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An Income 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 Income 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 Income Statement format and use the Income 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
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 = Income Target Income = Target Net Income 1 – Tax Rate Unit Sales = Fixed Costs + Target Income 1 – Tax Rate Unit CM
Note: A = Unit Sales, CM = Contribution Margin, CM Ratio = CM% = CM ÷ Sales
In our Income Statement approach, we use the Variable Costing Income Statement to perform CVP analysis. The Variable Costing Income Statement is shown horizontally as: Sales – Variable Costs – Fixed Costs = Income which also can be written vertically as:
Sales
- Variable Costs Contribution Margin
- Fixed Costs Income
Each of the above Sales and Variable Costs is an equation:
Left-side-view Right-side-view Sales Unit Selling Price x No. of Units
- Variable Costs Unit Variable Cost x No. of Units Contribution Margin
- Fixed Costs Income
When we complete the rest of the Income Statement, we get:
Left-side-view Right-side-view 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
- Fixed Costs Fixed Costs Income Income
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.
Left-side-view Right-side-view Sales 70 X (where X = number of units)
- Variable Costs 42 X Contribution Margin 28X
- Fixed Costs 84000 28X – 84000 = Income Income Income
The right-side-view of the company’s CVP Model has two unknowns, X and Income. Note that most of the CVP analysis can be done using the bottom three rows of the income statement, 28X – 84000 = Income, and the analysis revolves around asking students to solve for X or Income. 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 – 84000 = Income. Breakeven means that the bottom-line of the Income Statement is zero. Thus, let Income = 0^1 , and solve for X. 28X – 84000 = 0, and solving X = 3000.
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 + 84000. The CVP graph is presented as:
FIGURE 1 COST-VOLUME-PROFIT (CVP) GRAPH
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.
Total Costs = 42X + 84,
$ Sales = 70X
No. of units (X)
$84,
3,
Breakeven Point (in units)
Q: How to draw the Income graph? From the bottom three rows of the CVP Model, Income = 28X – 84000. Thus the Income graph is presented as: FIGURE 2 INCOME GRAPH
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 – 84000 = Income, we let Income = 4000, and solve for X. 28X – 84000 = 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 2500 4500 5000 Sales 70 X 70 (2500) 70 (4500) 70 (5000)
- Variable Costs 42 X 42 (2500) 42 (4500) 42 (5000) Contribution Margin 28X 28(2500) 28(4500) 28(5000)
- Fixed Costs 84000 84000 84000 84000 Income Income Income Income Income
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 Income as follows:
Number of units X 2500 4500 5000 Sales 70X 175000 315000 350000
- Variable Costs 42X 105000 189000 210000 Contribution Margin 28X 70000 126000 140000
- Fixed Costs 84000 84000 84000 84000 Income Income -14000 42000 56000
Income (^) Income = 28X – 84,
No. of units (X)
0
-$84,
Breakeven Point
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 – 84000 = NIBT and solve for X. Thus, 28X – 84000 = 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 = 2857.14. Next, we use equation (b) from the CVP Model; we put what we found from (a) into (b), and solve for X. Thus, 28X – 84000 = 2857.14, 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:
Left-side-view Right-side-view Sales Sales% x Sales
- Variable Costs Variable Costs% x Sales Contribution Margin Contribution Margin% x Sales
- Fixed Costs Fixed Costs Income Income
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% = Sales / Sales Variable Costs% = Variable Costs / Sales Contribution Margin% = Sales% - Variable Costs% = Contribution Margin / Sales
This CVP Percentage Model also has 2 unknowns. These are S (that is, Sales) and Income. 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% = 80000 / 80000 = 100% or 1. Variable Costs% = 20000 / 80000 = 25% or 0. Contribution Margin% = Sales% - Variable Costs% = Contribution Margin / Sales = 0.
The CVP Percentage Model for Ezen Company is:
Sales 1.00 S (where S = Sales)
- Variable Costs 0.25 S Contribution Margin 0.75S
- Fixed Costs 40000 0.75S – 40000 = Income Income Income
We use just the bottom three rows of the Model, 0.75S – 40000 = Income, to solve the CVP questions below.
Q: What is the breakeven point for Ezen Company? Breakeven is when the bottom-line is zero. Let Income = 0, and solve for S. Thus, 0.75S – 40000 = 0, S = $53,334.
Q: What do the CVP and Income 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 + 40000.
FIGURE 3 COST-VOLUME-PROFIT (CVP) GRAPH
The Income graph has 1 line, the Income line. Again, from the CVP Percentage Model for Ezen Company, Income = 0.75S – 40000.
Total Costs = 0.25S + 40,
$ Sales = 1.00S
Sales (S)
$ 40 ,
Breakeven Point (in sales dollars)
Sales 1.00 S (1.05) (where S = Sales)
- Variable Costs 0.25 S (1.05) Contribution Margin 0.75S (1.05)
- Fixed Costs 40000 + 8000 0.75S(1.05) – 48000 = Income Income Income
At S = 100000, the proposed Model shows Income = 0.75(100000)1.05 – 48000 = 30750. Since the proposal will bring in a lower income of $4,250 (or 35000 - $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:
Left-side-view Right-side-view Sales 1.00 S (where S = Sales)
- Variable Costs 0.25 S Contribution Margin 0.75S
- Fixed Costs 40000 0.75S – 40000 = NIBT (b) NIBT NIBT
- Tax 0.2 NIBT NIAT 0.8 NIBT (a)
The tax rate is assumed to be constant. As the Income 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 – 40000 = 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 = 2500. Next, we put NIBT = 2500 into (b). Thus, 0.75S – 40000 = 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 P Unit selling price $ 10 $ 6 $ 4 Unit variable cost 2 2 2 Unit contribution margin 8 4 2 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 2000 + 3000 + 5000 = 10000. The sales mix for P1 is 2000/10000 = 0.2, P2 is 3000/10000 = 0.3, and P3 is 5000/10000 = 0.5.
(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. Weighted Unit Variable Cost 2(0.2) 2(0.3) 2(0.50) 2. Weighted Contribution Margin 8(0.2) 4(0.3) 2(0.50) = 1.6 = 1.2 = 1 3. 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 5.8 T (where T = Total Company Sale Units)
- Variable Costs 2.0 T Contribution Margin 3.8T
- Fixed Costs 15000 3.8T – 15000 = Income Income Income
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 Income.
Q: What is the breakeven point? Breakeven is when the bottom-line is zero, 3.8T – 15000 = 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 Income of $60,000? To answer this question, we use the CVP Model which was set up above for West Company. Let Income = 60000, so 3.8T – 15000 = 60000. Solving, T = 19737. 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.
Left-side-view Right-side-view Sales 5.8 T (where T = Total Company Sale Units)
- Variable Costs 2.0 T Contribution Margin 3.8T
- Fixed Costs 15000 3.8T - 15000 = NIBT …...... (b) NIBT NIBT
- Tax 0.25 NIBT NIAT 0.75 NIBT ………..…………………….. (a) / We use two steps, (a) and (b), to answer most CVP questions.
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
Left-side-view Right-side-view 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
- Fixed Costs Fixed Costs Income Income
Panel B: CVP Model for a company where number of units is of interest, and the tax rate is given
Left-side-view Right-side-view 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
- Fixed Costs Fixed Costs Net Income Before Tax Net Income Before Tax
- Tax - Tax Rate x Net Income Before Tax Net Income After Tax (1 – Tax Rate ) x Net Income Before Tax
Panel C: CVP Model for a company where number of units is not of interest, and there is no tax given
Left-side-view Right-side-view Sales Sales Percentage x Sales
- Variable Costs Variable Costs Percentage x Sales Contribution Margin Contribution Margin Percentage x Sales
- Fixed Costs Fixed Costs Income Income
Panel D: CVP Model for a company where number of units is not of interest, and the tax rate is given
Left-side-view Right-side-view Sales Sales Percentage x Sales
- Variable Costs Variable Costs Percentage x Sales Contribution Margin Contribution Margin Percentage x Sales
- Fixed Costs Fixed Costs Net Income Before Tax Net Income Before Tax
- Tax - Tax Rate x Net Income Before Tax Net Income After Tax (1 – Tax Rate ) x Net Income Before Tax
Panel E: CVP Model for a company with multiple products and the sales mix is available, and there is no tax given
Left-side-view Right-side-view Sales Weighted Unit Selling Price x T
- Variable Costs Weighted Unit Variable Cost x T Contribution Margin Weighted Unit Contribution Margin x T
- Fixed Costs Fixed Costs Income Income
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
Left-side-view Right-side-view Sales Weighted Unit Selling Price x T
- Variable Costs Weighted Unit Variable Cost x T Contribution Margin Weighted Unit Contribution Margin x T
- Fixed Costs Fixed Costs Net Income Before Tax Net Income Before Tax
- Tax - Tax Rate x Net Income Before Tax Net Income After Tax (1 – Tax Rate ) x Net Income Before Tax
where T = Total Company Units
Note: In the right-side-view, model parameters in bold are assumed constant in CVP analysis.
