COST—VOLUME—PROFIT ANALYSIS Once a company determines its fixed and variable costs ,it can then conduct cost -volume-profit analysis .Basically，CVP analysis explores the relationships among costs，vo1ume or activity 1evels，and profit． 1．Break-Even Point One of the primary uses of CVP analysis is to calculate the break—even point．The break-even-point is the number of units a company must sell to earn a zero profit (i.e.，break-even)． At the point where sales revenue equals total costs (composed of fixed and variable cost) the company “breaks even”. 2．Profit Equation The calculation of the break-even point relies on the following profit equation： Profit=SP(x)-VC(x)-TFC where X=Quantity of units produced and sold SP = Selling price per unit VC=Variable costs per unit TFC=Total fixed costs As stated in the equation， profit is equal to revenues(selling price per unit times quantity) minus variable costs (variable costs per unit times quantity) minus total fixed costs．To calculate the break-even point，simply set profit to zero ,insert the appropriate selling price，variable costs，and fixed costs and solve for the quantity(x)． Suppose AA Company sells its deluxe in-1ine skates for $150 per unit(a pair of skates)．Variable costs are estimated to be $100 per unit，and total fixed costs are estimated to be $100000 per month．How many units must AA sell to break even in a given month? To answer the question, solve the equation above for a particular value of X． 0=$150(x)一$100(x) 一$100 000 0=$50(x)一$100 000 $50(x)=$100 000 x=2 000 Solving for x yields a break-even quantity of 2 000 pair of skates．If management prefers the break-even quantity expressed in dollars of sales，rather than in units，the quantity is simply multiplied by the selling price of $ 150 to yield $300 000． 3．Margin of safety Obviously，managers want a level of sales greater than break-even sales．To express how close they expect to be to the break—even level，managers may calculate the margin of safety，which is the difference between the expected level of sales and break-even sales．For example，AA Company’s break-even level of sales is $300 000，If it expects to have sales of $ 420 000，the margin of safety is $120 000． 4. Contribution Margin The profit equation can be rewritten by combining terms with them． Profit=(SP-VC)(x)-TFC The difference between the selling price and variable costs per unit is referred to as the contribution margin． Each unit sold contributes this amount to cover fixed costs and increase profits．Consider what happens when sales increase by one unit. The firm benefits from revenue equal to the selling price，but they also are unaffected by changes in volume，they do not enter into the analysis． If we solve the profit equation for the sales quantity in units (x)，we get the following expression： X=(Profit +TFC)／Contribution Margin This is a handy formula for calculating the break-even point and solving for the quantity needed to earn various profit 1evels. AA Company’s amount of fixed costs is $100 000 per month．With a selling price of $150 and variable costs Of $100，the contribution margin is $ 50．Using the formula implies that AA must sell 2 000 units to break each month． 2 000= (0+$100 000)／$50 Now AA Company’s management wants to know how many units the company must sell to achieve a profit of $40 000 in a given month．Using the formula implies that Union Skate must sell 2 800 units to achieve a profit of $40 000． 2 800=($40 000+$100 000)／$50