1. A Study on
C.V.P Analysis (under conditions of uncertainty-sensitivity)
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Need for the study
Scope of the study
Under sensitivity analysis
Assumptions of under lying break even analysis
Performa of C.V.P
3. Cost – Volume-Profit Analysis
In this article, the traditional cost-volume-profit (CVP) model is expanded to incorporate the cost of
capital. Using the principles of activity-based costing, the opportunity cost of invested funds is
traced to a product and is used to determine its operating income after taxes less the cost of capital or
economic income each period. When a product's economic income over its useful life is discounted
to when production will begin, it is equivalent to a product's net present value (NPV) (see Hartman,
2000; Shrives and Wachowicz, 2001). The NPV equation, or model, developed in this manner is
based on accounting, rather than cash flow, variables. Consequently, it provides a framework for
performing CVP analysis. As demonstrated in the article, the CVP model incorporating the cost of
capital can be used to compute a product's breakeven sales quantity, to measure the range of a
product's discounted economic income with respect to its sales, and to determine the rate of change
in its discounted economic income with respect to a unit change in sales. The CVP model also
facilitates measuring the trade-offs in alternative investment and cost structures, as well as
estimating the impact upon a product's profitability from a program of process improvement.
Resource :Paul A. Phillips, (1994) "Welsh Hotel: Cost-Volume-Profit Analysis and Uncertainty", International Journal of
Contemporary Hospitality Management, Vol. 6 Iss: 3, pp.31 - 36
management, Costs, Financial
measurement, Profitability, Uncertainty.
modeling, , Performance
Cost-volume-profit (CVP) analysis. CVP analysis examines the behavior of total revenues, total
costs, and operating income (profit) as changes occur in the output level, selling price, variable cost
per unit, and/or fixed costs of a product or service. The reliability of the results from CVP analysis
depends on the reasonableness of the assumptions. The Appendix to the chapter gives additional
insights about CVP analysis; it illustrates decision models and uncertainty.
C.V.P-analysis is an analytical technique for studying the relations among fixed costs, variables
costs and profits. If a firm’s costs were all variable, the problem of break – even volume would never
arise; but by having some variable and some fixed costs, the firm must suffer losses up to a given
Evidently, break – even analysis is a formal profit planning approach based on established relations
between costs and revenues. It is a device for determining the point at which sales will just cover
total costs. If the firm is avoid losses, its sales must cover all costs, those that vary directly with
production and those that do not change as production levels change.
Need for the Study:
The views expressed in this essay are purely personal and do not necessarily express the views of the
institutions is the associated with. This is a technical, academic and research output.
Scope of the Study:
Even though CVP assumptions simplify real-world situations, many companies have found
CVP relationships can be helpful in making decisions about strategic and long-range
planning, as well as decisions about product features and pricing. Managers, however, must
always assess whether the simplified CVP relationships generate sufficiently accurate
predictions of how total revenues and total costs behave. If decisions can be significantly
improved, managers should choose a more complex approach that, for example, uses
multiple cost drivers and nonlinear cost functions.
To know that Break-even analysis.
To Study Cost management.
To Evaluate Costs and Financial modeling.
To know that Profitability and Uncertainty .
This data collected from electronic sources collected from the electronic sources i.e., from
the Google and the related websites and also Class subject materials.
Review of literature:
5. 1. CVP analysis is based on several assumptions including:
a. Changes in the level of revenues and costs arise only because of changes in the number of
product (or service) units produced and sold (that is, the number of output units is the only driver of
revenues and costs).
b. Total costs can be separated into a fixed component that does not vary with the output level
and a component that is variable with respect to the output level.
c. When represented graphically, the behaviors of both total revenues and total costs are linear
(straight lines) in relation to the output level within the relevant range (and time period).
d. The analysis either covers a single product or assumes that the proportion of different
products when multiple products are sold will remain constant as the level of total units sold
Under sensitivity analysis:Even though CVP assumptions simplify real-world situations, many companies have found CVP
relationships can be helpful in making decisions about strategic and long-range planning, as well as
decisions about product features and pricing. Managers, however, must always assess whether the
simplified CVP relationships generate
Managers use CVP analysis to guide their decisions, many of which are strategic decisions.
For example, CVP analysis helps managers decide how much to spend on advertising, whether or
not to expand into new markets, and which features to add to existing products. Of course, different
choices can affect fixed costs, variable cost per unit, selling prices, units sold, and operating income.
Single-number “best estimates” of input data for CVP analysis are subject to varying degrees of
uncertainty, the possibility that an actual amount will deviate from an expected amount. One
approach to deal with uncertainty is to use sensitivity analysis another approach is to compute
expected values using probability distributions
Sensitivity analysis is a “what if” technique that managers use to examine how an outcome will
change if the original predicted data are not achieved or if an underlying assumption changes. In the
context of CVP analysis, sensitivity analysis examines how operating income (or the breakeven
point) changes if the predicted data for selling price, variable cost per unit, fixed costs, or units sold
are not achieved. The sensitivity to various possible outcomes broadens managers’ perspectives as to
what might actually occur before they make cost commitments. Electronic spreadsheets, such as
Excel, enable managers to conduct CVP-based sensitivity analyses in a systematic and efficient way.
An aspect of sensitivity analysis is margin of safety, the amount by which budgeted (or actual)
revenues exceed breakeven revenues. The margin of safety answers the “what-if” question: If
budgeted revenues are above breakeven and drop, how far can they fall below the budget before the
breakeven point is reached?
CVP-based sensitivity analysis highlights the risks and returns that an existing cost structure
holds for a company. This insight may lead managers to consider alternative cost structures. For
6. example, compensating a salesperson on the basis of a sales commission (a variable cost) rather than
a salary (a fixed cost) decreases the company’s downside risk if demand is low but decreases its
return if demand is high. The risk-return tradeoff across alternative cost structures can be measured
as operating leverage. Operating leverage describes the effects that fixed costs have on changes in
operating income as changes occur in units sold and hence in contribution margin. Companies with a
high proportion of fixed costs in their cost structures have high operating leverage. Consequently,
small changes in units sold cause large changes in operating income. At any given level of sales:
Degree of operating leverage
Contributi on margin
Knowing the degree of operating leverage at a given level of sales helps managers calculate the
effect of changes in sales on operating income.
Assumptions Underlying Break – Even Analysis
There are a number of assumptions underlying break – even analysis and these are as under:
Davison of Costs into Fixed and Variable –That the concept of cost variability is valid;
therefore costs can be classified realistically as fixed and variable.
Relevant Range - There is a relevant range of validity for all facets of the analysis.
Constant Selling Prices – The selling price does not change as physical volume of sales
No Material Change in Management’s Operational Policies – The basic managerial
policies relative to operations will not change materially.
Constant Sales Mix – There is only one product, or in case of multiple products that sales
mix remains constant.
Stable Price Level – which the general price level will remain essentially stable in the short
Synchronization between Production and Sales – There is synchronization between sales
and production, that is, inventory remains constant or is zero.
No Change in Efficiency and Productivity – The efficiency and productivity per person will
remain essentially unchanged.
Break – Even Point
Break – even point refers to the level of operations where there is no profit or no loss. It denotes the
activity level at which the total costs equal total sales revenue. The terminology of CIMA defines
7. break – even points as “The level of activity at which there is neither profit nor loss”. Break – even
point may be expressed in terms of units or value. The former is known as break – even volume
while the latter is called break – even sales – value.
The determination of break – even point requires knowledge of fixed cost and contribution per unit
or contribution – sales ratio. At break – even point, total contribution is equal to total fixed costs
accordingly, break – even volume may be calculated as under:
Contribution per unit
Similarly, break-even sales value is computed as under:
Sales value × Fixed cost
Sales value – Variable cost
Methods for Determining Break – Even Point
1) Break – Even Chart (or Graphical Method):
The Terminology of CIMA defines a break – even chart as “A chart which indicates
approximate profit or loss at different level of sales volume within a limited range. The level at
which neither profit nor loss is shown is termed the break – even point”.
A break – even chart is a graphical projection of income and expenses to show the
relationship of profits to volume under assumed conditions with references to mix, selling prices,
efficiency and costs. In other words, this is another mode of presentation of according data showing
the inter – relationship between the cost – volume – profit of a concern. It preparation is based upon
the assumption that certain costs vary with volume of production while other costs remain constant
or fixed regardless of volume produced. The hypothesis is that all cost can be classified as either
fixed or variable.
2) Utility of Break-Even Chart
Management has found the break-even chart a very useful tool. When future sales income has been
estimated, costs to generate this income can be forecast and projected profit and loss statement can
8. be prepared. The projected profit and loss data are then presented graphically on the break-even
charts which are also known as profit graphs or profit-volume graphs.
Thus, in market conditions where the demand for the product is elastic, the break-even chart may
be used to determine the optimum volume of production and selling price.
 Limitations of Break-Even Chart
i. The break-even chart in reality may show more than one break-even point.
ii. The basic assumptions on which they are based are not valid in the real world. Thus, variable
cost may not vary by a constant amount, sales mix may not remain constant, selling price
may change, fixed costs may change etc.
iii. The sales line and cost line are not straight lines in reality. In fact, they are curvilinear.
One way of expressing the relationships among costs, revenues and volumes is the contribution to
sales ratio. This ratio is the complement (thing that completes) of the variable cost ratio and denotes
(shows) the proportion increases with increase in volume. The ratio is expressed as under:
The contribution to sales ratio for any given product is assumed to remain constant overall
sales volumes. The contribution to sales ratio provides management with some useful information as
it tells an important fact about the profit making features of a film. If a firm is operating at a loss, the
ratio indicates how much the net loss will either profits than a smaller ratio as volume in rupees
increases above the break-even point. The reverse is the case when sales volume is below the breakeven point. It is most useful in some kinds of product analysis.
Margin of Safety
Margin of safety is the excess of normal or actual sales over sales at break-even point. It refers
to the decline (decrease) which may occur in sales from actual or budgeted levels to the break-even
The Terminology of CIMA defines margin of safety ratio
and indicates the percentage by which forecast
turnover exceeds or falls short of break-even.
Essentially, the margin of safety reveals (shows) the amount by which sales may decline
before losses occur. In other words, it indicates (shows) what portion of the sales are available to
generate profits for the firm. It is calculated as under:
Margin of safety
Actual sales – Break-even sales
9. This concept may be expressed (stated) as a ratio through the division of the rupee margin of
safety by budgeted or actual sales.
It is reasonable that the greater the margin of safety, the better it is for the firm.
Angle of Incidence
The angle which is formed by the intersection (cutting) of the total cost line and the sales line is
called the angle of incidence. The angle of incidence indicates the profit earning capacity of a
business. A large angle, namely a broad profit wedge shows a high rate of earnings after the breakeven point is reached. The reverse is the case when the angle is small.
Generally, firms which are highly stable have a small angle of incidence (i.e., narrow profit
edge), low break-even point, high margin of safety, low fixed cost and high variable costs per unit.
On the other hand, highly speculative or risky firms have a large angle of incidence, high break-even
point, low margin of safety, high fixed cost and low variable cost per unit.
Cost – Volume – Profit Analysis
Cost – Volume – profit analysis attempts to determine the effect that a change in volume, cost
price and product mix will have on profits. The Terminology of CIMA defines cost – volume
– profit analysis as “The study of the effects on future profits of changes in fixed cost,
variable cost, sales price, quantity and mix”. This technique is based on the employed only
for short term decisions making.
While making decisions, the management of a firm focuses its attention on the alternative
courses of action available for making profit. The cost of a product is dependent upon volume of
output, price of inputs, product is dependent upon volume of output, price of inputs, product mix
etc. the price of a product is subject to the influence of a number of factors, namely competitors’
actions, demand etc.
Utility of Cost – Volume – Profit Analysis
i.Analyzing a modernization or automation programs.
ii.Studying the effect of a general expansion in the level of operations.
iii.Making new product decisions.
iv.Determination of optimum selling price of products.
v.Estimation of profit or loss at different levels of output.
vi.Planning for cash requirements at a given volume of output.
vii.To exercise cost control.
viii.Making plant shutdown decisions.
Applications of Cost – Volume – Profit Analysis
1. Analyzing modernization or automation programmed
2. Studying the effects of general expansion in the level of operations
3. Making new product decisions
10. 4. Determination of optimum sale price of products.
5. Profit planning
The assumptions of the CVP model yield the following linear equations for total costs and total
These are linear because of the assumptions of constant costs and prices, and there is no
distinction between units produced and units sold, as these are assumed to be equal. Note that
when such a chart is drawn, the linear CVP model is assumed, often implicitly.
TC = Total costs
TFC = Total fixed costs
V = Unit variable cost (variable cost per unit)
X = Number of units
TR = S = Total revenue = Sales
P = (Unit) sales price
Profit is computed as TR-TC; it is a profit if positive, a loss if negative.
Break down:Costs and sales can be broken down, which provide further insight into operations.
One can decompose total costs as fixed costs plus variable costs:
Following a matching principle of matching a portion of sales against variable costs, one can
decompose sales as contribution plus variable costs, where contribution is "what's left after
deducting variable costs". One can think of contribution as "the marginal contribution of a unit to
the profit", or "contribution towards offsetting fixed costs".
C = Unit Contribution (Margin)
Subtracting variable costs from both costs and sales yields the simplified diagram and equation
for profit and loss.
TC = TR
Volume Production (or) Profit.
Diagram relating all quantities in CVP.
These diagrams can be related by a rather busy diagram, which demonstrates how if one
subtracts variable costs, the sales and total costs lines shift down to becomes the contribution and
fixed costs lines. Note that the profit and loss for any given number of unit sales is the same, and
in particular the break-even point is the same, whether one computes by sales = total costs or as
12. contribution = fixed costs. Mathematically, the contribution graph is obtained from the sales
graph by a shear, to be precise
, where V are unit variable costs.
Applications:CVP simplifies the computation of breakeven in break-even analysis, and more generally allows
simple computation of target income sales. It simplifies analysis of short run trade-offs in
Limitations:CVP is a short run, marginal analysis: it assumes that unit variable costs and unit revenues are
constant, which is appropriate for small deviations from current production and sales, and
assumes a neat division between fixed costs and variable costs, though in the long run all costs
are variable. For longer-term analysis that considers the entire life-cycle of a product, one
therefore often prefers activity or throughput accounting.
When we analyze CVP is where we demonstrate the neither point at which in a firm there will be
no profit or loss means that firm works in breakeven situation
Performa of C.V.P Analysis:Xxx, Inc. sells a single product. The company's most recent income statement is given below.
Sales (4,000 units)
Less variable expenses
Less fixed expenses
Contribution margin per unit is
If sales are doubled to $240,000,
Total variable costs will equal
If sales are doubled to $240,000,
total fixed costs will equal
If 10 more units are sold, profits will increase by
Compute how many units must be sold to break even.
f. Compute how many units must be sold
to achieve profits of $20,000.
********* per unit
The management would consider other factors before making the final decision. It is likely that
product quality would improve as a result of using state of the art equipment. Due to increased
automation, probably many workers will have to be laid off. Patel’s management will have to
consider the impact of such an action on employee morale. In addition, the proposal increases the
company’s fixed costs dramatically. This will increase the company’s operating leverage and