2.
Breakeven point
under variable
costing
=
per ton
margin
on
Contributi
costs
Fixed
=
$30
$320,000
=
10,667 (rounded) tons per year or 21,334 for two years.
If the company could sell 667 more tons per year at $30 each, it could get the extra
$20,000 contribution margin needed to break even.
Most students will say that the breakeven point is 10,667 tons per year under both
absorption costing and variable costing. The logical question to ask a student who answers
10,667 tons for variable costing is: “What operating income do you show for 2008 under
absorption costing?” If a student answers $120,000 (alternative 1 above), or $260,000
(alternative 2 above), ask: “But you say your breakeven point is 10,667 tons.
How can you show
an operating income on only 10,000 tons sold during 2008?”
The answer to the above dilemma lies in the fact that operating income is affected by
both sales and production under absorption costing.
Given that sales would be 10,000 tons in 2008, solve for the production level that will
provide a breakeven level of zero operating income. Using the formula in the chapter, sales of
10,000 units, and a fixed manufacturing overhead rate of $14 (based on $280,000 ÷ 20,000 units
denominator level = $14):
Let P = Production level
=
margin
on
contributi
Unit
produced
Units
units
in
sales
Breakeven
rate
overhead
manuf.
Fixed
income
operating
Target
costs
fixed
Total

×
+
+
10,000 tons
=
30
$
)
000
‚
10
(
14
$
0
$
000
‚
320
$
P

+
+
$300,000
= $320,000 + $140,000 – $14P
$14P
= $160,000
P
= 11,429 units (rounded)
Proof:
Gross margin, 10,000 × ($30 – $14)
$160,000
Productionvolume variance,
(20,000 – 11,429) × $14
$119,994
Marketing and administrative costs
40,000
159,994
Operating income (due to rounding)
$
6
928