Question

SmoothIt Inc is facing a problem with their 4th quarter absorption costing net operating income on December 23rd. The net operating income target is $2,000,000 and the data so far is as follows :

Sales Revenue : $25,000,000 ($500 per unit)
Variable Cost of Goods Sold : $10,000,000 ($200 per unit )
Fixed Overhead : $12,000,000
Fixed Selling and Adminstrative : $2,000,000
Variable Selling and Admin : 4% commission on sales
SmoothIt has a policy of having 0 inventories at the end of each quarter. No further sales are possible during the year and all the units that have been produced so far have been sold. The CEO is planning to produce items for inventory to meet net operating income target .
Question : How many units need to be produced for inventory to meet net operating income target if sales commission is left unchanged at 4% ?
A) 4,054 B) 30,000 C) 10,000 D) 15,000 E) None

Answer 1

Option (E) is correct.

Step-by-step explanation:

Let number of unit produced be "X"

Variable selling expense = 0.04 × X × 500

= 20X

Net operating income = Gross margin - Fixed selling - variable selling

2,000,000 = GM - 2,000,000 - 20X

Gross margin = 2,000,000 + 2,000,000 + 20X

= $4,000,000 + 20X

Unit produced (Selling price - Cost of goods sold) - Fixed overhead = Gross margin

X ($500 - $200) - 12,000,000 = 4,000,000 + 20X

300X - 20 X = 4,000,000 + 12,000,000

280X = 16,000,000

X = 16,000,000 ÷ 280

= 57,142.86 units

Hence, this much units need to be produced for inventory to meet the target.