Session 04 - CVP_in class

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Accounting 102 Session 4 Cost, Volume, Profit (CVP) Analysis
2 A Quick Review The following financial data apply to the production of a single unit of your company’s product: Manufacturing Cost per Unit Direct Materials $1.50 Direct Manufacturing Labor 0.80 Variable Manufacturing Overhead 0.70 Fixed Manufacturing Overhead 1.00 Total Manufacturing Costs $4.00 Variable manufacturing overhead varies with respect to units produced. Fixed overhead is general plant administration and building costs. Fixed overhead of $1 per unit is based on production of 150,000 units per month. Each unit currently sells for $5. A salesperson has asked the vice-president of marketing for permission to sell 10,000 units at $3.80 per unit to a customer who is not in its normal marketing channels.
Accounting 102 Session 4 Cost, Volume, Profit (CVP) Analysis
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Financial Modeling can provide an overview of a firm’s financial activities or help managers make specific decisions relies on the concepts of fixed and variable cost behavior financial models allow firms to test the interaction of economic variables in a variety of settings must develop a set of equations (i.e., a model) representing a firm’s operating and financial relations 4
Cost-Volume-Profit Model A cost-volume-profit (CVP) financial model summarizes the effects of volume changes on a firm’s costs, revenues, and income. allows “what-if” analyses when assessing alternatives analyses can be extended to determine the impact on profit of changes in selling prices, service fees, costs, income tax rates, and the mix of products and services 5
Break-Even Point The break-even point is the volume of activity that produces equal revenues and costs for the firm. no profit or loss at this point two approaches to determining break-even point equation approach contribution-margin approach 6
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7 A Simple Example Using Fixed and Variable Costs: Break-even Analysis The Facts: Unit price = $20 Variable manufacturing cost per unit = $7 Variable selling cost per unit = $3 Fixed manufacturing cost = $100,000 per mo. Fixed selling cost = $ 50,000 per mo. Expected sales volume = 13,000 units per month What is the break-even point in unit sales per month?
8 Sales Revenue Total Cost Fixed Cost Break-even Analysis Q B/E At Break-even : Total Revenue – Total Cost = 0 (= Profit @ Break-even) 20 x Q B/E [((7 + 3) x Q ̶ B/E ) + (100,000 +50,000)] = 0 Q B/E = 15,000 units Revenue/Cost
Equation Approach The equation approach to calculate break-even uses the following equation: Sales Revenue - Variable Costs - Fixed Costs = Operating Profit The Break-even point occurs where the operating profit equals zero Previous equation can be expanded algebraically to the following: Sales Price/Unit * Sales Volume - Variable Cost/Unit * Sales Volume - Fixed Costs = Operating Profit or (Sales Price/Unit - Variable Cost/Unit) * Sales Volume - Fixed Costs = Operating Profit 9
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10 Solving Breakeven Point Sales – Total Costs = 0 (profit at breakeven) Sales – Variable Costs – Fixed Costs = 0 Let Q B/E = Volume of Sales at Breakeven (20 – (7+3)) Q B/E (100K+50K) = 0 Q B/E = 15K per month Breakeven:
11 Contribution Margin: A Key Concept in Decision-making Contribution Margin (CM) = Revenues - All Variable Costs (including variable SG&A but excluding all fixed costs). Distinguish from: Gross Margin (GM) = Revenues - All Manufacturing Costs (including fixed manufacturing costs but excluding all SG&A costs). CM per unit is the contribution of each unit sold to: Covering fixed costs. Earning a profit.
Contribution Margin Approach Recall that contribution margin (CM) per unit is the selling price per unit less all variable costs per unit. Conceptually, the contribution margin is the amount of money you make from each sale to (1) pay off your fixed costs, and (2) contribute to profits (after you have paid off your fixed costs). break-even volume (or volume to reach a desired profit level) Q B/E = Fixed Costs (+ target profit) Contribution Margin per Unit 12
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13 Break-even Analysis Using Contribution Margin let Q B/E = Break-even quantity sold in units CM/unit = (Price/unit) - (VC/unit) = $20 – ($7 + $3) = $10 Q B/E = FC / (CM/unit) Q B/E = ($100,000 + 50,000) / $10 Q B/E = 15,000 units
14 How many units would the company have to sell in order to earn a before-tax profit (target profit) of $24,000?
15 Let Q BT = Quantity of sales needed to earn $24,000 before taxes Q BT = Fixed Cost + Target Profit CM/unit = 150,000 + 24,000 10 = 17,400 units How many units would the company have to sell in order to earn a before-tax profit (target profit) of $24,000?
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16 If the income tax rate is 40%, how many units would the company have to sell in order to earn an after-tax profit (target profit) of $24,000? If the income tax rate is t, then, in order to earn an after-tax profit of π, it would have to earn a before-tax profit of π 1 – t Let Q AT = Quantity of sales needed to earn $24,000 after taxes Q AT = Fixed Cost + Target Profit CM/unit = 150,000 + 24,000 1 – 0.40 10 = 19,000 units
17 If the income tax rate is 40%, how many units would the company have to sell in order to earn an after-tax profit (target profit) of $24,000? If the income tax rate is t, then, in order to earn an after-tax profit of π, it would have to earn a before-tax profit of π 1 – t Let Q AT = Quantity of sales needed to earn $24,000 after taxes Q AT = Fixed Cost + Target Profit CM/unit = 150,000 + 24,000 1 – 0.40 10 = 19,000 units
Sales Dollars as a Measure of Volume Break-even point and target profit can be calculated in sales dollars in addition to sales units Formulas remain essentially the same, except now we use the contribution margin ratio instead of contribution margin Contribution Margin Ratio = Contribution Margin Sales Price Break-even in Sales Dollars = Fixed Costs Contribution Margin Ratio Target Profit in Sales Dollars = Fixed Costs + Target Profit Contribution Margin Ratio 18
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Margin of Safety and Step Costs Margin of safety - excess of projected sales units over break- even sales level, calculated as follows: Sales Units - Break-Even Sales Units = Margin of Safety Provides an estimate of the amount that sales can drop before the firm incurs a loss Step costs can be factored into CVP analysis Requires break-even point calculation for each level of capacity 19
CVP with Step Costs Tim & Co. makes and sells one product, at a price of $50/unit. Tim can produce up to 15,000 units per year, with only a day shift. Fixed costs are $200,000 per year. VC is $35/unit. Tim can also operate a night shift to produce an additional 10,000 units. Fixed costs to run the night shift are an extra $64,000 per year. Variable costs per unit are 20 percent higher during the night shift than the day shift because of the higher wages required for night shift workers. What is the profit maximizing quantity? 20
Steps to Solve Calculate CM for day shift and night shift. Calculate the breakeven quantity for each shift [separately] Check that b/e point is within the relevant range Finally, identify profit maximizing quantity. If both shifts will breakeven within the relevant range---produce both! 21
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Cost Structure and Operating Leverage Cost structure refers to the proportion of fixed and variable costs to total costs Has a significant effect on the sensitivity of a firm’s profits to changes in sales volume Operating leverage refers to the extent to which a firm’s cost structure is made up of fixed costs The higher the firm’s operating leverage, the higher the break- even point For firms with high operating leverage, once break-even point is reached, further increases in sales increase profits significantly 22
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23 Low Leverage Fixed Cost: $50,000 Variable Cost: $10/unit Selling Price: $20/unit Break-even: 5,000 units Revenue Total Cost Revenue Total Cost High Leverage Fixed Cost: $100,000 Variable Cost: $5/unit Selling Price: $20/unit Break-even: 6,667 units
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Why Understanding Break-even Matters Why do you think that Saudi Arabia is not reducing its oil production in response to falling prices?
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Multiple Product Financial Modeling When a firm has multiple products, several alternatives are available to facilitate financial modeling 1) Assume a weighted-average contribution margin 2) Assume all products have the same contribution margin 3) Use sales dollars as a measure of volume 4) Treat each product line as a separate entity 25
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Multiple Product Financial Modeling 1) Assume a weighted-average contribution margin To determine break-even units, use the following formula: Fixed Costs ____ ___ Weighted Average Contribution Margin 26
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Multiple Product Financial Modeling 27 A company produces and sells two products: A, having a selling price of $9/unit and a variable cost of $4/unit, and B, with a selling price of $13/unit and a variable cost of $3/unit. A generally outsells B by 2:1 (i.e., for each unit of B it sells, it sells 2 units of A). If the firm’s fixed costs total $200, what is the break-even volume of sales for A and B. Let B be a “bundle” of products consisting of 2/3 units of A and 1/3 units of B. Then, the contribution margin for the bundle is CM B = (2/3 x ($9 – $4)) + (1/3 x ($13 – $3)) = $6.67 Let Q B/E = Break-even number of bundles Q B/E = FC/CM B = $200/($6.67) = 30 bundles And, to break-even, the firm must sell 20 (= 30 bundles x (2/3)) units of A, and 10 (= 30 bundles x (1/3)) units of B
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Multiple Product Financial Modeling 28 A company produces and sells two products: A, having a selling price of $9/unit and a variable cost of $4/unit, and B, with a selling price of $13/unit and a variable cost of $3/unit. A generally outsells B by 2:1 (i.e., for each unit of B it sells, it sells 2 units of A). If the firm’s fixed costs total $200, what is the break-even volume of sales for A and B. Let B be a “bundle” of products consisting of 2/3 units of A and 1/3 units of B. Then, the contribution margin for the bundle is CM B = (2/3 x ($9 – $4)) + (1/3 x ($13 – $3)) = $6.67 Let Q B/E = Break-even number of bundles Q B/E = FC/CM B = $200/($6.67) = 30 bundles And, to break-even, the firm must sell 20 (= 30 bundles x (2/3)) units of A, and 10 (= 30 bundles x (1/3)) units of B
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Multiple Product Financial Modeling 2) Assume all products have the same contribution margin This can be accomplished by grouping products so they have equal or near equal contribution margins However, this approach can be a problem when the products have substantially different contribution margins 29
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Multiple Product Financial Modeling 3) Use sales dollars as a measure of volume Can use weighted average contribution margin to calculate break-even dollar sales as follows: 30 Weighted Average Contribution Margin = Total Contribution Margin Weighted Average Price Total Sales Revenue
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Multiple Product Financial Modeling 31 A company produces and sells two products: A, having a selling price of $9/unit and a variable cost of $4/unit, and B, with a selling price of $13/unit and a variable cost of $3/unit. A generally outsells B by 2:1. If the firm’s fixed costs total $200, what is the break-even revenue for sales of A and B. CM from sale of 2 A and 1 B = [2 x (9 – 4)] + [1 x (13 – 3)] = $20 Revenue from sale of 2 A and 1 B = (2 x 9) + (1 x 13) = $31 CM Ratio = $20 = 0.6452 $31 BE Sales Revenue = $200 = $310 0.6452
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Multiple Product Financial Modeling 32 A company produces and sells two products: A, having a selling price of $9/unit and a variable cost of $4/unit, and B, with a selling price of $13/unit and a variable cost of $3/unit. A generally outsells B by 2:1. If the firm’s fixed costs total $200, what is the break-even revenue for sales of A and B. CM from sale of 2 A and 1 B = [2 x (9 – 4)] + [1 x (13 – 3)] = $20 Revenue from sale of 2 A and 1 B = (2 x 9) + (1 x 13) = $31 CM Ratio = $20 = 0.6452 $31 BE Sales Revenue = $200 = $310 0.6452
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Multiple Product Financial Modeling 4) Treat each product line as a separate entity Requires allocating indirect costs to product lines To the extent allocations are arbitrary, may lead to inaccurate estimates 33
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Multiple Product Financial Modeling 34 A company produces and sells two products: A, having a selling price of $9/unit and a variable cost of $4/unit, and B, with a selling price of $13/unit and a variable cost of $3/unit. If the firm’s fixed costs total $200, what is the break-even volume of sales for A and B. Assume that the fixed production and selling costs can be allocated to each of the product lines: $ 50 for A, and $ 150 for B. what is the break-even volume for A and B?
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CVP Model Assumptions Costs can be separated into fixed and variable components (maybe including step costs) Cost and revenue behavior is linear throughout the relevant range Total fixed costs, variable costs per unit, and sales price per unit remain constant throughout the relevant range Product mix remains constant 35
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CVP: an extension Kyle Industries is considering the introduction of a new product. Fixed costs for this product will be $800,000 for production of 75,000 units or less, and an additional $1.2 million if production exceeds 75,000 units. The ratio of variable costs to sales is 60% for the first 75,000 units. This ratio will change to 50% for units in excess of 75,000. If the product is expected to sell for $25 per unit, how many units must Kyle sell to break even? 36
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Treating CVP Analysis with Caution CVP analysis is merely a simplified financial model The usefulness of CVP analysis may be greater in less complex smaller firms, or stand-alone projects For larger firms, CVP analysis can be more valuable as a decision tool for the planning stages of new projects, services, and ventures 37
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