3.3. Break-even analysis

Total contribution versus contribution per unit

Break-even analysis is a technique widely used by production management and management accountants. It is based on categorising production costs between those which are "variable" (costs that change when the production output changes) and those that are "fixed" (costs not directly related to the volume of production).

Total variable and fixed costs are compared with sales revenue in order to determine the level of sales volume, sales value or production at which the business makes neither a profit nor a loss (the "break-even point").

The Break-Even Chart

In its simplest form, the break-even chart is a graphical representation of costs at various levels of activity shown on the same chart as the variation of income (or sales, revenue) with the same variation in activity. The point at which neither profit nor loss is made is known as the "break-even point" and is represented on the chart below by the intersection of the two lines:

Task 2: The management of an enterprise predict the best, worst and most likely demand for its new product at 20000 units, 10000 units and 15000 units respectively. The selling price per unit is $20 and the annual relevant fixed costs of the enterprise are estimated to be $120000. The variable cost per unit is $10.

Analyse the best, most likely and worst outcomes for this enterprise

A break-even chart and the following aspects of break-even analysis: break-even quantity, profit/loss, margin of safety, target profit output, target profit & target price

Break-even point

An important concept for decision-makers is breakeven. At a level of zero sales, the company’s total contribution will be zero; therefore, they will make a total loss equal to the level of their fixed costs. As sales revenues, the contribution will grow and will start to cover the fixed costs. Eventually a point will be reached where neither profit nor loss is made, this is the breakeven point. At this point the total contribution must exactly match the fixed costs. Any additional contribution made above this level will constitute profit.

Break-even point in units = Fixed costs/contribution per unit

For example, suppose that an organization manufactures a single product, incurring variable costs of $30 per unit and fixed costs of $20000 per month. If the product sells for $50 per unit, then the breakeven point can be calculated as follows:

Break-even point in units = $20000/($50-$30) = 1000 units per month

Task 4: AB Company manufactures a single product. The unit costs of the product are as follows:

The Margin of Safety

The margin of safety is the difference between the expected level of sales and the breakeven point. The larger the margin of safety, the more likely it is that a profit will be made, that is, if sales start to fall there is more leeway before the organization begins to incur losses.

• Margin of safety can be expressed in units or as a % of projected sales
• Margin of safety = projected sales – break even sales
• Margin of safety % = Projected sales – breakeven sales/projected sales x 100

Example

If a company has a breakeven level of sales of 1000 and is forecasting sales of 1700, the margin of safety can be calculated as follows:

Margin of safety = 1700 – 1000 = 700 units

Margin of safety = (1700 – 1000)/1700 = 41%

Using the margin of safety % puts it in perspective. To quote a margin of safety of 700 units without relating it to the projected sales figure is not giving the full picture.

Task 7: B Ltd manufactures a single product which it sells for $9 per unit. Fixed costs are $54000 per month and the product has a variable cost of $6 per unit. In a period when projected sales revenue was $180000, what was B Ltd’s margin of safety in units?

Task 8: Avoca Ltd presents you with the following information

Fixed Costs = $480,000

Variable Costs = $3 per unit

Selling Price = $9 per unit

Maximum factory capacity = 120,000 units

Current Demand = 100,000 units.

1. Calculate the break-even point
2. What is the break-even revenue (break-even output x selling price)?
3. What is the margin of safety?

Task 9: (a) Using the break-even formula, calculate the break-even point for Scooby Doo Ltd with

$660,000 of fixed overheads per month

Variable costs of $6.50 per unit

Selling price of $18.50

(b)If Scooby Doo Ltd expects to sell 78,000 units, what is its safety margin?

Illustration

RT organization manufactures one product. The product sells for $250, and has variable costs per unit of $120. Fixed costs for the month were $780000. The monthly projected sales for the product were 8000 units.

The breakeven sales point = Fixed costs/contribution per unit

$780000/($250-$120) = 6000 units

Margin of Safety in units = 8000 – 6000 = 2000 units

Margin of Safety % = (projected sales – breakeven sales)/projected sales

(8000 – 6000)/8000 = 25%

To calculate monthly profit

Contribution $130

Total Contribution ($130 x 8000) $1040000

Fixed Costs $780000

Profit $260000

Using MOS

Margin of safety = 2000 units per month

Monthly profit = 2000 x contribution per unit

2000 x $130 = $260000

Sales required for a required level of profit

Sales units required to achieve a profit of X = (Fixed Costs + X)/Contribution per unit

Example

Riding Breeches Ltd makes and sells a single product for which variable costs are as follows:

Direct materials 10

Direct labour 8

Variable Production overhead 6

24

The sales price is £30 per unit, and fixed costs per annum are £68000. The company wishes to make a profit of £16000 per annum.

Solution

Sales units required to achieve a profit of X = (Fixed Costs + X)/Contribution per unit

(68000 + 16000)/30-24

84000/6 = 14000 units

Target Profit

Profit = Sales – Total Variable Costs – Total Fixed Costs

Task 10: Up ltd is about to launch a new product on the market. The variable costs of making and selling the product amount to $10 per unit and its selling price is to be $20 per unit. Fixed costs are expected to amount to $100000 per annum.

Calculate the sales level which must be reached by Up Ltd if management require a profit of $70000 a year from the product.

Task 11: Down Ltd has just commenced operations and is deciding at what price the enterprise should sell its services in the market place.

The management accountant calculates the variable cost per unit of the service to be $15. Fixed costs are expected to run at $200000 per annum.

The marketing director of Down Ltd has made the following predictions as to selling price and related demand for the service provided by the enterprise.

Selling Price/unit Demand Units

$ Units

25 30000

20 50000

From the above information calculate the price at which Down Ltd should sell its services to maximise the profits earned by the enterprise

Task 12: An organisation currently provides a single service. The cost per unit of that service is as follows:

The effects of changes in price or cost on the break-even quantity, profit and margin of safety, using graphical and quantitative methods

Task 15: Changes in fixed costs, variable costs and selling price

1: On the basis that the unit sale price is £10, that the variable costs are £4 per unit and that fixed costs total £150,000 a year, calculate the break-even volume of sales.

(a) Calculate the break –even quantity using the formula:

Fixed Costs/Contribution

(b) Using the same values, calculate the break-even sales revenue.

(c) If the current level of output is 50,000 units, calculate the margin of safety.

Calculate the following values and illustrate the information in a break-even graph

Changes in Variable Costs

A change in variable costs will have the immediate effect of changing the contribution, and consequently the break-even point.

It is decided to improve the quality of a product by incorporating more expensive materials. As a result variable costs are increased by 10%. We take fixed costs as being £150,000.

(g) Calculate the new break –even quantity using the formula:

Fixed Costs/Contribution

(h) Calculate the break-even sales revenue.

(i) If the current level of output is 50,000 units, calculate the new margin of safety.

Calculate the following values and illustrate the information in a break-even graph

Changes in Selling Price

Successful profit planning through changes in selling prices depends upon management knowing how the market will react to these price changes. In other words, it is important to know the effect upon total revenue of changes in selling prices. This effect is measured through the price elasticity of demand.

Let us assume that a 10% increase in selling price will lead to a 10% reduction in the volume of sales. We take fixed cost as being £150,000

(j) Calculate the new break –even quantity using the formula:

Fixed Costs/Contribution

(k) Calculate the break-even sales revenue.

(l) If the current level of output is 50,000 units, calculate the new margin of safety.

Calculate the following values and illustrate the information in a break-even graph

Task 16: For the forthcoming year, E plc’s variable costs are budgeted to be 60% of sales value and fixed costs are budgeted to be 10% of sales value.

If E plc increases its selling prices by 10%, but if fixed costs, variable costs per unit and sales volume remain unchanged, what would be the effect on E plc’s contribution?