Break-Even and Cost-Volume-Profit Analysis Chapter 24

Break-even Analysis Determines at what level cost and revenue are in equilibrium Break-even point Obtained directly by mathematical calculations Usually presented in graphic form known as break-even chart

Determining the Break-Even Point Each expense must be analyzed to determine its fixed and variable portions Semi-variable expenses must be separated into their fixed and variable components Fixed portion is stated as a total figure Variable portion is stated as a rate or percentage

Determining the Break-Even Point Break-even analysis may be based on Historical data Future sales and costs

Determining the Break-Even Point Contribution margin ratio (C/M ratio) Also known as marginal income ratio or Profit-volume ratio Contribution 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

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

Income Statement Sales xxx Less variable expenses xxx Total contribution margin xxx Less fixed expenses xxx Profit xxx

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

Example The 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 Approach Profit= Sales revenue-variable expenses-fixed expenses (Unit sales price)*(sales volume)- (unit variable expenses)*(sales volume)-(Fixed expenses)

Determining the Break-Even Point Break-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 Chart Changes in Fixed expenses Original estimate new estimate Fixed utilities expenses $1,400 $2,600 Total Fixed expenses 48,000 49,200 Breakeven calculation 48,000 49,200 (FC/unit contribution margin) $6 $6 Break even point(units) 8,000units 8,200 units Break even point (dollars) $128,000 $131,200

Break even Chart Change in unit variable expenses Increase 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 Chart Change in sales price Increase 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 Profit We 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

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

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