RIZAL TECHNOLOGICAL UNIVERSITY

Boni Avenue, Mandaluyong City

College of Engineering and Industrial Technology

IE 300
WRITTEN REPORT
COST VOLUME PROFIT RELATIONSHIPS

GROUP 6
De La Cruz, Jeraldene C.
Ramos, Cheska Mae R.
Regidor, Jhane Valerie ES.
Sanchez, Julets Keah T.
Bagting, Shendy L.
CEIT 06 601A

COST VOLUME PROFIT RELATIONSHIPS

The Basis of Cost Volume Profit (CVP) Analysis

Managers are constantly faced with decisions about selling prices, variable costs and fixed costs.
To be able to choose from among the alternative actions, it is necessary to have a good estimate
of the probable cost that would result from each choice. Furthermore, management needs to know
the costs that are likely to be incurred under normal operating conditions and how they might vary
if conditions change.
Among the most frequently asked questions that require cost estimates and short run decisions are:
1.
How many units will be manufactured?
2.
What is the companys break even sales?
3.
Should the selling price be changed?
4.
Should the company spend more on advertising?
5.
What profit contribution can be realized if the organization performs as expected
for the period?
6.
Should the product be sold as is or should it be processed further?
7.
What would be the effects of the following changes in the next period?
a. Increase or decrease in the cost of materials?
b. Increase or decrease in the efficiency of production?

Long run decisions such as buying new plant and equipment

Significance of Cost Volume Profit Analysis

Cost Volume Profit (CVP) Analysis is one of the most powerful tools that managers have at their
command. It helps them understand the interrelationship between costs, volume and profit in an
organization by focusing on interactions between the following five elements:
1.
2.
3.
4.
5.

Prices of products
Volume or level of activity within the relevant range
Variable cost per unit
Total fixed cost
Mix of products sold

If the above items are known, the following relationships may be established

Contribution margin
Contribution margin ration

Example:

Dale own a company that manufactures bowling balls. These are the following
information on the unit pricing and variable cost for each unit of Bowling ball that she
produce and sell:

Unit Selling Price

Variable costs per unit
- Direct materials
- Direct Labor
- Variable portion of Mfg. OH
Total variable cost per unit

P10
P1
P2
P3
P6

CONTRIBUTION MARGIN PER UNIT

Unit Selling Price Variable cost per unit = Contribution Margin per unit
P10 P6 = P4

Contribution Margin per unit - This is the excess of unit selling price over variable cost per unit
and the amount each unit sold contributes toward.
1. Covering fixed cost
2. Providing operating profit

In the example,

P10 P6 = P4

- This is means that for each unit we produce and sell, we are left with P4 toward our
profit.
P4 is how much Bowling ball contributes to our margin (Profit).

CONTRIBUTION MARGIN RATIO

= Contribution Margin per unit
Unit selling price
= P10 P6
P10
= P4
P10
= P 0.40 or 40%

What if Dale produce and sell 1,000 units?

Sales Revenue ( 1,000 units x P10 per unit)
Variable costs (1,000 units x P6 per unit)
= CONTRIBUTION MARGIN

P10000
6000
P 4000

Contribution margin ratio

= P4000 / P10000
= 0.40 or 40%
What if this year Dale produce and sell 1,000,000 units and our total fixed costs for the
year are P2, 500,000?
Sales Revenue (1,000,000 X P10)
Variable Cost (1,000,000 X P6)
= Contribution Margin
Total Fixed Cost
NET INCOME

P 10,000,000
(6,000,000)
4,000,000
(2,500,000)
P 1, 500,000

The analysis above shows that if She sells each unit for P10, and the variable cost per unit is P6
and the total annual fixed cost are P2,500,000, if she sell 1 million units this year her net income
will be P1,500,000

CVP ANALYSIS FOR BREAK EVEN PLANNING

What if this year Dale produce and sell 625,000 units and our total fixed costs for the year
are P2, 500,000?
Sales Revenue (625,000 X P10)
Variable Cost (625, 000 X P6)
= Contribution Margin
Total Fixed Cost
NET INCOME

P 6,250,000
(3,750,000)
2,500,000
(2,500,000)
0

The analysis above shows that if our company sells each unit for P10, the variable
cost per unit is P6 and the total annual fixed costs are P2,500,000, if she sell 625,000 units
this year our net income will be 0.
This is known as the break-even point and it tells us how much we need to sell just to
cover our cost

Break even point is the level of sales volume where total revenues and the total expenses are
equal, that is, there is either profit or loss. This point can be determined using CVP analysis. Breakeven point can be computed as follows:

1.

Break even point (UNITS)

=

2.

3.

Total Fixed Costs

Contribution Margin per unit

Break even point (PESOS)

=
Total Fixed Costs
Variable cost
Sales
A. Break even sales for multi product firm (Combined units)
=
Total Fixed Costs
Weighted Average
Contribution Margin

B. Weighted contribution margin per unit

=
CM per unit x No. of units + CM per unit x No. of units
Per mix
Per mix
Total number of units per sales mix
4.

A. Break even sales for multi products firm (Combined Pesos)

=
Total Fixed Costs
Weighted CM Ratio

B. Weighted CM Ratio
=
Total weighted CM Ratio
Total weighted Sales

Break-even Analysis
The Income Statement for one of Manhattan Companys product shows:
Sales (100 units at P100 a unit).............................................. P10, 000
Cost of goods sold:
Direct Labor...............................
P1, 500
Direct materials used.................
1, 400
Variable factory overhead.......... 1, 000
Fixed factory overhead................
500
4,400
Gross profit.............................................................................
P 5, 600
Marketing expenses
Variable.....................................
P 600
Fixed.........................................
1,000
Administrative expenses
Variable....................................
500
Fixed........................................
1,000
3,100
Operating income.................................................................... P 2, 500
Required:
1.
Compute the break-even point in units
2.
If sales increase by 25%, how much will be the operating income?
3.
Compute the new break-even point in pesos if fixed factory overhead will
increase by
P1, 700.
Solution: Manhattan Company
(1) Break-even point = P500+P1, 000+P1000
P50
= 50 units
(2) Current Net Income
Add: Incremental Contribution
Margin (25 units x P50)
Operating Income

P2, 500
1,250
P3, 750

(3) Break-even point = P2, 500+P1, 700

50%
= P8, 400
CVP Analysis with changes in Cost Structure
The Don Company sold 100,000 units of its product at P20 per unit. Variable costs are P14 per
unit (manufacturing costs of P11 and marketing costs of P3). Fixed costs are incurred uniformly
throughout the year and amount to P792, 000 (manufacturing costs of P500, 000 and marketing
costs of P292, 000).

Required:
1.
The break-even point in units and in pesos.
2.
The number of units that must be sold to earn an income of P60, 000 before
income tax.
3.
The number of units that must be sold to earn an after-tax income of P90, 000.
Income tax rate is 40%
4.
The number of units required to break even if there is a 10% increase in wages
and salaries. Labor cost constitutes 50% of variable costs and 20% of fixed costs.
Solution:
(1)
BEP

BEP

= P792, 000
P6
= 132,000 units
= P792, 000
30%
= P2, 640,000

(2)
Desired net income
Add: Fixed costs
Contribution margin
Divided by: contribution margin unit
Total number of units
(3)
Desired net income after tax
Desired net income before tax
(P90, 000+ 60%)
Add: Fixed costs
Contribution margin
Divided by: contribution margin/unit
Total number of units
(4)
BEP

=
=

P60, 000
792,000
942,000
P6
157,000
P 90,000
P 150,000
792,000
P 942,000
P6
P157, 000

P 792,000+ [(20%xP792, 000) x10%]

P5.30
152, 423 units

Computation of Contribution margin/ unit:

Selling price per unit
Variable cost per unit:
Materials, overhead and
marketing (50% x P14)
Labor (50% x P14 x 110%)
Contribution margin per unit

P20.00
P7.00
7.70
P 5.30

14.70

CVP Analysis for a Multi-Products Firm

Lor, Inc. Produces only two products, A and B. These account for 60% and 40% of the total sales
pesos of Lors respectively. Variable costs as a percentage of sales pesos are 60% for A and
85% for B. Total fixed costs are P150, 000. There are no other costs.
Required: Compute
1.
The weighted contribution margin ratio.
2.
The break-even point in sales pesos.
3.
The sales pesos necessary to generate a net income of P9, 000 if total fixed costs
will increase by 30%.
Solution: Lor, Inc.
(1)
Sales mix ratio
Multiplied by: Contribution margin ratio
Weighted Contribution margin ratio

A
60%
40%
24%

(2)
BEP (P) = Fixed costs
Weighted CMR
= P150, 000
30%
= P500, 000
(3)
Desired net income
Add: Total Fixed costs
(P150, 000 x 130%)
Contribution margin
Divided by: Weighted CMR
Sales necessary to generate
desired net income

P 9,000
195,000
P204, 000
30%
P 680,000

B
40%
15%
+
6%
= 30%

CVP ANALYSIS FOR REVENUE AND COST PLANNING

In revenue planning, CVP analysis managers in determining the revenue required

to achieve a desired profit level.
FORMULA TO COMPUTE FOR TARGET SALES
SALES (UNIT) =

TOTAL FIXED COST + DESIRED PROFIT

CONTRIBUTION MARGIN PER UNIT

BREAK EVEN GRAPH

Under the graphical approach, sales revenue, variable costs and fixed costs are
plotted on the vertical axis while volume is plotted on the horizontal axis.

The break-even point is the point where the total sales revenue line intersects the
total.
EXAMPLE
The company has annual fixed cost of $40, a unit selling price of $10, and a unit variable
cost of $6. Total sales 200 units.

PROFIT-VOLUME CHART

This chart focuses more directly on how profits vary with changes in volume. Profits are
plotted on the vertical axis while units of output are shown on the horizontal axis.

150,000
100,000

PROFIT LINE

50,000
0
-50,000

10,0
00

B
E
P
20,000 30,000
40,000 50,000 60,000
VOLUME (UNITS)
37,500

ASSUMPTIONS AND LIMITATIONS OF CVP ANALYSIS

The following static assumptions will limit the precision and reliability of a given breakeven analysis.
ASSUMPTION/LIMITATION

COMMENT

1. The analysis is valid for a limited range of 1. Failure to observe this limits would the
values the relevant and limited period working with unrealistic data.
of time.
2. Semi variable costs present a problem that
can be solved by segregating fixed and
2. All cost can be categorized as fixed or
variable portion.
variable.
a.
Variable
costs
change
proportionately with volume within the
relevant volume
Range.
b. Fixed costs are constant within the
relevant volume range.

a. there is a danger that linear cost

and revenue relationship may be used
when nonlinearities are significant
b. non-linear curves often have
optimum quantities; linear ones do not
.

3. Revenue change proportionately with 3. Price is constant for all volumes within the
volumes with selling price remaining constant. relevant change.
4. Data should be adjusted for any shifts in
4. There is a constant product mix.
product mix.
5. There are other factors affecting costs and
5. Changes in volume alone are responsible
revenues, but they are lessened if narrow time
for changes in costs and revenues
and volume limits are applied.
6. There is no significant change in inventories 6. Data should be adjusted if inventories
(i.e. in physical units, sales volume equals change markedly
production volume.
7. Operation leverage questions can be dealt 7. This should be supported with capital
with in the CVP framework.
budgeting approaches that consider the time
value of money.
8. The analysis is deterministic and 8. Uncertainly and probabilities approach
appropriate data can be found.
can be introduced. This will change decisions
in some cases.

PREPARATION OF BREAK-EVEN GRAPH

Break-even is the point of zero loss or profit.

REQUIRED:
(a) Prepare a break-even graph for the company.
(b) From the graph, how many units must be sold to break-even?
(c) What is the margin of safety in units?
Break-even Graph
Revenue and Cost (P)

B. Break-even sales

7,500 units

C. Margin of Safety

10,000 7, 500

2,500 units

PREPARATION OF PROFIT-VOLUME GRAPH

Profit Volume Graph is the graphic that shows the relationship between a company's
earning (or losses) and its sales.

The Solimansing Company had the following revenue and cost data when 2,000 units
were sold:
Selling price per unit
Variable cost per unit
Fixed cost per unit
REQUIRED:
(A) Prepare a profit-volume graph for the company.
(B) Determine the break-even point from the graph.
(C) From the graph, determine how many must be sold to generate a net income of
P30,000.

Solution: Solimansing Company

a. Profit-Volume Graph

(b) Break-even point is 1,500 units

(c) To generate net income of P3,000

USE OF CVP IN DECISION-MAKING

Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume
affect a company's operating income and net income. In performing this analysis, there
are several assumptions made, including:

Sales price per unit is constant.

Variable costs per unit are constant.
Total fixed costs are constant.
Everything produced is sold.
Costs are only affected because activity changes.
If a company sells more than one product, they are sold in the same mix.

Woodstock is preparing its budget for the coming year and has made the
following projections about cost increases: materials 5%, labor 8% and all other costs
(including fixed), 6%. Production capacity is 200,000 units.

The President has been offered various proposals by the division manager as follows:
a. Maintain the present volume and sales price.
b. Produce and sell at capacity and reduce the unit price to P28
c. Raise the units price to P32, spend an extra P300, 000 on advertising and
produce and sell 180,000 units.
Required: Recommend action, based on quantification of alternatives

SENSITIVITY ANALYSIS OF CVP RESULTS

Margin of Safety
- measures the potential effect of the risk that sales will short of planned levels.

Margin of safety ratio =

Margin of safety
Actual or Planned Sales

Illustrative Problem 12.9 Margin Safety

Amflor Manufacturing Companys budget for the coming year revealed the following unit
data.
Budgeted net income for the year P 875,000
Unit Costs:
Variable

Fixed

P 14.00

P 12.00

Selling cost

2.50

5.50

General cost

0.25

7.00

Manufacturing cost

Unit selling price........P

Required:
1. Determine the budgeted sales volume (unit).
2. Determine the margin safety in peso amount and percentage.

Solution: Amflor Manufacturing Company

1. Budgeted sales volume (unit) =

Total Budgeted net income

Net income/unit

= P 875,000
P 8.75
= 100,000 units

50

Unit selling price

P 50.00

Less: Unit variable costs

Manufacturing

P 14.00

Selling

2.50

General

0.25

Contribution margin/unit

P 33.25

Less: Unit Fixed Cost

24.50

Net Income/unit

2. a.

Margin of Safety

16.75

P 8.75

= Budgeted sales Break- even sales

= P 5,000,000 P 24.50 x 100,000
66.5 %
= P 5,000,000 P 3,684, 211
= P 1, 315, 789

b.

Margin of Safety Ratio

Margin of Safety (P)

Budgeted Sales

= P 1, 315, 789
P 5,000,000
= 26%
Operating Leverage
- is the ratio of the contribution margin to profit

Operating Leverage =

Contribution Margin
Profit or Net Operating Income

Illustrative Problem 12.10 Operating Leverage

The sales and cost data(s) are for two companies in the transportation industry:
Company A
Amount

Company B
Percent of Sales Amount

Percent of

Sales
Sales

P100,000

Variables cost

60,000

Contribution Margin

P 40,000

Fixed cost

30,000

Net Income

P 10,000

100%
60
40%

P100,000
30,000
P 70,000

100%
30
70%

60,000
P 10,000

Required:
1. Calculate the operating leverage for each company. If sales increase, which company
benefits more? How do you know?
2. Assumes sales rise 10 percent in the next year. Calculate the percentage increase in
profit for each company. Are the results what you expected?

Solution:
1. Operating leverage =

contribution margin
Net income

As operating leverage = P40, 000 = 4

P10, 000
Bs operating leverage = P 70,000 = 7
P10, 000

2.
Company A
Amount
Sales

Percent of Sales

P110, 000

Variables cost
Contribution Margin
Fixed cost
Net Income

Company B

100%

66,000

60

P 44,000

40%

30,000

33,000
P 77,000

P 17,000

14 10 =40%
10

Bs change in profit =

P110, 000

60,000

P 14,000

As change in profit =

Amount

17 10 = 70%
10

Percent of Sales
100%
30
70%