A firm is selling two products—chairs and bar stools—each at $60 per unit. Chairs have a variable cost of $30, and bar stools $25. The fixed cost for the firm is $20,000.

If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break-even point in dollars of sales? In units of chairs and bar stools?
Note: Round the number of chairs to the nearest whole number BEFORE computing the number of bar stools. Use these rounded breakeven quantities in your calculation for the breakeven point in dollar sales.



To determine the break-even point in both units and dollars, we'll follow these steps:

### 1. Calculate the Contribution Margin per Unit for Each Product:
- **Contribution Margin per Chair** = Selling Price per Chair - Variable Cost per Chair  
  = $60 - $30  
  = $30

- **Contribution Margin per Bar Stool** = Selling Price per Bar Stool - Variable Cost per Bar Stool  
  = $60 - $25  
  = $35

### 2. Determine the Weighted Average Contribution Margin (WACM):
Since the sales mix is 1:1, the contribution margins are weighted equally.

\[
\text{WACM} = \frac{(30 + 35)}{2} = \frac{65}{2} = 32.5
\]

### 3. Calculate the Break-Even Point in Units:
The formula to find the break-even point in units is:

\[
\text{Break-even Units} = \frac{\text{Fixed Costs}}{\text{WACM}} = \frac{20,000}{32.5} \approx 615.38
\]

Since the sales mix is 1:1, you will need to round the units to the nearest whole number for chairs first. Therefore, round **615.38** to **615** chairs.

- **Chairs = 615**
- **Bar Stools** = Since the ratio is 1:1, **Bar Stools = 615**

### 4. Calculate the Break-Even Point in Dollar Sales:
The total sales in dollars is:

\[
\text{Dollar Sales} = (\text{Number of Chairs} \times \text{Price per Chair}) + (\text{Number of Bar Stools} \times \text{Price per Bar Stool})
\]

\[
\text{Dollar Sales} = (615 \times 60) + (615 \times 60) = 36,900 + 36,900 = 73,800
\]

### Final Answers:
- **Break-even Point in Units**:  
  615 chairs and 615 bar stools.

- **Break-even Point in Dollar Sales**:  
  $73,800

Would you like more details on any of these steps, or have any questions?

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**Related Questions:**
1. What would be the break-even point if the sales mix changed to 2 chairs for every bar stool?
2. How would a change in the fixed costs to $25,000 affect the break-even point?
3. What is the impact on the break-even point if the selling price of bar stools increases to $65?
4. How would a 10% increase in variable costs for chairs affect the break-even point?
5. What happens to the break-even point if the contribution margin for bar stools decreases by $5?

**Tip:** Always round unit quantities before performing final calculations for break-even analysis to avoid compounding rounding errors.

A firm is selling two products—chairs and bar stools—each at $60 per unit. Chairs have a variable cost of $30, and bar stools $25. The fixed cost for the firm is $20,000. If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break-even point in dollars of sales? In units of chairs and bar stools? Note: Round the number of chairs to the nearest whole number BEFORE computing the number of bar stools. Use these rounded breakeven quantities in your calculation for the breakeven point in dollar sales.

Calculate the break-even point in units and dollar sales for a firm selling chairs and bar stools at $60 each with variable costs of $30 and $25, respectively. Understand the break-even analysis process using weighted average contribution margin. Suitable for college-level accounting and finance students.

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