COST-VOLUME-PROFIT
(CVP) ANALYSIS
Cost-volume-profit (CVP) analysis (also called breakeven analysis) is a
tool for understanding
the effects of the behavior of fixed and variable
costs. It illuminates how changes in
assumptions about cost behavior and the relevant
ranges in which those assumptions are valid
may affect the relationships among revenues, variable
costs, and fixed costs at various
production levels.
Thus, CVP analysis allows management to discern the probable effects of
changes in sales volume, sales price, product mix,
etc.
1. The variables include
a. Revenue as a function of price per unit and quantity
produced
b. Fixed costs
c. Variable cost per unit or as a percentage of sales
d. Profit per unit or as a percentage of sales
2. The inherent
simplifying assumptions used in CVP
analysis are the following:
a. Costs and
revenues are predictable and are linear over the relevant range.
b. Total variable
costs change proportionally with activity level.
c. Changes in
inventory are insignificant in amount.
d. Fixed costs
remain constant over the relevant range of volume.
e. Prices remain
fixed.
f. Production equals
sales.
g. The product mix
is constant (or the firm makes only one product).
h. A relevant range
exists in which the various relationships are true for a given time span.
i. All costs are
either fixed or variable relative to a given cost object.
j. Productive
efficiency is constant.
k. Costs vary only
with changes in physical sales volume.
l. Unit variable
costs are unchanged.
m. The breakeven
point is directly related to costs and indirectly related to the udgeted
margin of safety
and the contribution margin.
3. Definitions
a. Fixed costs
remain unchanged over short periods regardless of changes in volume.
However, per-unit
fixed costs vary indirectly with the activity level.
b. Variable costs
vary directly and proportionally with changes in volume. However, the
variable cost per
unit remains constant.
c. The relevant range defines the limits within which the cost and revenue
relationships
remain linear and
fixed costs are fixed.
d. The breakeven point is the level of sales at which total revenues equal total expenses.
e. The margin of safety is the excess
of budgeted sales dollars over breakeven ales
dollars (or
budgeted units over breakeven units).
f. The sales mix is the composition of total sales in terms of various products,
i.e., the
percentages of
each product included in total sales. It
is maintained for all volume changes.
g. The unit contribution margin (UCM) is the unit selling price minus
the unit variable
It is the contribution from the sale of
one unit to cover fixed costs (and possibly a targeted profit).
1) It is expressed
as either a percentage of the selling price (contribution margin
ratio) or a dollar amount.
2) The slope of a
line (on a graph with the x axis as volume and the y axis as $)
equals the
contribution margin per unit of volume.
Breakeven Formula
a. P = S – FC – VC
S = XY
S = sales
FC = fixed
costs, in dollars
VC = variable
costs, as a percentage of sales or
dollars per unit
X = quantity
of units sold
Y = sales
price of units
b. EXAMPLE: Widgets are sold at $.60 per unit, and
variable costs are $.20 per unit. If
fixed costs are
$10,000, what is the breakeven point?
X = Units
of production and sales
$.60X (sales) = $10,000
of FC + $.20X of VC
$.40X = $10,000
X = 25,000
units
1) In other words,
the UCM is $.40 ($.60 sales price – $.20 variable cost).
2) To cover $10,000
of fixed costs, 25,000 units must be sold to break even.
a. The basic problem requires
equating sales with the sum of fixed costs and variable
costs.
1) EXAMPLE: Given a selling price of $2.00 per unit
and variable costs of 40%,
what is the
breakeven point if fixed costs are $6,000?
S = FC
+ VC
$2.00X = $6,000
+ $.80X
$1.20X = $6,000
X = 5,000
units at breakeven point
2) The same result can be
obtained by dividing fixed costs by the UCM.
3) The breakeven point in
dollars can be calculated by dividing fixed costs by the
contribution margin
ratio.
b. A specified profit, either
in dollars or as a percentage of sales, is frequently required.
1) EXAMPLE: If units are sold at $6.00 and variable
costs are $2.00, how many
units must be sold
to realize a profit of 15% ($6.00 × .15 = $.90 per unit) before
taxes, given fixed
costs of $37,500?
S = FC
+ VC + P
$6.00X = $37,500
+ $2.00X + $.90X
$3.10X = $37,500
X = 12,097
units at breakeven to earn a 15% profit
2) The desired profit of $.90
per unit is treated as a variable cost. If
the desired
profit were stated
in total dollars rather than as a percentage, it would be
treated as a fixed
cost.
3) Selling 12,097 units results
in $72,582 of sales. Variable costs
are $24,194 and
profit is $10,888
($72,582 × 15%). The proof is that
fixed costs of $37,500, plus
variable costs of
$24,194, plus profit of $10,888, equals $72,582 of sales.
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