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Breakeven & CVP Analysis

 

Recall from our discussion of variable costing that  revenue - variable costs = contribution margin, and that this works for totals (total revenue - total variable costs = total contribution margin) as well as per unit calculations.

The derivation of the breakeven point below uses the following notation:

  • SP = sales price/unit

  • TR = total revenues [ = quantity sold * sales price]

  • TC = total costs

  • TVC = total variable costs [ = quantity produced * variable cost per unit]

  • VC = variable cost/unit

  • TFC = total fixed costs

  • NI = net income

  • X = number of units

  • CM = contribution margin per unit

  • TCM = total contribution margin

  • CMR = contribution margin ratio

For simplicity, we'll assume that production equals sales; we won't worry about finished goods inventory Now we can derive the relationship for the breakeven point.

  1. TR - TC = NI

  2. but TR = SP(X), so we can substitute as follows:

  3. SP(X) - TC = NI

  4. but  TC = TFC + TVC, and TVC = VC(X), so we can substitute as follows:

  5. SP(X) - VC(X) - TFC = NI. Factoring out the common term, we get

  6. X[SP - VC] -TFC = NI, but

  7. SP - VC = CM, so we have

  8. CM(X) - TFC = NI, but at breakeven, NI = 0, so we can transpose and get

  9. CM(X) = TFC. To solve for X, divide both sides by CM:

  10. X = TFC/CM; recall that CM is contribution margin per unit.

    Therefore, the breakeven point in units = TFC/[CM/unit], and the breakeven in dollar sales = TFC/CMR, where CMR = CM/SP

The foregoing analysis assumes that there is only one product, or that all products have equal contribution margins. When there is more than one product, the contributions have to be weighted in proportion to each items relative sales volume. Suppose we produce 2 products: A and B. Product A constitutes 25% of our sales volume and Product B is 75%. The weighted average contribution margin would take these proportions into account as follows:

Weighted average CM = [CM (A) * .25] + [CM (B) * .75]

When we find the breakeven point, the answer we get will be a composite of one fourth product A and three fourths product B. To find the actual units of A and B, the breakeven in units has to be multiplied by the proportions in which the respective items are sold.

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Copyright © 2004 Gerald M. Myers. All rights reserved. This site has been developed as aid to instructors and students in managerial accounting. The scenarios contained herein are not intended to reflect effective or ineffective handling of managerial situations. Any resemblance to existing organizations is purely coincidental.
Last modified: August 03, 2005