The Puzzle Company had total revenue of $4,694,500, total fixed costs of $1,115,000, and total variable costs of $2,332,500. If the company aims to earn a net income of $1,000,000, what total sales volume must it achieve?

Hint: Express your answer as a function of the break-even volume n

To determine the total sales volume needed for the Puzzle Company to achieve a net income of $1,000,000, we can start by calculating the break-even point and then use that to find the required sales volume.

### Step 1: Calculate the Contribution Margin

The contribution margin (CM) per unit is calculated as:

\[
\text{CM} = \text{Total Revenue} - \text{Total Variable Costs}
\]

Given:
- Total Revenue = $4,694,500
- Total Variable Costs = $2,332,500

\[
\text{CM} = 4,694,500 - 2,332,500 = 2,362,000
\]

### Step 2: Calculate the Break-even Point in Sales

The break-even point in sales (n) can be calculated using the formula:

\[
\text{Break-even Sales} = \text{Total Fixed Costs} + \text{Total Variable Costs}
\]

Given:
- Total Fixed Costs = $1,115,000

The break-even point is when total sales equal total costs (fixed + variable):

\[
\text{Break-even Sales} = 1,115,000 + 2,332,500 = 3,447,500
\]

### Step 3: Calculate Required Sales Volume for Desired Net Income

To find the required total sales volume for a net income of $1,000,000, we need to cover both fixed costs and the desired profit:

\[
\text{Required Sales} = \text{Total Fixed Costs} + \text{Total Variable Costs} + \text{Desired Net Income}
\]

So:

\[
\text{Required Sales} = 1,115,000 + 2,332,500 + 1,000,000 = 4,447,500
\]

### Step 4: Express as a Function of Break-even Volume (n)

From the break-even point calculated, we know that:

\[
n = \frac{3,447,500}{\text{Price per Unit}}
\]

The required total sales volume $ S $ can be expressed as:

\[
S = n + \frac{1,000,000}{\text{CM per unit}}
\]

### Conclusion

The total sales volume needed to achieve a net income of $1,000,000 can be expressed in terms of the break-even volume $ n $.

If the contribution margin per unit is needed for a specific numeric answer, please provide the price per unit.

### Questions for Further Exploration:

1. How does the contribution margin affect overall profitability?
2. What strategies could the company employ to increase its contribution margin?
3. What would be the effect on required sales volume if fixed costs increased?
4. How can the company reduce variable costs to improve net income?
5. What are the implications of not reaching the required sales volume?

**Tip:** Always monitor fixed and variable costs closely, as changes can significantly impact your break-even point and profit margins.

The Puzzle Company had total revenue of $4,694,500, total fixed costs of $1,115,000, and total variable costs of $2,332,500. If the company aims to earn a net income of $1,000,000, what total sales volume must it achieve?

Explore how to calculate the total sales volume required for the Puzzle Company to achieve a net income of $1,000,000, considering fixed and variable costs. Detailed steps include contribution margin calculations and break-even analysis.

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