 Break-Even Analysis Topics:

# BREAK-EVEN ANALYSIS DEFINITION

The break-even point for a product is the point where total revenue received equals the total costs associated with the sale of the product (TR=TC).A break-even point is typically calculated in order for business to determine if it would be profitable to sell a proposed product, as opposed to attempting to modify an existing product instead so it can be made lucrative. Break-Even Analysis can also be used to analyze the potential profitability of an expenditure in a sales-based business.

Break-even point (for output) = fixed cost/ contribution per unit

Contribution (p.u) = Selling price (p.u) – Variable cost (p.u)

Break-even point (for sales) = fixed cost/ contribution (pu) *sp (pu)

# MARGIN OF SAFETY

In break-even analysis, margin of safety is how much output or sales level can fall before a business reaches its break-even point (BEP).

Margin of safety = ( (Budgeted sales- break-even sales)/ Budgeted sales) x100%

In Unit Sales

If the product can be sold in a larger quantity that occurs at the break-even point, then the firm will make a profit : below this point, a loss. Break-even quantity is calculated by:

Total fixed costs / (Selling price- average variable costs). Explanation-in the denominator, “price minus average variable cost” is the variable profit per unit, or contribution margin of each unit that is sold. This relationship is derived from the profit equation : Profit = Revenues –Costs where Revenues = (selling price * quantity of product ) and Costs= (average variable costs*quantity)+ total fixed costs. Therefore, Profit = (selling price*quantity)-(average variable costs* quantity +total fixed costs).Solving for Quantity of product at the breakeven point when profit equals zero, the quantity of product at breakeven is Total fixed costs/ (selling price-average variable costs).

Firms may still decide not to sell low- profit products, for example those not fitting well into their sales mix. Firms may also sell products that lose money-as a loss leader, to offer a complete line of products, etc. But if a product does not break does not break even, or a potential product looks like it clearly will not sell better than the break-even point, then the firm will not sell, or will stop selling, that product.

EXAMPLE

• Assume we are selling a product for \$2 each.

• Assume that the variable cost associated with producing and selling the product is 60 cents.

• Assume that the fixed cost related to the product (the basic costs that are incurred in operating the business even if no product is produced) is \$1000.

• In this example, the firm would have to sell (1000/2.00-0.60)=715)715 units to break even in that case the margin of safety value of NIL and the value of BEP is not profitable or not gaining loss.

Break Even =FC /(SP “VC)
Where FC is Fixed Cost, SP is selling Price and VC is Variable cost

# IN CAPITAL BUDGETING

Break-even analysis is a special application of sensitivity analysis. It aims at finding the value of individual variables at which the project’s NPV is zero. In common with sensitivity analysis, variables selected for the break-even analysis can be tested only one at a time.

The break–even analysis results can be used to decide abandon of the project if forecasts show that blow break even values are likely to occur.

In using Break-even analysis, it is important to remember the problem associated with Sensitivity analysis as well as some extension specific to the method:

• Variables are often interdependent, which makes examining them each individually unrealistic.

• Often the assumption upon which the analysis is based are mad by using past experience/ data which may not hold in the future.

• Variables have been adjusted one by one; however it is unlikely that in the life of the project only on variable will change until reaching the break-even point. Management decisions made by observing the behavior of only one variable are most likely to be invalid.

Break-even analysis is a pessimistic approach by essence. The figures shall be used only as a line of defense in the project analysis.

LIMITATIONS

Break-even analysis is only a supply side (i.e. . cost 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.

• It assumes average variable costs are constant per unit of output, at least in the range of likely quantities of sales. (i.e. linearity).

• It assumes that the quantity of goods produced is equal to the quantity of good sold ( i. e,. there is no change in the quantity of goods held in inventory at the beginning of the period and the quantity of goods held in inventory at the end of the period).

• In multi-product companies, it assumes that the relative proportions of each product sold and produced are constant (i.e. the sales mix is constant).

Branch of Cost-Volume –Profit (CVP) Analysis that determines the break-even point, which is the level of sales where total, costs equal total revenue. Thus, zero profit results. Break even sales is computed as follows:-

Break-even sales in units = Fixed costs / Unit contributions margin.

Break-even sales in dollars = Fixed costs /Contribution margin ratio.

For example, assume:

Fixed costs = \$ 15,000.

Unit contribution margin (selling price- unit variable cost )= \$15, and

Contribution margin ratio (unit CM/ selling price ) = .6

Then, break-even sales in units = \$ 15,000/\$15 = 1000 units and break-even sales in dollars = \$ 15,000/.6 =\$ 25,000.

A break-even chart is one in which sales revenue, variable costs, and fixed costs are plotted on the vertical axis while volume is plotted on the horizontal axis .The Break-Even Point is the Point at which the total sales revenue line intersects the total cost line.

See the example chart below. # PROFIT, COST AND QUANTITY ANALYSIS

Cost-Volume-profit (CVP) analysis is a mathematical representation of the economics of producing a product. The relationship between a product’s revenue and cost functions expressed within the CVP model are used to evaluate the financial implications of a wide range of strategic and operational decisions. For example, CVP analysis is employed to assess the financial implications of product mix, pricing, and product and process improvement decisions. Perhaps equally important, CVP analysis facilities measuring the sensitivity of a product’s profitability to variations in one or more of its underlying parameters. Finally, CVP analysis may be used to determine the trade-offs in profitability and risk from alternative product design and production possibilities. In effect, CVP is a quantitative model for developing much of the financial information relevant for evaluating resource allocation decisions.

## PRODUCT MIX DECISIONS AND CVP ANALYSIS

CVP analysis is generally implemented with financial data taken from the firm’s accounting system. Financial data is readily available, as well as congruent, with the accounting profit objective inherent in the use of CVP analysis. The financial data needed for CVP may be taken from either a traditional cost accounting or an activity-based costing (ABC) system. Traditional cost accounting system allocate overhead to products based on one or more volume-based measures of activity. However, products consume overhead resources based on batch-, facility-,and complexity-, as well as volume- or unit-level, activities, Consequently, traditional cost accounting systems can systematically misallocate overhead to products.

CVP analysis is used to measure the economic characteristics of manufacturing a proposed product. Based on accounting data, the CVP model is used to determine the sales quantity needed to break even, as well as the sales quantity required to earn a desired profit or profit margin. Managers then compare a product’s expected sales with the sales quantities required to break even and/or earn a target profit margin to determine whether the product should be produced.

## APPLICATION OF MARGINAL COSTING

Marginal costing is an important technique of managerial decision-making. It is a tool for cost control and profit planning. The advantages of Marginal costing technique are:

1. Simplicity: the statement under marginal costing can be easily followed as it breaks up the cost as variable and fixed.

2. Stock valuation: Stock valuation can be easily done and understood as it includes only variable cost.

3. Meaningful reporting: marginal costing serves as a good basis for reporting to management. The profits can be analyzed from the point of view of sales rather than production.

4. Effect of fixed costs: the fixed costs are treated as period costs and are charged to P&L A/C directly. Thus they have practically no effect on decision- making.

5. Profit planning: the cost- volume relationship is perfectly analyzed to reveal the efficiency of products, processes and departments. ‘Break-even point’ and margin of safety’ are the two important concepts helpful in profit planning. Most advantageous volume and cost to maximize profits within the existing limitations can be planned.

## LIMITATIONS OF MARGINAL COSTING

1. Classification of Cost: Break up of cost into variable and fixed portions is a difficult problem. Moreover clear-cut division of semi variable or semi fixed cost is complicated and cannot be accurate.

2. Not suitable for external reporting: Since fixed cost is not included in total cost, full cost is not available to outsider to judge the efficiency.

3. Lack of Long-term perspective: Marginal Costing is more suitable for decision making in the shot-term. It assumes that costs are classified into fixed and variable. In the long term all the costs are variable. Therefore it ignores time element and is not suitable for long-term decisions.

4. Under Valuation of Stock: Under marginal costing, only variable costs are considered and the outputs as well as stocks are undervalued and profit is distorted. When there is loss of stock the insurance cover will not meet the total cost of Marginal Costing in Business.

1. KEY FACTOR OR LIMITING FACTOR

Any factor concerned with production or sales, which imposes ‘limits’ on the production or sales can be called ‘limiting factor’ or key factor. It can be limited sales, limited production, and limited raw materials in us or limited finance.

Using a large number of parts or components assembles many durable products. Some of them may be made by the firm, which is assembling the product. It may buy some products from outside. When an assembling firm receives an offer from outside for a component it is already making, the ‘make or buy decision’ must be taken. Marginal Costing helps in taking the make or buy decision.

3. FIXATION OF SELLING PRICE

Marginal costing technique is widely used in the area of determining selling price. Prices will have to be fixed in different situations, under specific constraints, etc. total cost must be recovered and profit also to be mad by fixing appropriate selling price.

4. EXPORT DECISION

When idle capacity still exists, exporting is usually the most profitable strategy. So companies that have already recovered their fixed costs from local sales can export just above their variable cost and still make good profits. This is generally termed as dumping.

Review Questions
• 1. What is the significance of "Break Even Point".
• 2. "Marginal Costing is a valuable aid for managerial Decisions". Discuss.
• 3. Identify any four industries in which batch costing is employed.
• 4. Define "Standard cost".
• 5. Define Marginal cost.
• 6. Define "Marginal Costing".

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