Prepared by Diane Tanner University of North Florida ACG Basic Cost-Volume- Profit Analysis 4-2

Cost-Volume-Profit (CVP) Analysis  A very powerful decision making tool  Is what-if sensitive  Helps explain interactions between  Selling prices of products  Volume or level of activity  Per unit variable costs  Total fixed costs  Mix of products sold  Limitations  Companies often have multiple products with many different contribution margins  Sales mix may differ amongst periods  Calculations are estimates 2 Can be used to determine the sales volume needed to achieve breakeven, a target operating profit, or targeted net income

CVP Terminology  SP = Selling price  The amount for which one unit of product is sold  SR = Sales revenue  Selling price per unit multiplied by the number of units sold  VC = Variable cost  A variable cost per unit  TFC = Total fixed costs  Profit equation: 3 SR – TC = Profit SPx ‒ [VCx + TFC] = Profit SPx ‒ VCx ‒ TFC = Profit SR – TC = Profit SPx ‒ [VCx + TFC] = Profit SPx ‒ VCx ‒ TFC = Profit

Assumptions in CVP Analysis  Costs can be accurately separated into their variable and fixed components  If a cost is deemed to be mixed, use one of the cost estimation methods to determine the fixed and variable components.  Both unit variable costs and total fixed costs remain constant within the relevant range  Inventory levels are zero or do not change  Costs are linear  Sales mix is constant 4

Breakeven and Target Profit  The sales level needed to avoid an operating loss  The point where  Sales revenue equals total costs  Contribution margin equals total fixed costs  Profit is zero  Break-even profit equation SPx – VCx – TFC = 0  The level of profit a company desires to achieve  The point where  Sales revenue > total costs  Contribution margin > total fixed costs  Profit > 0  ‘Before tax’ target profit equation SPx – VCx – TFC = Target Profit  ‘After tax’ target profit equation (SPx – VCx – TFC)(1–TR) = Target Profit Where TR is the income tax rate Breakeven Point Target Profit Level

CVP Chart Fixed costs Units Dollars Total Cost Total Revenue 6 Profit Area Loss Area Break-even point Activity below the break-even point creates a loss Activity above the break-even point generates a profit

CVP Shortcuts When determining sales revenue (at breakeven or target profit) 7 Substitute the contribution margin ratio in place of ‘CM’. When determining unit sales (at breakeven or at target profit) Substitute the contribution margin per unit in place of ‘CM’ Using algebra, factor the ‘x’ variable out of the profit equation: SPx – VCx – TFC = profit (SP – VC)x – TFC = profit (CM)x – TFC = profit The CM ‘ratio’ is based on a portion of sales revenue. The CM ‘per unit’ is based on each unit to be sold.

CVP Breakeven Examples 8 TrayCo produces and sells bins. This product has a contribution margin per unit of $22 and a contribution margin ratio of 42%. During June, total fixed costs were $11,220. The income tax rate is 30%. Sales in units needed to achieve breakeven: (SP – VC)x – TFC = profit (CM)x – TFC = profit 22x – 11,220 = 0  X = 510 units Sales revenue needed to achieve breakeven: (SP – VC)x – TFC = profit (CM)x – TFC = profit 0.42x – 11,220 = 0  $X = $26, At the BEP, taxes are zero, so there is no need to consider.

CVP Target Profit Examples 9 TrayCo produces and sells bins. This product has a contribution margin per unit of $22 and a contribution margin ratio of 42%. During June, total fixed costs were $11,220. A profit of $4,500 is desired. The tax rate is 30%. Sales in units needed for profit of $4,500: (SP – VC)x – TFC = profit (CM)x – TFC = profit (22x – 11,220)(1 – 30%) = 4,500  X =  803 units Sales revenue needed for profit of $4,500: (SP – VC)x – TFC = profit (CM)x – TFC = profit (0.42x – 11,220(1 – 30%) = 4,500  $X = $42, Round up units to avoid a loss

Margin of Safety Margin of safety is……  The amount by which sales (revenue or units) can drop before losses begin to be incurred  A cushion available to management before trouble (a loss) occurs  Can be measured in  Unit sales or  Sales dollars Margin of safety = Total sales ‒ Breakeven sales Margin of safety = Total sales ‒ Breakeven sales 10 BEP

What-If Analysis  Using the profit equation, managers can change selected variables to see the effect on profit, units to be sold, or sales revenue.  Variables to be changed  Selling price  Total fixed costs  Unit variable costs 11 Which is better….a higher breakeven point or a lower breakeven point, and why? If the current period sales increases, what happens to the breakeven point?

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