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'''Cost–volume–profit''' ('''CVP'''), in [[managerial economics]], is a form of [[cost accounting]]. It is a simplified model, useful for elementary instruction and for short-run decisions.
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CVP analysis expands the use of information provided by breakeven analysis. A critical part of CVP analysis is the point where total revenues equal total costs (both fixed and variable costs). At this [[break-even point]], a company will experience no income or loss. This break-even point can be an initial examination that precedes more detailed CVP analysis.
 
CVP analysis employs the same basic assumptions as in breakeven analysis. The assumptions underlying CVP analysis are:
* The behavior of both costs and revenues is linear throughout the relevant range of activity. (This assumption precludes the concept of volume discounts on either purchased materials or sales.)
* Costs can be classified accurately as either fixed or variable.  
* Changes in activity are the only factors that affect costs.  
* All units produced are sold (there is no ending finished goods inventory).  
* When a company sells more than one type of product, the sales mix (the ratio of each product to total sales) will remain constant.
 
The components of CVP analysis are:
* Level or volume of activity
* Unit selling prices
* Variable cost per unit
* Total fixed costs
 
 
==Assumptions==
CVP assumes the following:
* Constant sales price;
* Constant [[variable cost]] per unit;
* Constant total [[fixed cost]];
* Constant sales mix;
* Units sold equal units produced.
These are simplifying, largely [[linear]]izing assumptions, which are often implicitly assumed in elementary discussions of costs and profits. In more advanced treatments and practice, costs and revenue are [[nonlinear]] and the analysis is more complicated, but the intuition afforded by linear CVP remains basic and useful.
 
One of the main methods of calculating CVP is profit–volume ratio
which is (contribution /sales)*100 = this gives us profit–volume ratio.
 
* contribution stands for sales minus variable costs.
Therefore it gives us the profit added per unit of variable costs.
 
==Model==
 
===Basic graph===
The assumptions of the CVP model yield the following linear equations for [[total cost]]s and total revenue (sales):
 
:<math>\text{Total costs} = \text{fixed costs} + (\text{unit variable cost} \times \text{number of units}</math>)
:<math>\text{Total revenue} = \text{sales price} \times \text{number of units}</math>
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.
 
In symbols:
:<math>\text{TC} = \text{TFC} + \text{V} \times \text{X}</math>
:<math>\text{TR} = \text{P} \times \text{X}</math>
where
* '''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:
:<math>\text{TC} = \text{TFC} + \text{V} \times \text{X}</math>
 
Following a [[matching principle]] of matching a portion of sales against variable costs, one can decompose sales as [[Contribution margin|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".
 
In symbols:
:<math>\begin{align}
\text{TR} &= \text{P} \times \text{X}\\
          &= \bigl(\left(\text{P} - \text{V} \right)+\text{V}\bigr)\times \text{X}\\
          &= \left(\text{C}+\text{V}\right)\times \text{X}\\
          &= \text{C}\times\text{X} + \text{V}\times \text{X}
\end{align}</math>
where
* '''C''' = '''Unit Contribution (Margin)'''
 
Subtracting variable costs from both costs and sales yields the simplified diagram and equation for profit and loss.
 
In symbols:
:<math>\begin{align}
\text{PL} &= \text{TR} - \text{TC}\\
          &= \left(\text{C}+\text{V}\right)\times \text{X}
          - \left(\text{TFC} + \text{V} \times \text{X}\right)\\
          &= \text{C} \times \text{X} - \text{TFC}
\end{align}</math>
 
[[File:CVP-TC-FC-VC-Sales-Contrib-VC-PL-compat.svg|thumb|right|240px|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 become 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 contribution = fixed costs. Mathematically, the contribution graph is obtained from the sales graph  by a [[shear mapping|shear]], to be precise <math>\left(\begin{smallmatrix}1 & 0\\ -V & 1\end{smallmatrix}\right)</math>, 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 operational decisions.
 
==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-based costing]] or [[throughput accounting]].<ref>[http://maaw.info/Chapter11.htm#The%20Controversy%20over%20the%20contribution%20margin%20approach The Controversy over the contribution margin approach], in MAAW, Chapter 11.</ref>
 
When we analyze CVP  is  where we demonstrate the point  at which in a firm  there will be no profit nor loss  means that  firm  works in breakeven situation
 
==See also==
*[[Contribution margin]]
 
==Notes==
{{Reflist}}
{{Library resources box
|by=no
|onlinebooks=no
|others=no
|about=yes
|label=Cost-volume-profit analysis }}
 
{{DEFAULTSORT:Cost-volume-profit analysis}}
[[Category:Costs]]
[[Category:Management accounting]]

Revision as of 07:14, 7 February 2014

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