Break-Even Analysis

  • Identify fixed and variable costs;

  • Perform break-even analysis to calculate break-even quantity.

  • Calculate required quantity to be manufactured to obtain certain profit (or to limit loss).

A breakeven analysis is used to determine how much sales volume your business needs to start making a profit.The breakeven analysis is especially useful when you’re developing a pricing strategy, either as part of a marketing plan or a business plan.

To conduct a breakeven analysis, use this formula:

\[\mathrm{BEQ} = \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\]

 

Fixed Cost

  • Fixed costs are costs that must be paid whether or not any units are produced. These costs are ’fixed’ over a specified period of time or range of production. e.g. cost of land, machinery and permits.

Variable Cost

  • Variable costs are costs that vary directly with the number of products produced. For instance, the cost of the materials needed and the labour used is directly proportional to the quantity manufactured.

  • In the above diagram, the fixed costs will always be represented by horizontal straight line (parallel to quantity axis) as it is independent of quantity.

  • The variable cost will always pass through the origin as no manufactured units means no variable cost.

Total Cost

  • The total cost is addition of fixed cost and variable cost. It will be represented by a line having same slope as that of variable cost. However, it will be ’lifted up’ by an amount equal to fixed cost. Which means the y-intercept of total cost line is always equal to fixed cost.

Revenue

  • Revenue line will be similar to variable cost line, passing through origin. However, its slope will be greater that that of variable cost.

Break-Even Point

  • Break-Even Point (BEP) is the intersection point of total cost and revenue.

Limitations:

Break-even analysis is only a supply side (i.e. costs only) analysis, as it tells you nothing about what sales are actually likely to be for the product at these various prices. It assumes that fixed costs (FC) are constant. Although, this is true in the short run, an increase in the scale of production is likely to cause fixed costs to rise.
Some fixed costs are not truly independent of quantities. e.g. a company may buy one machine initially but if the quantity increases then it may purchase another machine. In this scenario, the fixed cost may not be a straight line, but will be a step function showing sudden increase(step) at the quantity where additional machine is purchased.

Solved Examples

Solved Example:

17-3-01

Before break-even point, a company will have:

Solution:
Break-even point gives you minimum quantity to be manufactured so that the company will start earning profit. This means after break-even point, the company will have profit. Before that company will experience a loss.

Correct Answer: B

Solved Example:

17-3-02

The breakeven point is obtained at intersection of:

Solution:
Refer the above figure. At break-even quantity, there is no profit or no loss, which means revenues are equal to total cost. Hence, break even point is at the intersection of total revenue and total cost.

Correct Answer: A

Solved Example:

17-3-03

At breakeven point:

Solution:
At break-even quantity, there is no profit or no loss, which means revenues are equal to total cost.

Correct Answer: A

Solved Example:

17-3-04

Break-even analysis requires costs to be categorized as:

Solution:

Depending upon whether the costs vary based upon quantity, the costs can be divided into two categories, fixed and variable.
Fixed cost (FC): It is a cost that does not change with an increase or decrease in the amount of goods or services produced. Fixed costs are expenses that have to be paid by a company, independent of any business activity. For example:

  1. Initial investment made by the company in making plant and building, purchasing machinery and equipment etc. Rent. This is a periodic charge for the use of real estate owned by a landlord.

  2. Salaries. This is a fixed compensation amount paid to employees, irrespective of their hours worked.

  3. Utilities. This is the cost of electricity, gas, phones, and so forth. This cost has a variable element, but is largely fixed.

Variable Cost (VC): Variable cost line has a positive or upward slop starting from origin that indicates the effect of increasing variable expenses with the increase in production.
Variable costs are those that respond directly and proportionately to changes in product produced. For example:

  1. Direct raw materials. The most purely variable cost of all, are the raw materials that go into a product.

  2. Piece rate labor. This is the amount paid to workers for every unit completed.

  3. Production supplies. Things like machinery oil are consumed based on the amount of machinery usage, so these costs vary with production volume.

  4. Shipping cost: A business incurs a shipping cost only when it sells and ships out a product. Thus, freight out can be considered a variable cost.

Correct Answer: A

Solved Example:

17-3-05

In break-even analysis, if fixed costs are increased, then:

Solution:
If fixed costs are increased, then total costs will also increase. Hence the intersection point between total costs and sales revenue will also shift towards right.

Correct Answer: A

Solved Example:

17-3-06

In a graph of break even analysis, revenues are represented by:

Solution:

In a graph of break-even analysis,

  • Fixed costs are represented by a horizontal straight line with y-intercept equal to fixed costs.

  • Variable costs are represented by an inclined straight line passing through origin.

  • Total costs are represented by an inclined straight line having same slope as variable cost line but with a y-intercept equal to fixed costs.

  • Sales revenues are represented by an inclined straight line passing through origin, but its slope is more than slope of variable cost line.

Correct Answer: A

Solved Example:

17-3-07

The quantity required to have desired profit is:

Solution:
The required quantity should be able to recover fixed cost AND be able to give you profit, so it is total of both. Since each unit gives you contribution (net profit = sales price - variable cost), the required quantity will be ratio of them.

Correct Answer: A

Solved Example:

17-3-08

An industry is selling a product for \$10 per unit. The fixed cost for assets is \$40000 with variable cost of \$6 per unit. How many units should be produced to break even?

Solution:
Break Even Quantity (BEQ) is given by, \begin{align*} \mathrm{BEQ} &= \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\\ &= \dfrac{40000}{10-6}\\ &=10000 \end{align*}

Correct Answer: B

Solved Example:

17-3-09

You are opening a whiteboard marker factory, which requires fixed cost of \$14,500. Each marker will cost you \$0.60, and would sell for \$1.5 each. How many markers must be sold to realize a profit of \$1,450?

Solution:
\begin{align*} \mathrm{BEQ} &= \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\\ &= \dfrac{14500}{1.5-0.60}\\ &= 16111 \end{align*} Any sales after break even quantity generates profit. To get \$1450 profit, $\dfrac{1450}{1.5-0.6}$ = 1611 additional markers must be sold. Hence, total quantity to be sold = 16111+1611= 17722

Correct Answer: C

Solved Example:

17-3-10

Consider the following data projected for the year:

  • Selling price/unit: $14

  • Variable Cost/unit: $5 (this was for labor, materials and overhead required)

  • Fixed Costs: $100,000/year (rent, insurance, and other costs that do not depend on volume)

  • Projected volume: 70,000 units (sales based on previous year sales)

Calculate the break-even volume using the data above.

Solution:
BEP = $\dfrac{100000}{14-5}= 11,111$

Correct Answer: A

Solved Example:

17-3-11

A graphical device used to determine the break-even point and profit potential under varying conditions of output and costs, is known as:

Solution:

Let us look at the options individually.

  • A Gantt chart is a type of bar chart, that illustrates a project schedule. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project.

  • A flow chart is a graphical representation of a computer program in relation to its sequence of functions (as distinct from the data it processes).

  • A break-even chart calculated the break-even point, that is the point at which revenue is exactly equal to costs. At this point, no profit is made and no losses are incurred.

  • PERT:(Program Evaluation and Review Technique) A Project Management technique is a means of projecting task and project completion and organizing complex sequences of tasks. PERT is based on the probability of an event occurring at a specified time.

Correct Answer: C

Solved Example:

17-3-12

Break-even analysis consists of:

Solution:
Break-even analysis consists of fixed cost, which do not change with quantity manufactured, such as cost of land, machinery, license and registration, etc, as well as variable cost, which are directly proportional to the quantity manufactured, such as raw material cost and utility costs.

Correct Answer: C

Solved Example:

17-3-13

Break-even analysis shows profit when:

Solution:
Break-even analysis shows profit after break even point, when sales exceed total costs.

Correct Answer: A

Solved Example:

17-3-14

The break-even point represents:

Solution:
Break-even point represents no profit no loss scenario. Before break-even point there is loss and after it, there is a profit.

Correct Answer: B