# An Income Statement Teaching Approach for Cost-Volume-Profit (CVP) Analysis by Using a Company s CVP Model

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1 An Statement Teaching Approach for Cost-Volume-Profit (CVP) Analysis by Using a Company s CVP Model Freddie Choo San Francisco State University Kim B. Tan California State University Stanislaus This paper presents an Statement teaching approach for Cost-Volume-Profit (CVP) analysis by using a company s CVP Model that is intuitive and student-friendly. This approach would help students learn about CVP analysis and reduces their memorization of equations. INTRODUCTION This paper extends Wilner s (1987) focus on simplifying the teaching and learning of process costing. We present an alternative to the typical teaching approach for Cost-Volume-Profit (hereafter CVP) analysis (e.g., Garrison et. al 2010; Horngren et. al, 2009). The typical teaching approach is to teach students a series of equations for solving various questions relating to CVP analysis. In our approach, we collapse all the equations into its Variable Costing Statement format and use the Statement as a CVP Model of the company. We believe that this CVP Model provides students with an intuitive understanding of the CVP analysis and reduces their memorization of equations. DEVELOPING THE CVP MODEL The typical approach in teaching CVP analysis is to teach students a series of equations for solving CVP questions. Table 1 presents a sample of these equations. TABLE 1 SAMPLE EQUATIONS GIVEN IN TEXTBOOKS REGARDING COST-VOLUME-PROFIT (CVP) ANALYSIS From Garrison et al. (2010) and Horngren et al. (2009) Profit = Unit CM x A Fixed Costs Profit = CM ratio x Sales Fixed Costs Unit Sales to Attain Target Profit = Target Profit + Fixed Costs Unit CM Journal of Accounting and Finance vol. 11(4)

2 Dollar Sales to Attain Target Profit = Target Profit + Fixed Costs CM Ratio Unit Sales to Breakeven = Fixed Costs Unit CM Dollar Sales to Breakeven = Fixed Costs CM Ratio (Unit Selling Price x A) (Unit Variable Cost x A) Fixed Costs = Target = Target Net 1 Tax Rate Unit Sales = Fixed Costs + Target 1 Tax Rate Unit CM Note: A = Unit Sales, CM = Contribution Margin, CM Ratio = CM% = CM Sales In our Statement approach, we use the Variable Costing Statement to perform CVP analysis. The Variable Costing Statement is shown horizontally as: Sales Variable Costs Fixed Costs = which also can be written vertically as: Sales - Variable Costs Contribution Margin - Fixed Costs Each of the above Sales and Variable Costs is an equation: Sales Unit Selling Price x No. of Units - Variable Costs Unit Variable Cost x No. of Units Contribution Margin - Fixed Costs When we complete the rest of the Statement, we get: Sales Unit Selling Price x No. of Units - Variable Costs Unit Variable Cost x No. of Units Contribution Margin (Unit Selling Price Unit Variable Cost) x No. of Units The left-side-view shows the macro-view of a company. The right-side-view shows the micro-view of a company, and it shows the parameters of the company that can be varied or kept constant in a CVP analysis. In order to know which parameters can be varied or kept constant, some Cost Behavior knowledge is required. Therefore, CVP analysis is best taught after students have learnt the topic of Cost Behavior that Fixed Costs and Unit Variable Cost remain constant unless there is information provided to change them. 24 Journal of Accounting and Finance vol. 11(4) 2011

3 In CVP analysis, the Unit Selling Price also is assumed to be constant. Thus, at the right-side-view of the Statement, there are three constant parameters and these are shown in bold below: Sales Unit Selling Price x No. of Units - Variable Costs Unit Variable Cost x No. of Units Contribution Margin (Unit Selling Price Unit Variable Cost) x No. of Units Both the left- and right-side-views (as shown above and in Panel A of the Appendix) make up a CVP Model of a company. When students examine the right-side-view of the CVP Model, they see that there are 3 constant parameters (Unit Selling Price, Unit Variable Cost, and Total Fixed Costs) and that there are two unknowns, Number of Units and, and they realize the term C-V-P relates to how the three factors of Costs, Volume (No. of Units), and P () are related to a company. As the data given for companies can vary, we will limit our discussion in this paper to the following six company situations: 1. Number of units is of interest, and there is no tax given. Assume Jehan Company sells a single product. The unit selling price is \$70, the unit variable cost is \$42, and total fixed costs are \$84, Number of units is of interest, and tax rate is given. Assume Jehan Company sells a single product and has a tax rate of 30%. The unit selling price is \$70, the unit variable cost is \$42, and total fixed costs are \$84, Number of units is not of interest, and there is no tax given. Assume Ezen Company has revenue of \$80,000, variable costs \$20,000 and fixed costs \$40, Number of units is not of interest, and tax rate is given. Assume Ezen Company has revenue of \$80,000, variable costs \$20,000 and fixed costs \$40,000. It also has a tax rate of 20%. 5. Company has multiple products, sales mix is available, and there is no tax given. Assume West Company makes three products, P1, P2, and P3. The sales of P1, P2, and P3 are 2000, 3000, and 5000 units respectively. 6. Company has multiple products and tax, and sales mix information is available. Assume West Company makes three products, P1, P2, and P3. The sales of P1, P2, and P3 are 2000, 3000, and 5000 units respectively. The tax rate is 25%. We start with the first situation. Situation 1: Number of units is of interest, and there is no tax given. Assume Jehan Company sells a single product. The unit selling price is \$70, the unit variable cost is \$42, and total fixed costs are \$84,000. We first set up Jehan Company s CVP Model before we do CVP analysis. Based on the knowledge of Cost Behavior, the above data given pertains to the constant parameters that go into the right-side-view of the CVP Model is as follows: Journal of Accounting and Finance vol. 11(4)

4 Sales 70X (where X = number of units) - Variable Costs 42X Contribution Margin 28X - Fixed Costs X = The right-side-view of the company s CVP Model has two unknowns, X and. Note that most of the CVP analysis can be done using the bottom three rows of the income statement, 28X =, and the analysis revolves around asking students to solve for X or. Next we use the CVP Model to answer some questions related to CVP analysis. Q: What is the breakeven point in units? We use the bottom three rows from the right-side-view of the CVP Model, 28X =. Breakeven means that the bottom-line of the Statement is zero. Thus, let = 0 1, and solve for X. 28X = 0, and solving X = Q: What is the breakeven point in sales dollars? Since the first row of the CVP Model is Sales = 70X, Sales = 70(3000) = \$210,000. Q: How to draw the CVP graph? The CVP graph has two straight lines, Sales and Total Costs. To draw the CVP graph, we need the equations of these 2 lines. From the first row of the CVP Model, Sales = 70X. Since Total Costs = Variable Costs + Fixed Costs, we use the second and fourth rows of the CVP Model to get Total Costs = 42X The CVP graph is presented as: FIGURE 1 COST-VOLUME-PROFIT (CVP) GRAPH \$ Sales = 70X Total Costs = 42X + 84,000 \$84,000 3,000 Breakeven Point (in units) No. of units (X) From the CVP Graph, we can see that the company needs to sell more (less) than the breakeven point in order to make a profit (loss). A measure of how successful a company is the extent to which its sales exceed its breakeven point. 26 Journal of Accounting and Finance vol. 11(4) 2011

5 Q: How to draw the graph? From the bottom three rows of the CVP Model, = 28X Thus the graph is presented as: FIGURE 2 INCOME GRAPH = 28X 84,000 0 No. of units (X) Breakeven Point -\$84,000 Q: How many units must the company sell to make an income of \$4,000? From the bottom three rows of the CVP Model, 28X =, we let = 4000, and solve for X. 28X = 4000, X = 3143(rounding). Q: What is income if the company sells 2500, 4500, or 5000 units? Let X = 2500, 4500, and 5000 as follows: Number of units (X) X Sales 70X 70(2500) 70(4500) 70(5000) - Variable Costs 42X 42(2500) 42(4500) 42(5000) Contribution Margin 28X 28(2500) 28(4500) 28(5000) - Fixed Costs From the income statements above, we can see clearly how costs behave, that is, Fixed Costs and Unit Variable Cost remain constant. Furthermore, the Unit Selling Price also remains constant. We solve for as follows: Number of units X Sales 70X Variable Costs 42X Contribution Margin 28X Fixed Costs Journal of Accounting and Finance vol. 11(4)

6 Q: What is the company s breakeven point if the unit selling price increases by 10%, fixed costs decrease by 5%, and unit variable cost increases by 15%? How many units must the company sell to get a target income of \$5,000? Here, we need to update the CVP Model as its parameters (that is, unit selling price, unit variable cost and total fixed costs) which are usually assumed to be constant are changed. The CVP Model is updated as follows: Sales 70(1.10)X Unit Selling Price is increased by 10% - Variable Costs 42(1.15)X Unit Variable Cost is increased by 15% Contribution Margin?X Unit Contribution Margin has to be updated - Fixed Costs 84000(0.95) Fixed Costs are decreased by 5% The CVP Model now has a new set of constant parameters: Sales 77 X - Variable Costs 48.3X Contribution Margin 28.7X - Fixed Costs X = Instead of using the whole Statement, again we can use its bottom three rows, 28.7X =, to perform the CVP analysis as this shorter equation is sufficient and easy to solve. To find the breakeven point, we let the bottom-line be zero, that is, let = 0, and solve for X. Thus, 28.7X = 0, and X = 2781 (rounding). Next, to answer how many units the company must sell to get a target income of \$5,000, we let = Again, we use the bottom three rows of the CVP Model, 28.7X = 5000, thus X = 2955 (rounding). Situation 2: Number of units is of interest, and tax rate is given. Assume Jehan Company sells a single product and has a tax rate of 30%. The unit selling price is \$70, the unit variable cost is \$42, and total fixed costs are \$84,000. To incorporate tax, a CVP Model With Tax is set up. This is shown in Panel B of the Appendix. This Model also has two unknowns, X and NIBT (that is, Net Before Tax instead of ). In CVP analysis, the tax rate is assumed to be constant. Since this Variable Costing Statement is longer than the one shown in Panel A of the Appendix, we perform most CVP analysis using two steps labeled (a) and (b) below; the first step is to use equation (a) and the second step is to use equation (b). Sales 70X - Variable Costs 42X Contribution Margin 28X - Fixed Costs X = NIBT...(b) NIBT NIBT - Tax 0.3NIBT Note: Tax is calculated based on NIBT NIAT 0.7NIBT. (a) When the company needs to find its breakeven point or how many units to achieve a target income, step (a) is performed first whereby we let the bottom-line 0.7NIBT = 0 or 0.7NIBT = Target, and we solve for NIBT. Next, we put the NIBT that we found from step (a) into the equation for (b), and solve for X. 28 Journal of Accounting and Finance vol. 11(4) 2011

7 Q: What is the breakeven point in units? In sales dollars? Breakeven is when the bottom-line is zero. Thus, we use equation (a) by letting 0.7NIBT = 0. Solving, we get NIBT = 0. Next, we use equation (b). From (a), we found NIBT = 0 which we substitute into 28X = NIBT and solve for X. Thus, 28X = 0, X = 3000 units. To find breakeven in sales dollars, we use the first row of the income statement, Sales = 70X = 70(3000) = \$210,000. Q: If the company s income tax is 30%, how many units must the company sell to earn a target income (or income after tax) of \$2,000? Using the CVP Model with Tax from Panel B of the Appendix, we start with equation (a). The target income is \$2000, so we let the bottom-line 0.7NIBT = 2000, and get NIBT = Next, we use equation (b) from the CVP Model; we put what we found from (a) into (b), and solve for X. Thus, 28X = , and X = 3103(rounding). Thus, the company needs to sell 3103 units to get an income after tax of \$2,000. Situation 3: Number of units is not of interest, and there is no tax given. Assume Ezen Company has revenue of \$80,000, variable costs \$20,000 and fixed costs \$40,000. In some companies, there is no information regarding Number of Units. Thus, we cannot use the CVP Models in Panels A and B of the Appendix. We can use a CVP Percentage Model that is shown in Panel C of the Appendix and as shown below: Sales Sales% x Sales - Variable Costs Variable Costs% x Sales Contribution Margin Contribution Margin% x Sales Like the CVP Models in Panels A and B, the CVP Percentage Model in Panel C also has three constant parameters (shown in bold above). The percentages (of Sales) are calculated as follows: Sales% Variable Costs% Contribution Margin% = Sales / Sales = Variable Costs / Sales = Sales% - Variable Costs% = Contribution Margin / Sales This CVP Percentage Model also has 2 unknowns. These are S (that is, Sales) and. In most CVP analysis questions, we let one of the unknowns take on a value, and solve the remaining unknown. For Ezen Company, the percentages come to: Sales% = / = 100% or 1.00 Variable Costs% = / = 25% or 0.25 Contribution Margin% = Sales% - Variable Costs% = Contribution Margin / Sales = 0.75 The CVP Percentage Model for Ezen Company is: Journal of Accounting and Finance vol. 11(4)

8 Sales 1.00S (where S = Sales) - Variable Costs 0.25S Contribution Margin 0.75S - Fixed Costs S = We use just the bottom three rows of the Model, 0.75S =, to solve the CVP questions below. Q: What is the breakeven point for Ezen Company? Breakeven is when the bottom-line is zero. Let = 0, and solve for S. Thus, 0.75S = 0, S = \$53,334. Q: What do the CVP and graphs look like? The CVP graph has two lines, Sales and Total Costs. Their equations from the CVP Percentage Model are Sales = 1.00S and Total Costs = Variable Costs + Fixed Costs = 0.25S FIGURE 3 COST-VOLUME-PROFIT (CVP) GRAPH \$ Sales = 1.00S Total Costs = 0.25S + 40,000 \$40,000 Breakeven Point (in sales dollars) Sales (S) The graph has 1 line, the line. Again, from the CVP Percentage Model for Ezen Company, = 0.75S Journal of Accounting and Finance vol. 11(4) 2011

9 FIGURE 4 INCOME GRAPH = 0.75S 40,000 0 Sales (S) Breakeven Point -\$40,000 Q: How much sales must the company make to generate an income of \$12,000? The CVP Percentage Model has two unknowns, S and. To answer this question, we let = 12000, and solve for S. Thus, 0.75S = 12000, and S = \$69,334 (rounding). Q: What is income if sales are \$20000, \$25000, or \$80000? Using the bottom three rows of the Model, 0.75S =, we let S = \$20000, \$25000, and \$80000, and solve for. Sales (S) S Sales 1.00S 1.00(20000) 1.00(25000) 1.00(80000) - Variable Costs 0.25S 0.25(20000) 0.25(25000) 0.25(80000) Contribution Margin 0.75S 0.75(20000) 0.75(25000) 0.75(80000) - Fixed Costs Q: Assume the current sales are \$100,000. The company is considering a proposal to spend \$8,000 on advertising to increase its sales by 5%? Is the proposal a good idea? The current CVP Percentage Model for Ezen Company is: Sales 1.00S (where S = Sales) - Variable Costs 0.25S Contribution Margin 0.75S - Fixed Costs S = When S = , = 0.75(100000) = The proposed CVP Percentage Model is: Journal of Accounting and Finance vol. 11(4)

10 Sales 1.00S(1.05) (where S = Sales) - Variable Costs 0.25S(1.05) Contribution Margin 0.75S(1.05) - Fixed Costs S(1.05) = At S = , the proposed Model shows = 0.75(100000) = Since the proposal will bring in a lower income of \$4,250 (or \$30750), the proposal is not a good idea. Situation 4: Number of units is not of interest, and tax rate is given. Assume Ezen Company has revenue of \$80,000, variable costs \$20,000 and fixed costs \$40,000. It also has a tax rate of 20%. The CVP Percentage Model With Tax, as shown in Panel D of the Appendix, is set up for Ezen Company such that it has only two unknowns, S and NIBT: Sales 1.00S (where S = Sales) - Variable Costs 0.25S Contribution Margin 0.75S - Fixed Costs S = NIBT (b) NIBT NIBT - Tax 0.2NIBT NIAT 0.8NIBT (a) The tax rate is assumed to be constant. As the Statement with Tax is longer, we can use two short equations, starting with (a) and followed by (b). Q: What is the breakeven point? Since breakeven is when the bottom-line is zero, we use equation (a), and let 0.8NIBT = 0. Solving, we get NIBT = 0. The next step is to put NIBT = 0 into equation (b). Thus 0.75S = 0, and solving, we get S = \$53334(rounding). Q: How much sales to get a target income (that is, income after tax) of \$2,000? We use the CVP Percentage Model with Tax as shown in Panel D of the Appendix. We start with (a). Since the bottom-line is \$2,000, we let 0.8NIBT = 2000, and we get NIBT = Next, we put NIBT = 2500 into (b). Thus, 0.75S = 2500, and we get S = \$56,667. Situation 5: Company has multiple products, sales mix is available. and there is no tax given. Assume West Company makes three products, P1, P2, and P3. The sales of P1, P2, and P3 are 2000, 3000, and 5000 units respectively. Further information includes: P1 P2 P3 Unit selling price \$ 10 \$ 6 \$ 4 Unit variable cost Unit contribution margin The total fixed costs for West Company are \$15,000. Preliminary work is needed before we can set up a CVP Model for a company with multiple products. The preliminary work is to (i) determine the sales mix for the company and (ii) use this sales mix to determine a weighted contribution margin that is used as a constant parameter in the CVP model. (i) Sales Mix The total sales for the company are = The sales mix for P1 is 2000/10000 = 0.2, P2 is 3000/10000 = 0.3, and P3 is 5000/10000 = Journal of Accounting and Finance vol. 11(4) 2011

11 (ii) Weighted Contribution Margin We weight the first three rows by the sales mix: P1 P2 P3 West Weighted Unit Selling Price 10(0.2) 6(0.3) 4(0.50) 5.8 Weighted Unit Variable Cost 2(0.2) 2(0.3) 2(0.50) 2.0 Weighted Contribution Margin 8(0.2) 4(0.3) 2(0.50) = 1.6 = 1.2 = to get: P1 P2 P3 West Sales 2T 1.8T 2.0T 5.8T Variable Costs 0.4T 0.6T 1.0T 2.0T Contribution Margin 1.6T 1.2T 1.0T 3.8T where T = Total Company Sale Units. The West Company s CVP Model with Multiple Products is: Sales 5.8T (where T = Total Company Sale Units) - Variable Costs 2.0T Contribution Margin 3.8T - Fixed Costs T = The CVP Model for Multiple Products is similar to the earlier CVP Models (see Panels A to D of the Appendix) that we discussed. The CVP Model for Multiple Products also has two unknowns, T (No. of Company s Sales in Units) and. Q: What is the breakeven point? Breakeven is when the bottom-line is zero, 3.8T = 0. Solving, we get T = 3948 (rounding). To get the individual product sales, we use the sales mix; breakeven sales for P1 is 0.2(3948), P2 is 0.3(3948), and P3 is 0.5(3948). Q: How many units of P1, P2, and P3 must the company sell to make an of \$60,000? To answer this question, we use the CVP Model which was set up above for West Company. Let = 60000, so 3.8T = Solving, T = Using the sales mix information, sales of P1, P2, and P3 should be 0.2(19737), 0.3(19737), and 0.5(19737) respectively. Situation 6: Company has multiple products and tax, and sales mix information is available. Assume we use the same West Company as given in example 5, but includes a tax rate of 25%. We set up a CVP Model With Tax similar to what was set up in Panels B and D of the Appendix. For this example 6, the CVP Model has two unknowns, NIBT and T, where T = total company sales. Sales 5.8T (where T = Total Company Sale Units) - Variable Costs 2.0T Contribution Margin 3.8T - Fixed Costs T = NIBT... (b) NIBT NIBT - Tax 0.25NIBT NIAT 0.75NIBT.... (a) / We use two steps, (a) and (b), to answer most CVP questions. Journal of Accounting and Finance vol. 11(4)

12 Q: What is the breakeven point? Since breakeven is when the bottom-line is zero, we use equation (a) to get 0.75NIBT = 0, and solving we get NIBT = 0. The next step is to put NIBT = 0 into equation (b). Thus 3.8T = 0, and solving we get T = 3948(rounding). The breakeven sales of P1, P2, and P3 should be 0.2(3948), 0.3(3948), and 0.5(3948) respectively. Q: How much sales to get a target income (that is, income after tax) of \$60,000? We use the CVP Percentage Model with Tax as shown in Panel F of the Appendix. We start with (a). Since the bottom-line is \$60,000, we let 0.75NIBT = 60000, and we get NIBT = Next, we put NIBT = into (b) to get 3.8T = Solving, we get T = Furthermore, the sales of P1, P2, and P3 should be 0.2(25000), 0.3(25000), and 0.5(25000) respectively. CONCLUSION We present an Statement teaching approach for CVP Analysis using a company s CVP model. This approach would help students see which of the company s parameters are held constant and which of them can be varied in their learning of CVP analysis. This approach also would reduce students memorization of equations. ENDNOTES 1 Breakeven is when the bottom-line of the Statement is zero. Other ways of describing breakeven involves rearranging the Statement equation, that is, at breakeven, Sales Total Costs = 0 Sales = Total Costs Sales (Variable Costs + Fixed Costs) = 0 Sales Variable Costs = Fixed Costs Contribution Margin = Fixed Costs Unit Contribution Margin(Number of Units at breakeven) = Fixed Costs, that is, Number of Units at breakeven = Fixed Costs Unit Contribution Margin. REFERENCES Garrison, R.H., Noreen, E.W., & Brewer P.C. (2010). Managerial Accounting. Eleventh Edition. New York: McGraw-Hill Irwin. Horngren, C.T., Datar, S.M., Foster, G., Rajan, M., & Ittner, C. (2009). Cost Accounting A Managerial Emphasis. Thirteenth Edition. New Jersey: Pearson Prentice Hall. Wilner, N.A. (1987). A Simple Teaching Approach for Process Costing Using Logic and Pictures. Issues in Accounting Education, 2(2), Journal of Accounting and Finance vol. 11(4) 2011

13 APPENDIX COST-VOLUME-PROFIT (CVP) MODEL Panel A: CVP Model for a company where number of units is of interest, and there is no tax given Sales Unit Selling Price x No. of Units - Variable Costs Unit Variable Cost x No. of Units Contribution Margin (Unit Selling Price Unit Variable Cost) x No. of Units Panel B: CVP Model for a company where number of units is of interest, and the tax rate is given Sales Unit Selling Price x No. of Units - Variable Costs Unit Variable Cost x No. of Units Contribution Margin (Unit Selling Price Unit Variable Cost) x No. of Units Net Before Tax Net Before Tax - Tax - Tax Rate x Net Before Tax Net After Tax (1 Tax Rate) x Net Before Tax Panel C: CVP Model for a company where number of units is not of interest, and there is no tax given Sales Sales Percentage x Sales - Variable Costs Variable Costs Percentage x Sales Contribution Margin Contribution Margin Percentage x Sales Panel D: CVP Model for a company where number of units is not of interest, and the tax rate is given Sales Sales Percentage x Sales - Variable Costs Variable Costs Percentage x Sales Contribution Margin Contribution Margin Percentage x Sales Net Before Tax Net Before Tax - Tax - Tax Rate x Net Before Tax Net After Tax (1 Tax Rate) x Net Before Tax Journal of Accounting and Finance vol. 11(4)

14 Panel E: CVP Model for a company with multiple products and the sales mix is available, and there is no tax given Sales Weighted Unit Selling Price x T - Variable Costs Weighted Unit Variable Cost x T Contribution Margin Weighted Unit Contribution Margin x T where T = Total Company Units Panel F: CVP Model for a company with multiple products and the sales mix is available, and the tax rate is given Sales Weighted Unit Selling Price x T - Variable Costs Weighted Unit Variable Cost x T Contribution Margin Weighted Unit Contribution Margin x T Net Before Tax Net Before Tax - Tax - Tax Rate x Net Before Tax Net After Tax (1 Tax Rate) x Net Before Tax where T = Total Company Units Note: In the right-side-view, model parameters in bold are assumed constant in CVP analysis. 36 Journal of Accounting and Finance vol. 11(4) 2011

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