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Theoretical
Practical
Normal
Master Budget
Income with sales of 300,000 bulbs
$770,000
$770,000
$770,000
$770,000
Income with sales of 225,000 bulbs
327,500
398,750
567,500
620,000
Decrease in income when
there is over-production
$442,500
$371,250
$202,500
$150,000
Comparing these results, it is clear that for a given level of overproduction relative to sales, the
manager’s performance will appear better if he/she uses as the denominator a level that is lower.
In this example, setting the denominator to equal the master budget (the lowest of the four
capacity levels here), minimizes the loss to the manager from being unable to sell the entire
production quantity of 300,000 bulbs.
3. In this scenario, the manager of PLF produces 300,000 bulbs and sells 225,000 of them, and
the production volume variance is prorated. Given the absence of ending work in process
inventory or beginning inventory of any kind, the fraction of the production volume variance that
is absorbed into the cost of goods sold is given by 225,000/300,000 or 75%. The operating
income under various denominator levels is then given by the following modification of the
solution to requirement 3 of 9-36:
Theoretical
Practical
Normal
Master Budget
Revenue
$2,205,000
$2,205,000
$2,205,000
$2,205,000
Less: Cost of goods
sold
832,500
1,046,250
1,552,500
1,710,000
Less: Prorated
production-volume
variance a
585,000 U
371,250 U
(135,000) F
(292,500) F
Gross margin
787,500
787,500
787,500
787,500
Variable selling b
45,000
45,000
45,000
45,000
Fixed selling
220,000
220,000
220,000
220,000
Operating income
$ 522,500
$ 522,500
$ 522,500
$ 522,500
a (7/10) × 665,000, × 390,000, × 140,000, × (435,000)
b225,000 × 0.20
Under the proration approach, operating income is $522,500 regardless of the denominator
initially used. Thus, in contrast to the case where the production volume variance is written off to
cost of goods sold, there is no temptation under the proration approach for the manager to play
games with the choice of denominator level.
