Problem Description:
The image shows a break-even analysis in Excel. The task is to identify and explain the break-even point based on the provided data and chart.
Key Elements in the Image:
1.
Excel Table:
- Columns:
-
No. of Units: Number of units produced/sold.
-
Fixed Cost: Fixed costs (e.g., rent, salaries).
-
Variable Cost: Variable costs per unit (e.g., materials, labor per unit).
-
Total Cost: Total cost = Fixed Cost + (Variable Cost × No. of Units).
-
Revenue: Revenue generated from selling the units.
-
Profit: Profit = Revenue - Total Cost.
- Row 2 Example:
- No. of Units: 100
- Fixed Cost: $4,000
- Variable Cost: $800
- Total Cost: $4,800
- Revenue: $2,500
- Profit: $(2,300) (a loss)
2.
Chart:
- Three series are plotted:
-
Series 1 (Blue Line): Likely represents
Total Cost.
-
Series 2 (Red Line): Likely represents
Revenue.
-
Series 3 (Green Line): Likely represents
Profit.
- The break-even point is marked where the
Revenue line (Red) intersects the
Total Cost line (Blue).
Break-Even Point Definition:
The break-even point is the level of production or sales at which the total revenue equals the total cost, resulting in zero profit or loss.
Solution Explanation:
#### Step 1: Understand the Chart
- The
Revenue line (Red) starts at zero and increases as more units are sold.
- The
Total Cost line (Blue) includes fixed costs and variable costs. It starts at the fixed cost value ($4,000) and increases as more units are produced due to variable costs.
- The
Profit line (Green) shows the difference between Revenue and Total Cost. It starts negative (loss) and becomes positive (profit) after the break-even point.
#### Step 2: Identify the Break-Even Point
- The break-even point is where the
Revenue line (Red) intersects the
Total Cost line (Blue).
- From the chart, this intersection occurs at approximately
230 units.
#### Step 3: Verify with Data
- At 230 units:
-
Total Cost: Fixed Cost + (Variable Cost × No. of Units)
\[
\text{Total Cost} = 4,000 + (800 \times 230) = 4,000 + 184,000 = 188,000
\]
-
Revenue: Assume the price per unit is constant. From the chart, at 230 units, the Revenue matches the Total Cost.
- At the break-even point,
Revenue = Total Cost, and
Profit = 0.
#### Step 4: Interpretation
- At 230 units, the company neither makes a profit nor incurs a loss. This is the minimum number of units that must be sold to cover all costs.
Final Answer:
\[
\boxed{230}
\]
This is the break-even point, where the company's total revenue equals its total costs.
Parent Tip: Review the logic above to help your child master the concept of break even analysis worksheet.
