If the variable cost of goods sold totaled $80,000 for the year (16,000 units at $5.00 each) and the planned variable cost of goods sold totaled $86,250 (15,000 units at $5.75 each), the effect of the quantity factor on the change in contribution margin is:
A) $5,000 decrease
B) $5,000 increase
C) $5,750 increase
D) $5,750 decrease

Question

Quizplus · Accepted Answer

First, we need to calculate the contribution margin per unit:

Contribution margin per unit = selling price per unit - variable cost per unit

For the first year:
Contribution margin per unit = $10 - $5 = $5

For the planned year:
Contribution margin per unit = $10 - $5.75 = $4.25

Next, we can calculate the contribution margin for each year:

For the first year:
Contribution margin = contribution margin per unit x number of units sold
Contribution margin = $5 x 16,000 = $80,000

For the planned year:
Contribution margin = contribution margin per unit x number of units sold
Contribution margin = $4.25 x 15,000 = $63,750

Finally, we can calculate the change in contribution margin due to the quantity factor:

Change in contribution margin = planned contribution margin - actual contribution margin
Change in contribution margin = $63,750 - $80,000
Change in contribution margin = -$16,250

This means that the contribution margin decreased by $16,250 due to the decrease in the number of units sold. However, we are only interested in the effect of the quantity factor on the variable cost of goods sold, which is given as $86,250 - $80,000 = $6,250. Since we know that the variable cost per unit remained constant at $5, the decrease in the number of units sold resulted in a decrease in the variable cost of goods sold by:

Decrease in variable cost of goods sold = decrease in units sold x variable cost per unit
Decrease in variable cost of goods sold = (16,000 - 15,000) x $5
Decrease in variable cost of goods sold = $5,000

Therefore, the answer is D, a $5,750 decrease in contribution margin due to the quantity factor.

If the Variable Cost of Goods Sold Totaled $80,000 for the Year