244 13. 7.5 Graphical Approach to CVP Analysis (Break-Even Chart) A break-even chart is a graphical representation of the following on the same axes: 1. Fixed costs 2. Total costs at various levels of quantity produced 3. Total revenue at various levels of quantity sold The vertical axis (Y-axis) of the graph represents total cost or total revenue (in dollars) and the horizontal axis (X-axis) of the graph represents quantity of items produced or sold (in number of units). These graphs are useful tools in break-even analysis and make it easy to observe how total costs and total revenue change with the quantity produced and sold. It also makes it easy to see at which point neither profit is made nor loss is incurred in the business (i.e., break-even point) and the amount of profit or loss if the quantity produced and sold is known. Exhibit 7.5: Graph of Total Costs vs. Quantity Produced and Total Revenue vs. Quantity Sold The quantity produced and sold above the breakeven volume will result in a profit for a business while that below the break-even volume will result in a loss. As sales increase, net income becomes less negative until it equals zero (NI = 0). At this point, it reaches the break-even point. The intersection point of the two graphs represents the break-even point, where the total revenue and the total costs from the business are equal. Therefore, sales before the break-even point would result in a negative net income (NI < 0) indicating a loss, while sales after the break-even point will result in a positive net income (NI > 0), indicating a profit.
245 Creating and Understanding a Break-Even Chart Step I: Drawing and labelling the X-axis and Y-axis Draw a horizontal axis (X-axis) to represent the quantity (x) produced and sold. Use a suitable scale with equal incremental markings from 0 to the maximum quantity. Label the X-axis as "Quantity (x)". Draw a vertical axis (Y-axis) to represent the Total Revenue (TR) or Total costs (TC). Use a suitable scale and equal incremental markings from 0 to the maximum total revenue. Label the Y-axis as "Amount ($)". Mark the Point "O" where the X-axis and Y-axis intersect each other. The point "O" is the origin with co-ordinates (0, 0). Step II: Drawing the Fixed Costs Line Determine the Fixed Costs (FC) and mark a point "A" to represent this amount on the Y-axis. Through this point, draw a line "AB" parallel to X-axis. This is the "Fixed Costs line". Step III: Drawing the Total Revenue Line and Total Costs Line The Total Revenue function, TR = S x, is a linear function represented by line OC. The Total Costs function, TC = (VC x) + FC, is a linear function represented by line AD. Create a table of values by choosing the two end points (x = 0 and x = maximum quantity) and their corresponding TR and TC values to draw the two lines. To confirm the linearity of each line include another value for x between the two points (as a test point) in the table of values. Step IV: Determining the break-even point, break-even volume, break-even revenue, and the profit and loss areas The point "E", where the Total Revenue line (OC) and the Total Cost line (AD) intersect is the break-even point, where there is neither profit nor loss. The break-even volume is the x-coordinate of the break-even point E. The break-even revenue is the y-coordinate of the break-even point E. Any quantity produced and sold greater than the break-even volume will generate a profit. The profit area is the section ECD, where the Total Revenue line (OC) is above the Total Costs line (AD). The amount of profit for any quantity above the break even volume is represented by the vertical distance between the two lines EC and ED. Any quantity produced and sold less than the break-even volume will generate a loss. The loss area is the section OAE, where the Total Revenue line (OC) is below the Total Cost line (AD). The amount of loss for any quantity below the break even volume is represented by the vertical distance between the two lines AE and OE. Example 7.5 (a) Creating a Break-Even Chart, Determining Break-Even Revenue and Break-Even Volume, and Computing Break-Even as Percent of Capacity (Maximum Quantity) Johnathan's company has a capacity to produce and sell 300 chairs per month. The fixed costs are $5000 per month, variable costs are $30 per chair, and selling price is $70 per chair. (i) Draw a detailed break-even chart showing the fixed costs line, total costs line, total revenue line, break-even point, and (ii) Determine the break-even volume and break-even revenue, and compute the break-even as a percent of the Step I: Draw the X-axis and Y-axis as explained earlier. Step II: Drawing the Fixed Costs Line Draw the horizontal line (AB) from A (0, 5000) to represent the Fixed Costs line. Step III: Drawing the Total Revenue Line and Total Costs Line
246 continued. Graph the following linear functions: Total Revenue function, TR = S x = 70 x Total Costs function, TC = (VC x) + FC = (30 x) + 5000 Create a table of values when x = 0 and 300 (maximum quantity) and choose x = 100 (any number in between) as the third point. x 0 100 300 TR 0 7000 21,000 TC 5000 8000 14,000 Using these coordinates, construct OC to represent the Total Revenue line and AD to represent the Total Costs line. (ii) Determining the break-even volume The x-coordinate of the break-even point (E) is 125. Therefore, the break-even volume is 125 chairs. Determining the break-even revenue The y-coordinate of the break-even point (E) is $8750. Therefore, the break-even revenue is $8750. Computing the break-even as a percent of the capacity Break-even volume Break-even as a percent of capacity = Capacity = 125 # 100% = 41.67% 300 Therefore, the break-even as a percent of capacity is 41.67%. Example 7.5 (b) Using Break-Even Charts for CVP Analysis Answer the following referring to Example 7.5(a). (i) What was the amount of profit or loss if 210 chairs were produced and sold in a month? (ii) What was the amount of profit or loss if 60 chairs were produced and sold in a month? (iii) What is the maximum profit that can be expected in a month?
247 (i) Determining the amount of profit or loss if 210 chairs were produced and sold in a month If 210 chairs were produced and sold, then this was 85 chairs above the break-even volume of 125 chairs per month; therefore, a profit was made. The amount of profit is calculated by subtracting the value for the y-coordinate in line AD (i.e., TC), from the y-coordinate in line OC (i.e., TR), when x = 210. When x = 210, TR = $14,700, and TC = $11,300 TR - TC = 14,700-11,300 = $3400 Therefore, a profit of $3400 was made by producing and selling 210 chairs in a month. (ii) Determining the profit or loss made if 60 chairs were produced and sold in a month If 60 chairs were produced and sold, then this was 65 chairs below the break-even volume of 125 chairs per month; therefore, a loss was incurred. The amount of loss is calculated by subtracting the value for the y-coordinate in line AD (i.e., TC), from the y-coordinate in line OC (i.e., TR), when x = 60. When x = 60, TR = $4200, and TC = $6800 TR - TC = 4200-6800 = - $2600 Therefore, a loss of $2600 was made by producing and selling 60 chairs in a month. (iii) Determining the maximum profit that can be expected in a month Maximum profit can be expected at capacity, i.e., when x = 300. This is 175 chairs above the break-even volume of 125 chairs per month. The amount of profit is calculated by subtracting the value for the y-coordinate in line AD (i.e., TC), from the y-coordinate in line OC (i.e., TR), when x = 300. When x = 300, TR = 21,000 and TC = 14,000 TR - TC = 21,000-14,000 = $7000 Therefore, $7000.00 would be the maximum profit per month that can be expected.
248 Example 7.5 (c) Using Break-Even Charts for CVP Analysis when FC, VC, and S Change Answer the following referring to Example 7.5(a). If the fixed costs increased by 20% per month, variable costs increased by $10 per chair, and Jonathan increased the selling price per chair to $80, determine the new break-even volume and new break-even revenue. New FC = $5000(1 + 0.20) = $6000 per month New VC = $40 per unit New S = $80 per unit Creating the new break-even chart Drawing the New Fixed Cost Line Draw the new horizontal line (AB) from A (0, 6000) to represent the New Fixed Cost line. Drawing the New Total Revenue Line and New Total Cost Line Graph the following linear functions: Total Revenue function, TR = S x = 80 x Total Costs function TC = (VC x) + FC = (40 x) + 6000 Create a table of values when x = 0 and 300 (maximum quantity) and choose x = 100 (any number in between) as the third point. x 0 100 300 TR 0 8000 24,000 TC 6000 10,000 18,000 Using these coordinates, construct OC to represent the New Total Revenue line and AD to represent the New Total Cost line. Determining the new break-even volume The x-coordinate of the break-even point (E) is 150. Therefore, the break-even volume is 150 chairs. Determining the new break-even revenue The y-coordinate of the break-even point (E) is $12,000. Therefore, the break-even revenue is $12,000.
249 7.5 Exercises Answers to the odd-numbered problems are available at the end of the textbook 1. The market research for the production and sale of a new pair of boots indicates that it can be sold for $185 per pair. The cost details are as follows: variable costs: $95 per pair, fixed costs: $8100 per period, and production capacity: 180 pairs per period. point, and b. Determine the break-even volume and break-even revenue, and compute the break-even as a percent of the production 2. The market research for the production and sale of a new dress indicates that it can be sold for $175 per dress. The cost details are as follows: variable costs: $85 per dress, fixed costs: $7200 per period, and production capacity: 300 units per period. point, and production 3. Chenkowski Motors was selling an automotive component for $170 per unit. The cost details are as follows: variable costs: $80 per unit, fixed costs: $6300 per period, and production capacity: 190 units per period. production c. What was the amount of profit or loss if 50 components were sold in a period? d. What is the maximum profit that can be expected in a period? 4. An electronics manufacturer was selling an electronic gadget for $155 per unit. The cost details are as follows: variable costs: $65 per unit, fixed costs: $7200 per period, and production capacity: 250 units per period. production c. What was the amount of profit or loss if 150 gadgets were sold in a period? d. What is the maximum profit that can be expected in a period? 5. A firm manufactures a product which sells for $12 per unit. The variable costs consist of two parts: the variable manufacturing costs are $6 per unit and the variable selling costs are $1.50 per unit. The fixed costs are $2475 for the period. The capacity is 1500 units per period. c. What is the new break-even point in units if the fixed costs are increased by $1095 in a period and the variable manufacturing costs per unit are decreased by 10%?
250 6. A machine manufacturing firm sells a small component for $25 per unit. The variable costs consist of two parts: the variable manufacturing cost is $12.50 per unit and the selling cost is $2.50 per unit. The fixed cost for the period is $3600. The capacity is 600 units per period. point, and c. What is the new break-even point in units if the fixed costs are decreased by $625 in a period and the variable manufacturing costs per unit are increased by 10%? 7. A new product can be sold for $165 according to market research. The variable costs are $90 per unit, fixed costs are $8625 per period, and the production capacity is 475 units. point, and c. What is the new break-even point in units when the selling price is decreased by $5 and the fixed costs per period are increased to $10,150? 8. A new product can be sold for $175 according to market research. The variable costs are $95 per unit, the fixed costs are $9600 per period, and the capacity is 520 units. c. What is the new break-even point in units when the selling price is decreased by $5 and the fixed costs per period are increased to $10,875? 9. A publisher sells a new travel book for $65 per book. The fixed costs are $37,000 per year, publishing costs per book are $40, and the royalty paid to the author is 10% of the selling price per book. The publisher has a capacity to sell 10,000 books in a year. c. If the fixed costs increased by 20% per year, publishing costs increased by $5 per book, and the publisher increased the selling price per book to $80, determine the new break-even volume and new break-even revenue. 10. A new cookbook is being sold for $25 each. The publisher s fixed costs are $25,500 per year, publishing costs are $14 per book, and the royalty paid to the author is 10% of the selling price. The publisher has a capacity to sell 12,000 books in a year. c. If the fixed costs increased by 15% per year, publishing costs increased by $6 per book, and the publisher increased the selling price per book to $30, determine the new break-even volume and new break-even revenue.