Question
A company is currently selling 10,000 units per month of product for $40 per unit. The unit contribution margin is $27. The company believes that spending $50,000 on advertising will increase sales by 750 units per month and enable them to increase the selling price to $45 per unit. If this change is implemented, profits will Blank______.
Multiple choice question.
increase by $74,000
decrease by $29,750
increase by $24,000
increase by $3,750
Multiple choice question.
increase by $74,000
decrease by $29,750
increase by $24,000
increase by $3,750
Answers
GPT-4o mini
To determine the impact on profits from the proposed changes, we need to calculate both the additional contribution margin from the increase in sales and the cost of the advertising.
1. **Current Situation:**
- Units sold: 10,000
- Selling price per unit: $40
- Unit contribution margin: $27
- Total contribution margin: 10,000 units * $27 = $270,000
2. **Proposed Changes:**
- New selling price per unit: $45
- Expected increase in sales: 750 units
- New total units sold: 10,000 + 750 = 10,750
- New total contribution margin per unit: New selling price - Variable cost (which can be derived from the current unit contribution margin and selling price).
The current variable cost per unit can be calculated as:
\[
\text{Current Variable Cost} = \text{Selling Price} - \text{Contribution Margin} = 40 - 27 = 13
\]
The new contribution margin per unit with the increased selling price would be:
\[
\text{New Contribution Margin} = \text{New Selling Price} - \text{Variable Cost} = 45 - 13 = 32
\]
3. **Total Contribution Margin After Changes:**
- Contribution margin for original units (10,000 units): 10,000 units * $32 = $320,000
- Contribution margin for additional units (750 units): 750 units * $32 = $24,000
- Total new contribution margin = $320,000 + $24,000 = $344,000
4. **Advertising Costs:**
- Cost of advertising: $50,000
5. **Change in Profit:**
\[
\text{Change in Profit} = \text{Total New Contribution Margin} - \text{Original Contribution Margin} - \text{Advertising Cost}
\]
Original contribution margin = $270,000,
New contribution margin = $344,000,
Hence,
\[
\text{Change in Profit} = (344,000 - 270,000) - 50,000 = 74,000 - 50,000 = 24,000
\]
Thus, profits will **increase by $24,000.**
The correct answer is **increase by $24,000.**
1. **Current Situation:**
- Units sold: 10,000
- Selling price per unit: $40
- Unit contribution margin: $27
- Total contribution margin: 10,000 units * $27 = $270,000
2. **Proposed Changes:**
- New selling price per unit: $45
- Expected increase in sales: 750 units
- New total units sold: 10,000 + 750 = 10,750
- New total contribution margin per unit: New selling price - Variable cost (which can be derived from the current unit contribution margin and selling price).
The current variable cost per unit can be calculated as:
\[
\text{Current Variable Cost} = \text{Selling Price} - \text{Contribution Margin} = 40 - 27 = 13
\]
The new contribution margin per unit with the increased selling price would be:
\[
\text{New Contribution Margin} = \text{New Selling Price} - \text{Variable Cost} = 45 - 13 = 32
\]
3. **Total Contribution Margin After Changes:**
- Contribution margin for original units (10,000 units): 10,000 units * $32 = $320,000
- Contribution margin for additional units (750 units): 750 units * $32 = $24,000
- Total new contribution margin = $320,000 + $24,000 = $344,000
4. **Advertising Costs:**
- Cost of advertising: $50,000
5. **Change in Profit:**
\[
\text{Change in Profit} = \text{Total New Contribution Margin} - \text{Original Contribution Margin} - \text{Advertising Cost}
\]
Original contribution margin = $270,000,
New contribution margin = $344,000,
Hence,
\[
\text{Change in Profit} = (344,000 - 270,000) - 50,000 = 74,000 - 50,000 = 24,000
\]
Thus, profits will **increase by $24,000.**
The correct answer is **increase by $24,000.**