Break-Even Analysis

The objective of most business enterprises is to make as much profit as possible.  The purpose of break-even analysis is to determine the number of units of a product (the volume) to produce that will equate total revenue with total cost.  At this point, referred to as the break-even point, profit is zero.  The break-even point gives the manager a point of reference in determining how many units will be needed to ensure a profit.

The three components of break-even analysis are volume, cost and profit.

Volume is the level of production by a company.  Volume can be expressed as the number of units (quantity) produced and sold, as the dollar volume of sales or a percentage of total capacity available,

Costs
Two types of costs are typically incurred in the production of a product: fixed costs and variable costs.  Fixed costs are generally independent of the volume of units produced,  That is, fixed costs remain constant regardless of how many units of product are produced within a given range.  The costs of items such as the following, taken together, result in total fixed costs: Rent on plant and equipment, taxes, insurance, management and staff salaries, advertising, interest on investment, depreciation on plant and equipment, heat and light, janitorial services.

Variable costs are determined on a per-unit basis.  Thus, total variable costs depend on the number of units produced.  The costs of the following items are variable costs: raw materials and resources, direct labor, packaging, material and product handling, maintenance, freight

Total variable costs are function of the volume and the variable cost per unit.  This relationship can be expressed mathematically as :
 total variable cost = VCv
where: Cv = variable cost per unit; v = volume (number of units)

The total cost of an operation is computed by summing total fixed cost and total variable cost, as follows:
total cost = total fixed cost + total variable cost or TC = Cf +VCv where Cf = fixed cost

Profit
The third component in our break-even model is profit.  Profit is the difference between total revenue and total cost.  Total revenue is the volume multiplied by the price per unit.

Total revenue = vp where p (price per unit)

Total profit = total revenue - total cost

break - even volume = Cf/p - Cv

break-even sales volume = pv

break-even volume as percentage of capacity = v/k

1.  The Texas Electronics Company produces calculators.  The annual fixed cost of producing calculators is $280,000.  The variable cost of producing a calculator is $8.  The company sells the calculators for $26.  Given an annual volume of 60,000 calculators, determine the total cost, total revenue, profit, break-even volume, and break-even sales volume.  If production capacity is 80,000 calculators, determine the break-even volume as a percentage of capacity.

2. The Willow Furniture produces tables.  The fixed monthly cost of production is $8,000, and the variable cost per table is $65.  The tables sell for $180 apiece.  For a monthly volume of 300 tables, determine the total cost, total revenue, and profit, determine the monthly break-even volume for the Willow Furniture Company operation. Determine the break-even sales volume.

3.  The Retread Tire Company recaps tires.  The fixed annual cost of the recapping operation is $60,000.  The variable cost of the recapping a tire is $9.  The company charges $25 to recap a tire.  For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.  Determine the annual break-even volume.  Determine the break-even sales volume.  If the maximum operating capacity of the Retread Tire Company is 8,000 tires annually, determine the break-even volume as a percentage of capacity.

4.  The Rolling Creek Textile Mill produces cotton denim.  The fixed monthly cost is $21,000, and the variable cost per yard of denim is $0.45.  The mill sells a yard of denim for $1.30.  For a monthly volume of 18,000 yards of denim, determine the total cost, total revenue, and profit.  Determine the monthly break-even volume. If the maximum operating capacity of the Rolling Creek Textile Mill  is 25,000 yards of denim per month, determine the break-even volume as a percentage of capacity.