Break-Even Analysis

MBA Class of 2009-11

AIET

Break-Even Defined

• A technique that bases its decision on the cost trade-offs, associated with demand volume is break-even analysis.

Components of Break-Even

• The components of break even analysis are:

• Volume

• Revenue

• Cost

• profit.

Variable Costs

• A variable cost is a cost that changes in total in direct proportion to changes in the related total activity or volume.

• Numbers of orders processed, Number of lines billed in a billing department, Hours of labour worked in an assembly department, Number of rides in an amusement park, Seat-miles on an airline, Dollar sales in a grocery store, or some other index of volume.

Fixed Costs

• A fixed cost is a cost that is not affected in total by a decision to change the related total activity or volume during a given time-period.

Fixed costs, variable costs and Activity Volume

IF ACTIVITY VOLUME INCREASES (OR DECREASES) Type of Cost

Total Cost Cost per unit* Fixed Costs No Change+ Decrease (or increase) Variable Costs Increase (or decrease) No Change+ *Per unit of activity volume, for example, product units, passenger miles, sales dollars + When using data for making predictions, think of fixed costs as a total and variable costs as an amount per unit activity

Relevant Range

• A relevant range is the expected band of activity volume in which a specific form of budgeted sales and cost (expense) relationships will be valid.

• For example, the weekly volume of automobiles produced by an assembly plant for a forthcoming year might fluctuate between 10,000 units and 20,000 units. A fixed cost is fixed only in relationship to a given time – usually the budgeted period – and a given relevant range of activity.

Some Simplifying Assumptions

• Nearly every organization has some variable costs and some fixed costs. As you may suspect, it is often difficult to classify a cost as exactly variable or exactly fixed.

Some Simplifying Assumptions

• Many complications arise, including the possibility of costs behaving in some non linear way (not behaving as a straight line).

ACTIVITY VOLUMEACTIVITY VOLUME

Our assumptions for discussion

• A given variable cost (per unit) is associated with only one measure of volume

• The relationship between variable cost per unit and volume of activity is linear.

Break-even Point

• Break Even Volume in units = (Fixed Expenses)/(Contribution margin per unit)

Where,

• Contribution margin per unit = Unit sales price – Unit variable cost price

Break-even Point

• Break Even Volume in rupees = (Fixed Expenses)/(Contribution-margin ratio)

• Where,

• Contribution-margin ratio = (Contribution margin per unit)/sales price per unit

Problems

• Problem 1. Mikey W. Smitty, an emerging rapper, is getting ready to cut his first CD, called “Western Rap”. The cost of recording the CD is $ 5,000 but copies are $5 a piece. If the CDs can be sold for $15 each, how many CDs must be sold to break-even? What is the break even point in dollars?

Problems

• Problem 2. Mikey W. Smitty is confident that demand for his “Western Rap” CD will be substantially exceed the break-even point computed in the problem above. So, Mikey is contemplating having his CD cut at a classier (and pricier) studio. The cost to record the CD would rise to $9000. However, since this new studio works with a very high volume, production costs would fall to $2 per CD.

• What is the new break-even point for the new process?• Compare this process to the process proposed in the

problem above. For what volume of demand should Mikey choose the classier studio?

Limiting Assumptions

• The notion of relevant range discussed above is applicable to the entire break-even graph. Usually break even graphs are shown with revenue and cost lines extending back to the origin. However this not true because the graph is applicable only for the relevant range.

Limiting Assumptions

Total Expenses

Sales

Conventional Graph

Sales

Total Expenses

Modified Graph

Limiting Assumptions

• Total variable expenses vary directly with volume. Total fixed expenses do not change with volume.

• The behaviour of revenues and expenses is accurately potrayed and is linear over the relevant range.

• Efficiency and productivity will be unchanged• Sales mix will be constant. The sales mix is the relative

proportions or combinations of quantities of products that comprise total sales.

• The difference in inventory level at the beginning and at the end of a period is insignificant.

Multi-product Break -even Analysis

• Most companies produce or sell more than one product.

• The product mix is defined as the relative proportions or combinations of quantities of products that comprise total production and ultimately sales. If the proportions of the product mix changes, the cost volume-profit relation also changes.

Ramos Company

• Suppose Ramos Company has two products, wallets (W) and key cases (K). The income budget as follows:

Wallets(W) Key cases (K) Total Sales in units 300,000 75,000 375,000 Sales @ $8 and $5 $ 2,400,000 $375,000 $2,775,000 Variable Expenses @ $7 and $3

2,100,000 225,000 2,325,000

Contribution Margins @$1 and $2

$ 300,000 150,000 450,000

Fixed Expenses 180,000 Net Income $ 270,000

Ramos Company

• For simplicity, ignore income taxes. What would be the break-even point?

• The typical answer assumes a constant mix of 4 units of W for every unit of K.

• Let K = number of units of product K to break even

• 4K = number of units of product W to break even

Ramos Company

• Sales – variable expenses – fixed expenses – zero net income = 0

• $8(4K) + $5(K) - $7(4K) - $3(K) - $180000 = 0

• 32K + 5K – 28K -3K -180000 = 0

Ramos Company

• 6K = 180000• K = 30000• 4K = 120,000• The break-even point is 30000+120000 =

150000 units.• This is only break-even point for a sales

mix of 4 wallets for every key case. However, clearly, there are other break-even points for other sales mixes.

Ramos Company

• For instance, suppose only key cases were sold, fixed expenses being unchanged:

• Break-even point = (fixed expenses)/(contribution margin per unit)

• = $ 180,000/$2 = 90,000 key cases

• If only wallets were sold:• Break-even point = $ 180,000/$1 = 180,000

wallets

Ramos Company

• Managers are not primarily interested in the break-even point for its own sake. Instead they want to know how changes in a planned sales mix will affect net income.

• When the sales changes, the break-even point and the expected net income at various sales levels are altered.

Ramos Company

• For example, suppose overall actual total sales were equal to budgeted of 375,000 units.

• However, only 50,000 key cases were sold.:

Ramos Company

Wallets(W) Key cases (K) Total Sales in units 325,000 50,000 375,000 Sales @ $8 and $5 $ 2,600,000 $250,000 $2,775,000 Variable Expenses @ $7 and $3

2,275,000 150,000 2,325,000

Contribution Margins $1 and $2

$ 325,000 100,000 425,000

Fixed Expenses 180,000 Net Income $ 245,000

Ramos Company

• The change in the sales mix has resulted in a $245,000 actual net income rather than the $270,000 budgeted net income, an unfavourable difference of $25,000. The total budgeted and actual total sales in number of units were identical, but the proportion of the product bearing the higher unit contribution margin declined.

Ramos Company

• Managers usually want to maximize the sales of all their products. However faced with limited resources and time, executives prefer to generate the most profitable sales mix achievable.

Ramos Company

• Different advertising strategies may also affect the sales mix. Clearly if a sales budget is not actually attained, the budgeted net income will be affected by the individual sales volume of each product. The fewer the units sold, the lower the profit, and vice-versa.

Ramos Company

• All other things being equal, the higher the proportion of more profitable products, the higher the profit.