Chapter 4- cost volume profit analysis; a managerial planning tool
Cost volume-profit (CVP) analysis estimates how changes in costs (both variable and fixed),
sales volume, and price affect a company’s profit. CVP is a powerful tool for planning and
CVP is one of the most versatile and widely applicable tools used by managerial accountants to
help managers make better decisions.
The Break-even point is the point where total revenue equals total cost. (id. The point of zero
CVP analysis can address many other issues as well, such as the number of units that must be
sold to break even, the impact of a given reduction in a fixed cost on the break-even point and
the impact of an increase in price of profit.
In a CVP analysis, cost refer to all costs of the company-production, selling, and administration.
So variable costs are all costs that increase as more unit sold, including direct materials, direct
labour, variable overhead and variable selling and administrative costs.
Similarly, fixed costs include fixed overhead and fixed selling and administrative expenses.
The income statement format that is based on the separation of costs into fixed and variable
components is called the contribution margin income statement.
Contribution margin is defined as the excess of sales over variable costs:
Contribution margin= sales – variable costs
Contribution margin refers to the amount left after the variable costs are covered to contribute
toward fixed costs.
Contribution margin ratio indicates the percentage the percentage of each sales dollar available
to cover fixed costs and to provide income from operations.
Contribution margin ratio= contribution margin/ sales
The contribution margin ratio is most useful when the increase or decrease in sales volume in
CMR is also useful in developing business strategies
Unit contribution margin is also useful for analyzing the profit potential of proposed decisions
Unit contribution margin = sales price per unit- variable cost per unit
The unit contribution margin is most useful when the increase or decrease in sales volume is
measured in sales.
Change in income from operation = change in sales units x unit contribution margin
Operating income = Sales – total variable expenses – Total fixed expenses.
o Expanded .. =( price x number of units sold ) – ( variable cost per unit x number of units
sold) – total fixed cost.
The operating income equation can be rearranged as the following as well :
Break even units = total fixed cost/ price- variable cost per unit
If a company sells enough units for the contribution margin to just cover fixed costs, it will earn
zero operating income .. in other words, it will break even. units sold measure can be converted to a sales revenue measure by multiplying the unit selling
price by the units sold.
The contribution margin ratio is the proportion of each sales dollar available to cover fixed costs
and provide for profit.
Total contribution margin is the revenue remaining after total variable costs are covered, it
must be the revenue available to cover fixed costs and contribute to profit.
There are three possibilities that fixed costs to contribution margin effect operating income ..
1. Fixed costs can equal contribution margin – break even
2. Fixed costs can be less than contribution margin – company earns positive income
3. Fixed costs can be larger than contribution margin – company earns an operating loss
Break even sales = total fixed expenses/ contribution margin ratio
Equation formula approach to break even analysis :
Sales = VC = FC = PROFIT
BE = (P x Q) = Q x VCU + FC + O
P x Q – Q x VCU = FC
Q( P – VCU) = FC
QCM = FC
Q = FC/CM
*P = selling price per unit
*Q= quantity (volume or number of units)
* P(Q)= total revenue
*VCU= variable cost per unit
*VC(Q)= total variable cost
*FC= total fixed cost
Number of units to earn target income = fixed cost = target income / price – variable cost per
Assuming that fixed costs remain the same, the impact on a firms income resulting from a
change in the number of units sold can be assessed by multiplying the unit contribution margin
by the change in the units sold.
Sales dollars to earn target income = fixed cost = target income/ contribution margin ratio