# Cost Volume Profit Analysis

LEARNING OBJECTIVES

Students should be able to:

1. Explain the nature of CVP Analysis and name and illustrate planning and Decision-making situations in which it may be used,

2. Separate semi-variable (mixed) costs into their fixed and variable components. 3. Construct profit/volume charts given selling price, costs and volume data. 4. Construct a cost/volume/profit (CVP) model representing the data in a marginal costing profit and loss account 5. Define and calculate the breakeven point using various techniques 6. Apply the CVP model in multi-product situations.

7. Calculate budgeted sales volume required for a given target net income. 8. Calculate and explain the margin of safety.

9. Identify and explain the limitations of C-V-P analysis

KEY TOPICS

The following major topics are covered in this chapter (related learning objectives are listed for each topic).

1.Break-even point in units

2.Break-even point in sales dollars

3.Multiple-product analysis

4.Graphical representation of CVP relationships

5.Changes in the CVP variables

1.BREAK-EVEN POINT IN UNITS

2.BREAK-EVEN POINT IN SALES DOLLARS

Cost-volume-profit analysis enables a firm to determine the sales (in units or dollars) necessary to attain a desired level of profit. CVP analysis is useful in assessing the effect of operating changes (such as changes in selling price or variable cost or fixed costs) upon profit.

The break-even point is the point where total revenues equal total expenses, the point where profit equals zero. This can be expressed as:

Total revenue – Total variable cost – Total fixed cost = $0 or

Total revenue = Total variable cost + Total fixed cost

A.Shortcut to Calculating Break-Even Units

To determine how many units must be sold in order to break even, solve for X (the number of units) in the following equation: Total revenue = Variable cost + Fixed cost

(Selling price per unit)(X) = (Variable cost per unit)(X) + Fixed cost [pic]

[pic]

B.Unit Sales Needed to Achieve Targeted Profit

In order to earn a desired profit, total revenues must equal variable costs, fixed costs, and desired profit.

Total revenue = Total variable cost + Total fixed cost + Desired profit

To determine how many units must be sold in order to earn a desired profit, solve for X (the number of units) in the following equation:

Total revenue = Total variable cost + Total fixed cost + Desired profit (Selling price per unit)(X) = (Variable cost per unit)(X) + Total fixed cost + Desired profit [pic]

[pic]

After fixed costs are covered, the contribution margin per unit above break-even volume is profit per unit.

C.After-Tax Profit Targets

By substituting [(After-tax profit)/(1 – Tax rate)] for before-tax profit into the equation for CVP analysis, the equation becomes: [pic]

D.Break-Even Point in Sales Dollars

Break-even in sales dollars can be calculated using the following equation:

[pic]

3.MULTIPLE-PRODUCT ANALYSIS

Harvee Manufacturing Company produces two products, X and Y. The following information is presented for both products: X Y

Selling price per unit $46 $36

Variable cost per unit $38 $24

Sales Mix31

Total fixed costs are $234,000.

Determine the company’s break-even point in units.

SOLUTION

SPx - VCx - FC = 0 at the breakeven point

Let: x be units of Y.

3x be units of X

[46(3x) + 36x] - [38(3x) + 24x] - 234,000 = 0 [138x + 36x] -...

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