Break-even analysis examines the costs and revenues of a product to determine the quantity that needs to be sold to break even. It can be used to compare different production options and determine the best scenario. The analysis involves calculating fixed and variable costs to find the break-even point and profit levels using algebraic equations or graphical displays. It is an important tool for deciding whether a product or production method will be cost effective.
Acronyms and terms (Horngren “Cost Accounting” p. 63) Unit selling price: The price received by the manufacture per unit sold. Unit variable cost: Cost that change in proportion to the changes in the level of activity. Fixed cost: Cost that remain unchanged over a given period regardless of the change in activity.
Operating income:Total revenues from operation minus cost of goods sold and operating cost. Total revenue: Total revenue that a company takes in. Total cost: All cost related to the companies operations.
Total cost line is a linear line based on the equation: y = VC*Q + FC y = $5Q + $25,000 Total revenue line is a linear line based on the equation y = USP * Q y = $10 * Q Break-even point is where TR = TC.
Any quantity sold in the red colored region will produce a loss, while any quantity in the green region will produce a positive cash flow
Equation (Russel “Operational Management” p.240)
The first step in finding out which process and/or machine is preferred is to find out the break-even point of each option.
By analyzing the break-even analysis we can see that a quantity demanded of less than 600 units would produce a loss for both Machine A and Machine B.
Point of indifference identifies the quantity demanded amount where either machine (or process) will suffice. Below the point of indifference Machine A will be a good choice. The reason is that the fixed cost is lower and for smaller quantities demanded Machine A will cost less to operate. Above the point of indifference Machine B will be the best choice. The reason is that the variable cost is lower and for larger quantities demanded Machine B will cost less to operate.
The solution procedure for selecting the correct machine and/or process. Formulate a total cost equation for each variable. Calculate the point of indifference. Above the point of indifference choose the alternative with the lowest variable cost. Below the point of indifference choose the alternative with the lowest fixed cost.
The Machine A line is a linear line based on the equation: y = UVC*Q + FC y = $5Q + $3,000 The Machine B line is a linear line based on the equation y = UVC * Q + FC y = $2 * Q + $8,000 *The higher the VC the steeper the slope.
Red filled area is when neither machine should be purchased. The red area represents the quantity demanded between 0 and 600. Pink filled area is when Machine A should be purchased. The pink area represents quantity demanded between 600 and 1667. Green filled area is when Machine B should be purchased. The green area represents the quantities demanded of 1667 and above.
Company ABC will break even when they sell 5000 units of their widgets.
If answer is not a whole number then round to the nearest dollar.
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