Cost Volume Profit Analysis / Break Even Analysis – Part 2

Learning objectives

1. Calculation of Margin of safety

2. Interpretation of Margin of safety

3. Graphical Representation of BEP Analysis

4. Contribution margin approach profit statement

5. Calculation of target units

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Margin of Safety (MOS)

• The excess of actual or budgeted sales over the break even volume of sales is called margin of safety.

• At break even point costs are equal to sales revenue and profit is zero. Margin of safety, therefore, tells us the amount of sales that can be dropped before losses begin to be incurred.

• With a high margin of safety business have low risk of not breaking even and with a low margin of safety business have high risk of not breaking even.

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Margin of Safety = Total budgeted or actual sales − Break even sales

Margin of Safety Ratio:

The margin of safety can also be expressed in percentage form (Margin of safety ratio). This percentage is obtained by dividing the margin of safety in dollar terms by total sales. Following equation is used for this purpose.

Margin of Safety = Margin of safety in dollars / Total budgeted or actual sales

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Example:

Sales(400 units @ $250)$100,000

Break even sales$87,500Calculate margin of safety.

Calculation:

Sales(400units @$250)$100,000

Break even sales$ 87,500

Margin of safety in dollars$ 12,500 Margin of safety as a percentage of sales:

12,500 / 100,000

= 12.5%

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Contribution Margin Income Statement

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EXAMPLE

My Cake Shop’ is a cake and pastry business that you run. With the rising demand in customers asking for workshops for baking their own cakes you started weekend workshops for the same.

The revenue generated for the month was $7,500 which included direct sales of $6,000 and income from conducting Weekend Cake Workshops was $1,500.

Wages paid were $2,000 and the expense incurred in procuring materials summed up to a total of $1,500. Rent of $1,000 was paid and the insurance premium payment of $200 was also made. The contribution margin income statement would look like this:

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Break-Even Chart:This chart is constructed as follows:

1. A horizontal base line, the x-axis, is drawn and spaced into equal distances representing either plant capacity, sales volume or number of units. A physical index of output (units of product) is preferable because it is not influenced by changes in selling price, but when many products are involved a sales value index may be selected.

2. A vertical line, the j-axis is drawn on the left side of the chart and also spaced into equal parts. This line indicates sales revenue and also costs.

3. A line parallel to the horizontal line (x-axis) is drawn for fixed costs.

4. A total cost line is drawn starting at the y-axis fixed cost point and moving to the right. This total cost line represents at each point the total of all items of cost, fixed and variable.

.

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Break-Even Chart:

5. The sales line is drawn starting at the zero point on the vertical axis and ending at the top on the right side.

6. The total cost line intersects the sales line at a point which is known as the break-even point.

7. The area to the left of the break-even point between the total cost line and the sales line is the loss area the profit area lies to the right of the break-even point, above the total cost line

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Target Profit

• Units to Achieve a Target Income =

(Total Fixed Costs + Target Profit) / Contribution Margin Per Unit

• Sales value to Achieve a Target Income =

(Total Fixed Costs + Target Income Contribution Margin Ratio

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Assumptions of Break Even Analysis

(1) All costs can be categorized as fixed or variable costs.

(2) Total fixed costs remain unchanged for all output levels.

(3) Total variable costs fluctuate proportionately with output level resulting in no change in per unit variable cost.

(4) Sale price per unit remains the same for each output level.

(5) Costs and revenue behave in a linear fashion within a relevant range.

(6) No factor other than sales volume can affect costs and sales revenue.

(7) The analysis relates to businesses producing one product only or a constant product mix.

(8) The technology, production methods and efficiency remain unchanged.

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Limitations:

(1) The existence of semi variable costs is ignored, whereas most of the costs are not either perfectly fixed or perfectly variable.

(2) Fixed costs may change if output increases or decreases substantially.

(3) Possible changes in per unit variable costs due to various reasons like bulk buying discounts, overtime, etc., are ignored.

(4) Sales price may have to be reduced to win the extra sales or may be increased to cover increased costs.

(5) As discussed above selling prices and variable costs per unit vary at different output levels.

(6) Various external factors like inflation rate, economic state may also affect sales volume.

(7) This restricts its usefulness as it is difficult to experience in practice.

(8) The technology, production methods may change in practice.

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Example Items Amounts

Annual Volume 12 000 units

Selling Price Per Unit $48

Variable manufacturing cost per

unit

$20

Annual fixed manufacturing

costs

$16 000

Variable marketing and

distribution costs per unit

$12

Annual fixed non-manufacturing

costs

$4 000

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Questions

1) Calculate the break-even units

2) Calculate Contribution Sales ratio

3) Calculate the break-even Value(in dollars)

4) Calculate the Margin of safety in units and dollars

5) Draw a graph and explain the BEP concept

6) Calculate the profit achievable

7) If fixed cost increase by $ 5000 and variable cost per unit increase by 10 %,to achieve the same level of profit how many units need to be produced ?

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