# Study Unit 8. CVP Analysis and Marginal Analysis

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1 Study Unit 8 CVP Analysis and Marginal Analysis

2 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory CVP = Break-even analysis Allows us to analyze the relationship between revenue and fixed and variable expenses It allows us to study the effects of changes in assumptions about cost behavior and the relevant ranges (in which those assumption are valid) may affect the relationships among revenues, variable costs, and fixed costs at various production levels It considers the effects of: Sales volume Sales price Product mixes What else?

3 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory CVP analysis is done with what assumptions? See page 314 Simplifying assumptions of CVP What is the break-even point and where is it on a graph?

4 CVP Graph Break-Even Point

5 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory BEP = output level at which Total Rev = Total Exp It is also the point at which all fixed cost have been covered and operating income is zero Revenue \$100,000 Var. Cost \$ 80,000 Gross Margin \$ 20,000 Fixed Cost \$ 20,000 Oper. Income \$ 0

6 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory Other terms and def. Margin of safety = excess of budgeted sales over BE Sales Mixed costs - Costs that have both a fixed and variable component. For example, the cost of operating an automobile includes some fixed costs that do not change with the number of miles driven (e.g., operating license, insurance, parking, some of the depreciation, etc.) Other costs vary with the number of miles driven (e.g., gasoline, oil changes, tire wear, etc.). Revenue or sales mix Sensitivity analysis examines the effect on the outcome of not achieving the original forecast or of changing an assumption. Since many decisions must be made due to uncertainty, probabilities can be assigned to different outcomes ( what-if ). Continued

7 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory

8 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory Unit Contribution Margin (UCM) is an important term used with break-even point or break-even analysis is contribution margin. In equation format it is defined as follows: Contribution Margin = Revenues Variable Expenses The contribution margin for one unit of product or one unit of service is defined as: Contribution Margin per Unit = Revenues per Unit Variable Expenses per Unit

9 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory Break-even point in units Fixed costs UCM Break-even point in dollars Fixed costs CMR

10 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory - Question 1 Question 1 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis Cost-volume-profit (CVP) analysis is a key factor in many decisions, including choice of product lines, pricing of products, marketing strategy, and use of productive facilities. A calculation used in a CVP analysis is the breakeven point. Once the breakeven point has been reached, operating income will increase by the A. B. C. D. Gross margin per unit for each additional unit sold. Contribution margin per unit for each additional unit sold. Fixed costs per unit for each additional unit sold. Variable costs per unit for each additional unit sold.

11 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory Answer to Question 1 Correct Answer: B At the breakeven point, total revenue equals total fixed costs plus the variable costs incurred at that level of production. Beyond the breakeven point, each unit sale will increase operating income by the unit contribution margin (unit sales price unit variable cost) because fixed cost will already have been recovered. Incorrect Answers: A: The gross margin equals sales price minus cost of goods sold, including fixed cost. C: All fixed costs have been covered at the breakeven point. D: Operating income will increase by the unit contribution margin, not the unit variable cost.

12 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory - Question 2 Question 2 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis One of the major assumptions limiting the reliability of breakeven analysis is that A. B. C. D. Efficiency and productivity will continually increase. Total variable costs will remain unchanged over the relevant range. Total fixed costs will remain unchanged over the relevant range. The cost of production factors varies with changes in technology.correct Answer: C

13 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory Answer to Question 2 Correct Answer: C One of the inherent simplifying assumptions used in CVP analysis is that fixed costs remain constant over the relevant range of activity. Incorrect Answers: A: Breakeven analysis assumes no changes in efficiency and productivity. B: Total variable costs, by definition, change across the relevant range. D: The cost of production factors is assumed to be stable; this is what is meant by relevant range.

14 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory - Question 3 Question 3 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis The margin of safety is a key concept of CVP analysis. The margin of safety is the A. Contribution margin rate. B. C. D. Difference between budgeted contribution margin and breakeven contribution margin. Difference between budgeted sales and breakeven sales. Difference between the breakeven point in sales and cash flow breakeven.

15 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory Answer to Question 3 Correct Answer: C The margin of safety measures the amount by which sales may decline before losses occur. It is the excess of budgeted or actual sales over sales at the BEP. Incorrect Answers: A: The contribution margin rate is computed by dividing contribution margin by sales. The contribution margin equals sales minus total variable costs. B: The margin of safety is expressed in revenue or units, not contribution margin. D: Cash flow is not relevant.

16 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory - Question 4 Question 4 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis The breakeven point in units increases when unit costs A. B. C. Increase and sales price remains unchanged. Decrease and sales price remains unchanged. Remain unchanged and sales price increases. D. Decrease and sales price increases.

17 SU- 8.1 Cost-Volume-Profit (CVP) Analysis Theory Answer to Question 4 Correct Answer: A The breakeven point in units is calculated by dividing total fixed costs by the unit contribution margin. If selling price is constant and costs increase, the unit contribution margin will decline, resulting in an increase of the breakeven point. Incorrect Answers: B: A decrease in costs will cause the unit contribution margin to increase, lowering the breakeven point. C: An increase in the selling price will increase the unit contribution margin, resulting in a lower breakeven point. D: Both a cost decrease and a sales price increase will increase the unit contribution margin, resulting in a lower breakeven point.

18 SU- 8.1 Cost-Volume-Profit (CVP) Analysis - Theory Review: Diff. gross margin and contribution margin Effect of an increase in CM Effects on BEP by changes in CM

19 SU 8.2 CVP Analysis Basic Calculations CVP Applications Target Operating Income Multiple products Choice of products Degree of Operating Leverage (DOL) Problems 8, 9, 10, 12 & 13 starting on page 330

20 SU 8.3 CVP Analysis Target Income Calculations Target Operating Income Target Net Income Fixed costs + Target operating income UCM Fixed costs + Target net income / (1.0 tax rate) UCM Problem 15, 16 and 18 on page 333

21 SU 8.4 CVP Analysis Multiproduct Calculations Multiple Products (or Services) S = FC + VC = Calculated Weighted Average Contribution Margin Choice of Product decisions When resources are limited companies have to choose which products to produce Special Orders

22 SU- 8.4 CVP Analysis Multiproduct Calculations - Question 1 Moorehead Manufacturing Company produces two products for which the data presented to the right have been tabulated. Fixed manufacturing cost is applied at a rate of \$1.00 per machine hour. The sales manager has had a \$160,000 increase in the budget allotment for advertising and wants to apply the money to the most profitable product. The products are not substitutes for one another in the eyes of the company s customers. Per Unit XY-7 BD-4 Selling price \$4.00 \$3.00 Variable manufacturing cost Fixed manufacturing cost Variable selling cost

23 SU- 8.4 CVP Analysis Multiproduct Calculations - Question 1 Continued Suppose Moorehead has only 100,000 machine hours that can be made available to produce additional units of XY-7 and BD-4. If the potential increase in sales units for either product resulting from advertising is far in excess of this production capacity, which product should be advertised and what is the estimated increase in contribution margin earned? A. B. C. D. Product XY-7 should be produced, yielding a contribution margin of \$75,000. Product XY-7 should be produced, yielding a contribution margin of \$133,333. Product BD-4 should be produced, yielding a contribution margin of \$187,500. Product BD-4 should be produced, yielding a contribution margin of \$250,000.

24 Correct Answer: D SU- 8.4 CVP Analysis Multiproduct Calculations Answer to Question 1 The machine hours are a scarce resource that must be allocated to the product(s) in a proportion that maximizes the total CM. Given that potential additional sales of either product are in excess of production capacity, only the product with the greater CM per unit of scarce resource should be produced. XY-7 requires.75 hours; BD-4 requires.2 hours of machine time (given fixed manufacturing cost applied at \$1 per machine hour of \$.75 for XY-7 and \$.20 for BD-4). XY-7 has a CM of \$1.33 per machine hour (\$1 UCM.75 hours), and BD-4 has a CM of \$2.50 per machine hour (\$.50.2 hours). Thus, only BD-4 should be produced, yielding a CM of \$250,000 (100,000 \$2.50). The key to the analysis is CM per unit of scarce resource. Incorrect Answers: A: Product XY-7 actually has a CM of \$133,333, which is lower than the \$250,000 CM for product BD-4. B: Product BD-4 has a higher CM at \$250,000. C: Product BD-4 has a CM of \$250,000.

25 SU- 8.4 CVP Analysis Multiproduct Calculations - Question 2 Question 2 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis Product A accounts for 75% of a company s total sales revenue and has a variable cost equal to 60% of its selling price. Product B accounts for 25% of total sales revenue and has a variable cost equal to 85% of its selling price. What is the breakeven point given fixed costs of \$150,000? A. \$375,000 B. \$444,444 C. \$500,000 D. \$545,455

26 SU- 8.4 CVP Analysis Multiproduct Calculations Answer to Question 2 Correct Answer: B Using the relationship: sales = total variable costs + total fixed costs, the combined breakeven point can be calculated as follows: S = 0.75S(0.60) S(0.85) + \$150,000 S = 0.45S S + \$150,000 S S = \$150, S = \$150,000 S = \$444,444 Incorrect Answers: A: This amount is based on the contribution margin of Product A only rather than a weighted average. C: This amount is based on half of the required sales at B s contribution margin. D: This amount is based on an unweighted average of the two contribution margins.

27 SU- 8.4 CVP Analysis Multiproduct Calculations - Question 3 Question 3 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis Von Stutgatt International s breakeven point is 8,000 racing bicycles and 12,000 5-speed bicycles. If the selling price and variable costs are \$570 and \$200 for a racer, and \$180 and \$90 for a 5-speed respectively, what is the weighted-average contribution margin? A. \$100 B. \$145 C. \$179 D. \$202

28 SU- 8.4 CVP Analysis Multiproduct Calculations Answer to Question 3 Correct Answer: D Contribution margin equals selling price minus variable costs. The product contribution margins are: Racer: \$570 \$200 = \$370 5-Speed: \$180 \$90 = \$90 The sales mix is: Racer: 8,000 (8, ,000) = 40% 5-Speed: 12,000 (8, ,000) Multiply the CM by the sales mix for each product, and add the results. = 60% Weighted-average CM = (\$370 40%) + (\$90 60%) = \$148 + \$54 = \$202

29 SU- 8.4 CVP Analysis Multiproduct Calculations Answer to Question 3 Incorrect Answers: A: The sales mix dictates how much of the total CM will come from sales of each product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the UCM for racers must be added to 60% of the UCM for 5-speeds to get the weighted-average CM. B: The sales mix dictates how much of the total CM will come from sales of each product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the UCM for racers must be added to 60% of the UCM for 5-speeds to get the weighted-average CM. C: The sales mix dictates how much of the total CM will come from sales of each product. Unit sales are attributable 40% to racers and 60% to 5-speeds, so 40% of the UCM for racers must be added to 60% of the UCM for 5-speeds to get the weighted-average CM.

30 SU- 8.4 CVP Analysis Multiproduct Calculations - Question 4 Question 4 - CMA2 Study Unit 8: CVP Analysis and Marginal Analysis Catfur Company has fixed costs of \$300,000. It produces two products, X and Y. Product X has a variable cost percentage equal to 60% of its \$10 per unit selling price. Product Y has a variable cost percentage equal to 70% of its \$30 selling price. For the past several years, sales of Product X have averaged 66% of the sales of Product Y. That ratio is not expected to change. What is Catfur s breakeven point in dollars? A. \$300,000 B. \$750,000 C. \$857,142 D. \$942,857

31 SU- 8.4 CVP Analysis Multiproduct Calculations Answer to Question 4 Correct Answer: D A helpful approach in a multiproduct situation is to make calculations based on the composite unit, i.e., 2 units of Product X and 3 units of Product Y (a 66% ratio). The selling price of this composite unit is \$110 [(2 \$10) + (3 \$30)]. The UCM of the composite unit is \$35 {[2 (\$10 \$6)] + [3 (\$30 \$21)]}. Consequently, the breakeven point in composite units is 8, (\$300,000 FC \$35 UCM), and the breakeven point in sales dollars is \$942,857 (8, \$110). Incorrect Answers: A: This amount equals the fixed costs. B: This amount assumes a 40% contribution margin ratio. C: This amount assumes a 35% contribution margin ratio.

32 SU 8.5 Marginal Analysis Accounting Costs vs. Economic Costs Accounting Costs = The total amount of money or goods expended in an endeavor. It is money paid out at some time in the past and recorded in journal entries and ledgers. Economic Costs = The economic cost of a decision depends on both the cost of the alternative chosen and the benefit that the best alternative would have provided if chosen. Economic cost differs from accounting cost because it includes opportunity cost. As an example, consider the economic cost of attending college. The accounting cost of attending college includes tuition, room and board, books, food, and other incidental expenditures while there. The opportunity cost of college also includes the salary or wage that otherwise could be earning during the period. So for the two to four years an individual spends in school, the opportunity cost includes the money that one could have been making at the best possible job. The economic cost of college is the accounting cost plus the opportunity cost. Thus, if attending college has a direct cost of \$20,000 dollars a year for four years, and the lost wages from not working during that period equals \$25,000 dollars a year, then the total economic cost of going to college would be \$180,000 dollars (\$20,000 x 4 years + the interest of \$20,000 for 4 years + \$25,000 x 4 years).

33 SU 8.5 Marginal Analysis Explicit vs. Implicit Costs Implicit Costs = implicit cost, also called an imputed cost, implied cost, or notional cost, is the opportunity cost equal to what a firm must give up in order to use factors which it neither purchases nor hires. Explicit Costs = An explicit cost is a direct payment made to others in the course of running a business, such as wage, rent and materials.

34 SU 8.5 Marginal Analysis Accounting vs. Economic Profit See Utorial at Accounting Profit = book income exceeds book expenses Economic Profit = includes Accounting Profit + Implicit costs

35 SU 8.5 Marginal Analysis Marginal Revenue and Marginal Cost Marginal Revenue is the additional or incremental revenue of one additional unit of output. See page 321 See that Marginal Revenue is \$540 between generating 4 vs. 5 units of output. Marginal Cost is the additional or incremental cost incurred of one additional unit of output. Note that while cost decrease over some range they will at some point begin to increase due to the process becoming lest efficient. Profit Maximization is where MR = MC (see page 322)

36 SU 8.5 Marginal Analysis Short-Run Cost Relationship See graph on page 323 Other considerations/applications of CVP Make-or-Buy Capacity Constraints and Product Mix Disinvestments Sell-or-Process further

37 SU 8.6 Short-run Profit Maximization Pure Competition Monopoly Monopolistic Competition Oligopoly Law of Demand Calculating Price elasticity of demand Def. Greater than one Equal to one Less than one Infinite or perfectly elastic Equal to zero or perfectly inelastic

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