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## Cost-Volume-Profit Analysis

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**Cost-Volume-Profit Analysis**Chapter 3**Understand the assumptions**underlying cost-volume-profit (CVP) analysis.**Cost-Volume-Profit Assumptionsand Terminology**Cost volume profit analysis examines the behavior of total costs and operating income as changes occur in the output level, the selling price, the variable cost per unit, and /or the fixed costs of a product.**Explain the features**of CVP analysis.**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.**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)**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**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%**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.**Determine the breakeven point**and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods.**Breakeven PointEquation Method**Variable expenses Fixed expenses Sales – = Total revenues = Total costs**Abbreviations**SP = Selling price VCU = Variable cost per unit CMU = Contribution margin per unit = SP - VCU CM% = Contribution margin percentage FC = Fixed costs**Abbreviations**Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI = Target net income**Equation Method**Total revenues = Total costs (Selling price × Quantity sold) = (Variable unit cost × Quantity sold) + Fixed costs Let Q = number of units to be sold to break even $70Q – $42Q – $84,000 = 0 $28Q = $84,000 Q = $84,000 ÷ $28 = 3,000 units**Contribution Margin Method**PE in units = FC / CMU $84,000 ÷ $28 = 3,000 units $84,000 ÷ 40% = $210,000**Graph Method**Breakeven Revenue Total costs Fixed costs**Target Operating Income**(Fixed costs + Target operating income) / Contribution margin (per unit or ratio)**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**Understand how income**taxes affect CVP analysis.**Target Net Incomeand 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**Target Net Incomeand 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**Target Net Incomeand 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**Explain CVP analysis**in decision making and how sensitivity analysis helps managers cope with uncertainty.**Sensitivity Analysis andUncertainty 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.**Sensitivity Analysis andUncertainty 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**Sensitivity Analysis andUncertainty 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**Sensitivity Analysis andUncertainty 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**Use CVP analysis to plan**fixed and variable costs.**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.**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**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**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.**Apply CVP analysis to a company**producing different products.**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.**Effects of Sales Mix on Income**Contribution margin per shirt: $20 – $9 = $11 What is the contribution margin of the mix? $28 + (2 × $11) = $28 + $22 = $50**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**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**Effects of Sales Mix on Income**What is the weighted-average budgeted contribution margin? Pants: 1 × $28 + Shirts: 2 × $11 = $50 ÷ 3 = $16.667**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**Effects of Sales Mix on Income**Sales mix can be stated in sales dollars: PantsShirts Sales price $70 $40 Variable costs 42 18 Contribution margin $28 $22 Contribution margin ratio 40% 55%**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%**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