After studying this chapter you should be able to:
Understand the concept of break-even point.
Know the assumptions underlying break-even analysis.
Understand the methods for determining the break-even-point: (i) graphical method and (ii) equations approach.
Construct break-even charts.
Understand and compute P/ V ratio—contribution to sales ratio.
Know the concept of margin of safety and compute it.
Appreciate the impact of variable cost, fixed cost and selling price on P/ V ratio, break-even point and margin of safety.
Understand the meaning of cost-volume-profit (CVP) analysis and its uses.
Know well the applications of CVP analysis.
Understand and construct a profit-path chart.
Know how to increase P/ V ratio and margin of safely.
Apply the technique of CVP analysis in decision-making process.
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:
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.
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.
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:
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
NOTE: Preparation of statement of profit and loss is similar to marginal costing.
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
Illustration 17.2
Taking the same figures from the illustration 1, we may determine profitability when:
Solution
Repeat the first 4 steps as in illustration 1, and then continue:
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.
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”.
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.
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:
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.
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).
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.
The following methods can be adopted to determine the BEP:
Under this category, there are too methods, namely:
Under this category also, there are two methods:
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:
Illustration 17.4
For the same data in illustration 3, the contraction of graph is shown as follows:
(ii) Contribution break-even chart:
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:
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
B. Algebraic Methods:
(i) Contribution-margin approach:
or
or
or
or
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
Step 1 →
Step 2→
Step 1 →
Step 2 → Substituting the values in the formula, we get:
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. |
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. |
|
|
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):
[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 3 → BEP of output (in units) |
= 400 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.
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:
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.
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:
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 →
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.
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:
Under this approach,
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.
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. |
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) |
|
(ii) Product Q: % × 25 |
|
(iii) Product R: % × 20 |
|
(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
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:
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:
NOTE: The product is arranged in the descending order of P/ V ratio. C has a higher contribution. So, it is shown first.
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
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:
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.
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.
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:
Comment:
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:
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:
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:
[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
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:
Decision:
[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:
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:
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:
[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 |
|
(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 |
(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 |
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:
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 |
|
(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:
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 |
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
[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:
or
Actual sales − BE sales].
Substitute the figures in the formula to get the desired result:
Margin of safety = (Rs. 50,000 – Rs. 30,000) = Rs. 20,000.
Margin of safety = (Rs. 50,000 – Rs. 36,000) = Rs. 14,000.
(15,000 – 10% of 15,000: 1,500) = 13,500.
Margin of safety = (Rs. 50,000 – Rs. 27,000) = Rs. 23,000.
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.
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.
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.
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.
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:
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:
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 |
- |
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:
[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:
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:
[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:
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
[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).
As the margin of safety is 60% (given), BEP is (100 − 60): 40%.
∴ BEP is at 40% of units sold.
∴ No. of units sold
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. |
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.
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:
[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.
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.
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:
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.
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:
= Rs. 12.50 − Rs. 6.25
= Rs. 6.25*1.
New Formula
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:
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:
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:
[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:
[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
∴ Variable cost per unit (production overhead) = Re 1.
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:
∴ 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 |
(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.
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:
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:
BEP — It refers to the level of operations at which there will be neither profit nor loss.
Methods for determining BEP are as follows:
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:
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
Margin of safety may be improved by
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.
or
Sales value − Variable cost = Fixed cost + Profit (zero)
or
or
I: State whether the following statements are true or false
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)
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
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. From the following data, calculate the
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:
[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
[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:
[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:
[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:
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:
25% |
|
Product B |
40% |
Product C |
30% |
Product D |
5% |
You are required to calculate:
[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:
[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
[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:
[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)
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:
[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:
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:
[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 |
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
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:
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:
(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:
[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.]
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