,

17

Break-Even and Cost–Volume–Profit Analysis

The determination of profitability is an essential part of an accounting process. A careful analysis of the behaviour of costs and profits as a function of the expected volume of sales is very vital to make important managerial decisions. As these factors—cost, volume and profit (CVP)—are interrelated, one’s behaviour with respect to the other two factors has to be analysed in detail in determining the profitability of a business organization. CVP analysis is an effective tool of profit planning. In this chapter, the following are analysed with the technique of CVP analysis:

1. Behaviour of costs with respect to volume.
2. Volume (production or sales) at the level where the break-even occurs.
3. Sensitively of profits to variation in output.
4. Determination of profit for the desired sales volume.
5. Determination of production and sales for the predetermined profit level.

In the previous chapter, we have discussed the essential features of marginal-costing technique and its managerial applications. Managerial decisions demand an accurate knowledge of the behaviour of costs. A separation of fixed costs from the variable costs helped to a certain extent to make decisions. “Contribution” criterion plays a vital role in the marginal-costing technique. In this chapter, we have to analyse carefully the behaviour of costs and profits in relation to volume of sales. The factor cost of the product (price) can be determined at ease. The next factor is the volume of sales as one cannot predict exactly how much quantity will be sold in a specified future period—as profit has to be ascertained only when the volume of sales is known perfectly. Thus, the interlinking relationship among these three factors have to be analysed in-depth. This chapter aims at CVP analysis and the effect of changes in the volume of sales and profitability of the business enterprises.

17.1 FEATURES AND FORMULAE FOR PROFIT-VOLUME RATIO

One way of studying the relationship among costs, revenue and volumes is the profit-to-volume ratio. profit-volume ratio establishes a relationship between the contribution and the volume of sales (or sales value). This ratio is also known as marginal-income ratio, contribution to sales ratio and variable-profit ratio or P/ V ratio.

The formulae for P/ V ratio are:

It is the rate at which the profit increases with the increase in volume. Any increase in contribution will mean an increase in the profit because fixed costs are assumed to remain constant over all sales volumes. The P/ V ratio will remain constant at different levels of production because variable costs as a proportion to sales remain constant.

17.1.1 Ways to Increase P/ V Ratio

P/ V ratio is useful in product analysis. A comparison of P/ V ratios for different products will reveal the most profitable product. Higher the P/ V ratio, more will be the profit, and lower the ratio, lesser will be the profit. The management can try to increase the value of P/ V ratio by:

1. increasing the selling price per unit.
2. reducing the direct and variable costs.
3. switching over to products which show higher P/ V ratio.

P/ V ratio may be explained by way of an example as follows:

 

Sales	Rs.
	5,00,000
Variable costs	1,00,000
Fixed costs	75,000

By applying the formula

we can compute the variable costs as follows:

 

Variable costs	= Rs. 5,00,000 (1 − 0.8)
	= Rs. 5,00,000 × 0.2
	= Rs. 1,00,000.

 

Illustration 17.1

Comment on the profitability of each product from the following costing records:

Particulars	Product X per Unit Rs.	Product Y per Unit Rs.
Selling price	50	125
Material (Rs. 5 per kg)	10	40
Labour (Rs. 2.50 per hour)	12.50	25
Variable overhead	5	10
Total fixed costs are Rs. 6,000.

Solution

 

Result 1: If contribution per unit is the criterion, product Y is more profitable as Rs. 50 is the contribution per unit, whereas Rs. 22.50 is the contribution by the product X.

Result 2: If P/ V ratio is the criterion, product X shows a better ratio of 45% when compared to the product Y which shows only 40%. Hence, product X is more profitable.

Now, one may be able to understand the technique of P/ V ratio and differentiate from the marginal-costing technique where only contribution factor served as the deciding factor.

Important Note

1. If only “contribution per unit” and “P/ V ratios” are the available results, P/ V ratios should be considered to make decisions.
2. If “contribution per unit”, P/ V ratios, contribution per limiting factor are all available, it is better to make decisions on “contribution per limiting factor”.
3. However, an entire picture of the factory can be better understood, if analysis is carried out by taking all the three factors.

Illustration 17.2

Taking the same figures from the illustration 1, we may determine profitability when:

1. the raw material is in short supply.
2. labour is the constraint factor (production is limited).
3. the sales quantity is limited.
4. the sales value is limited.

Solution

 

Repeat the first 4 steps as in illustration 1, and then continue:

17.1.2 Results of Analysis (After Taking into Account the Various Limiting Factors)

1. When the raw material is in short supply, i.e., material is the key factor, the contribution per kg of product X is higher (Rs. 11.25), whereas the contribution per kg of product Y is lower (Rs. 6.25). So, product X will be more profitable.
2. When labour is the constraint factor, that is, the production capacity is limited, the contribution per hour of product Y is higher (Rs. 5) when compared to that of the product X which is lower (Rs. 4.50). Hence, product Y will be more profitable.
3. When the sales quantity is limited, the contribution per unit of product Y is higher (Rs. 50) when compared to that of the product X which is lower (Rs. 22.50). (Refer Step 3 of the illustration 1.) Therefore, product Y is more profitable.
4. When sales value is limited, P/ V ratio of product X is higher than that of product Y. (Refer Step 4 of the illustration 1.) As such, product X is more profitable.

17.2 COST–VOLUME–PROFIT ANALYSIS

The cost–volume–profit (CVP) analysis assists the management of any business entity in determining the relationship of costs and revenues to profit. CVP analysis aims at determining the effect that a change in volume, cost price and product mix will have no profits. This analysis is based on the assumption that the volume of production drives cost and revenue. We have to analyse the factors involved in this analysis, namely, cost of manufacture (C), volume of sales effected (V) and profit or revenue (P) earned. All these factors are interdependent. Generally, profits are affected to a great extent by the interplay of costs and volume. Of these, the cost factor is considered to be the major criterion in the CVP analysis as determining how costs change with output is a difficult task. Further, costs are divided into fixed and variable costs. Fixed costs remain constant. They do not change with production (volume). As such the amount per unit declines as the output increases. Because of this, we can say that fixed costs have a very little relationship with the volume of production. But the variable costs are directly associated with the level of activity. Variable costs may increase or decrease according to the increase or decrease of the level activity. Because of this, the amount per unit remains the same. The other factor, volume is generally expressed in terms of percentage of maximum sales or value of sales or unit of sales, and production capacity is expressed generally in terms of percentage of maximum production, production in revenue, physical terms, direct labour hours and machine hours. The CVP analysis tries to project a picture of profit at different levels of activity. To put in a nutshell, CVP analysis aims to determine the behaviour of profits in relation to output and sales.

17.2.1 Definition of CVP Analysis

This may be defined as, “The study of the effects on future profits of changes in fixed cost, variable cost, quantity and mix”.

The analysis of CVP requires an interaction of many factors, the important being (i) the volume of sales, (ii) the selling price, (iii) the product mix of sales and (iv) variable costs per unit.

Analysis of CVP is explained by way of illustrations, after explaining the technique “break-even analysis”.

17.3 OBJECTIVES (UTILITY) OF CVP ANALYSIS

The objectives of CVP are detailed as follows:

Determination of optimum selling price: Pricing plays an important part in the activity of a business. CVP analysis assists in framing the pricing policies of products with an aim on the profit.

profit planning: In order to estimate the profit or loss at different levels of activity, CVP analysis is essential.

Exercise cost control: CVP analysis assists in the evaluation of profit, cost incurred, and the like which facilitates the task of cost control.

Forecasting profit: To forecast precisely, it has become necessary to study the relationship between profits and costs on one side and volume on the other.

Decided alternative course of action: To make decisions accurately, CVP analysis helps to decide on the alternative courses of action, i.e., to make or buy, to continue or shut down, etc.

Planning for cash requirements: CVP analysis assists in planning for cash requirements at a given volume of output.

New product decisions: CVP analysis is very helpful in deciding to launch a new product (nature, volume of output, price, volume of sale).

Determination of overheads: CVP analysis helps in determining the amount of overhead cost to be charged at various levels of activity (operation) because overhead rates are generally predetermined to a selected volume of production.

Setting up flexible budgets: CVP analysis is helpful in setting up flexible budgets which indicate costs at different levels of activity.

Applications of CVP analysis are discussed, after explaining the concepts of break-even and margin of safety.

17.4 BREAK-EVEN ANALYSIS

Break-even analysis is a technique to formulate profit planning. As already explained, costs are divided into fixed costs and variable costs. Changes occur in such costs at different levels of production. The effect on profit due to these variations has to be studied for a proper profit planning. Break-even analysis is an analytical technique for studying the relationship between costs and revenues. It may be defined as, “a technique which shows the profit-ability or otherwise of an undertaking at various levels of activity and as a result indicates the point at which sales will equal total costs” (at which neither profit nor loss will occur). The break-even analysis depicts the following information at different levels of production (activities).

Features of Break-even Analysis are as follows:

1. Variable costs, fixed costs and total costs.
2. Sales value.
3. Break-even point, i.e., the point at which the total costs just equal (break-even) with sales. This is the point at which neither profit nor loss will occur.
4. profit or loss.

Break-even analysis is more or less similar to CVP analysis because break-even analysis also tries to depict the relationship between the factor cost of production, volume of production and profit (value of sales). It is useful to take important managerial decisions.

17.4.1 Assumptions Underlying Break-Even Analysis

Following are some of the assumptions underlying break-even analysis.

Cost variability concept: The concept of cost variability is valid. Costs can be classified into fixed and variable costs.

Fixed costs are constant: The fixed costs will remain constant. There are certain factors for which the costs may not change, whatever may be the level of activity.

Segregation of semi-variable costs: Semi-variable costs can be segregated into fixed and variable.

Constant selling price: The selling price does not change as the volume of sales changes.

No change in product: In case there is only one product, then there will not be any change in that product; if there is more than one product, then that sales mix will remain constant.

Management policy: The basic managerial policies will remain unchanged.

Short-term price level: In the short run, the general price level will remain stable.

Constant product mix: Like sales mix, the product mix will also remain unchanged.

Operating efficiency: Operating efficiency of the firm will neither increase nor decrease.

Synchronization between production and sales: The number of units of sales will coincide with the number of units of production so that inventory may remain constant or NIL (i.e., no opening and closing stock).

17.4.2 Break-Even Point

The terminology of CIMA defines the break-even point (BEP) as, “the level of activity at which there is neither profit nor loss”. It may be said otherwise as: BEP denotes the activity level at which the total costs equal the total revenue. If the level of activity is increased beyond this point, profit will accrue. If the level of activity is decreased below this point, loss will arise. BEP may be expressed in terms of units or value. If it is expressed in terms of units, it is called as break-even volume. Ifit is expressed in terms of value, then it is known as break-even sales value.

17.4.2.1 Definition and Formula to Determine BEP

1. Break-even volume is calculated as:
2. Break-even sales value is calculated as:

17.4.2.2 Methods for Determining BEPs

The following methods can be adopted to determine the BEP:

1. Graphic Presentation:

   Under this category, there are too methods, namely:

   1. Break-even chart and
   2. profit—volume chart.
2. Algebraic Methods:

   Under this category also, there are two methods:

   1. Contribution-margin approach and
   2. Equation technique.

Let us discuss one by one here:

(a) Graphic Presentation (or Graphical Method):

(i) Break-Even Chart (BEC)

Break-even chart is a graphic relationship between costs, volume and profits. This chart depicts the BEP. In addition, it shows the effects of costs and revenue at different levels of sales. CIMA of London defines the break-even chart as, “a chart which indicates approximate profit or loss at different levels of sales volume within a limited range”. Assumptions underlying break-even charts are similar to that of assumptions relating to break-even analysis, as explained earlier.

A break-even chart (BEC) may be presented in various forms.

First method:

Step 1: Take a graph paper. Draw X axis and Y axis. Fix the scale. For example: [1 cm = 1000 units or 1 cm = Rs. 1000]. According to the question, X line is known as the horizontal line or axis. Y line is known as the vertical line or axis.

Step 2: On the X axis of the graph, plot (fix the points or mark the points) the volume of output or production or quantities of sale according to the figures given in the question after converting them to scale.

Step 3: On the Y axis or the vertical line, plot costs/sales revenues (i.e., mark the points) according to the figures given in the question after converting them to scale.

Step 4: Mark the point on Y axis for fixed costs. From this point, draw a line parallel to that of X axis. This line is called “fixed cost line.”

Step 5: The variable costs for different levels of activity are marked over and above the fixed cost line. The marks are joined. This variable cost line is joined to the fixed cost line and this point is zero volume of production. This line is known as “total cost line”.

Step 6: Sales value at different levels of output are plotted (marked) from the origin and the marked points are joined. This line is known as “sales line”.

Step 7: The sales line so drawn will cut the total cost line at a point. This point of intersection of these two lines is referred to as “break-even point”. At this point, the total costs equal the total revenues.

Step 8: Join a line to Y axis from this intersection point. This gives the sales value of the product at BEP.

Step 9: Join a line to X axis from this intersection point. This gives the number of units produced at BEP.

Step 10: The angle at which the sales line makes with the total cost line while intersecting at BEP, is called the “angle of incidence”.

An overall view of this chart (reveals) depicts the approximate contribution at different levels of sales volume, but, of course, within a limited range of activity.

Illustration 17. 3

From the given data, construct a break-even chart and compute BEP:

Solution

NOTE: Follow the steps as explained earlier and construct the BEC as follows:

Second Method:

• This is a slight variation of the first method as explained previously. Contribution at various levels of output can automatically be seen.
• Same procedure has to be repeated.
• First, the variable cost line has to be drawn.
• Then, the fixed cost line is drawn above the variable cost line. This is the total cost line too.
• The sales line is drawn as described earlier.

Illustration 17.4

For the same data in illustration 3, the contraction of graph is shown as follows:

(ii) Contribution break-even chart:

• The contribution break-even chart shows the approximate amount of contribution at different levels of activity in addition to the BEP.
• Fixed cost line is drawn parallel to the horizontal axis.
• The contribution (sales–variable costs) line is to be drawn from the origin, i.e., which commences from O and proceeds evenly as the output increases.
• But here, the intersection of sales line with cost line does not arise.
• The point at which the contribution line intersects the total cost line is the BEP. Here, at this point CONTRIBUTION EQUALS FIXED COSTS (expenses).

Illustration 17.5

Taking the same figures as in illustration 3, the data are presented with contribution:

(iii) profit–Volume Graph

The profit–volume (P/ V) graph shows the relationship between profit and volume. The P/ V graph is a simplified form of break-even chart. It requires the same basic data for its construction. It suffers from the same limitations as that of BEC. A P/ V graph may be constructed if any two of the following data are provided:

1. Fixed overhead.
2. profit at a given level of activity.
3. BEP.

In constructing the P/ V graph, separate lines for costs and revenues are eliminated. Only figures relating to profit are plotted (marked).

Steps in the Construction of P/ V Graph:

Step 1: Take the graph paper. Draw the X axis (horizontal axis) and Y axis (Vertical axis).

Step 2: A scale for sales is selected (according to the figures shown in the problem). For horizontal X axis, points are plotted. The points are connected by a line. This is sales line.

Step 3: A scale for profit and fixed cost (according to the figures shown in the question) is selected for vertical Y axis.

NOTE: The graph is divided into two areas by a sales line, which are: (1) The vertical axis above the zero line represents “profit area” and (2) The vertical axis below the zero line represents “loss area” or fixed-costs area.

Step 4: Points are marked (plotted) for profits and fixed costs for the corresponding sales volume. The points are connected by a line. This line is known as “profit line”.

Step 5: The profit line intersects the sales line at the horizontal axis. This point of intersection is the required BEP.

Illustration 17.6

From the following data, you are required to construct a profit / Volume graph:

 

	Rs.
Sales	2,00,000
Variable costs	1,20,000
Fixed costs	50,000
Net profit	30,000

Solution

From the graph, it can be seen that

(i) BEP is Rs. 1,25,000.

This can be checked by applying the formula as

1. 
   
2. 
   

B. Algebraic Methods:

(i) Contribution-margin approach:

1. 

   or

2. 

   or

3. 

   or

4. 

   or

5. BEP (in Rs.) = BEP (units) × selling price per unit

NOTE: Depending on the cost data available, a suitable formula (one among the five different formulae mentioned above) should be selected and the figures should be substituted in the formula to determine the BEP.

(ii) Equation Technique:

Derivation of the equation may be explained as follows:

This technique is based on the income equation which is as follows:

Sales – Total costs = Net profit.

As the total costs can be segregated into fixed and variable, the equation may be rewritten as:

Sales – Fixed costs – Variable costs = Net profit

or

      Sales = Fixed costs + Variable costs = Net profit

This can be modified as:

      SP (S) = FC + VC (S) + P

Where:

      SP = Selling price per unit.

        S  = Number of units required to be sold to break-even.

      FC = Total fixed costs.

      VC = Variable cost per unit.

        P  = Net profit (zero).

Substituting the value of P, we get:

      SP (S) = FC + VC (S) + (Zero) 0.

      SP (S) = FC + VC (S).

      SP (S) – VC (S) = FC.

        S (SP – VC) = FC.

      

The level of sales required to earn a particular level of profit can be determined by using the formula:

Illustration 17.7

A product is sold at a price of Rs. 100 per unit and its variable cost is Rs. 80 per unit. The fixed expenses of the business are Rs. 10,000 per year. You are required to calculate: (i) BEP in units; (ii) BEP in values; (iii) profits made when sales is 620 units; and (iv) Sales to be made to earn a profit of Rs. 10,000 for the year.

Solution

First, the P/ V ratio has to be determined.

	Rs.
Step 1 → Selling price unit (given)	100
Step 2→ Less: Variable cost (given)	80
* Step 3→ Contribution per unit (2–3)	20

Step 4 → Select the appropriate formula

†Step 5 → Substituting the values, we get

1. Now, we can determine BEPs as follows (in units):

   Step 1 →

   Step 2→

2. BEP in Rs.

   Step 1 →

   Step 2 → Substituting the values in the formula, we get:

   
3. profit made when the sales is 620 units:

    

   Step 1 → Contribution per unit	= Rs. 20 (Ref Step 3).
   Step 2 → Total contribution of 620 units	= 620 x Rs. 20
   	= Rs. 14,400.
   Step 3 → Less: Fixed cost for the year	= Rs. 10,000 (given).
   Step 4 → profit (Step 2 – Step 3)	= Rs. 4,400.

    

4. Required sales to be made to earn a profit of Rs. 10,000:

   Step 1 → Formula or required sales =

   Step 2 → Substituting the values in the formula, we get:

   

∴ Required sales to earn a profit of Rs. 10,000 = Rs. 1,00,000.

Illustration 17.8

A factory manufacturing calculators had the capacity to produce 10,000 calculators per annum. The marginal cost of each calculator is Rs. 100 and each calculator is sold for Rs. 150. Fixed overheads are Rs. 20,000 per annum. Calculate the BEPs for output and sales and determine the profit of output as 80% capacity?

Solution

NOTE: For this type of problem, first gather the needed data by way of simple calculations before attempting to solve the problem.

 

1. Contribution per calculator (unit)	= Sales – Variable cost
	= Rs. 150 – Rs. 100 = Rs. 50.
2. Total contribution	= Contribution per unit x Total no. of units
	= Rs. 50 x 10,000 = Rs. 5,00,000.
3. Total sales	= Selling price/unit x Total sale of units
	= Rs. 150 x 10,000 = Rs. 15,00,000.
4. P/ V ratio	=

Now, going to the problem,

 

(a) BEP (in units) or (for output)
(b) BEP (for sales) in Rs.	= Output x Selling price/unit
	= 400 × Rs. 150 = Rs. 60,000.

 

Any formula can be used to compute BEP (in Rs.) or (for sales):

1. 
   
   
2. 
   
   
3. 
   
   
4. 
   
   

[Generally, selection of formula depends on the availability of data needed to substitute in.]

(c) Calculation of profit at 80% capacity:

 

Step 1 → Full capacity	= 10,000 calculators.
Step 2 → 80% capacity
Step 3 → BEP of output (in units)	= 400 calculators.
Step 4 → profit on 8,000 calculators	= (80% capacity – BEP) × contribution/unit
	= (8000 – 400) × Rs. 50
	= 7600 × Rs. 50
	= Rs. 3,80,000.

 

Important Note: Fixed overheads are recovered entirely at the BEP. Hence, the entire contribution beyond the BEP is profit.

17.5 CONCEPT OF SOME IMPORTANT TERMS

17.5.1 Cost BEP

• In case there are two alternatives and the costs under two alternatives are equal, then such condition is referred to as “cost BEP”. It is also called as “cost indifference point”.
• Its use is to decide which alternative is better to undertake the further level of activity.
• The formula for computing cost BEP is:

Illustration 17.9

A company intends to purchase a new plant. There are two alternative choices available:

Choice 1: Plant X: The operation of this plant will result in a fixed cost of Rs. 50,000 and variable costs of Rs. 6 per unit.

Choice 2: Plant Y: The purchase of this plant will result in a fixed cost of Rs. 75,000 and variable costs of Rs. 4 per unit.

You are required to advise the management which choice (plant) would be preferred and under what condition by using cost BEP.

Solution

Step 1 → First compute the cost BEP:

Results:

1. Purchase of plant Y will result in an increase of Rs. 25,000 in the fixed costs.
2. Saving of Rs. 2/unit in the variable cost.
3. The total cost of the two plants will be the same at an output of 12,500 units (Cost BEP).

Step 2 → Condition 1: If the output is to be less than 12,500 units, then purchase of plant × is preferable.

             Condition 2: If the output is to be more than 12,500 units, then purchase of plant Y is preferable.

             Condition 3: If the output is at BEP level, i.e., 12,500 units, then any one plant may be purchased.

17.5.2 Cash BEP

Cash BEP refers to the level of output (or sale) at which there will be no cash profit and no cash loss to the business entities. It refers to the level of activity where the cash inflow will equal the cash requirements to discharge (immediate) the cash liabilities.

To compute cash BEP, the formula is:

• The fixed costs have to be classified into two categories as: (i) Fixed costs that do not require immediate cash requirements, e.g., deferred expenses and depreciation and (ii) Fixed costs that require immediate cash requirements, e.g. wages and rent. This has to be taken into account.

Illustration 17.10

From the following data, you are required to compute the cash BEP:

	Rs.
Selling price	30
Variable cost/unit	18
Fixed costs	17,000

Fixed costs include Rs. 6,000 as depreciation: 50% of which has been taken as the variable cost and included in the variable cost per unit, given alone presuming an activity level of 1,500 units.

Solution

Step 1 →

• Fixed costs have to be classified and they require immediate cash requirements that will have to be taken.
• In this problem, fixed costs are shown as Rs. 17,000.
• In further information, it was given as follows: fixed costs include Rs. 6,000 as depreciation. 50% of it has to be treated as variable cost, i.e., 50% of Rs. 6,000 = Rs. 3,000. This Rs. 3,000 is included in the variable cost shown in the problem. Variable cost per unit has to be computed and deducted from the one that is given. Variable cost Rs. 2 per unit. he amount thus calculated has to be deduced from Rs. 18 to No. of units 1500 compute the cash contribution/unit.
• Cash fixed costs will be Rs. 17,000 – Rs. 3,000 = Rs. 14,000.
  

Important Note: If no detailed information is provided in the question, the entire depreciation amount has to be deducted to find the cash fixed costs. But in this case, details are furnished.

17.5.3 Composite BEP

A business entity may have different manufacturing establishments. Each establishment will have its own (or separate independent) production capacity and fixed costs, but will produce the same product. At the same time, the entity as a whole is a (one) unit having different establishments under the same management.

When more than one product is involved, BEP cannot be stated in units. This is because the sales volume of different products are expressed in different units of measurement. Some products may not be of a comparable nature and the contribution per unit may also differ. Hence, P/ V ratio has to be used to compute BEPs in terms of sales value (i.e., in rupee value). As all the products may not have the same P/ V ratio, we have to assume a constant sales mix at all levels of sales. Hence, the combined fixed costs have to be met by the combined BEP sales.

There are two approaches to determine BEP under such circumstances:

1. Constant (product or) sales mix
2. Variable (product or) sales mix

17.5.3.1 Constant Sales-Mix Approach

Under this approach,

1. The ratio in which the products of various establishments are mixed is constant.
2. Such mix must be maintained at BEP sales.

Illustration 17.11

Flora Ltd has two factories A and B producing the same cosmetic product whose selling price is Rs. 100 per unit. The following are the other factors:

	A	B
Capacity (in units)	20,000	30,000
Variable cost per unit	Rs. 75	Rs. 80
Fixed expenses	Rs. 3,00,000	Rs. 2,00,000

You are required to compute BEP for the two factories and for the company as a whole under constant sales-mix approach.

Solution

 

1. BEP for two factories separately:

Particulars	Factory A	Factory B
Step 1 → Sales value per unit	Rs. 100	Rs. 100
Step 2 → Variable cost per unit	Rs. 75	Rs. 80
Step 3 → Contribution (Step 1 – Step 2)	Rs. 25	Rs. 20
Step 4 → Fixed expenses	Rs. 3,00,000	Rs. 2,00,000
Step 5 → BEP
	= 12,000 units	= 10,000 units

2. Composite BEP: Constant sales-mix approach.

Step 1: Under this method, the fixed ratio of sales mix has to be calculated.

 

Units in Factory A	= 20,000.
Units in Factory B	= 30,000.
Total units in both factories	= 50,000.

Step 2: Combined P/ V ratio is to be computed.

Combined P/ V ratio = (Ratio of A × Contribution for A) × (Ratio of B × Contribution for B) /SP

Step 3: Combined fixed expenses:

[A: Rs. 3,00,000 + B: Rs. 2,00,000] = Rs. 5,00,000.

Step 4:

Step 5: As the sales price is uniform, the mix ratio will be the same as that of the capacity ratio, i.e., 2:3.

17.5.3.2 Variable Sales-Mix Approach

Illustration 17.12

Use the same figures as in the previous illustration.

Solution

Step 1 → Under this approach, the first contribution per unit is determined.

Ref: Solution to previous illustration.

Contribution per unit for A = Rs. 25 for B is Rs. 20.

Step 2 → Among the two, choose the one whose contribution is higher. Here, contribution for A is higher. Hence, it should be used first and that too with its full capacity. That means, 20,000 units should be produced before the production of B.

Step 3 → So, the contribution will be 20,000 (units) × Rs. 25 (contribution) = Rs. 5,00,000.

Step 4 → Total fixed expenses for both the factories (Rs. 3,00,000 + Rs. 2,00,000) = Rs. 5,00,000.

[As both are equal, no need arises to compute the additional contribution required to meet the fixed expenses in full—in this illustration.]

Illustration 17.13

Sathyam Ltd manufactures and sells four types of products under brand names P, Q, R and S. The sales mix comprises of P, Q, R and S, respectively. The total budgeted sales (100%) are Rs. 80,000 per month.

Operating (variable) costs are:

 

Product P	65% of selling price.
Product Q	75% of selling price.
Product R	80% of selling price.
Product S	40% of selling price.
Fixed costs	Rs. 16,000 per month.

1. Calculate the BEP for the products on an overall basis.
2. It has been decided to introduce a change in the sales mix as follows, when the total sales per month remaining Rs. 80,000.

Product	P 20%
Product	Q 45%
Product R	25%
Product S	10%

Assuming that the proposal is implemented, calculate the BEP.

 

[I.C.W.A. M.Com–Madras University–Modified]

Solution

 

Step 1 →	P/ V ratio (may be modified as): 100 – variable cost to sales ratio.
Step 2 →	(i) For Product P = 100 – 65% = 35%.
	(ii) For Product Q = 100 – 75% = 25%.
	(iii) For Product R = 100 – 80% = 20%.
	(iv) For Product S = 100 – 40% = 60%.
Step 3 →	Weighted average P/ V ratio = ∑ (Sales mix × P/ V ratio).
Step 4 →	Substitute figures as per Step 3:

 

	%
(i) Product P: % × 35 (given) (Step 2:1)	= 13.33.
(ii) Product Q: % × 25	= 10.42.
(iii) Product R: % × 20	= 3.33.
(iv) Product Q: 10% × 60	= 5.00.
	32.08.

 

Step 5 →

Step 6 → Substituting the figures in (Step 5) formula, we get:

Result: BEP for the products on an overall basis = Rs. 50,000.

Step 7:

Composite break-even sales is Rs. 50,000 (as calculated).

Break-up figures (shares) of the products:

(2) If the proposal is implemented:

(Step 1 and Step 2 may be repeated here.)

Step 3: Weighted average P/ V ratio: ∑ (Sales mix × P/ V ratio).

 

		%
Step 4:
(i)	Product P: 20% × 35	= 7.00.
(ii)	Product Q: 45% × 25	= 11.25.
(iii)	Product R: 25% × 20	= 5.00.
(iv)	Product S: 10% × 60	= 6.00.
		29.25.

Step 5:

Step 6:

Result:

(revised) composite BEP for the proposal = Rs. 54,700 per month.

Illustration 17.14

From the following, compute the composite BEP:

	Rs.
Total fixed costs:	1,00,000
Total sales for 5 products:	5,00,000
Total variable costs:	3,00,000

Solution

1. First, compute the composite P/ V ratio:
   
2. Then composite BEP is calculated as:
   

Illustration 17.15

From the following cost data, you are required to ascertain the composite BEP:

Solution

 

Step 7: Composite contribution per unit = Sum of P + Q + R + S

     = Rs. 1.50 + Rs. 2.10 + Rs. 0.75 + Rs. 0.80

     = Rs. 5.15.

Step 8: Composite BEP

Step 9: Break-even sales mix:

17.6 PROFIT-PATH GRAPH

Illustration 17.16

From the following data relating to a firm, prepare a graph of products and pass your comments:

Product	Sales Rs.	(Rs. in 000’s) Variable Cost Rs.
C	1000	500
D	500	300
Fixed cost = Rs. 300.

Solution

First, we have to collect (compute) the needed data to construct the graph.

STAGE I: Contribution, P/ V ratio and BEP may be computed in a usual manner.

STAGE II: A statement showing cumulative sales and cumulative profit has to be prepared as follows:

STAGE III: This is a multi-product graph, as more than one product is involved. It is prepared as follows:

Step 1 → Take a graph paper.

Step 2 → Draw X axis—horizontal line. Design the scale relating to sales (figures) value. Plot the sales on X axis.

Step 3 → Draw Y axis—vertical axis both below and above the horizontal axis. Draw a scale for the fixed cost—plot the fixed cost on the vertical axis below the horizontal axis.

Step 4 → Draw a line starting from the fixed cost point. Each line at the profit point is achieved by the latest product. (This is also known as “profit path”.)

Step 5 → The total profit line intersects the sales line at a point on X axis, known as BEP relating to a group of products.

Comment: Product C has a higher contribution. Hence, its production can be increased

17.7 MARGIN OF SAFETY

Definition and Computation

Margin of safety is excess of sales over and above BEP. It may also be said that margin of safety is the difference between the actual sales and the sales at BEP. In the break-even chart, it is the distance between the BEP and the present sales of output. The terminology of CIMA defines margin of safety ratio as,

Sales beyond break-even volume will result in profits. Such sales represent margin of safety.

Margin of safety may be expressed in sales volume or value or in percentage.

Example:

1. Margin of Safety: Total sales – Sales at BEP.

 

Present Sales	Break-Even Sales	Margin of Safety
(1)	(2)	(3) = (1) – (2)
(a) Rs. 5,00,000	Rs. 3,00,000	Rs. 2,00,000
(b) 50,000 units	30,000 units	20,000 units
(c)  –	–

 

Margin of safety can be calculated with the help of the formula:

2.

Example:

	Rs.
Sales	10,00,000
Fixed cost	2,00,000
Variable cost	6,00,000

In a simpler form, profit	= Total sales – Total cost
	= Rs. 10,00,000 – (Rs. 2,00,000 + 6,00,000)
	= Rs. 2,00,000.

or

Margin of safety is an indicator of the strength of the business. The higher the margin of safety, the better it is for the business. A high margin indicates high profit, whereas a low margin of safety will indicate a low profit. This is due to high fixed costs. To set right the low margin of safety, the following measures may be undertaken by the management:

1. Fixed costs may be reduced.
2. Variable costs too may be lowered to improve contribution.
3. Volume of sales can be increased.
4. Selling prices may be increased but it should not affect the market demand.
5. Product mix may be judiciously changed to maximize the contribution.

17.8 ANGLE OF INCIDENCE

17.8.1 Meaning and Significance

This is the angle between sales line and total cost line. This angle is formed by the intersection of the total cost line and the sales line (at the BEP). This angle is an indicator of profit-earning capacity over BEP. Large angle indicates the earning of high margin of profit. Small angle indicates a low margin of profit which, in turn, suggests that variable costs constitute a major chunk of cost of sales.

In general, a small angle of incidence indicates that firms are highly stable—with narrow profit margin, low BEP, high margin of safety, low fixed cost and high variable cost, whereas a large angle of incidence indicates that firms are highly risky—with high BEP, high fixed cost, low variable cost and low margin of safety.

If angle of incidence and margin of safety are considered together, the results will be more profitable. Impact of costs and selling price on profit and loss, BEP and margin of safety.

17.9 IMPACT OF VARIABLE COST, FIXED COST AND SELLING PRICE ON CONTRIBUTION, P/ V RATIO, BEP AND MARGIN OF SAFETY

This impact is explained in the following illustration:

Illustration 17.17

A & B Co. Ltd furnishes the following data for the year that ended on 31 December 2009:

 

Selling price per unit	Rs. 20
Production and sales	1,000 units
Variable cost per unit	Rs. 10
Fixed cost	Rs. 5,000

 

You are required to show the impact of the following actions on the P/ V ratio, BEP and margin of safety as follows:

(d) The variable cost increases to Rs. 12 per unit.

(e) The fixed cost increases to Rs. 7,500.

(c) The selling price increases to Rs. 30 per unit.

Solution

The contribution per unit, P/ V ratio, BEP and margin of safety for the current situation, and the proposed situation for each alternative course of action have to be determined.

From the results so obtained, each of its impact can be studied.

Solution

Now, compare the results with those shown in the chart shown earlier. Impact can be understood clearly.

17.10 APPLICATIONS OF CVP ANALYSIS

CVP analysis helps to make a decision on the 11.1 modernization of production:

Illustration 17.18

Renu Ltd is contemplating on a modernization programme. It has identified a machinery costing Rs. 2,00,000 to purchase. The machinery is expected to increase the output substantially from its existing level of 15,000 units to 25,000 units. The rate of depreciation applicable to the machinery is 25%. The introduction of the new machinery is expected to reduce the variable cost by Rs. 3 per unit due to reduction in the labour strength. No additional fixed costs will be incurred except for its depreciation. The existing cost structure is as follows:

Selling price per unit is Rs. 15.

Variable cost per unit is Rs. 8.

Fixed cost is Rs. 60,000 per annum.

As a cost accountant, analyse whether it is justifiable to go in for a modernization programme by installing a new machinery?

Solution

This is solved in the following order:

1. Contribution/unit has to be determined.
2. Present total contribution is to be calculated.
3. Desired total contribution is to be calculated.
4. Finally, the number of units required to be produced and sold so as to maintain the desired contribution, has to be ascertained.

Comment:

1. The firm must manufacture and sell 15,333 units of the products in order to maintain the existing level of contribution. At present, it is 15,000 units only.
2. By the modernization proposal, the new machinery increases the level of production from 15,000 units to 25,000 units. This additional production of 10,000 units would bring in an additional contribution of Rs. (10,000 units × Rs. 15) 1,50,000.
3. Modernization proposal is highly recommended, as it yields an additional contribution of Rs. 1,50,000.

This CVP analysis will be much helpful in studying the effects of general expansion in the level of operations:

Illustration 17.19

Vas Ltd. is engaged in the manufacture and sale of a consumer product. Its budget for the next year shows the following data:

 

	Rs.
Selling price/unit:	20
Variable cost/unit:	15
Fixed costs:	Rs. 50,000

 

A research agency suggested that the firm shall increase its production and sale by 25% by reducing its selling price by 10%. However, the firm is working in its full capacity (and producing 20,000 units). In order to increase its production and sale, it has to expand its factory. The expansion would lead to an increase in the fixed by Rs. 25,000.

You are required to advise the firm regarding the expansion.

Solution

Contribution per unit, total contribution, BEP and margin of safety have to be ascertained to take the decision, regarding the expansion of the firm.

 

Comment:

1. Expansion proposal reveals that such expansion raises the BEP (in units) to a substantially higher level from 10,000 units to 25,000 units.
2. Under-expansion proposal margin of safety is zero.
3. Contribution per unit also is lower by Rs. 2 for the expansion proposal.

Advise: It is not profitable to embark on an expansion proposal. It is profitable to carry on the business under the existing level.

This CVP analysis assists in designing a new product or diversifying the existing product line:

Illustration 17.20

M/s Bhagya & Co. is currently engaged in the manufacture and sale of a product EC. Its budget for the next year reveals the following:

 

Selling price/unit	: Rs. 15
Variable cost/unit	: Rs. 10
Fixed cost	: Rs. 50,000
Demand	: 25,000 units

 

It wants to diversity into product OK in order to reduce its market risks, and following are the estimated data for the new product OK.

 

Selling price/unit	: Rs. 18
Variable cost/unit	: Rs. 12
Fixed cost	: Rs. 30,000
Demand	: 10,000 units.

 

You are required to suggest whether a diversification is advisable?

Solution

As usual, calculate the contribution per unit, total contribution, BEP and margin of safety to decide on the issue.

 

Comments:

1. The new product OK has a low BEP, i.e., 5000 units.
2. The new product OK increases the total contribution by Rs. 60,000 (Rs. 1,25,000 + Rs. 60,000 = Rs. 1,85,000).
3. There is margin of safety but not higher than the existing product.

Advise: It is advisable to introduce the new product OK, subject to other market conditions.

This CVP analysis assists in profit planning:

Illustration 17.21

Mrs Panel has Rs. 3,00,000 investments in her business firm. She wants a 10% return on her money. From the analysis of the recent cost figures, she finds that her variable cost of operating is 70% of sales and her fixed cost is Rs. 90,000 per annum. Show computations to answer the following questions:

1. What sales volume must be obtained to break-even?
2. What sales volume must be obtained to get a 10% return on the investment?
3. Mrs Panel estimates that even if she closed the doors of her business, she would incur Rs. 30,000 as the expenses per year. At what sales would she be better off by locking her business up?

[I.C.W.A.I.–Modified]

Solution

 

This CVP analysis helps in determining the optimum sale price of products:

Illustration 17.22

In a purely competitive market, 15,000 FM sets can be manufactured and sold and a certain profit is to be generated. It is estimated that 3,000 FM sets need to be manufactured and sold in a monopoly market in order to earn the same profit. profit under both conditions is targeted at Rs. 3,00,000. The variable cost per FM set is Rs. 150 and the total fixed cost is Rs. 50,000.

You are required to find out the unit selling prices under both the conditions: competitive and monopoly.

 

[I.C.W.A.I. Inter–Modified]

Solution

Part I: Sale price under competitive conditions:

 

Step 1 → Let the selling price unit be taken as	= x.
Sales value (Total)	= x ×15,000 units.
Step 2 → Variable cost of production	= Variable cost/unit × No. of units
	= Rs. 150 × 15,000
	= Rs. 22,50,000.
Step 3 → Contribution (total) (Step 1–Step 2)	= 15,000 × – Rs. 22,50,000.
Step 4 → But, the total contribution	= Sum total of fixed cost + profit
	= (Rs. 50,000 (given) + Rs. 3,00,000 (given)
Step 5 →           Step 3	= Step 4
15,000x – 22,50,000	= Rs. 50,000 + Rs. 3,00,000
or 15,000x	= Rs. 50,000 + Rs. 3,00,000 + Rs. 22,50,000
or 15,000x	= Rs. 26,00,000
x	= Rs. 26,00,000 = Rs. 173.33.

 

[Answer: The selling price of one unit of FM set under competitive conditions = Rs. 173.33.]

Part II: Sale price per unit under monopoly conditions:

 

Step 1 → Let the selling price per unit be taken as y
Sales value (Price × No. of units)	= y × 3000 = 3000y.
Step 2 → Total variable cost of production
(Variable cost per unit × No. of units)	= Rs. 150 × 3,000 = Rs. 4,50,000.
Step 3 → Total contribution
(Sales value–Variable cost) (Step 1–Step 2)	= 3000 y – Rs. 4,50,000.
Step 4 → But, the total contribution	= Sum total of fixed cost +
	profit Rs. 50,000 + Rs. 3,00,000
Step 5 →           As Step 3	= Step 4
3000y–Rs. 4,50,000	= Rs. 50,00,000 + Rs. 3,00,000
or 3000 y	= Rs. 50,00,000 + Rs. 3,00,000 + Rs. 4,50,000
or 3000 y	= Rs. 8,00,000
or y
	=Rs. 266.67.

 

[Answer: The selling price of one unit of FM set under monopoly condition = Rs. 266.67.]

12. So far, we have discussed the various concepts associated with (i) marginal costing; (ii) P/ V ratio; (iii) BEP; and (iv) CVP analysis. In fact, each concept is interrelated to the other concept.

Interrelation of Concepts

1. By applying the marginal-costing technique we compute the contribution [Contribution = Sale – Variable cost]
2. Based on the contribution, we determine the P/ V ratio, i.e., contribution to sales ratio [ P/ V ratio = contribution per sales].
3. Applying the P/ V ratio, we compute the BEP
4. Combining all, we study CVP analysis. We have analysed these (basic tenets of each) by way of illustrations, so far. Now, we have to explain model-wise the above concepts in the forthcoming pages.

17.11 MODELS

Illustration 17.23

Model 1: Marginal costing (contribution) and P/ V ratio. (Determination of contribution and P/ V ratio and comparability of profit—Based on the results, decisions are to be taken.

From the following data, compute contribution and P/ V ratio and comment on the profitability of products:

Particulars	X Rs.	Y Rs.
Materials/unit	500	400
Wages/unit	200	300
Fixed overheads/units	700	200
Variable overheads/units	200	400
Sales per unit	2,000	2,000
Output per month	300 units	200 units

Solution

First, the contribution per unit has to be calculated.

Second, P/ V ratio has to be determined.

Third, the profit has to be ascertained.

Finally, based on the results, the decision has to be made.

 

Results:

1. Contribution/unit is higher for Product X, i.e., Rs. 1,100.
2. P/ V ratio is too higher for Product X, i.e., 55%.
3. But profit/unit and total profit is higher in case of Y, i.e., Rs. 700 and Rs. 1,40,000, respectively.

Decision:

1. Under normal circumstances (if there is no key factor), Product Y would be preferable since profit/unit is higher when compared to X.
2. In case the output in terms of units is the key factor, Product × would be more profitable.

[Students should observe here that though contribution and P/ V ratio are higher for Product X, profit/unit is lower for Product X. Decision has to be arrived at accordingly]

Illustration 17.24

Model 2: Contribution, P/ V ratio, BEP and profit

In the previous model, three factors were taken into account, whereas in this model, one more factor, i.e., BEP is clubbed to make decisions)

Take the same data as in the previous illustration and calculate the BEP in addition.

Solution

Repeat the steps from 1 to 7 as in the previous solution to illustration:

Step 8

Result:

Repeat 1 to 3 (as in the previous question).

4: BEP is higher with respect to product X, i.e., Rs. 3,81,818.

Decision:

Repeat 1 and 2 as in the previous question.

3: Product Y starts making profit when the sales exceeded Rs. 88,888 (BEP), whereas the Product × starts making profit only if the sales exceeded Rs. 3,81,818. Based on the BEP, as Product Y begins to earn profit earlier than Product X, Product Y is preferable.

Illustration 17.25

Model 3: Contribution, P/ V ratio, sales (volume) and profit]

From the following data, calculate:

1. BEP (in rupees) sales value.
2. Number of units that must be sold to earn a profit of Rs. 1,00,000 per year.
3. Number of units that must be sold to earn a net income of 20% on sales.

	Rs.
Sales price	25 per unit
Variable manufacturing costs	12 per unit
Variable selling costs	5 per unit
Fixed factory overheads	6,25,000 per year
Fixed selling costs	2,75,000 per year

[B.Com (Hons)–Delhi–Modified]

Solution

NOTE: First, compute the total fixed costs as:

 

Total fixed costs	= Fixed factory overheads + Fixed selling costs
	= Rs. 6,25,000 + Rs. 2,75,000
	= Rs. 9,00,000.

(a)

 

(b)

	Rs.
Step 1 →Fixed cost (Ref: Note)	9,00,000
Step 2 → Add: Profit expected (given)	1,00,000,
Step 3 → Total contribution required (Step 1 + Step 2)	10,00,000
Step 4 → Sales volume required to earn the desired contribution (profit)
Results: Sales volume required to earn a profit of Rs. 1,00,000 per year	= 1,25,000 units

(c) Let us assume that the units to be sold be × units.

Step 1 → Sales value:(Rs. 25 × x)	25x
Step 2 → Profit on sales: 20% of 25x (given) =	5x
Step 3 → Formula: Sales value = Variable cost + Fixed cost + Profit
Result → Sales volume required to earn a net income of 20% on sales	= 3,00,000 units

Decision: profit planning can be accordingly carried on as follows:

1. To earn a profit of Rs. 1,00,000 per annum, the sales volume should be 1,25,000 units.
2. To earn a net income of 20% on sales, the sales volume should be 3,00,000 units. Sales volume is planned thus.

Illustration 17.26

Model 4: Determination of sale price, recovering of total cost and BEP]

Cost data:

 

Sale price	Rs. 250 per unit
Variable	Rs. 150 per unit
Fixed costs (expenses)	Rs. 15,00,000

 

You are required to ascertain:

1. BEP
2. Sales per unit if BEP is brought up to 20,000 units.
3. Sales per unit if BEP is brought down to 12,000 units.

[B.Com.–Madras University–Modified]

Solution

 

Particulars	Amount Rs.
(a)
Step → 1: Sale price	250
Step → 2: Less: Variable cost	150
Step → 3: Contribution per unit (Step1 – Step 2)	100
Step → 4: BEP (in units) volume	Rs. 15,00,000
	Rs. 100 = 15,000 units.
(b)
Step → 1: Total variable cost (20,000 units (given) × Rs. 150 (given)) =	30,00,000
Step → 2: Total fixed cost (given)	15,00,000
Step → 3: Total cost to be recovered (it BEP is 20,000 units) [Add: Step (2) + Step(3)]	45,00,000
Step → 4: Sale price required to recover total cost when BEP is 20,000 units =	Rs. 45,00,000
=	Rs. 20,000 Rs. 225
(c)
Step → 1: Total variable cost (Rs. 150 × 12,000 units)	18,00,000
Step → 2: Total fixed cost (given)	15,00,000
Step → 3: Total cost to be recovered when BEP is brought down to 12,000 units. (Step 1 + Step 2)	33,00,000
Step → 4: Sale price required to recover total cost when BEP is 12,000 units.	Rs. 33,00,000
	12,000 Rs. 275

Illustration 17.27

Model 5: P/ V ratio, BEP, fixed cost, variable cost, margin of safety and profit

The cost data of a company are as follows:

Period	Sales Rs.	Profit Rs.
I	75,000	10,000
II	1,00,000	15,000

You are required to compute:

(a) P/ V ratio; (b) BEP; (c) fixed cost; (d) profit when sales is Rs. 80,000; (e) sales required to earn a profit of Rs. 30,000; (f) margin of safety; and (g) variable cost of Period II.

 

[B.Com.–Madras University–Modified]

Solution

NOTES:

1. In this problem, the data relating to two different periods are given. As such, P/ V ratio has to be calculated by applying the formula:
   
2. Fixed cost has to be calculated.
3. profit when sales is Rs. 80,000 has to be ascertained.
4. Then, the remaining questions have to be answered.

Particulars	Amount Rs.
(a) Computation of P/ V ratio:
(b) Determination of BEP (sales value):
(c) *Computation of fixed cost:
Step 1 → Sales in Period I	75,000
Step 2 → Contribution from sales of Period I (P/V ratio × Rs. 75,000) 20% of 75,000)	15,000
Step 3 → Less: Profit from sales of Period I	10,000
Step 4 → Fixed cost (Step 2 – Step 3)	5,000
(d) Computation of profit when the sales is Rs. 80,000:
Step1 → Contribution from sales (20% of Rs. 80,000) (Step 1) (given)	16,000
Step 2 → Less: Fixed cost (Ref = Step 4 of (c))	5,000
Step 3 → Profit when sales is Rs. 80,000 (Step 1 – Step 2)	11,000
(e) Computation of sales required to earn a profit of Rs. 25,000:
Step 1 → Fixed cost	5,000
Step 2 → Profit targeted (given)	25,000
Step 3 → Total contribution needed (Step 1 + Step 2)	30,000
Step 4 → Sales required to earn Rs. 25,000 profit	= 1,50,000
(f) Margin of safety (Actual sales – Break-even sales) Rs. 1,00,000 − Rs. 25,000.	Rs. 75,000
(g) Computation of variable cost for Period II:
Step 1 → Sales in Period II.	Rs. 1,00,000
Step 2 → Loss: Contribution from sale for this period (20% of Rs. 1,00,000).	Rs. 20,000
Step 3 → Variable cost for Period II. (Step 1 – Step 2)	Rs. 80,000

Method 1

Illustration 17.28

Model 6: Margin of safety, variable cost and net profit]

The profit-volume ratio of A Ltd is 50% and the margin of safety is 40%. You are required to compute the net profit.

The sales value is Rs. 2,50,000.

[C. A.–Inter–Modified]

Solution

NOTE 1:

 

Variable cost ratio	= 100% – P/ V ratio
	= 100%
	50%

 

NOTE 2:

1. Marginal cost = Actual sales – Break-even sales.
2. Total fixed costs (including variable costs up to break-even sales) are usually recovered at BEP. As such, the margin of safety consists of variable costs + net profit (Margin of safety = Variable costs + profit).
3. When variable costs are deducted from the margin of safety, profit can be ascertained. (profit = Margin of safety – Variable costs).

Particulars	Amount Rs.
Step 1 → Margin of safety	1,00,000
[40% of sales (Rs. 2,50,000]	(1,00,000)
Step 2 → Variable cost
[Variable cost ratio × Margin of safety)	50,000
[50% × Rs. 1,00,000]
Step 3 → Net profit
(Step 1 – Step 2)	50,000

Method 2: Another approach

The same problem can be solved by another way as follows:

We know that margin of safety

Step 1 → Let the excess sales over BE sales be taken as X.

Step 2 → Substituting the figures in the formula, we get:

Step 3 → BE sales = Rs. 2,50,000−1,00,000 = Rs. 1,50,000.

Step 4 → P/ V ratio = 50%.

Step 5 → Variable cost = 50% (100%−50%).

Step 6 → Variable cost = Rs. 1,50,000 − (1,50,000 × )

		= Rs. 75,000.
Step 7 →	Fixed cost = Rs. 1,50,000 – Rs. 75,000	= Rs. 75,000.
Step 8 →	Contribution on sale of Rs. 2,50,000 (50% P/ V ratio)	= Rs. 1,25,000.
Step 9 →	Less: Fixed cost	= Rs. 75,000.
Step 10 →	Profit (Step 8–Step 9)	= Rs. 50,000.

Students may opt either of the approach, to solve the problem.

Illustration 17.29

Model 7: P/ V ratio, BEP, margin of safety determining the effect of increase/decrease in fixed costs, variable costs and selling price

The following cost data relates to ABC Ltd for 2009:

Sales Rs.

Variable costs 50,000

Fixed costs 25,000

Fixed costs 15,000

1. You are required to compute P/ V ratio, BEP and margin of safety at this level.
2. Further, you are required to compute the effect of:
   1. 20% increase in fixed costs.
   2. 10% decrease in fixed costs.
   3. 20% decrease in variable costs.
   4. 10% increase in selling price.
   5. 10% increase in selling price with an increase of fixed overheads by Rs. 3,000.
   6. 10% decrease in sales price accompanied by a decrease of Rs. 2,500 in variable costs.
   7. 20% decrease in sales price.

[B.Com.–Madras University–Modified]

Solution

First, at the existing level, the required data can be computed as follows:

[Write the formulae that can be used:

1.  

   
2. 
3. Margin of safety

                   or

   Actual sales − BE sales].

Substitute the figures in the formula to get the desired result:

1. At the existing level:
   

   Margin of safety = (Rs. 50,000 – Rs. 30,000) = Rs. 20,000.

2. 1. 20% increase in fixed costs:
      

      Margin of safety = (Rs. 50,000 – Rs. 36,000) = Rs. 14,000.

   2. 10% decrease in the fixed costs:

              (15,000 – 10% of 15,000: 1,500) = 13,500.

      

      Margin of safety = (Rs. 50,000 – Rs. 27,000) = Rs. 23,000.

   3. 20% decrease in the variable cost:

      20% of Rs. 25,000 = Rs. 5,000, i.e., Rs. 25,000 – Rs. 5,000 = Rs. 20,000.

      

      Margin of safety = (Rs. 50,000 – Rs. 25,000) = Rs. 25,000.

   4. 10% increase in the selling price:

      10% of Rs. 50,000 = Rs. 5000, i.e., 50,000 + 5,000 = Rs. 55,000.

      

      Margin of safety = (55,000 – Rs. 27,502 ) = Rs. 27,498.

   5. 10% increase in the selling price and an increase of fixed overheads by Rs. 3,000:

      10% increase in sale = Rs. 50,000 + Rs. 5,000 = Rs. 55,000.

      Increase in the fixed cost = Rs. 15,000 + Rs. 3,000 = Rs. 18,000.

      
   6. 10% decrease in the sales price and a decrease of Rs. 2500 in VC:

      10% of Rs. 50,000 = Rs. 5,000 = 50,000 − 5,000 = Rs. 45,000.

      Decrease in variable cost = 45,000 − Rs. 2,500 = Rs. 22,500.

      

      Margin of safety = (Rs. 45,000 – Rs. 30,000) = Rs. 15,000.

   7. 20% decrease in selling price:

      20% of Rs. 50,000 = Rs. 10,000; (Rs. 50,000 − 10,000) = Rs. 40,000.

      

      Margin of safety = (Rs. 40,000 − Rs. 40,000) = NIL.

NOTE: Students can study the results based on how one factor (increase or decrease) affects the P/ V ratio, BEP and margin of safety, which would be useful to take decisions.

Illustration 17.30

Model 8: profit planning: In conditions of heavy demand and low demand

Two firms × & Co. and Y & Co. produce and sell the same type of product in the same market. Their budgeted profit and loss account (P&L A/c) for the year 2010 are as follows:

You are required to calculate:

1. At what sales value both the firms will earn an equal profit.
2. Which firm is likely to earn greater profits in condition of:
   1. heavy demand for the product.
   2. low demand for the product.

Give reasons.

 

[C.A. –Inter–Modified]

Solution

 

Particulars	X & Co. Rs.	Y & Co. Rs.
(A) Computation of sales value to earn equal profits:
Step 1 → Sales value (given)	6,00,000	7,50,000
Step 2 → Less: Variable cost (given)	4,50,000	4,50,000
Step 3 → Contribution (Step 1 − 2)	1,50,000	3,00,000
Step 4 →
Step 5 → Sales value required to earn equal profits
(B) (i & ii): BEP (sales value):

Decision:

1. Firm Y & Co. has a higher P/ V ratio (contribution to sales ratio), i.e., 40% compared to firm × & Co., where it is only 25%. This shows that firm Y & Co. earns a higher profit than × & Co.
2. When the sales exceed Rs. 6,66,666, Y & Co will earn a higher profit. At Rs. 6,66,666, both will earn equal profits.
3. But, below that level, i.e., Rs. 6,66,666, Firm × & Co. will earn higher.
4. Under the conditions of heavy demand for the product, firm Y & Co. will earn a higher profit.
5. Under conditions of low demand, the firm × & Co. will earn a higher profit.

Illustration 17.31

Model 9: Determination of costs (fixed and variable)

A manufacturer provides you the following data regarding his operations for the year:

 

		Rs.
Break-even sales	-	5,80,000
Direct materials	-	90,000
Gross profit	-	1,50,000
Contribution margin	-	2,00,000
Direct labour	-	2,00,000
Sales	-	8,00,000
Variable manufacturing overhead	-	10,000

You are required to calculate:

1. Fixed manufacturing overhead.
2. Fixed selling and administrative overhead.
3. Variable selling and administrative overhead.

[M.Com. – Bharathidasan University–Modified]

Solution

 

NOTE:	From sales, the gross profit cost of goods sold has to be calculated.
	From the cost of goods sold, the fixed factory overhead has to be calculated.
	From the fixed factory overhead, the fixed selling and administrative overhead and finally, variably selling and administrative overhead can be determined.

(a) Determination of fixed manufacturing (factory) overhead:

 

Step 1 → Cost of goods sold	=	Sales − Gross profit
	=	Rs. 8,00,000 − Rs. 1,50,000
	=	Rs. 6,50,000.

Step 2 → Let the fixed manufacturing overhead be taken as X.

Step 3 → Cost of goods sold = Direct materials + Direct labour + Variable manufacturing overhead + Fixed manufacturing overhead.

Step 4 → Substituting the figures in the above formula, we get:

 

Rs. 6,50,000	=	Rs. 90,000 + Rs. 2,00,000 + Rs. 10,000 + x
(Step 1)		(all given)         (assumed)
x	=	Rs. 6,50,000 – (Rs. 90,000 + Rs. 2,00,000 + Rs. 10,000)
	=	Rs. 3,50,000.
Fixed manufacturing overhead = Rs. 3,50,000.

(b) Determination of fixed selling and administrative overhead:

 

Step 1 → Sales value at BEP	= Rs. 5,80,000
Step 2 → Contribution	= Rs. 2,00,000
Step 3 → Total fixed cost (Step 1 – Step 2)	= Rs. 3,80,000
Step 4 → Less: Fixed factory overhead:	= Rs. 3,50,000
Step 5 → Fixed selling & administrative overhead (Step 3 – Step 4)	= Rs. 30,000

(c) Computation of variable selling and administrative overhead:

Step 1 → Sales variable cost = Contribution.

Step 2 → Substituting the figures in the above formula, we get:

or Rs. 8,00,000 − (Rs. 3,00,000 + x)	=	Rs. 2,00,000
or Rs. 5,00,000 + x	=	Rs. 2,00,000
or x	=	Rs. 2,00,000 − Rs. 5,00,000
	=	Rs. 3,00,000 (ignore − sign).

Step 3 → Variable selling and administrative overhead = Rs. 3,00,000.

Illustration 17.32

Model 10: Reducing selling price—Increase in the sales volume profit planning

X Ltd has planned to increase the volume of sales by reducing the price of its product by 25%. But there is no proposal to change the total fixed costs or variable costs per unit. They will remain unchanged. At the same time, the management desires to maintain the present level of profit. The cost data of the company are as follows:

 

	Selling price per unit	Rs. 20.
	Variable costs per unit	Rs. 7.50.
	Fixed costs (total)	Rs. 60,000.
	No. of units sold	20,000 units.

You are required to advice the management.

 

[B.Com.–Madras University–Modified]

Solution

STAGE I: First, the existing level of profit and P/ V ratio to be determined as:

 

	Rs.
Step 1 → Sales (20,000 × Rs. 20)	= 4,00,000
Step 2 → Less: Variable costs (20,000 × Rs. 7.50)	= 1,50,000
Step 3 → Contribution (Step 1 – Step 2)	= 2,50,000
Step 4 → Less: Fixed costs	= 60,000
Step 5 → profit (Step 3 – Step 4)	= 1,90,000
Step 6 → P/ V ratio

STAGE II: Reduction in selling price by 25%:

25% of Rs. 4,00,000 = Rs. 1,00,000.

(As it is assumed now that there is no increase in sales volume)

STAGE III: As per the proposal, the plan is:

1. Reduction of 25% in the selling price.
2. Maintain the existing level of profit.
3. Fixed costs will not change.

Now, we have to compute the sales volume required to meet the situation.

Sales volume required to maintain the desired level of profit after reduction of 25% in selling price

Result:

1. A reduction of 25% in the selling price requires an increase of 66% in the sales volume, to maintain the present level of profit.
2. Taking into consideration the other important factors like raw material, labour and factory-equipment capacity, the management will have to decide whether to embark on the proposal.

[The workings may be checked to verify its correctness as follows:

 

		Rs.
Sales	:	5,00,000
Less: Variable cost (33,333.33 × Rs. 7.50)	:	2,50,000 − (2,49,999.975) (Actual figure)
Contribution	:	2,50,000
Less: Fixed costs	:	60,000
Profit	:	1,90,000.

The same profit is arrived at. Hence, the workings are accurate without any mistakes.

NOTE: Students need not do this verification step.

        Only for academic interest, it is shown here.]

Illustration 17.33

Model 11: Merger planning

There are two plants manufacturing the same products under a single corporate management. The management proposes to merge the two plants.

Following are the particulars relating to these two plants:

Capacity Operation Level	Plant I 100%	Plant II 60%
Sales	Rs. 4,00,000	Rs. 1,80,000
Variable costs	Rs. 3,00,000	Rs. 1,20,000
Fixed costs	Rs. 75,000	Rs. 25,000

You are required to calculate for the proposal of the board of directors:

1. What would be the capacity of the merged plant to be operated for the purpose of break-even?
2. What would be the profitability on working at 80% of the merged capacity?

Solution

STAGE I: Sales and variable costs of Plant II must get adjusted for a 100% capacity (which at present is 60%) [before the merger of two plants].

Step 1 → Sales at 100% capacity

Step 2 → Variable costs at 100% capacity

Step 3 → Contribution (Step 1 − Step 2) = Rs. 2,00,000.

STAGE II: Determination of the capacity of the merged plants (both I & II) to break-even at 100% capacity:

 

	Rs.
Step 1 → Sales (Ref Stage I: Step 1)	7,00,000
Step 2 → Less: Variable costs (Step 2 in Stage I)	2,00,000
Step 3 → Contribution (Step 1 − 2)	5,00,000

Step 4 →

Step 5 → BEP (sales value)

[NOTE: In terms of percentage capacity, sales at BEP would be:]

STAGE III: Calculation of profit on working at 80% of the merged capacity:

	Rs.
Step 1 → Sales (80% of Rs. 7,00,000)	= 5,60,000
Step 2 → Less: Variable costs:

Step 3 → Contribution (Step 1 − Step 2)	= 1,20,000
Step 4 → Less: Fixed costs (Rs. 75,000 + 25,000)	= 1,00,000
Step 5 → Profit (Step 3 − Step 4)	= 20,000

Illustration 17.34

Model: 12 Fixation of selling price

A single product company sells its products at Rs. 50 per unit. In 2008, the company operated at a margin of safety of 60%. The fixed costs amounted to Rs. 4,00,000 and the variable cost ratio to sales was 60%. In 2009, it is estimated that the variable cost will go up by 10% and the fixed costs will increase by 5%. You are required to

1. Compute the selling price to be fixed in 2009 to earn the same P/ V ratio as in 2008.
2. Calculate the number of units to be produced and sold to earn the same profit as in 2008, assuming the same selling price of Rs. 50 per unit.

[Madurai Kamaraj University–Modified]

Solution

Before attempting to answer the questions, P/ V ratio and number of units sold, the profit earned with respect to the year 2008 have to be determined (step-wise – not followed).

1.  

   
2. Profit earned in 2008:
   

   As the margin of safety is 60% (given), BEP is (100 − 60): 40%.

   ∴ BEP is at 40% of units sold.

   ∴ No. of units sold

   
3. Profit earned in 2008:

   Profit	=	No. of units sold × contribution − Fixed costs
   	=	50,000 × Rs. 20 − Rs. 4,00,000
   	=	10,00,000 − Rs. 4,00,000
   	=	Rs. 6,00,000.

1. Now, coming to the main part of the problem, the fixation of selling price for the year 2009, has to be calculated as follows:

    

   Step 1 → Variable costs per unit in 2008	=	Rs. 30 + 10% of Rs. 30
   	=	Rs. 30 + Rs. 3 = Rs. 33.

    

   Step 2 → Fixed cost in 2009	=	Rs. 4,00,000 + 5% of Rs. 4,00,000
   	=	Rs. 4,00,000 + Rs. 20,000 = Rs. 4,20,000.

   Step 3 → P/ V ratio in 2008 = 40%.

               * [refer - (a)]

   Step 4 → Variable cost = 60% (100 − 40)

   Step 5 → Required selling price = = Rs. 55.

   Result: Selling price has to be fixed at Rs. 55 for the year 2009, to earn the same P/ V ratio as in 2008.

2. No. of units to be produced in 2009 is to be calculated as:

    

   Step 1 → Profit in 2008	= Rs. 6,00,000
   [Ref - c)]
   Step 2 → Fixed cost in 2009	= Rs. 4,20,000
   [Ref: Step 2]
   Step 3 → Desired contribution: (Step + Step 2)	= Rs. 10,20,000

    

   Step 4 → Contribution/unit in 2009	=	Selling price − Variable cost
   	=	Rs. 50 − Rs. 33 = Rs. 17.
   		(given) (Step 1)

   Step 5 → No. of units to be produced and sold in 2009

   

Result: Number of units to be produced and sold in 2009 to earn the same profit in 2008 = 24,706 units.

Illustration 17.35

Model 13: Segregation of costs and fixation of selling price

An American soft-drink company is planning to establish a subsidiary company in India to produce mineral water. Based on the estimated annual sales of 50,000 bottles of mineral water, cost studies produced the following estimates for the Indian subsidiary:

	Total Annual Costs Rs.	Percentage of Total Annual Cost that is Variable
Material	2,50,000	100%
Labour	1,00,000	80%
Overhead	75,000	60%
Administration	25,000	40%

The Indian production will be sold by the manufacturer’s franchisees who will receive a commission of 10% of the sale price. No portion of the American office expenses is to be allocated to the Indian subsidiary.

You are required to:

1. Compute the sale price per bottle to enable the company to realize an estimated 10% profit on the sale proceeds in India.
2. Calculate the BEP in rupee sales for the Indian subsidiary on the assumption that the sale price is Rs. 11 per bottle.

[B.Com (Hons)–Delhi; CA–Inter–Modified]

Solution

First, the selling price has to be computed by using the equation,

 

Then, on the given percentage, the total costs will have to be segregated into variable and fixed costs.

Finally, the break-even sales will be determined.

1. Calculation of selling price per unit:
   

   Step 1 → Total sales (50,000 units × Rs. x) = 50,000x.

   Step 2 → Total commission (10% on sales) = 5,000x.

   Step 3 → Total profit (10% on profit) = 5,000x.

   Step 4 → Total sales = Total cost + profit.

   Step 5 → Substituting the values in the equation, we get:

   

   Result → Rs. 11.25 per bottle is the sale price to be fixed to realize a 10% profit on sale in India.

2. Computation of BEP:

   Step 1 → Segregation of costs into variable and fixed costs:

   Particulars (VC)	Variable Cost Rs.	Fixed Cost Rs.
   (i) Materials (Rs. 2,50,000–100%)	2,50,000 (F.C)	–
   (ii) Labour (Rs. 1,00,000 × 80%)	80,000 – (20%)	20,000
   (iii) Overhead (Rs. 75,000 × 60%)	45,000 – (40%)	30,000
   (iv) Administration (Rs. 25,000 × 40%)	10,000 – (60%)	15,000

   			Rs.
   Step 2 →	Sales (50,000 units × Rs. 11):		5,50,000
   Step 3 →	Less: Variable costs:	Rs.
   	Materials [Ref Step 1 − (i)]	2,50,000
   	Labour [Ref Step 1 − (ii)]	80,000
   	Overhead [Ref Step 1 − (iii)]	45,000
   	Administration [Ref Step 1 − (iv)]	10,000
   	Sales commission (10% of Rs. 5,50,000)	55,000
   			4,40,000
   Step 4 →	Total contribution (Step 2 − Step 3)		1,10,000

   Step 5 → Break-even sales:

   (Ref Step 1 − Fixed cost column − add all):

   

   Result → BEP, if sale price is Rs. 11 per bottle                         = Rs. 3,25,000.

Illustration 17.36

Model 14: Computing variable cost at different level of capacity

X Ltd is experiencing recessionary difficulties and as a result, its directors are considering whether or not the factory should be closed down till the recession has passed. A flexible budget is compiled giving the following details:

Additional Information:

1. Present sales at 40% capacity are estimated at Rs. 25,000 per year.
2. Estimated costs of closing down are Rs. 4,000. Besides, the maintenance of plant and machinery is expected to be Rs. 1,000 per year.
3. Cost of reopening after being closed down is estimated to be Rs. 2,500 for overhauling of machines and Rs. 2,500 for the training of personnel.
4. Market research reveals that the sales should take an upward swing to around 60% capacity at prices which would produce a revenue of Rs. 80,000 in a year, approximately.

You are required to advise the directors of the company whether to close down for one year or continue operations without interruptions.

Solution

First, the variable costs at the present level, that is, at 40% capacity and then at a period when the economy recovers, that is, at 60% capacity have to be calculated.

1. Computation of variable cost for 40% capacity:

 

	Rs.
Step 1 → At 30% capacity the total costs are (given):	40,500.
Step 2 → At 50% capacity the total costs are (given):	51,000.

Step 3 → Variable costs for 1% capacity level

Step 4 → ∴ For 10% (increase in) capacity, the variable costs are	= 10 × Rs. 525
	= Rs. 5,250.
Step 5 → Hence, the total costs at 40% capacity will be	= Rs. 45,750.
(30% + 10% (i.e.) Rs. 40,500 Rs. 5,250)
Step 6 → Fixed costs (given)	= Rs. 17,000.

Step 7 →

2. Computation of variable costs for 60% capacity:

 

	Rs.
Step 1 → Total costs at 50% capacity (given)	= 51,000

Step 2 →

Step 3 → Total costs for 60% capacity
(Add Step 2 + Step 3)	= 56,250
Step 4 → Fixed costs (given)	= 17,000
Step 5 → Variable costs for 60% capacity
(Step 3 – Step 4)	= 39,250

Result: Loss will be higher by Rs. 1,250, if the plant is not shut down. It should not be shut down as loss is not much.

17.12 FOR PROFESSIONAL COURSE STUDENTS

Illustration 17.37

A company has an opening stock of 7,500 units of output. The production planned for the current period is 30,000 units and the expected sales for the current period amounted to 35,000 units. The selling price per unit of output is Rs. 12.50. The variable cost per unit is expected to be Rs. 7.50 per unit while it was only Rs. 6.25 per unit during the previous period.

What is the break-even volume for the current period if the total fixed costs for the current period are Rs. 1,07,500. Assume that FIFO system is followed.

 

[C.A.–Final–Modified]

Solution

NOTE:

1. FIFO method is followed.
2. Contribution per unit of opening stock = Selling price – Variable cost (previous period)

                       = Rs. 12.50 − Rs. 6.25

                       = Rs. 6.25^*1.

    

3. Contribution per unit of the current year’s production = Rs. 12.50 − Rs. 7.50 (current)
   = Rs. 5^*2.

    

4. As the contribution per unit relating to all the quantity to be sold in the current year will not be equal, the BEP would be:

   New Formula

   
5. Substituting the figures, we get:

Illustration 17.38

X Ltd manufactures three products A, B and C. The unit selling prices of the products are Rs. 75, Rs. 60 and Rs. 50, respectively. The corresponding unit variable costs are Rs. 55, Rs. 30 and Rs. 20. The propositions (quantity-wise) in which these products are manufactured and sold are 25%, 35% and 40%, respectively. The total fixed costs are Rs. 27,50,000.

Given above the information, you are required to work out the overall break-even quantity and the product-wise break-up of such quantity.

 

[I.C.W.A.I.–Modified]

Solution

 

Illustration 17.39

VRS Ltd has been offered a choice to buy one out of two machines—P and Q. You are required to compute:

1. BEP for each of the two machines.
2. The level of sales at which both machines would earn equal profit.
3. The range of sales at which one is more profitable than the other.

The relevant data are as follows:

	Machines
	P	Q
Annual output in units	20,000	20,000
Fixed costs	Rs. 60,000	Rs. 40,000
Profit at above level of production	Rs. 60,000	Rs. 50,000

The market price of the product is expected to be Rs. 10/unit.

Solution

First variable cost has to be computed as:

	Machine P (Rs.)	Machine Q (Rs.)
Step 1 → Sales value (20,000 units × Loss 10)	2,00,000	2,00,000
Step 2 → Less: Fixed cost	60,000	40,000
	1,40,000	1,60,000
Step 3 → Less: Profit	60,000	50,000
Step 4 → ∴ Variable cost	80,000	1,10,000

(1) Statement showing BEP

Particulars	Machine P (Rs.)	Machine Q (Rs.)
Step 1 → Sales value	2,00,000	2,00,000
Step 2 → Less: Variable cost	80,000	1,10,000
Step 3 → Contribution (Step 1.Step 2)	1,20,000	90,000
Step 4 → P/ V ratio (contribution to sales ratio)
Step 5 → Contribution per unit
Step 6 → BEP (sales value)
Step 7 → BEP (sales volume)	60,000/6 = 10,000 units

Statement showing sales value at which both firm’s profits are equal

Particulars	Amount (Rs.)
(i) Sales value required to earn equal profit:
	= 1,33,333.33
(ii) Sales volume:
	= 13,333.33 units

Result:

1. Machine Q has lower BEPs of 8,888.8 units than machine P which has 10,000 units.
2. Machine Q will be more profitable when the range of sales is 8,888 units to 13,333.3 units. The reason is that at 13,333.3 units, profits of both the machines are equal.
3. When the sale value exceeds 13,333.3 units, machine P will be more profitable because it has a higher contribution to sale ratio of 60%, comparing to machine ‘Q’ which has only 45% contribution to sales ratio. (Contribution to salesvratio and P/ V ratio are synonyms.)

Illustration 17.40

The budgeted results of ABC Ltd are as follows:

Sales of Products	Amount (in lakhs)	Variable Costs as % of Sales Value
P	4.00	50%
Q	3.00	60%
R	6.00	70%
S	2.00	55%
T	8.00	80%

Fixed costs for the period are Rs. 7,60,000.

You are required to:

1. Prepare a statement showing the amount of loss expected.
2. Recommend a change in the sales volume of each product which will eliminate the expected loss assuming that sale of only one product can be increased at a time.

[C.S.–Inter–Modified]

Solution

           ∴ Total contribution = Rs. 7,50,000.

                  Less: Fixed cost = Rs. 7,60,000.

Loss/under-recovery of fixed cost = (10,000).

Total : = Rs. 27,027 (approximately).

Decision: From the last step (Step 6), one can decide how much additional volume of sales is required for each product, for example, the company can increase the sales of product P by Rs. 20,000 or for product Q by Rs. 25,000 and so on.

Illustration 17.41

A company which recently launched a new product reviewed the operational performance after six months. The profit statements relating to last two quarters are as follows:

	Quarter I Rs.	Quarter II Rs.
No. of units sold	10,000 units	15,000 units
Selling price per units	12	12
Direct materials	25,000	40,000
Direct wages	25,000	35,000
Production overheads	35,000	40,000
Total	85,000	1,15,000
Gross profit	35,000	65,000
Selling ! administrative overheads	40,000	45,000
Net profit/loss	(5,000)	20,000

Required:

1. Calculate the BEP in units and the sales value for a quarter.
2. If the company supplies 5,000 units over and above the sales of the second quarter to a special customer (which sales will not affect the regular market), what selling price should be quoted to earn a profit of Rs. 3,000 after meeting the special expenses of Rs. 2,000?
3. If the selling commission is increased by 10% on sales, what quarterly unit sales will be required to earn a return of 15% on the investment of Rs. 1,00,000 in this line of product?
4. If in the third quarter, the company reduces the selling price by Re 1 and increases the advertisement expenses by Rs. 10,000, the sales volume will increase by 20% over that of the second quarter. Should this plan be implemented?

[I.C.W.A–Inter Modified; C.A.–Modified]

Solution

First, the segregation of costs into variable and fixed will have to be calculated.

I: Segregation of production overhead into variable and fixed elements:

Remember: Variable cost per unit

1. Substituting the values, we get:
   

   ∴ Variable cost per unit (production overhead) = Re 1.

2. Remember: Fixed cost = Total cost – (Variable cost/unit×No. of units)

   Substituting the values, we get:

   

   ^*1 ∴ Fixed cost (production overhead) = Rs. 25,000.

II: Segregation of selling and administrative overheads into variable and fixed elements:

1. Applying the same formula and substituting the values,
   

   ∴ Variable cost per unit (selling and administration overhead) = Re. 1.

   ^*2 (ii) Fixed cost = Rs. 40,000 − (Re 1 × 10,000)

                               (given I Qr)

                           = Rs. 30,000.

III: Fixed cost (total):

 

*1 i: Fixed production overhead	= Rs. 25,000.
*2 ii: Fixed selling and administration overhead	= Rs. 30,000.
	Rs. 55,000.

IV. Statement showing break-even and profit planning

Particulars	Rs.	Amount Rs.
(a)		12
Step 1 → Selling price
Step 2 → Variable costs:
(i) Direct materials =	2.50
(ii) Direct wages =	2.50
(iii) *1 Production overhead	1.00
(iv) *2 Selling and administration overhead	1.00	7
Step 3 → Contribution per unit		5
Step 4 →		41.67%
Step 5 → BEP (sales value):
		= Rs. 1,31,990 (approx)
Step 6 → BEP (sales volume):
		= Rs. 11,000 units
(b)
Step 1 → Special expenses (given)		2,000
Step 2 → Profit to be earned		3,000
Step 3 → Total contribution required (Step 1 + Step 2)		5,000
Step 4 → Contribution per unit		Re 1.00
Step 5 → Variable cost per unit [Step 2 (i + ii + iii + iv)]		7.00
Step 6 → Selling price per unit (Add: (Step 4 & Step 5))		8.00
(c)
Step 1 → Selling price/unit	Rs.	12.00
Step 2 → Less: Variable costs:
(i) Other variable costs: (Ref: Step 2)	7
(ii) Selling commission (10% or Rs. 12)	1.20	8.20
Step 3 → Contribution/unit	3.80
Step 4 → Fixed cost		55,000
Step 5 → Return on investment = 15 % of Rs. 1,00,000 = Rs. 15,000
		3,750
Step 6 → Desired contribution per quarter (Step 4 + Step 5)		58,750
Step 7 →		15,460.52 (units)
(d)
Step 1 → Selling price (Rs. 12 Less Re 1)		11
Step 2 → Less: Variable cost		7
Step 3 → Contribution per unit		4
Step 4 → Other fixed costs (Ref: III)		55,000
Step 5 → Increase in advertisement expenses (given in question)		10,000
Step 6 → Total fixed cost (Add Step 4 & Step 5)		65,000
Step 7 → Contribution − Total
(Rs. 4 × 20% increase over II Qr) Ref: Step 3
(Rs. 4 × 20% of 15,000 + 15,000 units)
(Rs. 4 × 3000 + 15,000 units = 18,000)		72,000
Step 8 → Profit/Loss (Step 6 − Step 7)		(7,000)

Decision: Proposal d involves a loss of Rs. 7,000.

The management is advised not to implement that proposal.

17.13 LIMITATIONS OF BREAK-EVEN ANALYSIS

Despite the fact that break-even analysis plays a very important role, as an effective tool for modern financial management, it is not without limitations, which are described as follows:

1. Break-even analysis is based on certain assumptions which are not true in practical situations.
2. The assumption that fixed costs will remain constant is not applied in certain conditions. Fixed costs also tend to vary.
3. The other assumption that variable costs always vary proportionally is also not true.
4. Sales revenue will not always change proportionately.
5. Break-even analysis is based on one more assumption that income is influenced by changes in sales, so that the changes in the inventory would not directly affect the income. But in practice, on many situations, the changes in the inventory can affect income. The reason is that absorption of fixed costs will depend on production and not on sales.
6. Break-even analysis ignores an important factor in any type of enterprise—which is growth and expansion.
7. When an enterprise is engaged in selling more than one product with different margins, break-even analysis may not be effective and fruitful.

17.14 USES OF CVP ANALYSI

1. Forecast: CVP analysis assists in forecasting costs and profits on account of change in volume–in both production and sales.
2. Determination of relative profit: This analysis extends a helping hand in the determination of profitability of each product.
3. Inter-firm comparison: By applying the CVP-analysis technique, interfirm comparison of profitability among firms can be easily made to assess the prevailing conditions in the market.
4. Studying the effect of change in volume: Any change in the volume of sales will have a deterrent impact on other important associated factors—cost and profit. CVP analysis assists in learning such impacts.
5. Segregation of costs: As costs can be segregated into fixed and variable, CVP analysis helps to a great extent in this task. As variable costs can affect to a great extent with respect to contribution, contribution to sales and, in turn, their impact on other related factors, such costs should be identified in order to forecast better planning.
6. Determination of cash requirements: CVP analysis assists in determining the cash requirements at a desired volume of production, at different levels of activity.
7. Making new product decisions: When the management is confronted with the problem whether to introduce new product or how effectively the existing product can be handled to maximize the profits. Under such circumstances, this analysis will give a proper solution.
8. Cost control: To exercise an effective cost control, this analysis will be of much help.
9. Shut-down decisions: To decide whether to shut down any unit or continue its operations, CVP analysis acts as an effective tool in the hands of management.
10. Modernization programme: CVP analysis helps in analysing a modernization or automation programme of an enterprise.

 

Break-even analysis is a technique for studying the relations among fixed costs, variable costs and profits.

Assumptions underlying break-even analysis are as follows:

1. Segregation of costs into fixed and variable.
2. Constant selling prices.
3. Constant sales mix.
4. Stable price level.
5. Inventory remains constant.
6. Specified and relevant range of activity.
7. No change in efficiency and productivity.

BEP — It refers to the level of operations at which there will be neither profit nor loss.

Methods for determining BEP are as follows:

1. Break-even chart—construction of graph—illustrated (Ref: illustrations)
2. Equation method
   1. sales value − variable cost = Fixed cost − profit
   2. at BEP, contribution = fixed cost.

      Contribution to sales ratio or ratio

      

Margin of safety: Total (actual) sales–Break-even sales.

Angle of incidence is the angle formed by the intersection of the total cost line and the sales line.

CVP Analysis: The study of the effects on the future profits of changes in fixed cost, variable cost, sales price, quantity and mix.

Utility of CVP analysis:

1. To analyse the impact of modernization programme.
2. To make new product decisions.
3. To determine the selling price.
4. To study the effects of expansion.
5. To plan the profit.
6. To plan for cash requirements.
7. To make shut-down decisions.
8. To exercise cost control.

Applications of CVP analysis: The above factors are analysed by applying CVP technique (Refer illustrations 17.12 to 17.22).

Multi-product-profit graph: This is used by firms which produce and sell more than one product with a different profitability. Explained in illustration.

ratio may be improved by

1. reducing direct material cost.
2. reducing direct labour cost.
3. reducing direct expenses and variable overheads.
4. increasing the selling price.
5. changing the product mix to boost profit.

Margin of safety may be improved by

1. increasing the selling price.
2. increasing the sales volume.
3. reducing the variable cost.
4. reducing the fixed cost.

Break-Even Analysis: An analytical technique for studying the relations among costs and profits. A profit-planning device based on the established relations between costs (fixed and variable) and revenues.

Break-Even Chart: A mathematical or graphical representation, depicting profit or loss (approximate) of an enterprise at different levels of activity within a limited range.

Break-Even Point: Refers to the level of operations at which there is no profit or no loss.

Cash Break-Even Point: Refers to the level of operations where there is neither a cash profit nor a cash loss.

Cash Break-Even Point or Cost Indifference Point: Refers to the level of activity where the total costs under two alternatives are the same.

Contribution to Sales Ratio or P/ V Ratio: Establishes a relationship between the contribution and the sales value.

CVP Analysis: A managerial tool analysing the various interrelated factors of profit planning, namely, cost, selling price, profit and volume of activity.

Angle of Incidence: Angle which is formed by the intersection of the total cost line and the sales line.

Margin of Safety: Excess of total sales over break-even sales.

Profit–Volume Graph: A chart showing the expected relationship between cost and revenue at different volumes with profit.

1. Bhabatosh Banerjee, “The Cost Accounting”, The World Press Private Ltd., Calcutta.
2. Charles T. Horngreen, Srikant M. Datar, George Foster, “Cost Accounting: A Managerial Emphasis; Pearson Education; New Delhi.
3. Manash Datta; “Cost Accounting: Principles and Practice”; Pearson Education, New Delhi.

 

1.  

   

   or

   
2. ratio of merged plant
   
3. Sales (volume) required to earn desired profit
   
4. Sales (value) required to earn the desired profit
   
5. Additional sales required to earn additional profit
   
6. Additional sales required to eliminate loss
   
7. Sales value required to earn equal profit by two firms of
   
8. BEP (sales volume) (in units)
   
9. 
   
10. BEP (sales value)

    Sales value − Variable cost = Fixed cost + Profit (zero)

    or

    
11. BEP of merged plant (sales value in Rs.)
    
12. Margin of safety = Total sales (Actual sales) − Break even sales

    or

    
13. Fixed cost = Break-even sales × ratio.
14. Net profi = Margin of safety × ratio.
15. Total sales = Margin of safety + Break-even sales.
16. Selling price required to recover the total cost at BEP
    
17. New selling price per unit to recover variable cost
    
18. Straight-line (linear) equation = y = mx + C
19. 
20. Composite BEP (in units)
    

QUESTION BANK

I: State whether the following statements are true or false

1. Break-even analysis is a formal profit-planning process based on the established relationship between costs and revenues.
2. BEP is the point at which an enterprise makes profit.
3. Variable costs vary according to the variations in the level of activity, whereas the fixed costs remain constant.
4. Excess of sales over variable cost will result in profit.
5. When a firm’ costs are all fixed costs, the question of break-even will never arise.
6. Break-even analysis is based on the assumption that costs cannot be classified into fixed and variable.
7. Break-even analysis assumes that the selling price charges in proportion with the volume of sales changes.
8. Break-even analysis is based on the assumption that the price level will be stable.
9. BEP denotes the activity level at which the total costs equal the total revenue.
10. The ratio or percentage of contribution to sales is known as the break-even ratio.
11. A break-even chart indicates accurate profit for various products in the long run.
12. BEP (in Rs.) may be calculated by dividing the fixed costs by P/ V ratio.
13. To compute the level of sales required to earn a particular level of profit, the formula is:

     

    

     

14. At the BEP, contribution = Fixed cost.
15. P/ V ratio may be improved by increasing the selling price per unit.
16. P/ V ratio may be improved by increasing the variable costs.
17. A high P/ V ratio will generate a low profit.
18. Margin of safety = Actual sales – Break-even sales.
19. CVP analysis analyses the relation among the factors–cost, volume and profit.
20. The angle of incidence indicates the profit-earning capacity of an entity.

Answers:

 

1. True	2. False	3. True	4. True
5. True	6. False	7. False	8. True
9. True	10. False	11. False	12. True
13. False	14. True	15. True	16. False
17. False	18. True	19. True	20. True

II: Fill in the blanks with apt word(s)

1. Break-even analysis is an analytical technique for studying the relations among fixed costs, variable costs and __________.
2. Break-even point is the point at which the total __________ equals the total costs.
3. Break-even point is the point at which an enterprise makes neither loss nor any __________.
4. The problem of break-even will never arise if a firm' costs are all __________ costs.
5. If a firm has some variable and some fixed costs, then such a firm must suffer __________ up to a given volume.
6. Break-even analysis is based on the assumption that selling prices are __________.
7. Break-even analysis is based on the assumption that the price level will be stable in the short run.
8. Break-even analysis assumes that inventory remains constant or __________.
9. BEP, when expressed in terms of units, is known as __________.
10. BEP when expressed in terms of value, is known as __________.
11. At the BEP, total __________ is equal to total fixed costs.
12. 
13. 
14. The ratio or percentage of contribution margin to sales is known as __________ or __________.
15. The formula for P/ V ratio is .
16. P/ V ratio can be improved by increasing the __________ price/unit.
17. P/ V ratio can be improved by __________ direct and variable costs.
18. The P/ V ratio for any given product is assumed to remain constant over all __________.
19. When sales volume is below the BEP, the net result will be __________.
20. A high P/ V ratio will generate __________.
21. The excess of total sales over sales at BEP is referred to as __________.
22. The margin of safety may be improved by lowering __________.
23. Margin of safety may be improved by __________ volume of sales.
24. Margin of safety may be improved by increasing the __________.
25. The angle which is formed by the intersection of __________ line and __________ line is called the angle of incidence.
26. An increase in the variable cost per unit will __________ the P/ V ratio, whereas a decrease in the variable cost per unit will __________ the P/ V ratio.
27. An increase in the fixed cost would __________ the BEP, whereas a decrease in the fixed cost would __________ the BEP.
28. An increase in the selling price will __________ the BEP, whereas a decrease in the selling price will __________ the BEP.
29. A chart which indicates an approximate profit or loss at different levels of sales volume units in a limited range is known as __________.
30. The profit/volume graph is a simplified form of __________.

Answers:

 

1. profit	2. Revenue
3. profit	4. Variable
5. Losses	6. Constant
7. Stable	8. Zero
9. Break-even volume	10. Break-even sales value
11. Contribution	12. Contribution
13. P/V ratio	14. P/V ratio (or) Contribution to sales ratio
15. Marginal cost	16. Selling
17. Decreasing	18. Sales volume
19. Loss	20. Higher profit
21. Margin of safety	22. Fixed costs
23. Increasing	24. Selling price
25. Total cost; sales	26. Decrease; increase
27. Increase; decrease	28. Decrease; increase
29. Break-even chart	30. Break-even chart

III: Choose the correct answer

1. Break-even analysis is a technique for studying
   1. fixed costs only.
   2. fixed and variable costs.
   3. fixed costs and profit.
   4. relations among fixed costs, variable costs and profit.
2. CVP analysis highlights the
   1. cost factor to earn profit.
   2. sales volume required to avoid loss.
   3. volume of production needed to fix the selling price.
   4. effect of changes in volume, cost, price and product mix on a firm’ profit.
3. BEP is a point at which the
   1. total costs equal total revenue.
   2. loss incurs.
   3. profit occurs.
   4. none of these.
4. The most important assumption underlying breakeven analysis is:
   1. profit is predetermined.
   2. division of costs into fixed and variable.
   3. only one product is dealt with.
   4. sales mix may vary.
5. BEP may be expressed in terms of:
   1. units only.
   2. rupees only.
   3. units and rupees.
   4. none of these.
6. Contribution is
   1. excess of fixed cost over profit.
   2. excess of selling price over marginal cost.
   3. selling price over profit
   4. selling price over fixed cost
7. P/ V ratio shows:
   1. the volume of profit.
   2. the volume of sales.
   3. the net profit.
   4. the volume of production.
8. A break-even chart provides information on:
   1. the sales value required to maintain production.
   2. the amount of sales required to prevent loss.
   3. the relationship among sales values, variable cost and fixed cost at different activity levels.
   4. none of these.
9. Which of the following is used to compute break-even sales:
   1. Actual sales–Break-even sales.
   2. 
   3. 
   4. By margin of safety ratio.
10. Which one of the following formula is used to compute break-even sales in units:
    1. 
    2. 
    3. 
    4. 
11. P/ V ratio can be increased by
    1. increasing the selling price of products.
    2. increasing the direct material cost.
    3. increasing the direct labour cost.
    4. increasing all variable costs.
12. An increase in the variable cost per unit will lead to
    1. an increase in the contribution.
    2. a reduction in the contribution.
    3. an increase in the P/ V ratio.
    4. none of these.
13. An increase in the fixed cost will lead to
    1. an increase in the BEP.
    2. a decrease in the BEP.
    3. a decrease in the P/ V ratio.
    4. none of these.
14. When a firm has negative contribution, to attain break-even, it has to:
    1. increase the fixed overhead.
    2. reduce the variable cost per unit.
    3. reduce the fixed overhead.
    4. none of these.
15. Margin of safety can be improved by
    1. increasing the fixed cost.
    2. increasing the variable cost of product.
    3. decreasing the sales volume.
    4. increasing the selling price of products.

Answers:

 

1. (d)	2. (d)	3. (a)	4. (b)
5. (c)	6. (b)	7. (a)	8. (c)
9. (c)	10. (b)	11. (a)	12. (b)
13. (a)	14. (b)	15. (d)

1. What is meant by break-even analysis?
2. Define “break-even point”.
3. Name any four assumptions underlying break-even analysis?
4. Write down the formula for calculating (i) break-even volume and (ii) break-even sales value.
5. Define “break-even chart”.
6. What is meant by contribution break-even chart?
7. What are the limitations of break-even chart?
8. What is meant by P/ V graph?
9. What do you mean by contribution to sales P/ V ratio?
10. What is meant by margin of safety?
11. How will you increase the margin of safety?
12. How can P/ V ratio be improved?
13. What do you mean by angle of incidence.
14. Write short notes about the impact of variable cost, fixed cost and selling price on P/ V ratio, BEP and margin of safety.
15. Write short notes on CVP analysis.
16. Write a short note on the role of cost in product-mix decisions.
17. State the objectives of CVP analysis.
18. profit is the product of P/ V ratio and margin of safety. Explain.
19. Distinguish between break-even analysis and profit planning.
20. What are the uses of CVP analysis?
21. What is the formula for computing BEP (in Rs.) of the merged plant?
22. What is the formula for computing sales volume required to earn the desired profit?
23. What is the formula for computing sales value required to earn the desired profit.
24. How will you calculate the sales value required to earn profit by two firms or products?
25. Differentiate between “cost indifference point” and BEP.

1. What are the assumptions underlying BEP? In practice do you agree on it? Substantiate your answer with reasons.
2. How would you determine BEP by the graphical method. Explain the steps involved in constructing a graph, using an illustration.
3. What is a multi-product profit graph? Explain.
4. What are the advantages of break-even chart? What are its limitations?
5. What is meant by P/ V ratio? Explain its uses to the management.
6. Describe in detail the role of cost in product-mix decision.
7. What do you understand by P/ V graph? What happens to P/ V ratio, BEP and margin of safety when
   1. the unit selling price of the product increases.
   2. the unit variable cost increases.
   3. the total field cost increases.
   4. the number of units sold increases.
8. Can there be two BEPs? Show with the help of graph.
9. Explain in detail the impact of variable cost, fixed cost, and selling price on P/ V ratio, BEP and margin of safety.
10. Enumerate the applications of CVP analysis with simple illustrations.
11. What steps would you take to improve
    1. P/V ratio and
    2. margin of safety.
12. The effect of a price reduction is always to reduce the P/ V ratio, to raise BEP and to shorten the margin of safety. Explain and illustrate by simple examples.
13. What are the advantages and limitations of break-even analysis.
14. Explain the significance of CVP analysis. How is it useful in the decision-making process? Enlist a few such areas.
15. What do you mean by “make or buy” decision? State the quantitative as well as qualitative considerations influencing “make or buy” decision.

1. From the following data, calculate the

1. BEP in Rs. and units.
2. profits made when the sales is 600 units.
3. Sales to be made to earn a net profit of Rs. 15000 for the year when:

Selling price of the product per unit: Rs. 100.

Variable cost per unit: Rs. 80.

Fixed expenses are Rs. 10,000 per year.

[Ans: P/ V ratio = 20%; BEP (in Rs.) = Rs. 50,000; BEP in units: 500; profit made when the sales is 600 units = Rs. 2,000; and Required sales to earn a net profit of Rs. 15,000 = Rs. 1,25,000.]

2. From the following data, calculate the break-even sales for a company producing three products:

Product	Sales Rs.	Variable Cost Rs.
A	20,000	12,000
B	10,000	5,000
C	10,000	4,000
	40,000	21,000

Total fixed expenses amounted to Rs. 38,000.

[Ans: Rs. 80,000]

3. The budget sales of a company is extracted from its records, showing as follows:

 

Budgeted sales in units:	5,000
Budgeted selling price/unit, Rs:	4
Budgeted variable cost/unit, Rs:	3
Budgeted fixed expenses (total):	Rs. 3,000
Budgeted capacity:	80%

From the above, you are required to compute:

1. The budgeted profit.
2. The budgeted BEP.

1. The budgeted margin between BEP and the budgeted sales as a percentage of the total capacity.
2. The impact on profit of a ± 10% deviation in the budgeted sales.

[Ans: Rs. 2,000; P/ V ratio = 25%; BEP (in Rs.): Rs. 12,000; Margin of safety = Rs. 8,000; Increase or decrease in profit: Rs. 500.]

4. The following are the costs drawn of a company:

 

Production and sales:	4,000 units
Selling price per unit:	Rs. 40
Variable cost per unit:
Direct materials:	Rs. 10.
Direct labour:	Rs. 5
Variable overhead:	100% of direct
	labour cost
Fixed cost (total):	Rs. 50,000

Required: (a) (i) P/ V ratio; (ii) BEP; and (iii) margin of safety.

(b) Find the effect on P/ V ratio, BEP and margin of safety of changes when there is

1. 20% decrease in the fixed cost and
2. 10% decrease in the sales volume.

[Ans:	(a) (i) P/ V ratio: 50%; (ii) BEP (in Rs.): Rs. 1,00,000; and (iii) Margin of safety: Rs. 60,000.
	(b)(1)(i) P/ V ratio: Nil effect; (ii) Rs. 80,000; and (iii) Rs. 10,00,000.
	(2) (i) P/ V ratio; (ii) BEP: Nil effect; and (iii) Rs. 44,000.]

5. you are required to compute the BEP from the following:

 

Selling price per unit:	Rs.  20
Direct material cost per unit:	Rs.   8
Direct labour cost per unit:	Rs.   2
Direct expenses cost per unit:	Rs.   2
Variable overheads per unit:	Rs.   3
Fixed overheads (total):	Rs. 20,000

If the sales is 20% above the BEP, then ascertain the net profit.

 

[M.Com–Calcutta University]

6. By making and selling 7,000 units of its product, a company would lose Rs. 10,000, whereas in the case of 9,000 units, it would make a profit Rs. 10,000 instead.

Calculate:

1. The amount of fixed expenses.
2. The no. of units to break-even.
3. The profit or loss for 10,000 units.
4. The no. of units to earn a profit of Rs. 40,000.

[M.Com–Calcutta University]

[Ans:	(i) Rs. 80,000,
	(ii) 8,000 units.
	(iii) profit of Rs. 20,000.
	12,000 units.

7. X Ltd has an annual fixed cost of Rs. 3,00,000. In the Year 2009, the sales amounted to Rs. 15,00,000 when compared to Rs. 11,25,000 in 2008, and the profit for 2009 was Rs. 1,25,000 higher than that in 2008. you are required to:

1. Estimates the profits for 2010 on forecasting a sales volume of Rs. 21,00,000 on the assumption that this would not involve any addition to the company' capacity.
2. Calculate the break-even sales value.

[C.S.–Inter–Modified]

[Ans: (i) Rs. 3,75,000 and (ii) Rs. 9,00,000]

8. A factory manufacturing an electronic product has the capacity of producing 1000 machines. The marginal cost of each machine is Rs. 400 and each machine is sold for Rs. 500. Fixed overheads are Rs. 20,000 per annum. you are required to calculate the BEPs for output and sales and ascertain the profit if the output is of 80% capacity.

 

[B.com – Bharathidasan University]

[Ans:	(i) BEP (output): 200 machines.
	(ii) BEP (sales): Rs. 1,00,000.
	(iii) profit @ 80% capacity: Rs. 6,00,000.]

9. From the following data, calculate:

1. P/ V ratio.
2. profit when the sales is Rs. 50,000.
3. New BEP if the selling price is reduced by 25%.

   Fixed Expenses = Rs. 5,000.

    BEP = Rs. 10,000.

 

[Ans:	(i) P/ V ratio: 50%.
	(ii) profit when the sales is Rs. 50,000 = Rs. 20,000.
	(iii) New BEP when the selling price is reduced by 25% = Rs. 15,015.]

10. From the following details, compute composite BEP:

[Ans: Composite BEP = 2000 units; Break-even sales mix (units) = P: 400 Q: 500 R: 500 S: 600]

11. A company producing four products has a total sales value of Rs. 2,00,000, total variable costs of Rs. 1,00,000 and the total fixed costs are Rs. 75,000. Compute the composite BEP.

[Ans: Composite P/ V ratio = 50%; Composite BEP = Rs. 1,00,000.]

12. Vijendra Hard Chrome Products manufactures and sells four types of products under brand names of A, B, 1 C and D. The sales mix in the value comprises of A, B, C and D, respectively. The total budgeted sales is Rs. 60,000 per month.

The operative costs of the enterprise are as follows:

 

Product A	60% of the sale price.
Product B	68% of the sale price.
Product C	80% of the sale price.
Product D	40% of the sale price.
Fixed costs	Rs. 14,700 per month.

The firm proposes to change the sales mix for the next month as follows, and it is estimated that the total sales would be maintained at the same level as the current month:

 

Product A	25%
Product B	40%
Product C	30%
Product D	5%

You are required to calculate:

1. BEP for all the products on an overall basis for the current month.
2. BEP for the products on an overall basis for the next month, assuming that the proposal is implemented.
3. Explain the shift in the BEP to a new position.

[B.Com (Hons)–Delhi University]

[Ans:	(i) Composite BEP = Rs. 42,000.
	(ii) Composite BEP = Rs. 46,226.
	(iii) BEP has shifted upwards.

Reason: A decline in the proportion of more profitable products A and D and a corresponding increase in the proportion of less profitable products B and C]

13. The following data are extracted from the records of a company:

	I Year Rs.	II Year Rs.
Sales	60,000	80,000
Profit	10,000	15,000

You are required to compute:

1. P/ V ratio.
2. BEP.
3. profit or loss when the sales is Rs. 70,000.
4. Sales required to earn a profit of Rs. 25,000.

[B.Com–University of Madras]

[Ans:	(a) 25%.
	(b) Rs. 20,000.
	(c) When the sales is Rs. 70,000, then the profit will be Rs. 23,000.
	(d) Required sales to earn a profit of Rs. 25,000 will be Rs. 1,20,000.]

14. X Ltd and Y Ltd sell all their production of sugar in the same market at a uniform price of Rs. 20 per kg. Their budget for the year that ended on 31 December 2009 is as follows:

	X Ltd Rs.	Y Ltd Rs.
Sales	30,00,000	30,00,000
Less: Variable costs	24,00,000	20,00,000
Fixed costs	3,00,000	7,00,000
Net profit	3,00,000	3,00,000

You are required to

1. Compute the BEP of each company.
2. State the impact on each company when the year ended with production exceeding the budget by 20% and had to be sold at a price 10% lower than the budgeted. The variable and fixed cost increased by 5% over the budget.

[I.C.W.A.–Modified]

[Ans: (a) X Ltd: Rs. 15,00,000.

Y Ltd: Rs. 21,00,000.

15. (a) Ascertain the profit when sales = Rs. 2,00,000.

                Fixed cost = Rs. 40,000.

                BEP = Rs. 1,60,000.

15. (b) Ascertain the sales when fixed cost = Rs. 20,000.

                profit = Rs. 10,000.

                BEP = Rs. 40,000.

 

[C.A.–Inter–Modified]

[Ans: (a) Rs. 10,000 and (b) Rs. 60,000]

16. Two business companies ABC Ltd and PQR Ltd produce and sell the same type of product in the same type of market. Their budgeted P&L A/c for the year ending 31 March 2010 are as follows:

Particulars	ABC Ltd Rs.	PQR Ltd Rs.
Sales	4,50,000	4,50,000
Less: Variable cost	Rs. 3,60,000	Rs. 3,00,000
Fixed cost	45,000	1,05,000
	4,05,000	4,05,000
Net budgeted profit	45,000	45,000

You are required to compute:

1. P/ V ratio.
2. Break-even sales of each business.
3. State which business is likely to earn greater profits in conditions of:

1. heavy demand for the product and
2. low demand for the product.

[I.C.W.A.–Modified]

	ABC Ltd	PQR Ltd
[Ans: (a) P/ V ratio	20%

(b) Break-even sales: Rs. 2,25,000; Rs. 3,15,000.

(c)

1. In case of heavy demand, PQR Ltd will do better than ABC Ltd. That is, if the sales exceeds Rs. 4,50,000, PQR Ltd will earn greater profits as its P/ V ratio is also greater than ABC Ltd.
2. In case of low demand, that is, if the sales level will go down below Rs. 4,50,000, ABC Ltd will earn higher profits than PQR Ltd, as its break-even is lower than PQR Ltd.]

17. A public limited company produces and sells three products. All products are manufactured in the same facilities under a common administrative control. The budgeted income statement for 2009 is as follows:

Fixed expenses are allocated among the products in proportion to their budgeted sales volume:

1. Compute the budget BEP of the company as a whole.
2. What would be effect on the budgeted income if half of the budgeted sales volume of product Y was shifted to products X and Z in equal rupee amounts, so that the total budgeted sales in rupees remain the same?
3. What would be the effect of the shift in the product-mix suggested in (b) above on the budgeted BEP of the whole company?

[C.A.–Inter–Modified]

[Ans:	(a) Rs. 16,00,000 (P/ V ratio = 32.5%).
	(b) Increase in net income: Rs. 28,500.
	(c) BEP: Rs. 14,91,040–(Reduced by Rs. 1,08,960).

[Hints:

1. Variable expenses as percentage of sales for products X–60%; Y–72%; and Z–65%.
2. Fixed expenses in proportion to budgeted sales are: P–Rs. 1,69,000; Q–Rs. 1,30,000; and Z: Rs. 2,21,000.]

18. A multi-product company furnishes the following data relating to the year 2009:

	I half of the Year Rs.	II half of the Year Rs.
Sales	1,35,000	1,50,000
Total cost	1,20,000	1,29,000

Assuming that there is no change in the prices and variable costs and that the fixed expenses are incurred equally in the two half-year periods, you are required to calculate for the year 2009, the following:

1. the profit–volume ratio.
2. the fixed expenses.
3. the break-even sales.
4. the percentage of margin of safety to total sales.

[I.C.W.A.–Inter–Modified]

[Ans:	(a) P/ V ratio: 40%.
	(b) Fixed expenses: Rs. 78,000.
	(c) BE sales = Rs. 1,95,000.
	(d) 31.58%.]

19. The overall P/ V ratio of a company is 60%. The marginal cost of the product of that company is Rs. 225. Compute the selling price of that product.

[Ans: Rs. 562.50]

20. The cost reduction is to be pursued by a company which seeks to improve its competitive pricing position by an increased output from the existing plant. The current profit before tax is 15% of the sales value and 30% of the value of the capital employed. Other working ratios are: Gross margin–35%; Margin of safety–43%; and Capital turnover: 2%. The actual figures for the year are as follows:

	Rs.
Total sales value	30,00,000
Variable costs	19,50,000
Fixed costs	6,00,000
Capital employed	1,50,000
BEP	17,10,000

The proposal is to reduce sales price by 10% and 20% to the output. No change in fixed costs is expected. The cost reduction is expected to be Rs. 1,05,000.

You are required to explain whether the proposal is favourable?

 

[Ans:	(i) BEP	Present 57% of sales	Proposed 60% of sales
	(ii) Margin of safety	43%	40%
	(iii) Capital turnover ratio	2	2.16
	(iv) profit as % of capital	30%	27%
	(v) Gross margin	35%	31%
	(vi) profit as % of sales	15%	12.5%

Hence, the proposal is not favourable. It should be dropped.]

[Model: Break-even charts]

21.(a) From the following particulars, draw a break-even chart and find out the BEP:

 

	Rs.
Variable cost per unit	7.50
Fixed expenses	27,000
Selling price per unit	10.00

(b) What should be the selling price per unit, if the BEP should be brought down to 3,000 units?

[I.C.W.A.–Inter–Modified]

22. From the following data draw a break-even chart:

 

	Rs.
Selling price per unit: Trade discount @ 5%	20
Direct material cost per unit	6
Fixed overheads	4
Fixed overheads	Rs. 10,000

Variable overhead–100% on the direct labour cost.

If the sales are 10% and 20% above the break-even sales volume, then determine the net profits.

 

[I.C.W.A.–Inter–Modified]

23. From the following figures, ascertain the break-even sales by means of a graph. Also draw a profit–volume chart:

 

	Rs.
Sales	4,00,000
Fixed costs	1,00,000
Variable costs	2,00,000

 

[C.S.–Inter–Modified]

(Hint: P/ V ratio 50%; BE sales: Rs. 2,00,000.)

24. Draw P/ V graph from the following data:

 

	Rs.
Sales	2,00,000
Variable costs	1,20,000
Fixed costs	50,000
profit	30,000

 

[I.C.W.A.–Modified]

(Hint: P/ V ratio: 40%; BEP: Rs. 1,25,000.)

25. From the following data, construct an analytical break-even chart:

 

	Rs.
Direct labour (per unit):	5.
Direct material (per unit):	10.
Variable overhead–100% of direct material.
Fixed overheads (total):	50,000.
Selling price (per unit):	100.

(Hint: Draw a table to get the needed figures to plot, showing each element of cost for different outputs and then proceed to construct the graph.)

26. The following figures relate to a manufacturing company producing a wide range of products which may be classified into three main groups:

Product Group	Annual Sales Rs.	Variable Cost Rs.
L	3,00,000	1,00,000
M	3,00,000	2,00,000
N	3,50,000	3,00,000

Fixed costs are (total) Rs. 2,50,000.

You are required to plot on a graph the marginal income slopes for the product groups in an alphabetical order to enable you to plot the average marginal income slope for the total output.

 

[I.C.W.A.–Modified]

27. A company has the option of buying one machine, from the two machines that are available AB and CD. From the information given below, compute

1. BEP for each.
2. The level of sales at which both are equally profitable.
3. The range of sales at which one is more profitable than the other.

	Machine AB	Machine CD
Output (units)	20,000	20,000
Fixed costs per annum	Rs. 60,000	Rs. 32,000
Profit at full capacity (Rs.)	60,000	48,000

The annual market demand for such product is 20,000 units @ Rs. 10 per unit. (Both the machines will produce identical products.)

 

[C.A.–Inter–Modified]

[Ans:

1. Break-even sales value: AB → Rs. 1,00,000; CD → Rs. 80,000. (Volume): AB → 10,000 units; CD → 8,000 units.
2. At 14,000 units, both the machines will be equally profitable.
3. Machine CD will yield more profit at an output range of 8,000 units to 13,999 units.

Machine AB will yield more profit in the range of 14,001 units to 20,000 units.]

28. Joy Ltd manufactures and sells four types of products under brand names Q, R S and T. The sales mix comprises respectively. The total budgeted sales (100%) are Rs. 2,00,000 per month. Operating costs are:

Variable costs

Product Q–60% of selling price.

Product R–68% of selling price.

Product S–80% of selling price.

Product T–40% of selling price.

Fixed cost–Rs. 58,800.

You are required to find the following:

1. To compute the BEP for the products on an overall basis.
2. Is planning a change in the sales mix as follows desirable?

(The total sales remain unaffected.)

 

[I.C.W.A.–Modified]

[Ans:	(a) BEP = Rs. 1,68,000.
	(b) BEP = Rs. 1,84,905.66.

 

Hence, the change in the sales mix is not advisable, as the BEP is higher]

29. The following is the budget of ABC Ltd:

Compute the BEPs in the following independent situations, if:

1. a 10% increase is effected in the fixed costs.
2. a 10% increase is effected in the variable costs.
3. a 10% increase is effected in the sales price which will result in a reduction in units sold by 5%.
4. a 10% increase in the fixed costs and a 5% decrease in the variable costs is effected.

[C.S.–Modified]

[Ans:		BEP (Sales Volume) (units)	BEP (Sales Value) (Rs.)
	(a) 10% increase in fixed costs:	33,000	8,25,000
	(b) 10% increase in variable costs:	33,645	8,41,121
	(c) 10% increase in sale price & 5% decrease in sales volume	24,828	6,82,753
	(d) 10% increase in fixed cost & 5% decrease in variable cost	31,304	7,82,610
	(e) Budget	30,000	7,50,000]

30. X Ltd manufactures three products A, B and C. The selling prices of the products are Rs. 25, Rs. 20 and Rs. 12.50, respectively. The corresponding unit variable costs are Rs. 12.50, Rs. 10 and Rs. 5, respectively. The propositions (quantity-wise) in which these products are manufactured and sold are 20%, 30% and 50%, respectively. The total fixed costs is Rs. 9,25,000.

Given the above information, you are required to work out the overall break-even quantity and the product-wise break-up of such quantity.

 

[I.C.W.A.–Inter–Modified]

[Ans: BEP of overall sales volume: 1,00,000 units. Product-wise break-up:

                        A – 20,000 units.

                        B – 30,000 units.

                        C – 50,000 units.]