3 3.1 3.2 3.2

(Costing-Volume-Profit Relationship Analysis)190419222050

3.1 1 () 1 2

3.1 2(abp)

3.1 3

3.1 4

3.2 3.2.1 3.2.2 3.2.3 3.2.4

3.2.1 1(Contribution Margin) (cm) (p)(b) (Tcm) (px)(bx) (pb)x

3.2.1 2 (cm)(p) (b)(p)

3.2.1 3(Operating Leverage)

3.2.2

(Break-even Point )() =0 0 pXbXa Xa(pb) ()

0 x y y = a + b xy = p x

5332000 () 32000(53) 16000() 32000 [(53) 5] 80000()

1()

33300

ABC332083002000-20108.3-1076.64-1031.66-3320024900332061420664008300016600166000()405010100()50302037

(1) () 40505030102037(2) 3330037%90000(3) A 900004036000 B 900005045000 C 90000109000

2

33300

A1200ABC

1.333001200614200.52A12000.523320018551B0.522490013014C0.52332017352.A185515037102B130143043380C1735208675

3

33300

BABC0.410.2410.4A1B0.25C

1.0.4201100.2418.3200.410170.2416.6412.6 2012.67.42.333007.44500()3.A45000.41800B450014500C45000.2411085

1 (Margin of Safety) (Margin of Safety ratio) ()

0 x y

2. 1.

2

3.2.3 () ()

3.2.4

1(0 x y y = a + b xy = p xy = p x

20 x y y = a + b xy = p xy = a+ b x

3 0 x y y = a + b xy = a+bxy = p x

00 px-bx- a 0

=TCM P 1

.

=TCM P 1=p-TCM

3.3

0 10 20 30 40 50 60 70 80 90 100 110 %

x

TR=5.6x-0.05x2 TC=10-0.4x+0.7x2

1 TR=5.6x-0.05x2 TC=10-0.4x+0.7x2 M=TR-TC =5.6x-0.05x2-10-0.4x+0.7x2 =-0.75x2+6x-10

M =0-0.75x2+6x-10=0X1=2.367( X2=5.633(X1=2.367( X2=5.633(

2 M = -0.75x2+6x-10 M = -1.5x+6 M=0 : x=4

1 2 3 4

COSTVOLUMEPROFIT ANALYSISOnce a company determines its fixed and variable costs, it can then conduct cost-volume-profit analysis. BasicallyCVP analysis explores the relationships among costsvo1ume or activity 1evelsand profit 1.Break-Even Point One of the primary uses of CVP analysis is to calculate the break-even pointThe break-even point is the number of units a company must sell to earn a zero profit At the point where sales revenue equals total costs (composed of fixed and variable cost) the company breaks even.

2Profit 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 costsAs stated in the equationprofit is equal to revenues (selling price per unit times quantity) minus variable costs (variable costs per unit times quantity) minus total fixed costsTo calculate the break-even pointsimply set profit to zero ,insert the appropriate selling pricevariable costsand 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 unitand total fixed costs are estimated to be $100000 per monthHow 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)-$100(x) -$100 000 0=$50(x)-$100000 $50(x)=$100000 x=2000Solving for x yields a break-even quantity of 2000 pair of skatesIf management prefers the break-even quantity expressed in dollars of salesrather than in unitsthe quantity is simply multiplied by the selling price of $ 150 to yield $300000

3Margin of safetyObviouslymanagers want a level of sales greater than break-even salesTo express how close they expect to be to the breakeven levelmanagers may calculate the margin of safetywhich is the difference between the expected level of sales and break-even salesFor exampleAA Companys break-even level of sales is $300 000If it expects to have sales of $ 420 000the margin of safety is $120 000

4. Contribution MarginThe profit equation can be rewritten by combining terms with them Profit=(SP-VC) (x)-TFCThe difference between the selling price and variable costs per unit is referred to as the contribution marginEach unit sold contributes this amount to cover fixed costs and increase profitsConsider what happens when sales increase by one unit. The firm benefits from revenue equal to the selling pricebut they also are unaffected by changes in volumethey do not enter into the analysisIf we solve the profit equation for the sales quantity in units (x)we get the following expression X=(Profit +TFC)Contribution MarginThis is a handy formula for calculating the break-even point and solving for the quantity needed to earn various profit 1evels.

AA Companys amount of fixed costs is $100000 per month.With a selling price of $150 and variable costs of $100the contribution margin is $ 50.Using the formula implies that AA must sell 2000 units to break each month 2000= (0+$100000)$50 Now AA Companys management wants to know how many units the company must sell to achieve a profit of $40000 in a given month. Using the formula implies that Union Skate must sell 2800 units to achieve a profit of $40000 2800=($40000+$100000)$50