Questions: Daimler Inc. sells a product for 75 per unit. The variable cost is 50 per unit, while fixed costs are 5,400,000. Determine (a) the break-even point in sales units and (b) the break-even point if the selling price were increased to 80 per unit a. Break-even point in sales units units b. Break-even point if the selling price were increased to 80 per unit units

Daimler Inc. sells a product for 75 per unit. The variable cost is 50 per unit, while fixed costs are 5,400,000. Determine (a) the break-even point in sales units and (b) the break-even point if the selling price were increased to 80 per unit a. Break-even point in sales units units b. Break-even point if the selling price were increased to 80 per unit units
Transcript text: Daimler Inc. sells a product for $\$ 75$ per unit. The variable cost is $\$ 50$ per unit, while fixed costs are $\$ 5,400,000$. Determine (a) the break-even point in sales units and (b) the break-even point if the selling price were increased to $\$ 80$ per unit a. Break-even point in sales units $\square$ units b. Break-even point if the selling price were increased to $\$ 80$ per unit $\square$ units
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Solution

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Solution Steps

To determine the break-even point in sales units, we need to calculate the point at which total revenue equals total costs (both fixed and variable). The formula for the break-even point in units is given by:

\[ \text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \]

We will use this formula to calculate the break-even point for both scenarios: (a) with the original selling price of $75 per unit, and (b) with the increased selling price of $80 per unit.

Solution Approach
  1. Calculate the break-even point in units using the original selling price of $75.
  2. Calculate the break-even point in units using the increased selling price of $80.
Step 1: Calculate Break-even Point with Original Selling Price

To find the break-even point in sales units with the original selling price of \( \$75 \), we use the formula:

\[ \text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \]

Substituting the values:

\[ \text{Break-even point (units)} = \frac{5400000}{75 - 50} = \frac{5400000}{25} = 216000 \]

Step 2: Calculate Break-even Point with Increased Selling Price

Next, we calculate the break-even point in sales units if the selling price is increased to \( \$80 \):

\[ \text{Break-even point (units)} = \frac{5400000}{80 - 50} = \frac{5400000}{30} = 180000 \]

Final Answer

The break-even points are:

  • (a) \( \boxed{216000} \) units
  • (b) \( \boxed{180000} \) units
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