 2. Compute the contribution margin percentage for each product. 3. Compute the break even point of each product. 4. Compute the break even point of the business as a whole. 5. Explain how it is possible for each product to break even yet the business as a whole is operating at a loss. 6. Suppose the sales mix ratio rather than 1:2:3 becomes 3:1:2. How would this change in the sales mix ratio affect the variable cost percentage? Exercise 7.7 Computing Target Income Point After Taxes The Acme Manufacturing Company income statement for the year ended was as follows: Sales (10,000 units) $ 200,000 Variable expenses 120,000 Contribution margin $ 80,000 Fixed expenses 60,000 Net income $ 20,000 Tax expense 8,000 Net income after taxes $ 12,000 Required: The company would like to have an after tax income of $50,000. What level of sales is required to attain this level of after tax net income?
Management Accounting 303 Segmental Profitability Analysis and Evaluation Unless a business is a not-for-profit business, all businesses have as a primary goal the earning of profit. In the long run, sustained
Management Accounting 63 Management Accounting Theory of Cost Behavior Management accounting contains a number of decision making tools that require the conversion of all operating costs and expenses into
Management Accounting 243 Pricing Decision Analysis The setting of a price for a product is one of the most important decisions and certainly one of the more complex. A change in price not only directly
Management Accounting 137 Comprehensive Business Budgeting Goals and Objectives Profit planning, commonly called master budgeting or comprehensive business budgeting, is one of the more important techniques
Management Accounting 305 Return on Investment Profit or net income without question is a primary goal of any business. Any business that fails to be profitable in the long run will not survive or will
Chapter 6 Cost-Volume-Profit Relationships 6-2 LEARNING OBJECTIVES After studying this chapter, you should be able to: 1. Explain how changes in activity affect contribution margin. 2. Compute the contribution
Cost-Volume-Profit Analysis Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there
Chapter 6 Cost-Volume-Profit Relationships Solutions to Questions 6-1 The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety
Accounting Building Business Skills Paul D. Kimmel Chapter Fourteen: Cost-volume-profit Relationships PowerPoint presentation by Kate Wynn-Williams University of Otago, Dunedin 2003 John Wiley & Sons Australia,
1. CVP analysis and purposes: Profit per unit of a product depends on its selling price and cost of sales. Total profit depends on sales volume which in turn depends inter alia on selling price. By and
Management Accounting 31 Financial Statements for Manufacturing Businesses Importance of Financial Statements Accounting plays a critical role in decision-making. Accounting provides the financial framework
Summary Chapter Five Cost Volume Relations & Break Even Analysis 1. Introduction : The main aim of an undertaking is to earn profit. The cost volume profit (CVP) analysis helps management in finding out
9 Break-Even Point and Cost-Volume-Profit Analysis Objectives After completing this chapter, you should be able to answer the following questions: LO.1 LO.2 LO.3 LO.4 LO.5 LO.6 What is the break-even point
1. Introduction The cost volume profit (CVP) analysis helps management in finding out the relationship of costs and revenues to profit. Cost depends on various factors like Volume of production Product
Part Five Cost Volume Profit Analysis COST VOLUME PROFIT ANALYSIS Study of the effects of changes of costs and volume on a company s profits A critical factor in management decisions Important in profit
Management Accounting 51 Classification of Manufacturing Costs and Expenses Introduction Management accounting, as previously explained, consists primarily of planning, performance evaluation, and decision
Chapter 4 Solutions Question 4.1 A) Explain the following The term marginal cost refers to the additional costs incurred in providing a unit of product or service. The term contribution refers to the amount
Management Accounting 175 Incremental Analysis and Cost Volume Profit Analysis: Special Applications Incremental analysis is a flexible decision-making tool that may be used in making many different kinds
Cost-Volume-Profit Analysis Cost-Volume-Profit Assumptions and Terminology 1 Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced
C 6 - ACRONYMS notesc6.doc Instructor s Supplemental Information ACRONYMS (ABBREVIATIONS) FOR USE WITH MANAGERIAL ACCOUNTING RELATING TO COST-VOLUME-PROFIT ANALYSIS. CM Contribution Margin in total dollars
Accounting 610 2C Cost-Volume-Profit Relationships Page 1 I. OVERVIEW A. The managerial accountant uses analytical tools to advise line managers in decision making functions. C-V-P (CVP) analysis provides
Assumptions of CVP Analysis Cost-Volume-Profit Analysis Expenses can be classified as either variable or fixed. CVP relationships are linear over a wide range of production and sales. Sales prices, unit
12 CHAPTER Managerial Accounting and Cost-Volume-Profit When asked by a marketing or production manager what a certain item or activity costs, the management accountant who asks Why do you want to know?
385 356 PART FOUR Capital Budgeting a large number of NPV estimates that we summarize by calculating the average value and some measure of how spread out the different possibilities are. For example, it
COST & BREAKEVEN ANALYSIS http://www.tutorialspoint.com/managerial_economics/cost_and_breakeven_analysis.htm Copyright tutorialspoint.com In managerial economics another area which is of great importance
CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS NOTATION USED IN CHAPTER 3 SOLUTIONS SP: Selling price VCU: Variable cost per unit CMU: Contribution margin per unit FC: Fixed costs TOI: Target operating income 3-1
Management Accounting 161 Incremental Analysis and Decision-making Costs Nature of Incremental Analysis Decision-making is essentially a process of selecting the best alternative given the available information
Chapter 5 Break-even analysis (CVP analysis) 1 5.1 Introduction Cost-volume-profit (CVP) analysis looks at how profit changes when there are changes in variable costs, sales price, fixed costs and quantity.
Paper 3A: Cost Accounting Chapter 9 CA. Dharmendra Gupta Introduction Cost classification Profit Volume Ratio ( P V ) ratio Break Even Point Margin of Safety Shut Down Point Cost Indifference Point Cash
Management Accounting 319 Financial Statement Ratio Analysis Financial statements as prepared by the accountant are documents containing much valuable information. Some of the information requires little
Management Accounting 195 Inventory Decision-Making To be successful, most businesses other than service businesses are required to carry inventory. In these businesses, good management of inventory is
Chapter 6-1 Chapter 6 Cost-Volume-Profit Relationships McGraw-Hill /Irwin The McGraw-Hill Companies, Inc., 2007 Basics of Cost-Volume-Profit Analysis Contribution Margin (CM) is the amount remaining from
Chapter 25 Cost-Volume-Profit Analysis Questions 1. Cost-volume-profit analysis is used to accomplish the first step in the planning phase for a business, which involves predicting the volume of activity,
Chapter 22 Helena Company reports the following total costs at two levels of production. 10,000 Units 20,000 Units Direct materials $20,000 $40,000 Maintenance 8,000 10,000 Direct labor 17,000 34,000 Indirect
Slide 1.3.1 1. Accounting for decision making 1.3 Cost-volume volume-profit relationships Slide 1.3.2 Introduction This chapter examines one of the most basic planning tools available to managers: cost
TM 5-1 COST-VOLUME-PROFIT RELATIONSHIPS Cost-volume-profit (CVP) analysis is concerned with the effects on net operating income of: Selling prices. Sales volume. Unit variable costs. Total fixed costs.
Managerial Accounting Prof. Dr. Vardaraj Bapat Department of School of Management Indian Institute of Technology, Bombay Lecture - 26 Cost Volume Profit Analysis Dear participations in our early session,
COST DATA FOR SHORT-RUN TACTICAL DECISION MAKING To decide on the acceptance or rejection of a special order from a supplier, marginal costing and contribution analysis should be applied. The company may
Breakeven, Leverage, and Elasticity Dallas Brozik, Marshall University Breakeven Analysis Breakeven analysis is what management is all about. The idea is to compare where you are now to where you might
BREAK-EVEN ANALYSIS In your business planning, have you asked questions like these? How much do I have to sell to reach my profit goal? How will a change in my fixed costs affect net income? How much do
12 Marginal Costing Learning Objectives When you have finished studying this chapter, you should be able to Understand the difference between absorption costing and marginal costing Understand the concept
Part Three Cost Behavior Analysis Cost Behavior Cost behavior is the manner in which a cost changes as some related activity changes An understanding of cost behavior is necessary to plan and control costs
Harvard Business School 584-149 Rev. September 29, 1986 Basic Quantitative Analysis for Marketing Simple calculations often help in making quality marketing decisions. To do good numbers work, one needs
Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis QUESTIONS 1. A variable cost is one that varies proportionately with the volume of activity. For example, direct materials and direct labor (when
HOSP 2110 (Management Acct) Learning Centre Cost-Volume-Profit Analysis The basic principles of CVP analysis were covered in business math. CVP analysis can be done both graphically, through plotting the
Journal of Construction Education Spring 1999, Vol. 4, No. 1, pp. 26-37 Copyright 1999 by the Associated Schools of Construction 1522-8150/99/$3.00/Educational Practice Manuscript Practical Business Application
Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solution to Problem #11 This problem focuses on being able to work with both total cost and average per unit cost. As a brief review,
Chapter 18 Identify how changes in volume affect Total variable change in direct proportion to changes in the volume of activity Unit variable cost remains constant Units produced 3 5 Total direct materials
Chapter 5 Revenue & Cost Analysis 1. General Cost data are subject to great misunderstanding than are value data. The main reason: although the various categories of costs have precise meaning to the accountant,
01 technical cost-volumeprofit relevant to acca qualification paper F5 In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could look into a crystal ball and find
Financial Analysis, Modeling, and Forecasting Techniques Course #5710B/QAS5710B Course Material TECHNIQUES OF FINANCIAL ANALYSIS, MODELING, AND FORECASTING Delta Publishing Company Copyright 2011 by DELTA
MANAGERIAL ACCOUNTING 7e Al L. Hartgraves Wayne J. Morse Learning Objective 1 CHAPTER 3 Cost Volume Profit Analysis and Planning Identify the uses and limitations of traditional cost volume profit analysis.
MANAGEMENT ACCOUNTING Cost-Volume-Profit Analysis Zofia Krokosz-Krynke, Ph.D., MBA firstname.lastname@example.org Wroclaw University of Technology, Building B4 Room 521 http://www.ioz.pwr.edu.pl/pracownicy/krokosz/
Financial Analysis, Modeling, and Forecasting Techniques Course #5710A/QAS-5710A Course Material Financial Analysis, Modeling, and Forecasting Techniques (Course #5710A/QAS-5710A) Table of Contents PART
12 Marginal Costing BASIC CONCEPTS AND FORMULAE Basic Concepts 1. Absorption Costing: a method of costing by which all direct cost and applicable overheads are charged to products or cost centers for finding
Chapter 6 Notes Page 1 Cost-Volume-Profit Analysis Understanding the relationship between a firm s costs, profits and its volume levels is very important for strategic planning. When you are considering
c04.qxd 6/2/06 2:53 PM Page 124 CHAPTER 4 LEARNING OBJECTIVES 1 2 3 4 5 6 Identify common cost behavior patterns. Estimate the relation between cost and activity using account analysis and the high-low
CHAPTER 22 Cost-Volume-Profit Relationships ASSIGNMENT CLASSIFICATION TABLE Study Objectives Questions Brief Exercises Exercises A Problems B Problems * 1. Distinguish between variable and fixed costs.
The Role of the Basic Profit Equation in Selecting a Selling Price Ted Mitchell Consider the following three exam questions: #1 A person bought a wagon at $4 and sold it at a price that provides the desired
Example Summary of how to calculate Six Sigma Savings: Six Sigma calculations are based on current period actual activity vs. prior period actual activity. Reported Six Sigma Direct Savings must therefore
2.0 Chapter Introduction In this chapter, you will learn to use cost-volume-profit analysis. Assumptions. When you acquire supplies or services, you normally expect to pay a smaller price per unit as the
Financial ratio analysis A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Liquidity ratios 3. Profitability ratios and activity ratios 4. Financial leverage ratios 5. Shareholder
Dear Profit Master, Congratulations for taking the next step in improving the profitability and efficiency of your company! Profit Guard will provide you with comparative statistical and graphical measurements
19 Cost-Volume-Profit Analysis Learning Objectives 1 Identify how changes in volume affect costs 2 Use CVP analysis to compute breakeven points 3 Use CVP analysis for profit planning, and graph the CVP
CSUN GATEWAY Managerial Accounting Study Guide Table of Contents 1. Introduction to Managerial Accounting 2. Introduction to Cost Terms and Cost Concepts 3. Allocation of Manufacturing Overhead Costs 4.
Chapter 3: Cost-Volume-Profit Analysis and Planning Agenda Direct Materials, Direct Labor, and Overhead Traditional vs. Contribution Margin Income Statements Cost-Volume-Profit (CVP) Analysis Profit Planning
CHAPTER 7 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will
Medicare versus Private Health Insurance: The Cost of Administration Presented by: Mark E. Litow, FSA Consulting Actuary January 6, 2006 Medicare versus Private Health Insurance: The Cost of Administration
Management Accounting 337 Statement of Cash Flow Cash is obviously an important asset to all, both individually and in business. A shortage or lack of cash may mean an inability to purchase needed inventory
USE OF THE COST/VOLUME/PROFIT ANALYSIS IN TERMS OF EARNINGS Ms. Indu Patni Dept.: Applied science and humanities Assistant Professor, Institute of Technology Gopeshwar Chamoli, India e-mail: email@example.com
Break-even analysis On page 256 of It s the Business textbook, the authors refer to an alternative approach to drawing a break-even chart. In order to survive businesses must at least break even, which
Finance for Cultural Organisations Lecture 9. Capital Budgeting: Project Analysis and Evaluation Lecture 9. Capital Budgeting: Project Analysis & Evaluation Understand forecasting risk and sources of value
Learning Objectives After reading Chapter 3 and working the problems for Chapter 3 in the textbook and in this Workbook, you should be able to: Employ marginal analysis to find the optimal levels of activities
Chapter 11 Project Analysis and Evaluation McGraw-Hill/Irwin Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Understand forecasting risk and sources of value
5-1 Cost-Volume-Profit Managerial Accounting Fifth Edition Weygandt Kimmel Kieso 5-2 study objectives 1. Distinguish between variable and fixed costs. 2. Explain the significance of the relevant range.
Basic Accounting & Budgeting February 4, 2009 The Nature of Accounting Systems Accounting is the process of recording, classifying, summarizing, reporting and interpreting information about the economic