**Basic Assumptions**** **

n **Changes in production/sales volume are the sole cause for cost and revenue changes**** **

n **Total costs consist of fixed costs and variable costs**** **

n **Revenue and costs behave and can be graphed as a linear function (a straight line)**** **

n **Selling price, variable cost per unit, and fixed costs are all known and constant**** **

n **In many cases only a single product will be analyzed. If multiple products are studied, their relative sales proportions are known and constant**** **

n **The time value of money (interest) is ignored**** **

**Basic Formula**** **

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**Contribution Margin**** **

n **Contribution Margin equals sales less variable costs **** **

**CM = S – VC**** **

n **Contribution Margin per unit equals unit selling price less variable cost per unit **** **

**CMu = SP – VCu **** **

n **Contribution Margin also equals contribution margin per unit multiplied by the number of units sold**

n **CM = CMu x Q**

n **Contribution Margin Ratio (percentage) equals contribution margin per unit divided by selling price**

n **CMR = CMu ÷ SP**

**Contribution**** ****Margin **** ****Income Statement Derivations**

n **A horizontal presentation of the Contribution Margin Income Statement:**

n **Sales – VC – FC = Operating Income (OI)**

n **(SP x Q) – (VCu x Q) – FC = OI**

n **Q (SP – VCu) – FC = OI**

n **Q (CMu) – FC = OI**

n **Remember this last equation, it will be used again in a moment**

**CVP, Graphically**

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**Breakeven Point**

n **Recall the last equation in an earlier slide:**

n **Q (CMu) – FC = OI**

n **A simple manipulation of this formula, and setting OI to zero will result in the Breakeven Point (quantity):**

n **BEQ = FC ÷ CMu **

n **At this point, a firm has no profit or loss at a given sales level**

n **If per-unit values are not available, the Breakeven Point may be restated in its alternate format:**

n **BE Sales = FC ÷ CMR**

**Breakeven Point, extended: Profit Planning**

n **With a simple adjustment, the Breakeven Point formula can be modified to become a Profit Planning tool**

n **Profit is now reinstated to the BE formula, changing it to a simple sales volume equation**

n **Q = (FC + OI) **

** CM**

**CVP and Income Taxes**

n **From time to time it is necessary to move back and forth between pre-tax profit (OI) and after-tax profit (NI), depending on the facts presented**

n **After-tax profit can be calculated by:**

n **OI x (1-Tax Rate) = NI**

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