Lotts Company produces and sells one product. The selling price is $10, and the
unit variable cost is $6. Total fixed costs are $10,000.
Required
1. Prepare a CVP graph with “Units Sold” as the horizontal axis and “Dollars” 
as the vertical axis. Label the break-even point on the horizontal axis.
2. Prepare CVP graphs for each of the following independent scenarios:
a. Fixed costs increase by $5,000.
b. Unit variable cost increases to $7.
c. Unit selling price increases to $12.
d. Assume that fixed costs increase by $5,000 and unit variable cost is $7.
3. Prepare a profit-volume graph using the original data. Repeat, following the scenarios in Requirement 2.
4. Which of the two graphs do you think provides more information? Why?

Let's work through this step by step, starting with the requested Cost-Volume-Profit (CVP) graphs and profit-volume graphs.

### 1. **CVP Graph for the Original Data**
- **Selling price** = $10 per unit
- **Variable cost** = $6 per unit
- **Fixed costs** = $10,000

The CVP graph will have the following characteristics:
- **Horizontal axis**: Units sold
- **Vertical axis**: Dollars
- **Break-even point**: This is where total revenue equals total cost (fixed + variable costs).

The formula for the **break-even point** in units is:

\[
\text{Break-even units} = \frac{\text{Fixed Costs}}{\text{Selling Price} - \text{Variable Cost per unit}} = \frac{10,000}{10 - 6} = 2,500 \text{ units}
\]

To create the CVP graph:
- Draw a horizontal line at $10,000 to represent fixed costs.
- Plot the total cost line starting from $10,000 with a slope of $6 per unit sold.
- Plot the total revenue line starting from zero with a slope of $10 per unit sold.
- Mark the break-even point where total revenue equals total cost.

### 2. **CVP Graphs for Independent Scenarios**
For each scenario, we will adjust the variables accordingly and create a new break-even point.

#### a. **Fixed costs increase by $5,000**
- **Fixed costs** = $15,000
- **Selling price** = $10
- **Variable cost** = $6

Break-even units:
\[
\text{Break-even units} = \frac{15,000}{10 - 6} = 3,750 \text{ units}
\]

#### b. **Unit variable cost increases to $7**
- **Fixed costs** = $10,000
- **Selling price** = $10
- **Variable cost** = $7

Break-even units:
\[
\text{Break-even units} = \frac{10,000}{10 - 7} = 3,333.33 \text{ units}
\]

#### c. **Unit selling price increases to $12**
- **Fixed costs** = $10,000
- **Selling price** = $12
- **Variable cost** = $6

Break-even units:
\[
\text{Break-even units} = \frac{10,000}{12 - 6} = 1,666.67 \text{ units}
\]

#### d. **Fixed costs increase by $5,000 and unit variable cost is $7**
- **Fixed costs** = $15,000
- **Selling price** = $10
- **Variable cost** = $7

Break-even units:
\[
\text{Break-even units} = \frac{15,000}{10 - 7} = 5,000 \text{ units}
\]

### 3. **Profit-Volume Graphs**
A profit-volume graph plots profit (not total revenue and cost) against the number of units sold.

#### **Original Data Profit Formula:**
Profit = (Selling Price - Variable Cost) × Units - Fixed Costs

So, the profit equation for the original data is:
\[
\text{Profit} = (10 - 6) \times \text{Units} - 10,000 = 4 \times \text{Units} - 10,000
\]

#### Profit at the break-even point:
\[
\text{Profit at } 2,500 \text{ units} = 4 \times 2,500 - 10,000 = 0
\]

Now, we will use the same approach for the scenarios provided:
- **Scenario a:** Profit = 4 × Units - 15,000
- **Scenario b:** Profit = 3 × Units - 10,000
- **Scenario c:** Profit = 6 × Units - 10,000
- **Scenario d:** Profit = 3 × Units - 15,000

### 4. **Which Graph Provides More Information?**
- The **CVP graph** shows both revenue and cost lines, which help in visualizing the total cost structure, break-even point, and safety margin.
- The **profit-volume graph** directly illustrates how profit varies with sales, which can be more straightforward when the focus is solely on profitability.

In conclusion:
- The **CVP graph** provides more comprehensive information because it shows the relationship between total revenue, total cost, and profit. 
- The **profit-volume graph** is simpler for tracking profits but doesn't offer insights into cost behavior or the structure of fixed and variable costs.

Would you like to see a plotted version of these graphs?

Lotts Company produces and sells one product. The selling price is $10, and the unit variable cost is $6. Total fixed costs are $10,000. Required 1. Prepare a CVP graph with 'Units Sold' as the horizontal axis and 'Dollars' as the vertical axis. Label the break-even point on the horizontal axis. 2. Prepare CVP graphs for each of the following independent scenarios: a. Fixed costs increase by $5,000. b. Unit variable cost increases to $7. c. Unit selling price increases to $12. d. Assume that fixed costs increase by $5,000 and unit variable cost is $7. 3. Prepare a profit-volume graph using the original data. Repeat, following the scenarios in Requirement 2. 4. Which of the two graphs do you think provides more information? Why?

Explore the Cost-Volume-Profit (CVP) analysis for Lotts Company with a selling price of $10 and variable cost of $6 per unit. Learn to calculate the break-even point and see how changes in fixed costs, variable costs, and selling prices affect the graph. Includes scenarios such as fixed costs increase and unit price adjustments. Suitable for college-level business students.

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