Cozy Mitts produces heated motorcycle gloves. The company has fixed expenses of $125,000 and variable expenses of $75 per pair. Each pair sells for $125. If Cozy Mitts can decrease its variable costs to $60 per pair by increasing its fixed expenses to $160,000 how many more or fewer pairs will Cozy Mitts have to sell to continue to generate $100,000 operating income if these changes are made?

Question

Quizplus · Accepted Answer

First, we need to calculate the current sales volume to attain $100,000 operating income:
Profit = Revenue - Total Cost
$100,000 = $125x - $125,000 - $75x
$100,000 = $50x - $125,000
$225,000 = $50x
x = 4,500 pairs
Now, we need to calculate the new variable cost per pair:
New variable cost = $60
New total cost per unit = $60x + $160,000
New revenue per unit = $125
New profit = $125x - $60x - $160,000 - $125,000 = $65x - $285,000
To achieve $100,000 profit:
$100,000 = $65x - $285,000
$385,000 = $65x
x = 5,923 pairs
The difference is 1,423 pairs, which represents 31.6% more units. However, we need to calculate the difference based on the original sales volume:
1,423/4,500 = 0.316
0.316 x 100% = 31.6%
Therefore, Cozy Mitts needs to sell 500 fewer pairs to achieve the same profit level with the new cost structure.

Cozy Mitts Produces Heated Motorcycle Gloves