Management Consulting/managerial economics

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Question
sir,

An analytical tool frequently employed by managerial economists is the break even chart,an important application of cost functions.
discuss this statement giving examples from any firm.

thank you.

Answer
“An analytical tool frequently employed by managerial economists is the break even chart, an important application of cost functions.” Discuss this statement giving examples from any firm.
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:
The  BREAK EVEN  POINT  is , in  general ,the  point  at which the  gains  equal
the  losses. A break even  point defines when an  investment
will generate a positive return. The point where sales or revenues equal expenses. Or also the point where total costs equal total revenues. There is no profit made or loss incurred at the break-even point. This is important for anyone that manages a business, since the break¬even point is the lower limit of profit when prices are set and margins are determined.
Achieving Break-even today does not return the losses occurred in the past. Also it does not build up a reserve for future losses. And finally it does not provide a return on your investment (the reward for exposure to risk).
The Break-even method can be applied to a product, an investment, or the entire company's operations and is also used in the options world. In options, the Break-even Point is the market price that a stock must reach for option buyers to avoid a loss if they exercise. For a Call, it is the strike price plus the premium paid. For a Put, it is the strike price minus the premium paid.
THE RELATIONSHIP BETWEEN FIXED COSTS, VARIABLE COSTS AND RETURNS
Break-even analysis is a useful tool to study the relationship between fixed costs, variable costs and returns. The Break-even Point defines when an investment will generate a positive return. It can be viewed graphically or with simple mathematics. Break-even analysis calculates the volume of-production at a given price necessary to cover all costs. Break-even price analysis calculates the price necessary at a given level of production to cover all costs. To explain how break-even analysis works, it is necessary to define the cost items.
Fixed costs, which are incurred after the decision to enter into a business activity is made, are not directly related to the level of production. Fixed costs include, but are not limited to, depreciation on equipment, interest costs, taxes and general overhead expenses. Total fixed costs are the sum of the fixed costs.
Variable costs change in direct relation to volume of output. They may include cost of goods sold or production expenses, such as labor and electricity costs, feed, fuel, veterinary, irrigation and other expenses directly related to the production of a commodity or investment in a capital asset. Total variable costs (TVC) are the sum of the variable costs for the specified level of production or output. Average variable costs are the variable costs per unit of output or of TVC divided by units of output.
The Break-even Point analysis must not be mistaken for the Payback Period, the time it takes to recover an investment.
In Value Based Management terms, a break-even point should be defined as the Operating Profit margin level at which the business / investment is earning exactly the minimum acceptable Rate of Return, that is, its total cost of capital.
BREAK-EVEN POINT CALCULATION
Calculation of the BEP can be done using the following formula:
BEP = TFC / (SUP - VCUP)
where:
• BEP = break-even point (units of production)
• TFC = total fixed costs,
• VCUP = variable costs per unit of production,
• SUP = selling price per unit of production.
BENEFITS OF BREAK-EVEN ANALYSIS
The main advantage of break-even analysis is that it explains the relationship between cost, production volume and returns. It can be extended to show how changes in fixed cost-variable cost relationships, in commodity prices, or in revenues, will affect profit levels and break-even points. Break-even analysis is most useful when used with partial budgeting or capital budgeting techniques. The major benefit to using break-even analysis is that it indicates the lowest amount of business activity necessary to prevent losses.
LIMITATIONS OF BREAK-EVEN ANALYSIS
• It is best suited to the analysis of one product at a time;
• It may be difficult to classify a cost as all variable or all fixed; and
• There may be a tendency to continue to use a break-even analysis after the cost and income functions have  changed.



Break-Even and Target Income
CVP analysis is used to build an understanding of the relationship between costs, business volume, and profitability. This analysis will drive decisions about what products to offer and how to price them. CVP is at the heart of techniques used to calculate break-even, volume levels necessary to achieve targeted income levels, and similar computations. The starting point for these calculations is the contribution margin.
The contribution margin is revenues minus variable expenses. Do not confuse the contribution margin with gross profit. Gross profit is calculated after deducting all manufacturing costs associated with sold units, whether fixed or variable.
Instead, the contribution margin reflects the amount available from each sale, after deducting all variable costs associated with the units sold. Some of these variable costs are product costs, and some are selling and administrative in nature. The contribution margin is generally calculated for internal use and is not externally reported.
MARGIN: AGGREGATE, PER UNIT, OR RATIO?
One might refer to contribution margin on an aggregate, per unit, or ratio basis. This point is illustrated for Leyland Sports, a manufacturer of scoreboards. The production cost is $500 per sign, and Leyland pays its sales representatives $300 per sign sold. Thus, variable costs are $800 per sign. Each signs sells for $2,000. Leyland’s contribution margin is $1,200 ($2,000 - ($500 + $300)) per sign. In addition, assume that Leyland incurs $1,200,000 of fixed cost.
Following are schedules with contribution margin information, assuming production and sales of 1,000, 2,000, and 500 units:

Notice that changes in volume only impact certain amounts within the “total column.” Volume changes did not impact fixed costs, nor change the per unit or ratio calculations. By reviewing the data, also note that it is necessary to produce and sell 1,000 units to achieve break-even net income. At 2,000 units, Leyland managed to achieve a $1,200,000 net income. Conversely, if only 500 units are produced and sold, the result will be a $600,000 loss.
BREAK-EVEN CHART
Leyland’s management would probably find the following chart very useful. Dollars are represented on the vertical axis and units on the horizontal.

Be sure to examine this chart, taking note of the following items:
•   The total sales line starts at “0” and rises $2,000 for each additional unit.
•   The total cost line starts at $1,200,000 (reflecting the fixed cost) and rises $800 for each additional unit (reflecting the addition of variable cost).
•   “Break-even” results where sales equal total costs.
•   At any given point, the width of the loss area (in red) or profit area (in green) is the difference between sales and total costs.
BREAK-EVEN ALGEBRA
Break-even occurs when there is no profit or loss. As noted, the break-even point results where sales and total costs are equal:
Break-Even Sales = Total Variable Costs + Total Fixed Costs
For Leyland, the math works out this way:
(Units X $2,000) = (Units X $800) + $1,200,000
Solving:
Step a:       (Units X $2,000) = (Units X $800) + $1,200,000
        
Step b:       (Units X $1,200) = $1,200,000
        
Step c:       Units = 1,000

It is possible to “jump to step b” above by dividing the fixed costs by the contribution margin per unit. Thus, a break-even short cut is:
Break-Even Point in Units = Total Fixed Costs / Contribution Margin Per Unit
1,000 Units = $1,200,000 / $1,200
Sometimes, one may want to know the break-even point in dollars of sales (rather than units). This approach is especially useful for companies with more than one product, where those products all have a similar contribution margin ratio:
Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,000,000 = $1,200,000 / 0.60
TARGET INCOME
Breaking even is not a bad thing, but hardly a satisfactory outcome for most businesses. Instead, a manager may be more interested in learning the necessary sales level to achieve a targeted profit. The approach to solving this problem is to treat the target income like an added increment of fixed costs. In other words, the margin must cover the fixed costs and the desired profit. Assume Leyland wants to know the level of sales to reach a $600,000 target income:
Solving:
Step a:       (Units X $2,000) = (Units X $800) + $1,200,000 + $600,000
        
Step b:       (Units X $1,200) = $1,800,000
        
Step c:       Units = 1,500

Again, it is possible to “jump to step b” by dividing the fixed costs and target income by the per unit contribution margin:
Units to Achieve a Target Income
=
(Total Fixed Costs + Target Income) / Contribution Margin Per Unit
1,500 Units = $1,800,000 / $1,200
If one wants to know the dollar level of sales to achieve a target net income:
Sales to Achieve a Target Income
=
(Total Fixed Costs + Target Income) / Contribution Margin Ratio
$3,000,000 = $1,800,000 / 0.60
CRITICAL THINKING ABOUT CVP
CVP is more than just a mathematical tool to calculate values like the break-even point. It can be used for critical evaluations about business viability.
For instance, a manager should be aware of the “margin of safety.” The margin of safety is the degree to which sales exceed the break-even point. For Leyland, the degree to which sales exceed $2,000,000 (its break-even point) is the margin of safety. This will give a manager valuable information as he or she plans for inevitable business cycles.
A manager should also understand the scalability of the business. This refers to the ability to grow profits with increases in volume. Compare the income analysis for Leaping Lemming Corporation and Leaping Leopard Corporation:

Both companies “broke even” in 20X1. Which company would one rather own? If one knew that each company was growing rapidly and expected to double sales each year (without any change in cost structure), which company would be preferred? With the added information, one would expect the following 20X2 outcomes:

This analysis reveals that Leopard has a more scalable business model. Its contribution margin is high and once it clears its fixed cost hurdle, it will turn very profitable. Lemming is fighting a never-ending battle; sales increases are met with significant increases in variable costs. Be aware that scalability can be a double-edged sword. Pull backs in volume can be devastating to companies like Leopard because the fixed cost burden can be consuming. Whatever the situation, managers need to be fully cognizant of the effects of changes in scale on the bottom-line performance.

Sensitivity Analysis
Cost structures can be anticipated to change over time. Management must carefully analyze these changes to manage profitability. CVP is useful for studying sensitivity of profit for shifts in fixed costs, variable costs, sales volume, and sales price.
CHANGING FIXED COSTS
Changes in fixed costs are perhaps the easiest to analyze. To determine a revised break-even level requires that the new total fixed cost be divided by the contribution margin. Return to the example for Leyland Sports. Recall one of the original break-even calculations:
Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,000,000 = $1,200,000 / 0.60
If Leyland added a sales manager at a fixed salary of $120,000, the revised break-even would be:
$2,200,000 = $1,320,000 / 0.60
In this case, the fixed cost increased from $1,200,000 to $1,320,000, and sales must reach $2,200,000 to break even. This increase in break-even means that the manager needs to produce at least $200,000 of additional sales to justify his or her post.
CHANGING VARIABLE COSTS
In recruiting the new sales manager, Leyland became interested in an aggressive individual who was willing to take the post on a “4% of sales” commission-only basis. Let’s see how this would change the break-even point:
Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,142,857 = $1,200,000 / 0.56
This calculation uses the revised contribution margin ratio (60% - 4% = 56%), and produces a lower break-even point than with the fixed salary ($2,142,857 vs. $2,200,000). But, do not assume that a lower break-even defines the better choice! Consider that the lower contribution margin will “stick” no matter how high sales go. At the upper extremes, the total compensation cost will be much higher with the commission-based scheme. Following is a graph of commission cost versus salary cost at different levels of sales. Note that the commission begins to exceed the fixed salary at any point above $3,000,000 in sales. In fact, at $6,000,000 of sales, the manager’s compensation is twice as high if commissions are paid in lieu of the salary!

What this analysis does not reveal is how an individual will behave. The sales manager has more incentive to perform, and the added commission may be an excellent inducement. For example, the company will make more at $6,000,000 in sales than at $3,000,000 in sales, even if the sales manager is paid twice as much. At a fixed salary, it is hard to predict how well the manager will perform, since pay is not tied to performance.
 
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