Question

Operating income effects of denominator-level choice and disposal of production-volume variance

1. If ELF sells all 220,000 bulbs produced, what would be the effect on operating income of using each type of capacity as a basis for calculating manufacturing cost per unit?

2. Compare the results of operating income at different capacity levels when 200,000 bulbs are sold and when 220,000 bulbs are sold. What conclusion can you draw from the comparison?

3. Using the original data (that is, 220,000 units produced and 200,000 units sold) if ELF had used the proration approach to allocate the production-volume variance, what would operating income have been under each level of capacity? (Assume that there is no ending work in process.

Answer 1

Operating income effects of denominator-level choice and disposal of production-volume variance

1.         

Since no beginning inventories exist, if ELF sells all 220,000 bulbs manufactured, its operating income will be the same under all four capacity options. Calculations are provided below:

	Theoretical	Practical	Normal	Master Budget
Revenue	$1,980,000	$1,980,000	$1,980,000	$1,980,000
Less: Cost of goods sold a	825,000	990,000	1,430,000	1,650,000
Production volume variance	725,000 U	560,000 U	120,000 U	(100,000) F
Gross margin	430,000	430,000	430,000	430,000
Variable selling b	55,000	55,000	55,000	55,000
Fixed selling	250,000	250,000	250,000	250,000
Operating income	$ 125,000	$ 125,000	$ 125,000	$ 125,000

a220,000 × 3.75, × 4.50, × 6.50, × 7.50

b200,000 × 0.25

 

2.

If the manager of ELF produces and sells 220,000 bulbs, then all capacity levels will result in the same operating income of $125,000 (see requirement 1 above). If the manager of ELF is able to sell only 200,000 of the bulbs produced and if the production-volume variance is closed to cost of goods sold, then the operating income is given as in requirement 3 of 9-37. Both sets of numbers are reproduced below.

 

	Theoretical	Practical	Normal	Master Budget
Income with sales of 220,000 bulbs	$125,000	$125,000	$125,000	$125,000
Income with sales of 200,000 bulbs	25,000	40,000	80,000	100,000
Decrease in income when
there is over production	$100,000	$ 85,000	$ 45,000	$ 25,000

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 220,000 bulbs.

 

3.        

In this scenario, the manager of ELF produces 220,000 bulbs and sells 200,000 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 200,000/220,000 or 10/11. The operating income under various denominator levels is then given by the following modification of the solution to requirement 3 of 9-37:

 

	Theoretical	Practical	Normal	Master Budget
Revenue	$1,800,000	$1,800,000	$1,800,000	$1,800,000
Less: Cost of goods sold	750,000	900,000	1,300,000	1,500,000
Prorated production-volume variance a	659,091 U	509,091 U	109,091 U	(90,909) F
Gross margin	390,909	390,909	390,909	390,909
Variable selling b	50,000	50,000	50,000	50,000
Fixed selling	250,000	250,000	250,000	250,000
Operating income	$ 90,909	$ 90,909	$ 90,909	$ 90,909

a (10/11) × 725,000, × 560,000, × 120,000, × 100,000

b200,000 × 0.25

 

Under the proration approach, operating income is $90,909 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.

Under the proration approach, operating income is $90,909 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.