Break even point

A number of assumptions are made to ensure that the analysis can be carried out. The important assumptions are:

1. All costs can be classified into fixed and variable components.
2. Total fixed cost remains constant at all levels of output.
3. Total costs and total revenue are linear functions of output.
4. Profits are calculated on a variable costing basis, i.e., contribution minus fixed costs.
5. Sales price per unit remain constant.
6. Sales volume or output is the only factor affecting costs.
7. All outputs are sold, or there is no change in inventory levels.

A business may be selling a large amount of the products to incredible customers. This is not a proof that, such a business makes profit. It needs an understanding of important analysis, which can be undertaken to determine the total cost incurred versus the revenue, so as to know if they are really making profit or just selling many products. A break-even analysis, is the calculation that allows business owners to figure out reasonable quantity of the product to be sold, and to come up with pricing strategies that will be able to cover the total costs incurred, and generate a profit thereon. A break-even point is the level of activity at which the company is making neither profit nor loss. At this point the total costs is equal to the total revenue. Usually the management is very much interested to know the activity level at which there is neither profit nor loss. This is because, the break-even point helps the management to ascertain the cost of doing business and the relevance of the prices they charge.

The break-even point (BEP) can be calculated arithmetically from the following formula:

$\text{BEP in units} = \frac{\text{Total Fixed Cost}}{\text{Selling price per unit} - \text{Variable cost per unit}}$

But: Selling price per unit – Variable cost per unit = Contribution margin per unit

Hence:

$\text{BEP in amounts} = \frac{\text{Total Fixed Cost}}{\text{Contribution margin per unit}} \times \text{Selling price per unit}$

Alternatively:

$\text{BEP in amounts} = \text{Break-even point in units} \times \text{Selling price per unit}$

Example

The following information extracted from DQP Ltd. relates to the production projections of Blue pure drinking water for the forthcoming year of production

Required: Compute the break-even point in units and in TZS

Solution

Break-Even Point (BEP) Calculation

The break-even point is the point at which total revenue equals total costs, meaning there is no profit or loss.

Formula for BEP in Units:

BEP (units) = Total Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)

Example Calculation:

Let's assume:

• Total Fixed Costs: TZS 150,000,000
• Selling Price per Unit: TZS 500
• Variable Cost per Unit: TZS 300

Then:

BEP (units) = 150,000,000 / (500 - 300)

BEP (units) = 150,000,000 / 200

BEP (units) = 750,000 units

Formula for BEP in Revenue:

BEP (revenue) = BEP (units) × Selling Price per Unit

Example Calculation:

BEP (revenue) = 750,000 × TZS 500

BEP (revenue) = TZS 375,000,000

Conclusion:

The break-even point is 750,000 units, which translates to TZS 375,000,000 in revenue.

This means DQP Ltd. has to produce and sell at least 750,000 bottles of water, to be able to cover the total costs (variable costs and fixed costs). Note that, at this level of sales, they will not be able to earn any profit, but just cover the costs (no profit, no loss level).

Contribution can be simply defined as the amount remaining to cover fixed cost, after deducting the variable costs from sales. Arithmetically, contribution is obtained by taking sales minus variable costs. Under the variable costing system, total profit is equal to total contribution minus fixed costs. Contribution can also be calculated for each unit, as selling price per unit minus variable cost per unit.

Contribution margin ratio is a measure of how much contribution is earned from each TZS 1 of sales. This is also called contribution to sales ratio and it is expressed as a percentage of contribution to sales or contribution per unit to selling price per unit. The contribution margin ratio can be calculated using the contribution margin per unit, or the total contribution as follows:

Contribution margin and break-even point calculations

The contribution margin is the amount of revenue that contributes to covering fixed costs and then generating profit. It can be expressed per unit or as a ratio.

Contribution Margin per Unit:

Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit

Contribution Margin Ratio:

The contribution margin ratio expresses the contribution margin as a percentage of sales. It can be calculated in two ways:

Method 1: Using Per-Unit Values

Contribution Margin Ratio = (Contribution Margin per Unit / Selling Price per Unit) × 100

Method 2: Using Total Values

Contribution Margin Ratio = (Total Contribution Margin / Total Sales) × 100

Break-Even Point (BEP) in Amounts (Revenue):

The break-even point in amounts (revenue) is the total sales revenue required to cover all fixed costs.

Formula for BEP in Amounts:

BEP in Amounts = Total Fixed Costs / Contribution Margin Ratio

Example (Continuing from Previous Example):

Let's use the previous example's data:

• Total Fixed Costs: TZS 150,000,000
• Selling Price per Unit: TZS 500
• Variable Cost per Unit: TZS 300

Contribution Margin per Unit:

Contribution Margin per Unit = TZS 500 - TZS 300 = TZS 200

Contribution Margin Ratio:

Using Method 1:

Contribution Margin Ratio = (TZS 200 / TZS 500) × 100 = 40%

Break-Even Point in Amounts:

BEP in Amounts = TZS 150,000,000 / 0.40 = TZS 375,000,000

(Note: We use the decimal form of the percentage (40% = 0.40) in the calculation.)

Conclusion:

The break-even point in amounts (revenue) is TZS 375,000,000, which matches the result we obtained by multiplying the break-even point in units by the selling price per unit. After obtaining the BEP in amounts, BEP in units can be calculated by dividing the BEP in revenue with the sales price per unit, if it is known

The margin of safety is the difference between the budgeted sales and the break-even amount of sales. The margin of safety formula is equal to targeted/budgeted sales level minus the break-even sales, divided by the targeted/budgeted sales level. It is usually expressed as a percentage.

$\text{Margin of safety} = \frac{\text{Budgeted sales} - \text{BEP in amounts}}{\text{Budgeted sales}} \times 100$

It is called margin of safety because it is the maximum amount by which actual sales can be lower than budgeted sales without incurring a loss for a particular period. A high margin of safety therefore indicates a low risk of making a loss.

ARORA Company Ltd. budgets to sell 40,000 units of its product Arora toilet soaps in the year to December, 2023. Arora toilet soap has a selling price of TZS 2,000 and a variable cost of TZS 1,500. Fixed costs for the period are expected to be 12,500,000.

Required: Calculate the expected margin of safety for ARORA Company Ltd. for the year 2023.

Solution

Margin of safety = Budgeted sales – Break-even sales

The break-even point = TZS 12,500,000 / (TZS 2,000 – 1,500) = 25,000 units.

The budgeted sales are 40,000 units.

= 40,000 – 25,000 = 15,000

Margin of safety = 15,000 units

The margin of safety is often expressed as a percentage of budgeted sales as:

$\text{Margin of safety} = \frac{\text{Budgeted sales} - \text{BEP in amounts}}{\text{Budgeted sales}} \times 100$

$= \frac{40,000 - 25,000}{40,000} \times 100 = \frac{15,000}{40,000} \times 100 = 37.5\%$

This means, the company will start making loss if it allows its sales volume to decrease by 37.5% or more. Otherwise, the sales volume can decrease and the company still makes profit.

Managers may also obtain an understanding of break-even analysis if the information is presented in graphical format. A graphical presentation of break-even analysis is also known as the break-even chart. Break-even charts are used by managements to: plan the production of a company's product; market a company's products; and give a visual display of break-even arithmetic. With the break-even chart the sales and fixed costs are plotted. The total cost line is derived by adding variable costs to fixed costs, and it is drawn parallel to the variable cost line because fixed costs are assumed to be a constant sum throughout the output range. The intersection of the sales line and the total costs line is the break-even point. This is the point where total costs are matched exactly by total revenue. The distance between the break-even point and the expected (or budgeted) sales in units, indicates the margin of safety. The break-even charts do not highlight the profit or loss at different output levels and must be ascertained by comparing the differences between the total cost and total revenue lines.

Example

NAG Ltd. is a firm dealing with the production and distribution of biscuits, which are packed in small packets of 200 grams each. The budgeted annual output of NAG Ltd. is 4,000 packets. The fixed overheads amount to TZS 1,000,000 and the variable costs are TZS 500 per packet of biscuits. After being well packed, each packet is sold at TZS 1,000.

Required:

1. Use the provided information to create a table showing the amounts for all variables at different production levels up to the present maximum capacity.
2. Construct a break-even chart showing the current break-even point and profit earned up to the present maximum capacity

a. A table showing the amounts for all variables at different production levels

From the table created, NAG Ltd. will break-even at the level of 2,000 units at which point the total cost is TZS 2,000,000, and total revenue is also TZS 2,000,000.

b. Break-even chart

The break-even chart indicates that NAG Ltd. will start earning profits at the level of 2,000 units and above. This is because from the break-even point, the total revenue is higher than the total cost