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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 and sold. 2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.
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Cost-Volume-Profit Assumptions and Terminology 3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range (and time period). 4. The unit selling price, unit variable costs, and fixed costs are known and constant.
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Cost-Volume-Profit Assumptions and Terminology 5. The analysis either covers a single product or assumes that the sales mix when multiple products are sold will remain constant as the level of total units sold changes. 6. All revenues and costs can be added and compared without taking into account the time value of money.
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Cost-Volume-Profit Assumptions and Terminology Operating income = Total revenues from operations – Cost of goods sold and operating costs (excluding income taxes) Net income = Operating income – Income taxes
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Essentials of Cost-Volume-Profit (CVP) Analysis Example Assume that the Pants Shop can purchase pants for $32 from a local factory; other variable costs amount to $10 per unit. The local factory allows the Pants Shop to return all unsold pants and receive a full $32 refund per pair of pants within one year. The average selling price per pair of pants is $70 and total fixed costs amount to $84,000.
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Essentials of Cost-Volume-Profit (CVP) Analysis Example How much revenue will the business receive if 2,500 units are sold? 2,500 × $70 = $175,000 How much variable costs will the business incur? 2,500 × $42 = $105,000 $175,000 – 105,000 – 84,000 = ($14,000)
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Essentials of Cost-Volume-Profit (CVP) Analysis Example What is the contribution margin per unit? $70 – $42 = $28 contribution margin per unit What is the total contribution margin when 2,500 pairs of pants are sold? 2,500 × $28 = $70,000
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Essentials of Cost-Volume-Profit (CVP) Analysis Example Contribution margin percentage (contribution margin ratio) is the contribution margin per unit divided by the selling price. What is the contribution margin percentage? $28 ÷ $70 = 40%
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Essentials of Cost-Volume-Profit (CVP) Analysis Example If the business sells 3,000 pairs of pants, revenues will be $210,000 and contribution margin would equal 40% × $210,000 = $84,000.
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Breakeven Point Sales Variable expenses Fixed expenses – = Total revenues = Total costs
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Abbreviations SP = Selling price VCU = Variable cost per unit CMU = Contribution margin per unit CM% = Contribution margin percentage FC = Fixed costs
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Abbreviations Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI = Target net income
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Equation Method $70Q – $42Q – $84,000 = 0 $28Q = $84,000 Q = $84,000 ÷ $28 = 3,000 units Let Q = number of units to be sold to break even (Selling price × Quantity sold) – (Variable unit cost × Quantity sold) – Fixed costs = Operating income
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Graph Method Revenue Total costs Breakeven Fixed costs
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Target Operating Income (Fixed costs + Target operating income) divided either by Contribution margin percentage or Contribution margin per unit
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Target Operating Income Assume that management wants to have an operating income of $14,000. How many pairs of pants must be sold? ($84,000 + $14,000) ÷ $28 = 3,500 What dollar sales are needed to achieve this income? ($84,000 + $14,000) ÷ 40% = $245,000
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Target Net Income and Income Taxes Example Management would like to earn an after tax income of $35,711. The tax rate is 30%. What is the target operating income? Target operating income = Target net income ÷ (1 – tax rate) TOI = $35,711 ÷ (1 – 0.30) = $51,016
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Target Net Income and Income Taxes Example How many units must be sold? Revenues – Variable costs – Fixed costs = Target net income ÷ (1 – tax rate) $70Q – $42Q – $84,000 = $35,711 ÷ 0.70 $28Q = $51,016 + $84,000 Q = $135,016 ÷ $28 = 4,822 pairs of pants
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Target Net Income and Income Taxes Example Proof: Revenues: 4,822 × $70 $337,540 Variable costs: 4,822 × $42 202,524 Contribution margin $135,016 Fixed costs 84,000 Operating income 51,016 Income taxes: $51,016 × 30% 15,305 Net income $ 35,711
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Using CVP Analysis Example Suppose the management anticipates selling 3,200 pairs of pants. Management is considering an advertising campaign that would cost $10,000. It is anticipated that the advertising will increase sales to 4,000 units. Should the business advertise?
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Using CVP Analysis Example 3,200 pairs of pants sold with no advertising: Contribution margin $89,600 Fixed costs 84,000 Operating income $ 5,600 4,000 pairs of pants sold with advertising: Contribution margin $112,000 Fixed costs 94,000 Operating income $ 18,000
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Using CVP Analysis Example Instead of advertising, management is considering reducing the selling price to $61 per pair of pants. It is anticipated that this will increase sales to 4,500 units. Should management decrease the selling price per pair of pants to $61?
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Using CVP Analysis Example 3,200 pairs of pants sold with no change in the selling price: Operating income = $5,600 4,500 pairs of pants sold at a reduced selling price: Contribution margin: (4,500 × $19) $85,500 Fixed costs 84,000 Operating income $ 1,500
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Sensitivity Analysis and Uncertainty Example Assume that the Pants Shop can sell 4,000 pairs of pants. Fixed costs are $84,000. Contribution margin ratio is 40%. At the present time the business cannot handle more than 3,500 pairs of pants.
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Sensitivity Analysis and Uncertainty Example To satisfy a demand for 4,000 pairs, management must acquire additional space for $6,000. Should the additional space be acquired? Revenues at breakeven with existing space are $84,000 ÷ .40 = $210,000. Revenues at breakeven with additional space are $90,000 ÷ .40 = $225,000
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Sensitivity Analysis and Uncertainty Example Operating income at $245,000 revenues with existing space = ($245,000 × .40) – $84,000 = $14,000. (3,500 pairs of pants × $28) – $84,000 = $14,000
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Sensitivity Analysis and Uncertainty Example Operating income at $280,000 revenues with additional space = ($280,000 × .40) – $90,000 = $22,000. (4,000 pairs of pants × $28 contribution margin) – $90,000 = $22,000
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Alternative Fixed/Variable Cost Structures Example What is the new contribution margin? Decrease the price they charge from $32 to $25 and charge an annual administrative fee of $30,000. Suppose that the factory the Pants Shop is using to obtain the merchandise offers the following:
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Alternative Fixed/Variable Cost Structures Example $70 – ($25 + $10) = $35 Contribution margin increases from $28 to $35. What is the contribution margin percentage? $35 ÷ $70 = 50% What are the new fixed costs? $84,000 + $30,000 = $114,000
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Alternative Fixed/Variable Cost Structures Example Management questions what sales volume would yield an identical operating income regardless of the arrangement. 28x – 84,000 = 35x – 114,000 114,000 – 84,000 = 35x – 28x 7x = 30,000 x = 4,286 pairs of pants
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Alternative Fixed/Variable Cost Structures Example Cost with existing arrangement = Cost with new arrangement .60x + 84,000 = .50x + 114,000 .10x = $30,000 x = $300,000 ($300,000 × .40) – $ 84,000 = $36,000 ($300,000 × .50) – $114,000 = $36,000
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Operating Leverage Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold. Organizations with a high proportion of fixed costs have high operating leverage.
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Operating Leverage Example Degree of operating leverage = Contribution margin ÷ Operating income What is the degree of operating leverage of the Pants Shop at the 3,500 sales level under both arrangements? Existing arrangement: 3,500 × $28 = $98,000 contribution margin
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Operating Leverage Example $98,000 contribution margin – $84,000 fixed costs = $14,000 operating income $98,000 ÷ $14,000 = 7.0 New arrangement: 3,500 × $35 = $122,500 contribution margin
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Operating Leverage Example $122,500 contribution margin – $114,000 fixed costs = $8,500 $122,500 ÷ $8,500 = 14.4 The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating income.
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Effects of Sales Mix on Income Pants Shop Example Management expects to sell 2 shirts at $20 each for every pair of pants it sells. This will not require any additional fixed costs.
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Effects of Sales Mix on Income What is the contribution margin of the mix? Contribution margin per shirt: $20 – $9 = $11 $28 + (2 × $11) = $28 + $22 = $50
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Effects of Sales Mix on Income $84,000 fixed costs ÷ $50 = 1,680 packages 1,680 × 2 = 3,360 shirts 1,680 × 1 = 1,680 pairs of pants Total units = 5,040
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Effects of Sales Mix on Income What is the breakeven in dollars? 3,360 shirts × $20 = $ 67,200 1,680 pairs of pants × $70 = 117,600 $184,800
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Effects of Sales Mix on Income What is the weighted-average budgeted contribution margin? Pants: 1 × $28 + Shirts: 2 × $11 = $50 ÷ 3 = $16.667
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Effects of Sales Mix on Income The breakeven point for the two products is: $84,000 ÷ $16.667 = 5,040 units 5,040 × 1/3 = 1,680 pairs of pants 5,040 × 2/3 = 3,360 shirts
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Effects of Sales Mix on Income Sales mix can be stated in sales dollars: Pants Shirts Sales price $70 $40 Variable costs 42 18 Contribution margin $28 $22 Contribution margin ratio 40% 55%
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Effects of Sales Mix on Income Assume the sales mix in dollars is 63.6% pants and 36.4% shirts. Weighted contribution would be: 40% × 63.6% = 25.44% pants 55% × 36.4% = 20.02% shirts 45.46%
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Effects of Sales Mix on Income Breakeven sales dollars is $84,000 ÷ 45.46% = $184,778 (rounding). $184,778 × 63.6% = $117,519 pants sales $184,778 × 36.4% = $ 67,259 shirt sales
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Multiple Cost Drivers Example Suppose that the business will incur an additional cost of $10 for preparing documents associated with the sale of pants to various customers. Assume that the business sells 3,500 pants to 100 different customers. What is the operating income from this sale?
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Multiple Cost Drivers Would the operating income of the Pants Shop be lower or higher if the business sells pants to more customers? The cost structure depends on two cost drivers: 1. Number of units 2. Number of customers
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