c. Multiple products
may be involved in calculating a breakeven point.
1) EXAMPLE: If A and B account for 60% and 40% of
total sales, respectively, and
variable costs
are 60% and 85%, respectively, what is the breakeven point,
given fixed costs
of $150,000?
S = FC
+ VC
S = $150,000
+ .6(.6S) + .85(.4S)
S = $150,000
+ .36S + .34S
.30S = $150,000
S = $500,000
a) In effect, the result
is obtained by calculating a weighted-average
contribution
margin ratio (30%) and dividing it into the fixed costs to arrive
at the breakeven
point in sales dollars.
b) Another approach
to multiproduct breakeven problems is to divide fixed
costs by the unit
contribution margin for a composite unit (when unit
prices are known)
to determine the number of composite units.
The
number of
individual units can then be calculated based on the stated
mix.
d. Sometimes CVP
analysis is applied to analysis of the profitability of special orders.
This application
is essentially contribution margin analysis.
1) EXAMPLE: What is the effect of accepting a special
order for 10,000 units at
$8.00, given the
following operating data?
Per Unit Total
Sales $12.50 $1,250,000
Manufacturing
costs -- variable $ 6.25 $ 625,000
-- fixed 1.75 175,000
-- total $ 8.00 $ 800,000
Gross profit $ 4.50 $ 450,000
Selling expenses
-- variable $ 1.80 $ 180,000
-- fixed 1.45 145,000
-- total $ 3.25 $ 325,000
Operating income $ 1.25 $ 125,000
a) Because the
variable cost of manufacturing is $6.25, the UCM is $1.75,
and the increase
in operating income is $17,500 ($1.75 × 10,000 units).
b) The assumptions
are that idle capacity is sufficient to manufacture 10,000
extra units, that
sale at $8.00 per unit will not affect the price or quantity of
other units sold,
and that no additional selling expenses are incurred.
6. The degree
of operating leverage (DOL) is the change in operating income
(earnings
before interest
and taxes) resulting from a percentage change in sales. It measures the
extent to which a
firm incurs fixed rather than variable costs in operations.
Operating leverage=
a .Percentage change in operating
income
------------------------------------
Percentage change in sales
b. The assumption is that companies with larger
investments (and greater fixed costs)
will have higher
contribution margins and more operating leverage.
1) Thus, as companies invest in
better and more expensive equipment, their
variable production
costs should decrease.
2) EXAMPLE: If sales increase by 40% and operating
income increases by 50%,
the operating
leverage is 1.25 (50% ÷ 40%). Given that Q
equals the number of units sold, P is unit price, V is unit variable cost, and F is fixed
cost, the DOL can also be calculated from the formula below, which
equals total
contribution margin divided by operating income (total contribution margin minus
fixed cost). This formula is derived
from the operating leverage formula on the previous
page, but the derivation procedure is not given.
Q(P – V)
Q(P – V) - F
The DOL is
calculated with respect to a given base level of sales. The significance of the DOL is that a
given percentage increase in sales yields a percentage increase in operating income
equal to the DOL for the base sales level times the percentage increase in
sales.
4.2 VARIABLE AND
ABSORPTION COSTING
1. Accountants have two different views
about whether fixed manufacturing overhead costs
should be
assigned to products.
a. The prevailing
view for external reporting purposes is that product cost should include
all manufacturing
costs: direct labor, direct
materials, and overhead. This method
is
commonly known as
absorption costing.
1) It is required
for external reporting under GAAP and for tax purposes.
2. However, variable (direct) costing has won increasing support.
a. This method
assigns only variable manufacturing costs to products.
b. The term direct costing may be misleading because it suggests traceability, which
is
not what cost
accountants mean when they speak of direct costing.
1) Many accountants
believe that variable costing is a more suitable term, and
some even call
the method contribution margin reporting.
3. Variable and absorption costing are just
two of a continuum of possible inventory costing
methods. At one extreme is supervariable costing,
which treats direct materials as the
only variable
cost. At the other extreme is superabsorption costing, which treats costs
from all links in
the value chain as inventoriable. For
income tax reporting purposes, the
IRS requires that
some design and administrative costs, as well as manufacturing costs, be
treated as
product costs.
4. Under variable costing, all direct
labor, direct materials, variable overhead costs, and selling
and
administrative costs are accounted for in the same manner as under absorption
costing. Only fixed manufacturing overhead costs
are treated differently.
a. Absorption
costing includes a provision for fixed overhead in the total cost of each
product
manufactured.
b. In variable
costing, the inventoriable or product cost includes only the variable costs.
Variable overhead
is part of product cost, but fixed overhead is treated as an
expense of the
accounting period (as are selling and administrative expenses).
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