Session 14 - Accounting 102 Session 14 Cost-Volume-Profit...

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Session 14 Accounting 102
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Cost-Volume-Profit Analysis A Tool for Decision Making
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The Basis for Cost-Volume-Profit Analysis The Cost-Volume-Profit (CVP) Model Operating Profit ( π ) = Total Revenue (TR) - Total Cost (TC) Assuming that: 1) Q represents units both produced and sold (ignoring inventory considerations); 2) the cost function is linear , of the form TC = F + VxQ (where F denotes the fixed costs and V the variable costs per unit); 3) the revenue function is linear , of the form TR = PxQ (where P is the price/unit for any quantity sold). Then, the operating profit can be written as π = PxQ - (F + VxQ) And, cost-volume-profit analysis, is the analysis of how total revenues, total costs, and profit change in response to changes in the quantity sold, Q, the price, P, and the firm’s cost structure, V and F.
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Identifying the Breakeven Point The Breakeven Point is the level of output at which total revenues and total costs are equal. (The location of the breakeven point is often of interest to start-up firms and to firms introducing new products.) To determine the breakeven point, set the operating profit to zero and solve the equation for Q B/E 0 = PxQ B/E -(F+VxQ B/E ) Then, Q B/E = And, recalling that Contribution Margin/unit = CM = (P – V) Then, Q B/E = CM F P – V F
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Example : A firm is trying to decide whether to introduce a new product to the market. Production and marketing costs are expected to be: $6/unit, variable, and $200, fixed. It believes that a reasonable selling price would be $10/unit. What is the breakeven sales volume (in units)? Substituting for the variables in Q B/E = 200/(10 – 6) = Q B/E 50 = Gives P - V F
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Example: (Analyzing the trade-off between fixed and variable costs.) For a fixed annual fee, an outside supplier has offered to provide certain services to the firm that, currently, are being provided “in-house”. If the firm accepts the offer, its variable costs would be reduced to $5/unit. What is the maximum fee that the firm would be willing to pay for the services if its objective is to maintain its breakeven point at 50 units? 10 - 5 F = 250 P - V F = F 50 = = Q B/E Maximum annual fee = 250 – 200 = 50
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Margin of Safety A concept related to the Breakeven point, the margin of safety measures the excess of actual or projected sales volume over the breakeven volume. In the previous example, suppose actual sales were 70 units (compared to the breakeven sales of 50 units). Then, the firm's Margin of Safety would be 20 units.
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Target Profit Level If the firm wants to reach some before tax target profit level , π T , it must produce and sell an amount Q T that solves the equation π T = P Q T -(F+VQ T ) So, P - V π T + F = Q T Example : In the preceding example, suppose the firm wants to earn a profit of $40. How many units must it produce and sell? Substituting in the equation above, we get 60 units = 10 – 6 40 + 200 = Q T
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Breakeven in Dollars Rev Rev – Var. Cost = Contribution Margin per $ of Revenue = Contribution Margin Ratio For some firms (e.g., service firms), output cannot be measured physically (in units).
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This note was uploaded on 10/06/2010 for the course FNCE 100 taught by Professor Jaffe during the Spring '10 term at UNC Asheville.

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Session 14 - Accounting 102 Session 14 Cost-Volume-Profit...

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