A company has provided the following data:
If the dollar contribution margin per unit is increased by 10%,total fixed cost is decreased by 20%,and all other factors remain the same,what will the outcome be for operating income?
A) Increase by $61,000.
B) Increase by $20,000.
C) Increase by $3,500.
D) Increase by $11,000.

Question

A company has provided the following data: 
If the dollar contribution margin per unit is increased by 10%,total fixed cost is decreased by 20%,and all other factors remain the same,what will the outcome be for operating income?
A) Increase by $61,000. 
B) Increase by $20,000. 
C) Increase by $3,500. 
D) Increase by $11,000.

Quizplus · Accepted Answer

We do not know the original dollar contribution margin per unit, but if we assume it is $x, then the new contribution margin per unit will be 1.1x. If we assume the original total fixed cost is $y, then the new total fixed cost will be 0.8y.

Let's calculate the original operating income:
Revenue= $11ea82f6_1e62_84dd_9299_d137b692d655_TB2484_00 
= $11,000,000
Total variable cost= (number of units)(dollar contribution margin per unit) 
= ea82f6_1e62_84dd_9299_d137b692d655
Let's assume this is $n per unit. Then total variable cost will be: 
(number of units)(n)=(11ea82f6_1e62_84dd_9299_d137b692d655)(n)
Therefore, the original operating income will be:
Revenue-Total variable cost-Total fixed cost
=$11,000,000-(11ea82f6_1e62_84dd_9299_d137b692d655)(n)-y

Now, let's calculate the new operating income:
Revenue= $11ea82f6_1e62_84dd_9299_d137b692d655_TB2484_00 
= $11,000,000
New total variable cost= (number of units)(1.1x)
=(11ea82f6_1e62_84dd_9299_d137b692d655)(1.1x)
New total fixed cost=0.8y

Therefore, the new operating income will be:
Revenue-New total variable cost-New total fixed cost
=$11,000,000-(11ea82f6_1e62_84dd_9299_d137b692d655)(1.1x)-0.8y

Subtracting the original operating income from the new operating income, we get:
New operating income-Original operating income
= $11,000,000-(11ea82f6_1e62_84dd_9299_d137b692d655)(1.1x)-0.8y
-($11,000,000-(11ea82f6_1e62_84dd_9299_d137b692d655)(n)-y)
= $11ea82f6_1e62_84dd_9299_d137b692d655(0.1x)+0.2y

Since we do not have values for x or y, we cannot calculate the exact value of the increase in operating income. However, we can see that the increase will be positive and larger than $10,000, which eliminates choices A and C. Choice B is also too small of an increase, so the best answer is D.

A Company Has Provided the Following Data