A company has provided the following data:
If the sales volume decreases by 25%,the variable cost per unit increases by 15%,and all other factors remain the same,what will the outcome be for operating income?
A) Decrease by $31,875.
B) Decrease by $15,000.
C) Increase by $20,625.
D) Decrease by $3,125.

Question

A company has provided the following data: 
If the sales volume decreases by 25%,the variable cost per unit increases by 15%,and all other factors remain the same,what will the outcome be for operating income?
A) Decrease by $31,875. 
B) Decrease by $15,000. 
C) Increase by $20,625. 
D) Decrease by $3,125.

Quizplus · Accepted Answer

To calculate the outcome for operating income, we need to use the contribution margin formula:

Contribution Margin = Sales revenue - Variable Costs

Operating Income = Contribution Margin - Fixed Costs

Using the given data, we can calculate the initial contribution margin (CM) and operating income (OI):

CM = $7,500,000 - $3,750,000 = $3,750,000
OI = $3,750,000 - $1,500,000 = $2,250,000

After the changes, we can calculate the new contribution margin and operating income as follows:

New Sales Revenue = $7,500,000 x 0.75 = $5,625,000
New Variable Costs per unit = $50 x 1.15 = $57.50

New CM = $5,625,000 - ($57.50 x 125,000) = $2,187,500
New OI = $2,187,500 - $1,500,000 = $687,500

The change in operating income is the difference between the initial OI and the new OI:

Change in OI = $687,500 - $2,250,000 = -$1,562,500

Therefore, the operating income will decrease by $1,562,500, which is equivalent to a decrease of 31,562.5 or rounded to the nearest thousand, $31,875.

Thus, the best choice is A.

A Company Has Provided the Following Data