Chapter 3: Cost-Volume-profit (CVP) Analysis

Cost-volume-profit analysis is a technique for evaluating the effect of changes in cost and
volume on profit. Costs include variable and fixed costs that are expenses of the period.
Volume represents the level of sales activity, either in units or in dollars. Profit for the firm
may be net income or operating income. The role of this analysis is to help managers answer
questions that relate to certain decisions. For example, given the selling price, fixed costs and
variable costs of the products, management can determine how many units must be sold to
break even – to have a net income of zero. The break-even point is that level of volume at
which the firm earns zero profit. Analyzing costs and volume in order to determine the break-
even point is referred to as break-even analysis.

Uses of CVP analysis:

CVP enables the management to reach planning and policy making decisions more
intelligently. This analysis is used in the following cases:
1. Determination of profit which will result from any given volume of sales.
2. Analysis of effect of changes in selling price.
3. Effect of changes in product mixture.
4. Additional sales volume needed to support an additional expenditure.
5. Lowest price at which business may be accepted to utilize facilities and contribute
something towards net profit.
6. The particular products to be emphasized to reflect the highest net profit.
7. Determination of unit costs at various volume levels.
8. Determination of probable effect of investment in new plant and equipment.
9. Determination of most profitable use of scarce materials.
10. Determination of how many units must be sold to earn a specific net income or a
minimum desired rate of return.
11. Determination the necessary selling price of a product, given expected volume, costs and
desired profit.

Assumptions in CVP Analysis:

1. Costs have been accurately distinguished as variable and fixed.
2. Fixed costs remain constant within the relevant range of analysis.
3. Total variable costs are affected only by changes in volume.
4. Revenues are linear
5. No change in inventory levels
6. Sales-mix is constant for multiple product firm

Techniques used in CVP analysis:

1. Equation Technique:
Sales = Fixed Costs + Variable Costs + Desired Net Income
Example- Selling price per unit Tk.30, Fixed costs Tk.200000, Variable Cost per unit Tk.15
and Desired net income Tk.80000. Determine sales in units and in amount.

Let, Sales is X units

30X = 200000 + 15X + 80000
or, 15X = 280000
or, X = 280000/15 = 18667

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Sales in unit 18667 and in amount Tk.(18667*30) 560010

2. Contribution margin technique:

Break-even point = Fixed Costs / Contribution margin ratio
Required sales for a desired net income = (Fixed Costs + Desired net income) / Contribution
margin ratio
Example- Selling price per unit Tk.40, Variable cost per unit Tk.25, Fixed Costs Tk.300000
and Desired net income Tk.50000.

Break-even point sales = 300000 / {(40-25)/40}

= 300000 / 0.375
= 800000
Required sales for a desired net income = (Fixed Costs + Desired net income) / Contribution
margin ratio = (300000+50000) / {(40-25)/40}
= 350000 / 0.375 = 933333
3. Graphical analysis: The relationship between costs, sales and profit at different levels of
activity can be presented diagrammatically by using a break-even chart. It is possible to seat a
glance the estimated results of trading at various levels of activity. The chart shows fixed and
variable costs and sales revenue so that profit or loss at any given level of production or sales
can be ascertained. The chart also shows quite clearly the break-even point and the margin of
safety. In a break-even graph, costs and sales revenues are shown on the vertical axis and
volume either in units or in amount on the horizontal axis. Three lines are required to draw
for presenting graphically such as total fixed cost line, total costs line and sales revenue line.

Company Bag Ltd. produces and sells the bags in the market and wants to conduct the break-
even analysis of its business. The accountant in charge of the company determined that the
fixed cost of the company consisting of salaries of the employees, rent cost, property tax, etc.
will remain the same at $1000000. The variable cost, which is associated with the production
of one unit of the bag, will come to $20. The bag is sold in the market at a premium price of
$120. Prepare the break-even chart for Company Bag Ltd.

Calculation of different costs and revenue for different number of units sold:

Break-Even Chart

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Margin of safety: Margin of safety is a useful concept in the context of Cost-Volume-profit
analysis. It is defined as the excess of actual sales over the break-even level of sales. The
margin of safety is a particularly important measurement for management when they are
contemplating an expansion or new product line because it shows how safe the company is
and how much lost sales or increased costs the company can absorb. Formula is:
Margin of safety = Actual sales – Break-even sales. The size of the margin of safety
determines to a considerable extent the soundness of the business and indicates whether the
business is susceptible to a drop in demand.
Bob’s current sales are Tk.100000 and his breakeven point is Tk.75000. Bob achieves a
Tk.25000 safety margin. This means that his sales could fall Tk.25000 and he will still have
enough revenues to pay for all his expenses and won’t incur a loss for the period. Translating
this into a percentage, we can see that Bob’s buffer from loss is 25 percent of sales.

Operating leverage: Operating leverage represents a measurement of the effect on net

income of changes in sales volume. Operating leverage = Contribution margin / Net income.
An operating leverage of 3 means that the percentage change in net income will be three
times the percentage change in sales. The following information pertains to last week's
operations of XYZ Company. The company sold 2500 units at Tk.25 each. Variable cost per
unit is Tk.15.
Sales Revenue Tk.62500
Less: Variable Costs 37500
Contribution Margin 25000
Less: Fixed Costs 15000
Operating Income 10000

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The degree of operating leverage is: DOL = Contribution margin/Operating income =
25000/10000 = 2.5 times

Analysis: If sales revenue changes by a certain percentage, operating income will change by
2.5 times the percentage change in sales. A 10% increase in sales will result in a 25%
increase in operating income.
Old New
Sales Revenue (Tk.25/unit) Tk.62500 Tk.68750
Less: Variable Costs (Tk.10/unit) 37500 41250
Contribution Margin 25,000 27500
Less: Fixed Costs 15000 15000
Operating Income 10000 12500
In the table above, sales revenue increased by 10% (Tk.62500 to Tk.68750). However, it
resulted in a 25% [(12500-10000)/10000] increase in operating income (Tk.10000 to
Tk.12500).

Problem 1: Laraby Company produces a single product. It sold 25000 units last year with the
following results (Tk.):
Sales 625000
Variable cost 375000
Fixed costs 150000
Net income 100000

In an attempt to improve its products, Laraby is considering replacing one of its component
parts with a new and better one in the coming year. The part presently used has a cost of
Tk.2.5 per unit; the new part would cost Tk.4.5 per unit. A new machine would also be
needed to increase plant capacity. The machine would cost Tk.18000 with a useful life of 6
years and no salvage value. The company uses straight-line depreciation on all plant assets.
Required:
a) What was Laraby’s break-even point in number of units last year?
b) How many units of product would Laraby company have had to sell in the last year to earn
Tk.85000 in net income?
c) If Laraby company holds the sales price constant and makes the suggested changes, how
many units of product must it sell in the coming year to break-even?
d) If Laraby company holds the sales price constant and makes the suggested changes, how
many units of product will the company have to sell to make the same net income as last
year?
e) If Laraby company wishes to maintain the same contribution margin ratio, what selling
price per unit of product must it charge next year to cover the increased material cost?

Problem 2: Given,
Products: A B C D
Selling price per unit (Tk.) 120 135 70 94
(-) Variable cost per unit (Tk.) 75 95 43 58
Contribution margin 45 40 27 36
% of sales 15 25 20 40

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Fixed cost for the period is Tk.1800000.
i) Determine break-even point sales in units for the above sales-mix.
ii) Determine required sales in units for earning net income Tk.750000.

Problem 3: CBL sales 40000 units for Tk.10000000, materials cost Tk.4000000, variable
overheads Tk.1000000, labor charge Tk.2000000 and fixed overheads Tk.1800000, net profit
Tk.1200000. Calculate the followings:
i) number of units to be sold for which the company will neither loss or gain.
ii) sales needed to earn a profit of 20% on sales.
iii) extra units which should be sold to obtain the present profit if it is proposed to reduce the
selling price by 20% and 25%.
iv) selling price to be fixed to bring down its break-even point to 50000 units under present
conditions.