Questions: You've opened a retail store selling hoodies. Given total fixed costs of 200,000, unit variable cost of 9, and hoodie selling price of 59, what volume is necessary to break even?

You've opened a retail store selling hoodies. Given total fixed costs of 200,000, unit variable cost of 9, and hoodie selling price of 59, what volume is necessary to break even?

Transcript text: You've opened a retail store selling hoodies. Given total fixed costs of $\$ 200,000$, unit variable cost of $\$ 9$, and hoodie selling price of $\$ 59$, what volume is necessary to break even? 400,000 22,222 3,390 4,000

Solution

Solution Steps

To find the break-even volume, we need to determine the number of hoodies that must be sold to cover both fixed and variable costs. The break-even point is where total revenue equals total costs. The formula for the break-even volume is:

\[ \text{Break-even volume} = \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \]

Step 1: Identify the Given Values

We are given the following values:

Total fixed costs: $ \$200,000 $
Unit variable cost: $ \$9 $
Hoodie selling price: $ \$59 $

Step 2: Set Up the Break-Even Formula

The break-even volume can be calculated using the formula: \[ \text{Break-even volume} = \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \]

Step 3: Substitute the Given Values into the Formula

Substitute the given values into the formula: \[ \text{Break-even volume} = \frac{200,000}{59 - 9} \]

Step 4: Simplify the Expression

Simplify the expression inside the denominator: \[ 59 - 9 = 50 \]

Step 5: Calculate the Break-Even Volume

Now, calculate the break-even volume: \[ \text{Break-even volume} = \frac{200,000}{50} = 4,000 \]