Break-Even and Cost-Volume-Profit AnalysisChapter 8

Break-even AnalysisDetermines at what level cost and revenue are in equilibriumBreak-even pointObtained directly by mathematical calculationsUsually presented in graphic form known as break-even chart

Determining the Break-Even PointEach expense must be analyzed to determine its fixed and variable portionsSemi-variable expenses must be separated into their fixed and variable components

Fixed portion is stated as a total figureVariable portion is stated as a rate or percentage

Determining the Break-Even PointBreak-even analysis may be based onHistorical dataFuture sales and costs

Determining the Break-Even PointContribution margin ratio (C/M ratio)Also known as marginal income ratio or Profit-volume ratioContribution of each dollar towards covering fixed costs and making a profit

Contribution margin ratio = 1 (Variable costs/Sales)OR Contribution margin ratio = unit contribution margin/unit sales price

Contribution margin= sales variable costs

ExampleThe ABC Lodge has sales of $4500,000. The fixed expense was $1,200,000 and the variable expense totaled $1,800,000.

Contribution margin ratioContribution margin

Income StatementSalesxxxLess variable expensesxxxTotal contribution marginxxxLess fixed expensesxxxProfitxxx

Determining the Break-Even PointBreak-even = Fixed costs sales volume ($) Contribution margin ratio

Break-even = Fixed costs sales volume ($) 1 (Variable costs/Sales)

Determining the Break-Even Point

Break-even = Fixed costs sales in units Contribution margin/unit

Break-even = Break-even sales in dollars sales in units Unit sales price

ExampleThe ABC Lodge has sales of $4500,000. The fixed expense was $1,200,000 and the variable expense totaled $1,800,000.

Break even point in dollars

Equation ApproachProfit= Sales revenue-variable expenses-fixed expenses

Profit=

(Unit sales price)*(sales volume)- (unit variable expenses)*(sales volume)-(Fixed expenses)

Determining the Break-Even PointBreak-even capacity %age = Break-even sales in dollars Normal sales volume in dollars

Margin of Safety ratio =Sales Break-even sales Sales

Profit % = CM ratio x Margin of safety ratio

Break even Chart

Break even ChartChanges in Fixed expenses Original estimatenew estimateFixed utilities expenses$1,400 $2,600Total Fixed expenses48,000 49,200

Breakeven calculation 48,000 49,200(FC/unit contribution margin) $6 $6

Break even point(units)8,000units 8,200 unitsBreak even point (dollars)$128,000 $131,200

Break even ChartChange in unit variable expensesIncrease in unit variable expenses will cause a decrease in unit contribution margin.

Break even will now be achieved at a higher output level.

Break even ChartChange in sales priceIncrease in sales price will cause an increase in unit contribution margin.

Break even will now be achieved at a lower output level.

However, careful analysis by the management is required as the increase in sales price might also cause a decline in output sold.

Profit-Volume Analysis

Target Net ProfitWe can use break-even analysis to find the sales required to reach a target level of profit.

Number of sales units required to earn target profit:= Fixed expenses+ Target net profit Unit contribution margin

ExampleCalculate the number of units the company needs to sell in order to realize a Profit of $500,000?Given:Fixed costs= $100,000Sale price= $10Variable cost per unit= $5

Constructing a Break-even ChartExample:Fixed costs = $1,600,000Sales = $5,000,000Sales/unit = $4Variable cost/unit = $2.4/unitConstruct Break-even chart