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Chapter 6

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Brock University
Norman Chasse

ACTG 1P11 MA CHAPTER 7: COST-VOLUME-PROFIT ANALYSIS 1. Cost-Volume-Profit (CVP) Basics a. CVP assumptions i. A change in volume is the only factor that affects costs. 1. Fixed costs remain fixed and the unit variable cost remains fixed throughout the relevant range ii. Managers can classify each cost (or the components of mixed costs) as either variable or fixed. These costs are linear throughout the relevant range of volume. iii. Revenues are linear throughout the relevant range of volume. 1. Implies a constant selling price per unit iv. Inventory levels will not change. 1. Units sold = units produced v. The sales mix of products will not change. b. Unit contribution margin i. Sales – Variable Costs = Contribution Margin ii. On a PER UNIT basis: 1. Unit Selling Price (USP) – Unit Variable Cost (UVC) = Unit Contribution Margin (UCM) 2. UCM remains constant so long as USP and UVC remains constant 3. UCM represents the dollar amount that each unit sold contributes to covering fixed costs and ultimately providing a profit c. Contribution margin ratio i. Contribution Margin Ratio (CMR) = Contribution margin (total or unit) ÷ Sales (total or unit) ii. CMR tells us how much of every dollar sold is available to pay fixed costs and provide a profit above fixed costs 2. Using CVP analysis to find break-even points and target profit volumes. a. BE is the point where revenues = expenses and net income is zero b. Based on the PROFIT EQUATION: i. USP (x) – UVC (x) – FC = Profit 1. USP = Unit Selling Price 2. UVC = Unit Variable Cost 3. FC = Fixed Costs 4. x = # of units sold ii. Break-even point is the point at which profit=0; i.e. 1. USP (x) – UVC (x) – FC = 0, i.e. 2. Revenue = Total cost, i.e. 3. USP(x) = UVC(x) + FC 4. FC = USP(x)-UVC(x) 5. x = BEP in units = FC÷UCM c. Break-even point (BEP) in dollars: i. Sales (in dollars) = VC + FC ii. FC = Sales – VC iii. BEP (dollars) = FC ÷ CMR d. Target profit point (before taxes) in sales units: i. Target profit = USP (x) – UVC (x) – FC ii. Target profit = UCM (x) – FC iii. x = (FC + Target Profit) ÷ UCM e. Target profit point (before taxes) in sales dollars: i. $X = (FC + Target Profit) ÷ CMR f. To factor in income taxes in the profit equation: i. After-tax profit = [SP (x) – VC (x) – FC] (1 – t) 1. t = tax rate ii. Or, find the pre-tax equivalent profit (After-tax ÷ (1-t)) and use basic before tax formulas g. Formulas i. BE point in units = fixed costs / CM per unit ii. BE point in sales revenue = fixed costs / CM ratio iii. Target profit volume in units = (fixed costs + target profit) / CM per unit iv. Target profit volume in sales revenue = (fixed costs + target profit) / CM ratio EX: Nord Corporation, a bicycle manufacturer, presents the following contribution margin format income statement for its most recent month. Use this information to calculate: 1) The unit contribution margin and contribution margin ratio 2) The break-even point in units and in dollars 3) The number of units needed to be sold to earn a target profit of $70,00 Total Sales (500 bikes) ...................$250,000 Less variable expenses ...............150,000 Contribution margin ..................100,000 Less fixed expenses ...................80,000 Net income ..........................$ 20,000 3. Graphing CVP relationships a. Step 1: Choose a sales volume b. Step 2: Draw the fixed expense line c. Step 3: Draw the total expense line d. Step 4: Identify the break-even point i. BEP is the point of intersection between the total revenue (TR) and total cost (TC) lines e. Step 5: Mark the operating income and operating loss areas i. Where TR > TC: profit ii. Where TR < TC: loss 4. Perform sensitivity analysis: “what if” a. Changing the sales price i. New USP means new UCM and new BEP ii. Calculate new BEP and target profit volume 1. Higher USP decreases BEP 2. Lower USP increases BEP b. Changing variable costs i. New UVC means new UCM and new BEP 1. Lower UVC means lower BEP 2. Higher UVC means higher BEP ii. A change in UVC has same effect as an equal change in USP c. Changing fixed costs i. New BEP will result 1. higher FC = higher BEP 2. lower FC = lower BEP) ii. No change to the contribution margin 5. Multiproduct companies a. Changing the mix of products offered for sale i. Sales mix is how many of each product a company sells
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