CHAPTER - ONE
COST -VOLUME -PROFIT (CVP) ANALYSIS
1.1 IntroductionThe first step in CVP analysis classifying costs as variable and fixed based on their behavior. Variable Cost - is a cost that changes in direct proportion to changes in the cost driver.
Fixed Cost- is a cost that remains constant over a given period called relevant range. Variable cost per unit is constant -where as fixed cost per unit changes in opposite direction with an increase in cost driver Relevant Range: is the limit of cost driver activity with in which a specific relation ship b/n the cost & the cost driver is valid.
CVP Analysis: is one of the most powerful tools that managers have at their command. It helps them understand the interrelationship between cost, volume, and the profit of an organization and hence, it helps to make important decisions like for example:
what products to manufacture or sell
what price policy to follow
what marketing strategy to apply 1.2 Basics of CVP Analysis
Consider the following example: Mary Alebachew plans to sell a home-office software package at a heavily attended two-month computer convention (Exhibition) in Addis. Mary can purchase this software from computer software wholesaler at Br.120 per package. The packages will be sold at Br 200 each. She has already paid Br. 2000 for the booth rental for a month convention. Assume there are no other costs and number of units sold is 100.
Summary of the data:
Number of units sold 100 units Selling price per unit Br.200 Variable cost per unit 120 Monthly fixed costs 2000 A. Contribution Margin
. Total Per unit
Sales Br. 20,000 Br. 200 Less: VC 12,000 120 Contribution Margin Br. 8,000 Br. 80 Less: Fixed Costs 2000
Operating Income Br. 6,000
Notice that sales, variable expenses and contribution margin are expressed on a per unit basis as well as in total.
B. Contribution Margin Ratio:
The contribution margin as a percent of total sales is referred to as the contribution margin ratio.
CM percentage (CM ratio) =
CM per Unit
Selling
Pr
ice
= 80/200 =40% CM % -Shows CM achieved per dollar of revenue.1.3 BREAKEVEN POINT (BEP) Analysis
Breakeven point is an important aspect of CVP analysis. Managers usually ask ‘what volume of sales do we need to breakeven? ’when they starting a new product line. Breakeven point is the level of out put where total revenues equal total costs i.e. company’s profit is zero. It tells mgrs what level of sales they must generate to avoid a loss.
THREE METHODS TO DETERMINE BEP
A. EQUATION METHOD
It is used to determine the BEP and focus on the contribution margin approach. It expresses the income statement in equation form as follows:
Net Income = Revenues - Variable costs - Fixed costs = (SP x Q) - (V x Q) - FC
= Q = FC/(SP-VC) For Mary, the BEP is:
0 = (200 x Q) - (120 x Q) – 2000 80Q= 2000 Q = 25 units.
IF Mary sells fewer than 25 units, she will have a loss; if she sells 25 units she will break even; and if she sells more than 25 units, she will make a profit.
B. CONTRIBUTION MARGIN METHOD
It uses the equation method to determine the BEP. Taking the above general Equation we've:
NI = (SP x Q) - (V x Q) – FC NI + FC = Q(SP - V) Q =
NI
+
FC
SP
−
V
but SP - V = contribution per unit and by definition, at BEP, NI equals zero.
∴Q
FC
CM per unit
i.e. Break even in quantity
Fixed Cost
Contribution M
arg
in Per Unit
Break even in quantity =
2000
80/unit = 25 units
Break even Revenue = Break even quantity x Price per unit
BE Rev. =
FC
UCM/SP , UCM/SP = CM %
BE
Re
v
.
=
FC
CM
%
BEP in revenue for the above example =
2000
40% = $ 5,000
C. Graph Method
CVP Relationships in Graphic Form: the relationships among revenue, cost, profit, and volume can be expressed graphically by preparing a CVP graph. A CVP graph highlights CVP relationships over wide range of activity and can give managers a perspective that can be obtained in no other way.
How to Read the BEP Graph?
a) BEP- BEP is determined by the intersection of the total revenue line and the total expense line. The company in our example breaks even at 25 units, or $ 5,000 of sales. This agrees with the calculation made earlier.
b) Profit and loss area - The CVP graph discloses more information than the BEP calculation. From the graph, a manager can see the effects on profits of changes in volume. The vertical distance between the lines on the graph represents the profit and loss area at a particular sales volume. If sales are fewer than 25 units, the organization will suffer a loss. The magnitude of the loss increases as sales decline. The organization will have a profit if sales exceed 25 units a month.
c) Implications of the Breakeven Point - The position of the breakeven point within the organization's relevant range of activity provides important information to management.
Managers can also use CVP analysis to determine the total sales, in units & dollars, needed to reach a target profit.
Target sales - Variable costs - Fixed costs = Target NI. SPQ - VQ - FC = NI
Q (SP-VC) = NI + FC
Q
=
NI
+
FC
UCM
Example: If Mary considers Br. 2,000 the minimum acceptable net income, how many units she must sell?
Q
=
NI
+
FC
UCM
=2000
+
2000
80
= 50 UnitsIf Mary wants to get a minimum NI of Br. 2000 she has to sell 50 units.
Target Sales volume in dollars =
NI
+
FC
CM
%
=2000
+
2000
40 %
= $ 10,000 Consideration of Income Tax under Target Profit AnalysisNI after tax = Operating Income - Income tax. SPQ - VQ -FC = Target NI
Q (SP-V) =
NI
1−R + FC
Q
=
NI
+
FC
(
1
−
TR
)
UCM
(
1
−
TR
)
Example: Suppose Mary considers Br. 2400 minimum acceptable net income and pays an income and pays an income tax of 40 %, how many units she must sell?
Target sale =
Q
=
NI
+
FC
(
1
−
TR
)
UCM
(
1
−
TR
)
=
2400
+
2000
(
0.6
)
80
(
0
−
60
)
=3600
48 = 75 units
1.5 Margin of Safety:
Margin of Safety (MOS) = planned sales - BEP unit sales.
It can be expressed in ratio by dividing the MOS amount to the expected sales. 1.6 Sensitivity Analysis
Sensitivity analysis involves studying the effects of changes in variable costs, fixed costs, sales price, and sales volume, on the company’s profitability.
Per unit Percent of sale
Sales Price $250 100%
Less: Variable Exp. 150 60%
Contribution margin 100 40%
Total monthly fixed expenses = $35, 000
1) Change in fixed cost and sales volume
The company is currently selling 400 units per month (monthly sales of $100, 000). The sales manager feels that a $10,000 increase in the monthly advertising budget would increase monthly sales by $30,000. Should the advertising budget be increased?
Incremental cm ($30,000*40%) $12,000 Less: Incremental advertising Expense 10,000
Incremental Net Income 2,000
Assuming there are no other factors to be considered, the increase in the advertising budget should be approved since it would lead to an increase in net income of $2,000.
2) Change in variable costs and sales volume
Refer back to the original data. Recall that the co. is currently selling 400 units per month. Management is contemplating the use of high quality components, which would increase variable costs (and thereby reduce the contribution margin) by $10 per unit. However, the sales manager predicts that the higher overall quality would increase sales to 480 units per month. Should the higher quality components be used?
The $10 increase in variable costs will cause the unit contribution margin to decrease from $100 to $90.
Expected total contribution margin with higher quality
Components: 480 units x $90 $43,200
Increase in total contribution margin $ 3,200
Yes, based on the information above, the higher quality components should be used. Since fixed costs will not change, net income should increase by the $3,200 increase in cm shown above.
3) Change in fixed cost, sales price, and sales volume
Refer to the original data and recall again that the company is currently selling 400 units per month. To increase sales, the sales manager would like to cut the selling price by $20 per unit and increase the advertising budget by $15,000 per month. The sales manager argues that if these two steps are taken, unit sales will increase by 50% to 600 units per month. Should the changes be made?
A decrease of $20 per unit in the selling price will cause the unit contribution margin to decrease from $100 to $80.
Expected total contribution margin with lower selling price
600 units x $80 $48,000
Present total contribution margin: 400 units x $100 40,000 Incremental contribution margin 8,000 Less: Incremental fixed costs 15,000 Reduction in Net Income $ (7,000) No, Based on the information above, the changes should not be made.
4) Change in variable cost, fixed cost, and sales volume
Refer to the original data. As before, the company is currently selling 400 units per month. The sales manager would like to place the sales staff on commission basis of $15 per unit sold, rather than on flat salaries that now total $6,000 per month. The sales manager is confident that the change will increase monthly sales by 15% to 460 units per month. Should the change be made?
Changing the sales staff from a salaried basis to a commission basis will affect both fixed and variable costs. Fixed costs will decrease by $6,000, from $35,000 to $29,000. Variable costs will increase by $15, from $150 to $165, and the unit contribution margin will decrease from $100 to $85.
Expected total contribution margin with sales staff on
Commissions: 460 units x $85 $39, 100
Increase in Net Income $ 5, 100 Yes, based on the information above, the changes should be made.
5) Change in regular sales price
Refer to the original data where the company is currently selling 400 units per month. The company has an opportunity to make a bulk sale of 150 units to a wholesaler if an acceptable price can be worked out. This would not disturb the company’s regular sales. What price per unit should be quoted to the wholesaler if the company wants to increase its monthly profits by $3,000?
Variable cost per unit $150
Desired profit per unit ($3, 000/150 units) 20
Quoted price per unit $170
Notice that no element of fixed cost is included in the computation. This is because fixed costs are not affected y the bulk sale, so all of the additional revenue that is in excess of variable costs goes to increasing the profits of the company.
1.7 CVP Analysis with Multiple Products
For any organization selling multiple products, the relative proportion of each type of product sold is called the sales mix.
Sales mix - is the relative proportion or combinations of quantities of products that comprise total sales. It is an important assumption in multi-product CVP analysis and is used to compute the weighted average unit contribution margin.
Example: Suppose Mary intends to sell two soft ware products X & Y for the next convention & budgets the following.
X Y Total
Units Sold. 60 40 100 Revenues, $200 $100 per unit $12,000 $ 4,000 $16,000 Variable Costs, $120 $70 per unit 7,200 2,800 10,000 Unit Contribution Margin, $80 $ 30 per unit $ 4,800 $ 1200 $ 6,000
Fixed Costs 4,500
Operating Income $ 1,500
Weighted - Average Contribution Margin per unit =
CMUx. X+CMUy.Y
X+Y
=
80x60+30x40 60+40 =
6000
100 = $ 60
OR the CM of each will be multiplied by its sales mix i.e. (80*60%) + (30*40%) = $60
BEP =
FC
WA UCM
= 604,500 = 75, units. I.e. 60 % x 75 = 45 units of X40 % X 75 = 30 units of Y
To Compute the BER (total revenues required to break even)
Weighted - Average CM % =
Total WCM
Total
Re
venues
= 80200xx6060++30100x40x40 = 0.375 or 37.50% BER =
FC
WA CM
%
=4,500
0.375 = $ 12,000
1.8 Assumptions and limitations of CVP analysis
For any CVP analysis to be valid, the following important assumptions must be satisfied with in the relevant range:
The total revenue line and the total expenses line must be straight line, i.e. the selling price per unit, the variable cost per unit, and the total fixed cost must remain the same within the relevant range.
In multi-product companies, the sales mix remains constant over the relevant range.
