CVP and Breakeven Analyses

6.4 Break-Even Chart

A break-even chart, also known as a break-even analysis or graph, visually represents the relationship between costs, revenue, and profit levels at various levels of sales volume. The chart displays fixed costs, variable costs per unit, total costs, total revenue, and the break-even point (where total revenue equals total costs) on a graph. It helps businesses determine the minimum level of sales needed to cover all expenses and start generating profit. This analysis is crucial for decision-making regarding pricing strategies, production volume, and overall business planning.

 

Example 6.4.1: Creating a Break-Even Chart

Jina’s small business has the capacity to make and sell 200 bags per month. Each bag is sold for $100. The fixed costs are $7000 and the variable cost per bag is $30.

a) Draw a break-even chart showing the total revenue, total costs, and fixed costs lines.

b) Determine the break-even point in volume and sales dollars.

c) Calculate the break-even as a percent of capacity.

Show/Hide Solution

 

a)

Step 1: Let X represent the number of units, and Y represent dollar values. Draw and label the X- and Y-axis. We only need the positive sides of the axes. The intersection of the axes is the origin. The capacity or the maximum quantity is 200 units. Thus, the X-axis should extend to at least 200. The revenue at capacity is $100*200 = $20,000. So the Y-axis should extend to at least 20,000.

Step 2: Draw the fixed costs, which should be a horizontal line parallel to the X-axis starting from point (0, 7000) on the Y-axis.

Step 3: Draw the total revenue and total cost lines.

  • The total revenue function is [asciimath]TR=SP*X=100X[/asciimath]
  • The total cost function is [asciimath]TC=VC*X+FC=30X+7000[/asciimath]

We create a table of values for the function at zero and maximum quantities.

 [asciimath]X[/asciimath]  [asciimath]TR[/asciimath]  [asciimath]TC[/asciimath]
0 0 7000
200 20,000 13,000
  • Locate points (0,0) and A(200,20000) and connect them to form a straight line. That will be the total revenue line.
  • Locate points (0,7000) and B(200,13000) and connect them to form a straight line. That will be the total cost line.

Step 4: Mark the point where the total revenue (TR) and total cost (TC) lines intersect. That is the break-even point.

Break-even chart showing lines for total revenue, total costs, and fixed costs, with a break-even point at 100 units and $10,000. Fixed costs are indicated at $7,000. The chart has a capacity of 200 units, with areas marked for profit above and loss below the break-even point.

b) The X-coordinate of the break-even point is the break-even volume, which is 100 units. The Y-coordinate of the break-even point is the break-even revenue, which is $10,000.

c) Break-even as a percent of capacity [asciimath]= "Break-even volume"/"Capacity" xx 100%[/asciimath]

 [asciimath]=100/200xx100%[/asciimath]

 [asciimath]=50%[/asciimath]

 

Key observations from the Break-even Chart: 

  • If the number of units sold is below the break-even point (100 units), Total Costs (TC) exceed Total Revenue (TR), as indicated by the TC line being above the TR line. This scenario results in a loss.
  • Conversely, when the number of units sold surpasses the break-even point (100 units), Total Revenue (TR) is higher than Total Costs (TC). This is shown by the TR line being above the TC line, indicating a profit.

 

Try an Example

 

 

As we saw in the previous example, a Break-even Chart uses straight lines to demonstrate the relationship between total revenue, total costs, and the fixed cost functions, offering an easy-to-understand visual representation of how these elements interact. Figure 6.4.1 illustrates a typical Break-even Chart that includes all of these components.

 

Example of a break-even chart, depicting two intersecting lines on a graph. The horizontal axis is labeled 'Quantity', and the vertical axis is labeled 'Amount ($)'. One line represents the Total Cost, which begins at a point above the origin and slopes upward, indicating fixed and variable costs. Another line, representing Total Sales Revenue, starts from the origin and slopes upward, reflecting revenue per unit sold. The point where these two lines intersect indicates the break-even point. The third line is a horizontal line that begins where the total cost line starts. This line represents the fixed cost.

Figure 6.4.1: Break-even Chart

 

Here is a breakdown of the key components of a Break-even Chart:

  • X-axis (Horizontal): Represents the number of units produced and sold (sales volume).
  • Y-axis (Vertical): Represents the dollar amount of revenue and costs.
  • Total Revenue Line: Starts from the origin and slopes upward. Its slope represents the selling price per unit (SP). As sales volume increases, the total revenue increases linearly.
  • Fixed Costs Line: This is a straight, horizontal line that runs parallel to the X-axis because fixed costs stay the same regardless of the quantity produced.
  • Total Cost Line: This begins at a point equivalent to the fixed costs (since fixed costs are incurred even when no units are produced) and slopes upward. Its slope represents the variable costs per unit (VC), and its y-intercept equals the fixed costs. The increase in the production volume leads to an increase in total cost.
  • Break-even Point: The point where the Total Revenue Line intersects the Total Cost Line. At this point, the business neither makes a profit nor incurs a loss. The X-coordinate of this point gives the number of units that need to be sold to break even ([asciimath]X_B[/asciimath]), while the Y-coordinate gives the corresponding dollar amount of sales or revenue ([asciimath]TR_B[/asciimath]).
  • Profit Area: The space between the Total Revenue Line and the Total Cost Line above the break-even point; when the number of items produced exceeds the break-even volume, the total revenue surpasses total costs, leading to a profit.
  • Loss Area: The space between the Total Revenue Line and the Total Cost Line below the break-even point; when the number of items produced is below the break-even volume, the total revenue falls short of total costs, causing a loss.

A break-even chart provides a visual tool for businesses to quickly assess the impact of changes in costs, prices, and other variables on their profitability. It’s particularly useful for understanding how variations in sales volume can affect profit or loss situations.

 

Example 6.4.2: CVP Analysis Given the Break-Even Chart

A break-even chart of a certain product is given below. Use the chart to answer the following questions.

a) What is the break-even volume?

b) What is the revenue at break-even?

c) How much are the fixed costs?

d) What is the unit selling price?

e) What is the unit variable cost?

f) What is the amount of the profit or loss if 80 units are produced and sold?

Break-even chart with three distinct lines: Total Cost, Total Sales Revenue, and Fixed Costs. The horizontal axis is labeled 'Quantity,' with a maximum indicated capacity of 100 units, and the vertical axis is labeled 'Amounts,' extending up to $6,000. The Fixed Costs line is horizontal, representing a constant $3,000 across all unit sales. The Total Cost line starts from this fixed cost point and slopes upward, indicating the addition of variable costs per unit. The Total Sales Revenue line, originating from the graph's origin, rises steeply, showing increasing revenue with each unit sold. The intersection of the Total Cost and Total Sales Revenue lines is marked at the coordinate (60, $3,600). At full capacity of 100 units, the Total Revenue line reaches $6,000.

Show/Hide Solution

 

a) The break-even point is the intersection of the total revenue (TR) and the total costs (TC) lines. This point has the coordinates of (60,3600). The X-coordinate of the break-even point is the volume at break-even. So [asciimath]X_B=60[/asciimath] units.
b) The Y-coordinate of the break-even point is the revenue or sales at break-even. So [asciimath]TR_B=$3600.[/asciimath]
c) The fixed costs amount is the y-intercept of the total costs or the fixed costs line, which is 3000. So [asciimath]FC=$3000[/asciimath].
d) Given that the total revenue (TR) line is represented by the equation [asciimath]TR = SP * X[/asciimath], and knowing that the break-even point (60,3600) lies on this TR line, we can plug in the coordinates of the break-even point into the TR equation and solve for unit selling price (SP).

 [asciimath]TR=SP*X[/asciimath]

 [asciimath]3600=SP(60)[/asciimath]

 [asciimath]SP=3600/60[/asciimath]

 [asciimath]SP=$60[/asciimath]

e) Given that the total costs (TC) line is represented by the equation [asciimath]TC = VC * X+FC[/asciimath], and knowing that the break-even point (60,3600) also lies on the TC line, we can use the fixed costs amount (FC = $3000) and the coordinates of the break-even point to solve for the unit variable cost (VC).

 [asciimath]TC = VC * X+FC[/asciimath]

[asciimath]3600 = VC(60)+3000[/asciimath]

[asciimath]3600-3000=60VC[/asciimath]

[asciimath]600=60VC[/asciimath]

[asciimath]VC=$10[/asciimath]

f)

Graphically: To determine the net income when X = 80 units, draw a vertical line at the 80-unit mark. Where this line intersects the TC (Point A) and TR (Point B) lines will give us the corresponding revenues and costs. The Y-value at the intersection with the TR line shows the total revenue is $4800 for 80 units. The Y-value at the intersection with the TC line indicates the total cost is $3800 for 80 units. The net income is the difference between these two values.

Diagram illustrating how to find net income from a break-even chart at X = 80 units. A vertical line is drawn at the 80-unit mark intersecting the Total Cost (TC) line at Point A and the Total Revenue (TR) line at Point B. The intersection with the TR line indicates total revenue of $4,800 for 80 units, while the intersection with the TC line shows total costs of $3,800 for the same quantity. Net income, calculated as the difference between total revenue and total costs, is depicted visually.

[asciimath]NI = TR-TC[/asciimath]

[asciimath]=4800-3800[/asciimath]

 [asciimath]=$1000[/asciimath] Profit

Algebraically: Given we have the values for unit selling price (SP = $60), variable cost (VC = $10), fixed costs (FC = $3000), and quantity (X = 80), we can use Formula 6.6a to find the net income (NI):

[asciimath]NI=SP*X-(VC*X+FC)[/asciimath]

 [asciimath]=60(80)-(10(80)+3000)[/asciimath]

[asciimath]=4800-(800+3000)[/asciimath]

[asciimath]=$1000[/asciimath] Profit

 

Try an Example

 

Section 6.4 Exercises

  1. break-even chart of a certain product is given below. Use the chart to answer the following questions. a) What is the break-even volume? b) What is the revenue at break-even? c) How much are the fixed costs? d) What is the unit selling price? e) What is the unit variable cost? f) What is the net income if 105 units are produced and sold?Break-even chart featuring three distinct lines: Total Cost, Total Revenue, and Fixed Costs. The horizontal axis, labeled 'Quantity,' shows a scale up to 135 units, while the vertical axis, labeled 'Amounts,' extends to $10,800. The Fixed Costs line runs horizontally across the graph at $4,125, indicating this cost remains constant regardless of units sold. The Total Cost line begins at the fixed cost level of $4,125 and slopes upward, reflecting increasing variable costs with each additional unit. In contrast, the Total Sales Revenue line starts from the origin and ascends more steeply, illustrating rising revenue for each unit sold. The Total Cost and Total Sales Revenue lines intersect at the coordinate (75, $6,000). Also, two points are highlighted: Point A at (105, $6,750) on the Total Cost line, and Point B at (105, $8,400) on the Total Revenue line, representing specific cost and revenue values at 105 units.
    Show/Hide Answer

     

    a) X = 75 Units

    b) TR = $6000

    c) FC = $4125

    d) SP = $80

    e) VC = $25

    f) NI = $1650

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