,

16

Marginal Costing

We know that overheads can be classified into fixed overheads and variable overheads. Similarly, costs can also be classified into fixed and variable parts. Some eminent accountants opine that it is not fair to apportion fixed costs to production. They advocate for charging them against the amount arising out of excess of selling price over total variable cost. Marginal-costing technique is based on this concept. In this chapter, the concept of marginal costing, its special features, and all its related factors are dealt with and how this marginal-costing technique is used for making essential decisions are explained by way of illustrations.

Marginal costing is a technique of ascertaining costs. Cost per unit is ascertained only on the basis of variable costs. Fixed costs are not taken into account to ascertain cost per unit under marginal-costing technique. Its aim is to assess the effect on profit due to changes in volume or the type of output. It is a technique of applying the costing methods in a specified way so as to bring out the relationship between profit and volume or the type of the output. The important components of marginal costing are: (i) classification of costs into fixed and variable; (ii) ascertainment of marginal costs; and (iii) Determination of effect on profit due to changes in the volume or the type of output. The term “marginal costing” is synonymous with “variable costing” or “direct costing.”

16.1 MARGINAL COST

Economists defined marginal cost as, “the amount as any given volume of output by which aggregate costs are changed if the volume of output is increased or decreased by one unit”. This can be explained through an example. Assume that the cost of production of 25,000 units of a product in a business enterprise is Rs. 10,00,000 and that of 25,001 units is Rs. 10,00,050. The cost of producing one additional unit is Rs. 50. (Rs. 10,00,050 – Rs. 10,00,000). That is, Rs. 50 is the marginal cost of one unit, which comprises the direct cost—cost of materials (inventory) used, cost of labour employed and the cost of variable overhead which would not have been incurred but for producing this additional one unit.

16.1.1 Concept of Marginal Cost—View of Economists and Accountants

But according to accountants, the marginal cost is the aggregate of variable costs which will be prime costs plus variable overhead. For example, if we assume that for producing 10,000 units of a product of an enterprise, Rs. 50,000 for direct materials, Rs. 30,000 for wages, Rs. 20,000 for variable overhead and Rs. 15,000 for fixed overhead are incurred, then the marginal cost can be determined as follows:

First determine the prime cost and then determine the marginal cost as marginal cost = prime cost + variable overhead.

 

		Rs.
	Materials	50,000
	Add: Wages	30,000
	Prime cost	80,000
	Add: Variable overhead	20,000
	∴ Marginal cost	1,00,000

Marginal cost per unit

16.2 ABSORPTION COSTING

First, one has to understand the meaning of absorption costing in order to learn the intricacies involved in the marginal-costing system. Under absorption costing, also known as conventional costing, both fixed and variable costs are charged to product costs. According to CIMA, “Absorption costing is a principle whereby fixed as well as variable costs are allotted to cost units. Under this system, cost per unit includes fixed expenses in addition to variable costs”. As all costs (variable and fixed) are identified to production, this system is also referred to as “product costing.”

16.2.1 Salient Features of “Absorption Costing”

1. Fixed as well as variable costs are allotted (charged) to cost units and total overheads are absorbed according to the activity level.
2. Absorption costing aims at linking all costs (variable and fixed) to production.
3. Absorption costing allocates costs to the finished products and inventories.
4. For variable costs, the proportionate allocation for the inventories passing through various stages of production (process) may be accurately made.
5. But for fixed costs, the allocation of costs, that is, transfer of fixed costs from one period to another, cannot be accurately made.
6. Administration, selling and distribution expenses are treated as period costs and are not allotted (charged) to cost units.
7. Under absorption costing, not only fixed overhead but also direct material, direct labour, direct expenses and variable factory overhead are treated as the product cost.
8. Absorption costing may also be designed as the job order or process cost for which the actual or standard costs are utilized.
9. Any changes in the volume of stock carried from one period to another will affect the profit earned.
10. Correct and proper apportionment of overheads cannot be possible which results in the distortion of product costs.
11. All fixed costs are not charged to the profit and loss account (P&L A/c) of the period in which they are incurred. Real problem lies in the allocation of fixed costs.
12. Under absorption costing, the costs are not segregated into variable and fixed categories.

16.3 MARGINAL COSTING

Marginal costing is a unique technique of costing, in which only variable costs are accumulated and the cost per unit is ascertained only on the basis of variable costs. For ascertaining the value of inventories, prime costs and variable overheads are taken into account. Generally, fixed costs are not controllable as they tend to vary with time rather than with level or the type of output. Hence, fixed costs are not taken into account under marginal costing. Marginal costing is defined as, “the accounting system in which variable costs are charged to cost units and fixed costs of the period are written-off in full against the aggregate contribution. Its special value is in decision-making”. CIMA defines marginal costing as, “The principle whereby marginal costs of cost units are ascertained. Only variable costs are charged to cost units, the fixed cost attributable to a relevant period being written off in full against the contribution for that period”. Marginal costing is based on the assumption that all costs can be segregated into two parts, namely, variable and fixed. Under marginal-costing technique, variable costs are assigned to products and matched with revenues (revenues from the related products and not the period). But periodic costs are matched with revenues in the “period” in which the costs are incurred.

Definition of marginal costing and main features of marginal costing—segregation of costs and its allocation explained.

16.3.1 Salient Features of Marginal Costing

Segregation of costs: Costs are separated into fixed and variable elements and semi-variables are also to be separated.

Variable cost as product cost: Only variable costs are considered as product costs.

Fixed cost as period cost: The fixed costs which are incurred during a period are excluded from the product cost. They are treated as period costs and charged to the P&L A/c.

Valuation of stocks: Only the variable costs are taken into account for computing the value of stocks of work-in-progress (WIP) and finished products. They are valued at the marginal cost of production.

Prices: Prices are based on marginal costs and contribution margin. In the normal course, prices would cover costs in total.

Profit: Any change in stock carried from one period to another will not affect the profit earned. Profit would be consistent from period to period. Profit is determined in terms of marginal contribution.

Combination of techniques: Marginal costing combines the techniques of cost recording and cost reporting.

Average variable cost: The unit cost of a product means the average variable cost of manufacturing the product.

16.4 CONTRIBUTION OF GROSS MARGIN

16.4.1 Meaning and Method of Computing Contribution

Importance of contribution or gross margin arises here. Gross margin or contribution is the difference between sales and marginal cost of sales. The terminology of CIMA defines contribution as follows:

1. Contribution per unit: The difference between the selling price of a unit of a product or service and its marginal cost.
2. Contribution in total: The difference between the sales value and the marginal cost of such sales.

It represents the amount each unit contributes towards absorbing fixed costs and generating profit. It is determined by deducting from sales revenue for a particular segment of the business the variable costs which relate to that revenue. It can also be determined by multiplying total sales (for the segment) by the profit–volume ratio (for the segment). Contribution includes both fixed cost as well as profit. Marginal-costing technique itself is based on the assumption that the contribution provides a pool out of which fixed cost is met and any surplus being the net profit or margin.

Products may be sold under different situations such as profit or loss or no profit and no loss, that is, at cost. As such, the character of contributions has the following composition under different situations:

1. Selling price containing profit (sales at profit):
   Contribution = Fixed cost + profit
2. Selling price at cost: (Sales: No profit – No loss):
   Contribution = Fixed cost
3. Selling price at loss: (Sales at loss)
   Contribution = Fixed cost – loss.

16.5 ASCERTAINMENT OF INCOME (PROFIT) UNDER MARGINAL-COSTING AND ABSORPTION-COSTING TECHNIQUES

16.5.1 Marginal Costing

1. Only factory-overhead costs which tend to vary with volume are charged to product cost in addition to prime cost.
2. For inventory valuation, only direct materials, direct labour and variable factory overhead are included which are treated as product costs.
3. An important point to be noted here is that fixed factory overhead is never included in the inventory.
4. Fixed factory overhead is to be treated as a period cost and charged against the revenue when incurred.

16.5.2 Absorption Costing

1. All manufacturing costs both fixed as well as variable costs are charged to cost units (product costs).
2. All fixed expenses, especially, fixed production overheads are included in addition to the variable cost to ascertain the cost per unit.
3. Profit is determined after charging all costs—both fixed and variable costs.

The main aspect under marginal-costing technique in income determination is that the profit is ascertained by charging fixed-expense costs to “contributions”. As already described, contribution is the difference between the selling price and the marginal cost. Fixed costs have to be written off against contribution during the period when occurred.

Contribution = Selling price – Variable cost (Marginal cost)

Under marginal-costing technique,

Profit = Contribution – Fixed costs

If profit and fixed costs are known:

Then the equation may be transformed as:

Fixed costs + Profit = Contribution.

From this, the basic marginal equation is obtained as:

Sales – Marginal costs = Contribution.

where Contribution = Fixed costs + Profit.

Substituting this in the above equation, we get

Sales – Marginal costs = Fixed costs +Profit

(or)

Sales = Marginal costs + Fixed costs + Profit

Profit ascertained by marginal-costing technique may differ from that which was ascertained by the absorption costing. The difference is mainly due to the factor—fixed overhead, which is explained by way of the following:

Illustration 16.1

Prepare a profit and loss statement under

(i) Absorption costing and (ii) Marginal costing from the following data:

 

	Total units produced	5000 units
	Total units sold	4000 units
	Selling price per unit	Rs. 10
	Total fixed overheads	Rs. 15,000
	Cost structure:
	(Per unit)
	Direct material:	Rs. 2
	Direct wages:	Rs. 2
	Variable overhead:	Rs. 2
	Fixed overhead:	Rs. 3.

Solution

Step 1 → Closing stock has to be calculated as follows:

 

	Units produced:	5000 units (given)
	Less: Units sold:	4000 units (given)
	Closing stock:	1000 units

Step 2 → Calculation of the unit of production (absorption costing) has to be worked out as follows:

 

		Rs. unit
	Direct material	2
	Direct wages	2
	Variable overhead	2
	Fixed overhead	3
		9

Step 3 → Calculation of marginal cost of production has to be done as: (marginal costing).

 

		Rs. unit
	Direct material	2
	Direct wages	2
	Variable overhead	2
		6

Step 4 → Ascertainment of profit/loss under absorption costing:

 

Particulars		Amount Rs.
Sales value (Units sold × selling price/unit: 4000 × Rs. 10)		40,000
Less: Cost of goods sold:	Rs.
Opening stock	Nil
Cost of production (5000 units × Rs. 9)	45,000
	45,000
Less: Closing stock:
(1000 units × Rs. 9)	9,000	36,000
Gross profit		4,000

NOTE:

1. Production: 5,000 units
2. Sales: 4,000 units
3. Closing stock is valued at variable cost + Fixed factory overhead.
4. Fixed overhead is included.

Step 5 → Ascertainment of profit/loss under marginal costing

 

Particulars		Amount Rs.
Sales value (4000 units × Rs. 10)		40,000
Less: Marginal cost of goods sold:	Rs.
Opening stock	Nil
Marginal cost of production: (5000 units × Rs. 6)	30,000
	30,000
Less: Closing stock (1000 units × Rs. 6)	6,000	24,000
Hence, Contribution		16,000
Less: Fixed overheads		15,000
GROSS PROFIT		1,000

NOTE:

1. Production: 5000 units
2. Sales: 4000 units
3. Closing stock (i.e., 1000 units) has been valued at marginal cost (i.e., Rs. 6/unit)
4. Fixed overhead is excluded.

Comments:

1. Gross profit under absorption costing is Rs. 1,000 higher when compared with the profit under marginal costing.
2. Reason for the difference:

   Not all of the current manufacturing overheads are deducted from sales because the closing stock will include a portion of fixed overheads, that is, in absorption-costing inventory, is valued at a higher figure. Hence, the profit is more under absorption costing. In this case, the company produces more units (5000 units) than it sells (4000 units). (The position will be just reverse in case if the company produces less than it sells)

The differences between these two methods can be explained in detail through the following illustration:

Illustration 16.2

You are required to ascertain profit and loss under (i) marginal-costing- and (ii) absorption-costing method from the following data:

Basic production data:

 

Normal volume of production      = 20,000 units per period.

	Sales price	= Rs. 5 per unit.
	Variable cost	= Rs. 3 per unit.
	Fixed cost	= Re 1 per unit.
	Total fixed cost	= Rs. 20,000 (20,000 × Re 1).

Selling and distribution costs (not available).

The opening and closing stocks consist of both finished goods as well as equivalent units of WIP.

Additional data:

Solution

Step 1 → Marginal cost of production has to be calculated. In this question, straightaway variable cost and fixed cost are given. Hence, variable cost represents the marginal cost per unit, that is, Rs. 3 per unit.

Step 2 → Unit of production is to be computed under absorption costing as follows:

 

	Variable cost	= Rs. 3 per unit
	Fixed cost	= Re. 1 per unit
		Rs. 4 per unit

Step 3 → Under marginal costing, profit is arrived in the following order:

1. For each period, cost of goods sold has to be calculated.
2. Contribution has to be computed, that is, contribution = Sales – Cost of goods sold.
3. Fixed cost has to be deducted from contribution.
4. The net result (profit) is showing as follows:

Step 4 → Statement of Profit/Loss under Marginal-Costing Method:

Step 5 → Under absorption-costing method, profit is arrived at the order as mentioned as follows:

1. For each period, cost of sales hast to be computed.
2. Over-absorbed fixed cost has to be calculated and deducted..
3. Under-absorbed fixed cost has to be calculated and added.

I Overabsorption of fixed costs has to be calculated as follows:

Look at the Period II Production – Over Production (25,000 units – 20,000 units) = 5000 units. For this 5000 units, the fixed cost @ Re 1 will be Rs. 5,000. Similarly, for the Period IV, Over Production:(25,000 units – 20,000 units (Normal production) = 5000 units and @ Re 1 per unit Rs. 5,000 will be the overabsorption of fixed costs.

II Underabsorption of fixed costs: Look at the Period III. Number of units produced are 18,000 only which is below the level of normal production by 2000 units. Underabsorption of overhead will be 2000 × Rs. 1 = Rs. 2,000.

Step 6 → Statement of Profit/Loss under Absorption Costing:

The above illustration reveals the following features:

1. In the accounting period I, the profit under both the methods is the same, that is, Rs. 20,000. The reason is due to the fact that there is no opening or closing stock. The production level is normal and hence, there is neither overabsorption nor underabsorption of the fixed costs under absorption-costing method.
2. In the accounting period II, the marginal-costing method shows a profit of Rs. 15,000 whereas the absorption-costing method shows a profit of Rs. 20,000. The reason is due to the fact that a portion of the fixed cost, instead of being charged against the profit for the period is charged to the closing stock and carried over to the next period.
3. In the accounting period III, the profit calculated under absorption costing is Rs. 24,000, whereas the profit shown under marginal costing is Rs. 27,000. In this period, the sales exceeds the output. A portion of the fixed cost carried over as a part of the opening stock under absorption costing is charged to the product sold in the current period.
4. In the accounting period IV, the profit calculated under the absorption costing is Rs. 32,000, which is lesser than that of the marginal costing where it is Rs. 34,000. This is due to the fact that the fixed cost relating to the opening stock of 2000 units now sold is brought over to the current accounting period.
5. In the long run, when the sales level and the production level equals, there may not be much difference in profit under both the methods. In this illustration also, if the net profit for the four accounting periods are taken together, it will be the same, that is, Rs. 96,000.

The features described above may be summarized as follows:

How profit will be affected under different situations? Reasons for such effect are explained in the following table:

Situation	Effect Upon Profit Under Marginal & Absorption Costing	Reasons for the Effect
1. When production (output) is equal to sales.	Profit under marginal costing and absorption costing will be the same.	There is no opening or closing stock. The total fixed costs incurred during the period are charged against the income of the period.
2. When sales exceed production.	Profit under absorption costing is lower than that shown in the marginal costing.	Closing stock decreases. Under absorption costing, the fixed costs charged against Profit exceed the amount incurred during the year. This is due to the fact that fixed costs deferred previously in stock are charged against the income in the period in which goods are sold.
3. When production exceeds sales.	Profit under absorption costing is higher than that shown in the marginal costing.	Closing stock increases. Under absorption costing, the total fixed costs charged against income are lower than the amount incurred. This is because a portion of the fixed costs is deferred to future by including in the closing stock.
4. When sales volume remains constant the production fluctuates.	Profit under marginal costing remains constant. But under absorption costing, the profit will fluctuate.	Changes in the level of inventory will not affect profit under the marginal costing.
5. When the output volume is constant the volume of sales fluctuates.	The profit figure may not be the same but its movement will be in the same direction and there will not be any advance effect.	profit is directly proportional to sales under these methods.

16.5.3 Distinction Between Absorption Costing and Marginal Costing

Having studied the salient features and techniques of marginal costing and absorption costing, now one can distinguish absorption costing from marginal costing. The distinction between the two methods may be presented in tabular form as follows:

Basis of Distinction	Absorption Costing	Marginal Costing
1. Segregation of costs.	Under absorption costing, costs are never classified into fixed and variable.	Costs must be classified into fixed and variable under this technique.
2. Treatment of fixed-production overheads.	Fixed-production overheads are included in the cost per unit.	Fixed-production overheads are not included in the calculation of cost per units.
3. Valuation of stocks.	Stocks are valued at total cost (variable + fixed).	Stocks are valued only at variable costs.
4. Absorption of certain costs.	Variable portion of administration, selling, distribution research and development costs will be absorbed in this technique.	Variable portion of administration, selling, distribution research and development costs are treated as capable of being absorbed by production.
5. Ascertainment of profit.	profit is ascertained by computing the difference between the sales and costs of goods sold.	profit is ascertained by computing the contribution and then deducting the total fixed expenses, where contribution = sales – variable cost.
6. Change in inventories and their effect on profit: (a) Increase in inventory (b) Decrease in inventory	(a) If inventories increase, this method will show more profit. (b) If inventories decrease, less profits will be shown under this method.	a) If inventories increase, this method will reveal lesser profit than absorption costing. b) If inventories decrease, this method will show more profit than absorption costing.
7. Arbitrary apportionment of fixed costs and its effect.	Fixed costs are apportioned arbitrarily. Due to this, under- or overabsorption of overheads will result. Adjustments for recovery of such under- or overabsorption have to be made.	No such arbitrary apportionment of fixed costs arises under this technique. As such there is no resulting of under- or overabsorption of overheads and the question of adjustments for recovery does not arise here.

16.6 SEGREGATION OF SEMI-VARIABLE OVERHEADS

The reliability and accuracy of marginal costing depends upon with the segregation of costs into fixed and variable elements. Fixed costs can be picked up individually without any difficulty. Variable overheads can also be ascertained from the previous ledger postings. But the real difficulty arises in segregating the variable and fixed portions from semi-variable overheads. Any of the following methods may be used in segregating semi-variable costs into their fixed and variable parts:

Segregation of semi-variable overheads. Different methods are illustrated.

1. Levels of output compared to levels of expenses method.
2. Range method.
3. Degree of variability method.
4. Scatter-graph method.
5. Equation method.
6. Method of least squares.

Segregation of semi-variable heads can be ascertained by the methods mentioned above by way of an illustration as follows:

Illustration 16.3

Segregate the semi-variable overheads into fixed and variable by applying the methods (one by one).

16.6.1 Method 1: Levels of Output Compared to Levels of Expenses

As per this method, the output at two different levels are compared with the corresponding level of expenses. Fixed expenses remain constant. Variable overheads are determined by using the formula:

Step 1 → Take figures for different months from the illustration and present as follows:

Month	Output (Units)	Semi-Variable Overheads (Rs.)
January	25	125
July	45	185
	20	60

Step 2 → Difference.

Step 3 → Variable element
	= Rs. 3 per unit.

Step 4	→	Variable overhead for January = 25 × Rs. 3 = Rs. 75.
Step 5	→	Fixed overhead for January = (Rs. 125 − Rs.75) = Rs. 50.
Step 6	→	Semi-variable overhead for January Rs. 125 is segregated into Rs. 75 as variable and Rs. 50 as fixed.
Step 7	→	In a similar manner, for July it can be determined as
		Variable overhead for July = 45 × Rs. 3 = Rs. 135
		∴ Fixed overhead for July = (Rs. 185 − 135) = Rs. 50
Step 8	→	Semi-variable overhead for July Rs. 185 is segregated into Rs. 135 as variable and Rs. 50 as fixed.
Step 9	→	Variable overheads for January 2010 is:

 

	30 units × Rs. 3 per unit	= Rs. 90
	(Given) (Calculated as above)
	Fixed overheads	= Rs. 50
	(Same as for other months)
	∴ Total semi-variable overheads for January 2010	= Rs. 140

16.6.2 Method 2: Range Method or “High and Low” Method

This method is similar to the above method but the levels of highest and lowest expenses are compared with one another and related to the output attained in those periods.

From the illustration, the highest production is in the months of April and the lowest in the months of January, and the figures of these two months are taken and presented as follows:

Step 1 →

	Units	Semi-Variable Overheads (Rs.)
Highest (April)	47	191
Lowest (January)	25	125
	22	66

Step 2 → Difference or change → 22

Step 3 → Variable element
	Rs. 3 per unit

Step 4	→	Variable overhead for April	= 47 × Rs. 3 = Rs. 141
		Fixed overhead for April	= (Rs. 191 − Rs. 141) = Rs. 50
Step 5	→	Variable overhead for January 2009	= 25 × Rs. 3 = Rs. 75
		Fixed overhead for January 2009	= (Rs. 125 − Rs. 75) = Rs. 50
Step 6	→	Variable overhead for January 2010	= 30 × Rs. 3 = Rs. 90
		Fixed overhead for January 2010	= Rs. 50
		Total semi-variable overheads for January 2010	= Rs. 140

16.6.3 Method 3: Degree of Variability Method

Under this method, the degree of variability is noted for each item of semi-variable expenses. Some semi-variable items have 30% variability while others have 20% variability. (Look at the illustration—for one unit, the variance is Rs. 3, i.e., 30% variability).

In this case, the degree of variability is 30%

Take figures for the months of February:

 

	Total expenses	= Rs. 140
	Variable element	= 30%
	That means 30% of Rs. 140
	∴ Fixed element	= Rs. 140 . Rs. 42 = Rs. 98.

On this basis for January 2010 it is determined as follows:

On the basis of variable expenses of Rs. 42 for the production of 30 units (30%), the variable expenses for 30 units (2010 January)

Fixed element     = Rs. 98.

∴ Total semi-variable expenses for January 2010 = Rs. 42 + Rs. 98 = Rs. 140.

NOTE: In case the degree of variability varies, the value of variable elements too will vary. But the task of fixing the degree of variability level is difficult.

16.6.4 Method 4: Equation Method

Under this method, the straight-line equation is used.

 

	The equation is	=	Y = M X + C
where	Y	=	Total semi-variable cost
	M	=	Variable cost per unit
	X	=	Output
	C	=	Fixed cost included in the semi-variable cost

Step 1: Take figures for any two periods and substitute them in the equation as follows:

 

	February: 140 = M (30) + C	(1)
	March:       155 = M (32) + C	(2)

Step 2: Subtracting equation (1) from (2), we get: 15 = M (5) (3)

Step 3: Substituting the value of (M) in equation (1), we get = 140 = 3 × 30 + C

 

Step 4: Fixed cost included in semi-variable = Rs. 50.

             ∴ Variable portion = (Rs. 140 − Rs. 50) = Rs. 90.

16.6.5 Method 5: Method of Least Squares

Of all the methods explained so far, this is the most accurate method. This is based on the mathematical technique of fitting an equation with the help of number of observations.

As shown in the previous illustration, the straight line equation is: y = mx + C.

For each period, we have an equation in the following form:

Adding the above equations, we get:

[N = Number of observations]

A Curvilinerar equation can be got by multiplying both sides of the equation by x:

Adding the above equations, we get

 

With the help of equations 1 and 2, the values of ‘m’ and ‘c’ can be determined and the pattern of cost line can be ascertained.

Step 1 → Pattern of cost line may be determined by taking figures for the first 3 months in order to explain the method of least squares as follows:

Step 2: → Substituting these values in the equations, we get

 

	420 = 90m + 3C	(3)
	12,750 = 2750m + 90C	(4)

Step 3 → Multiply (3) by 30:

 

Step 4 → Subtracting (4) – (5), we get 150 = 50m

Step 5 → Substituting the value of m in equation (3), we get

 

	90 (m) + 3C	= 420
	90 × 3 + 3C	= 420
	3C	= 420 − 270
	C	=

Step 6 → Now we get the straight-line equation as

                                 y = mx + C

                (Where m = 3; C = 50)

                                y = 3x + 50.

∴ Rs. 50 is the amount of fixed overhead present in the total semi-variable overhead and the variable overhead is Rs. 3/unit.

Step 7 → Now, for January 2010, when the production is 30 units, then the total overhead is: y = 3 x 30 + 50

                                           = 90 + 50 = Rs. 140.

              Fixed overhead = Rs. 50

        Variable overhead = Rs. 90 (30 × Rs. 3).

16.6.6 Method 6: Scattergraph Method

Under this method, the given data will be plotted on a graph paper (whose abscissa will represent the output at various levels of activity and the ordinate will represent the respective semi-variable overheads).

Procedure:

Step 1 → The volume of production or sales is plotted on the horizontal axis and the costs are plotted on the vertical axis.

Step 2 → Expenses relating to each volume of production are plotted on the paper, thereby several points appearing on it.

Step 3 → A straight line is drawn connecting all the points marked on the paper. This line is known as “the line of best fit”. It is also called as “the total cost line”. The point where this line intersects the vertical axis is taken to be the amount of fixed element.

Step 4 → A line parallel to the horizontal axis is drawn from the point where the line of best fit intersects the vertical axis. This represents the fixed cost and the line is known as the fixed cost line.

Step 5 → From this graph, the variable element at any level of output may be determined. [It is the difference between the fixed cost line and the total cost line.]

*From the graph (drawn on the next page), we can determine the fixed expenses as Rs. 45.

* For the month of January 2010, for 30 units of production, the semi-variable expenses are 140. Hence, the variable expenses are (Rs. 140 − Rs. 45) Rs. 95.

*For any volume of production, these can be easily ascertained from the graph by a mere look.

From the graph it is noted that for the 30 units of production in January 2010, the semi-variable expenses are Rs. 140.

16.7 ADVANTAGES OF MARGINAL COSTING

Elimination of profit fluctuations: Fluctuations in profits arise due to the differences between the volume of output and the sales during a period. The use of marginal-costing technique eliminates such fluctuations in profits.

Availability of cost–volume–profit relationship data: Cost–volume–profit data are readily available in the books of accounts, that is, regular financial statements. Otherwise, the same ought to be calculated separately which involves additional time, labour and money. But under marginal-costing technique, such data are readily available in regular accounting statements, thereby saving time and money.

Allocation of fixed costs: Under marginal-costing technique, it is not necessary to allocate fixed costs to departments and products. As the fixed costs are treated as period costs, they are charged against the profit of the period in which they are incurred. Hence, less allocations are possible and sufficient.

Profit not affected by changes: When direct cost is in use, profits will not be affected by changes in the absorption of fixed expenses.

Facilitates appraisal of several factors: Marginal-costing technique makes the task of relative appraisal of products, area of operation, types of customers and the like factors easy.

Better control: Marginal-costing technique provides a better control over fixed overhead costs.

An effective tool: Marginal-costing technique is employed as an effective tool in making managerial decisions such as product pricing, optimizing product mix, make or buy decision, shut-down decision, profit planning and so on.

Determination of break-even point: This is the only basis on which the break-even point can be ascertained. But for this, the determination of break-even point will be difficult.

Substitute of budget-control system: In case there is no budgetary-control system in the entities, this acts as a substitute by way of showing the fixed costs in total in the income statement.

16.8 DISADVANTAGES OF MARGINAL COSTING

Segregation of costs: Costs are classified into fixed and variable in marginal costing. It is difficult to classify with accuracy. Further, many expenses considered to be variable or fixed may not be exactly the same at various levels of activity of the business. They differ from situation to situation. Besides, in marginal costing, there is no place of semi-variable or semi-fixed overheads which have to be segregated into fixed and variable elements.

Undervaluation of inventory: Inventories are valued at a marginal or at a variable cost. Total cost does not come into picture. As such, inventories are undervalued in marginal costing.

Limitations of Marginal Costing

Fluctuations of monthly profits: The income statement of each month will show the same amount of fixed costs irrespective of the volume of sales. During above-average months, the profit will be higher and during the below-average months the profit will be lower. It fluctuates in a wide range.

Dominance of single factor: Under marginal-costing technique, the focus is “one contribution”. Decisions based on the single factor may result in losses or low profits. The other important factors such as fixed cost, capital employed and so on are ignored.

Cost control: Effective cost control can be achieved with using some other techniques such as standard costing and budgetary control.

Long-term assessment: Marginal costs may be suitable for a short-term assessment of profit. But long-term assessment is determined with accuracy on a full-cost basis only, which cannot be possible by using marginal-costing technique.

Assumption in sale price per unit: Marginal-costing technique is based on the assumption that sales price per unit will remain the same on different levels of production. But in real situation the assumption is not true.

Not suitable for technology-oriented entities: In an era of scientific revolution, technical advancement cannot be relegated to background alone. Heavy investment is inevitable for technology advancement. Consequently, impact of fixed costs on product is more. By ignoring the fixed costs, which are naturally very high in such a scenario, marginal-costing system may be of less importance, as it will not reflect true financial results.

No provision for the evaluation of performance: This technique does not provide any standard to evaluate the performance. Further, the marginal contribution data are insufficient for evaluation, compared to the data obtained from variance analysis.

Under- or overabsorption of variable overheads: While the problem of under- or overabsorption of fixed overheads is eliminated, the problem of under- or overabsorption of variable overheads still persists.

Not acceptable by government agencies: Valuation of stocks, WIP, transfer from one process to another and so on at marginal costs are not acceptable to the government agencies and tax authorities. They serve the purpose as internal financial statements. They differ from published reports.

16.9 MANAGERIAL APPLICATIONS OF MARGINAL COSTING

The concepts of marginal costing and how it differs from absorption costing have been discussed so far. Now, we have to study how the various concepts can be applied to make appropriate decisions on the managerial level and how to provide an effective mechanism to control the activities of the entities. By making use of marginal-costing techniques one can achieve the main objectives of business organization, such as—(1) Better decision-making and (2) A proper device to control needs.

The task of arriving at a proper decision-making is facilitated by the application of marginal-costing technique making decisions relating to fixation of selling prices, selection of profitable product mix, diversification of products, make or buy decisions, alternative methods of manufacture, shut-down decisions, cost control, profit planning, evaluation of performance, accepting an offer or exporting a below normal price, offering quotations, cost control, problem of key factors and so on have to be studied in detail with the help of illustrations in the forthcoming pages of this chapter.

16.9.1 Optimizing the Product Mix

“Contribution” is the main criteria to decide the profitability of any business concern. The product which gives the highest contribution is generally considered to be the most profitable one. In order to maximize the profit, the resources have to be mobilized towards the product which gives the highest contribution. In business, these resources include working capital, available hours, machine capacity, raw materials, production capacity and sales potential. The product mix which gives the maximum contribution is selected and produced in maximum possible quantities.

A business enterprise which manufactures more than one product, must decide in what proportion would these products be produced or sold. The technique of marginal costing helps the management in determining the most profitable product mix. To determine the best product mix, the contribution under different mixes will have to be ascertained. The mix which gives the highest contribution will be selected for production.

In the absence of any key factor, the selection of the most profitable mix is explained in this illustration

Illustration 16.4

A company engaged in plantation activities has 400 hectares of virgin land which can be used for growing jointly or individually tea, coffee and cardamom. The yield per hectare of the different crops and their selling price per kg are as follows:

	Yield (kgs)/Hectare	Selling Price (Rs.)
Tea	2000	40
Coffee	500	80
Cardamom	100	500

Cost data:

(b) Total fixed cost per annum is Rs. 62,00,000.

You are required to calculate (i) the priority of production and (ii) the most profitable product mix, if the policy of the company for maximum and minimum usage of cultivation will be:

	Max. Area (Hectare)	Min. Area
Tea	320	240
Coffee	100	60
Cardamom	60	20

Solution

STAGE I: Contribution per kg and contribution per hectare are to be calculated.

1. Contribution per kg = Selling price/kg – Total variable cost/kg.
2. Contribution per kg has to be multiplied by yield per hectare to know the contribution per hectare.
3. This has to be computed for tea, coffee and cardamom separately as follows:

Decision 1: Order of priority of production to maximize the profit will be coffee, tea and cardamom.

STAGE II:

1. For optimum product mix:
   1. Coffee has to be cultivated in a maximum area on the basis of ranking (i.e.) 100 hectares (given).
   2. The minimum area that has to be cultivated for cardamom will be 20 hectares (as per third rank).
   3. The balance (400 hectares − 100 hectares (for coffee) − 20 hectares for cardamom) 280 hectares will be used for cultivation of tea.
2. For optimum product mix:
   

3. Maximum profit may be calculated as follows (even though it is not asked in question, it is shown here):

   

16.9.2 Problems of Limiting Factor or Key Factor

16.9.2.1 Concept of Limiting Factors and Method of Computing Contribution Related to Limiting Factors

As discussed above, we have come to understand that the product which gives the greatest contribution will be the most profitable one. But in practice, there are several factors which limits the production and or sales even if the products give a high contribution. These factors, usually termed as limiting factors or key factors, limit the volume of output at a particular period. These constraints are also called as scarce factors, limiting factors, principal budget factors or governing factors. In such a case, if there is any limiting factor, care should be taken before arriving at a decision. Contribution per unit of key factor has to be computed, and the product which gives the greatest contribution per unit of key factor is considered highly profitable and such product is taken for production to maximize the profit. The list of limiting factors is vast and the most important limiting factors are: sale labour, raw material, plant capacity and availability of capital.

Illustration 16.5 (One limiting factor only)

From the following information, you are required to decide the profitable product during a labour shortage:

	Product A	Product B
Selling price	Rs. 60	Rs. 50
Direct material	Rs. 20	Rs. 20
Labour hours (Re 1. per hour)	20 hours	10 hours
Variable overheads	50% of direct wages

Solution

NOTE 1: *Labour is shortage (given). Hence, labour is the key factor.

NOTE 2: *Profitability is to be ascertained by using the formula

Key factor is labour: For Product A = 20 hours (given)

                                For Product B = 10 hours (given)

 

Step 1 → Selling price (given)	Product A	Product B
	Rs.	Rs.
	60	50
Step 2 → Less: Variable costs:
(i) Direct material	20	20
(ii) Direct labour	20	10
	(20 × Re. 1)	(10 × Re 1)
(iii) Variable overheads (50% of Direct labour)	10	5
Step 3 → Total variable costs (2 (i) + (ii) + (iii))	50	35
Step 4 → Marginal contribution (Step 1 – Step 3)	10	15
Step 5 → Profitability

1. For Product
2. For Product

Step 6 → Decision: Product B is more profitable than Product A during the labour shortage.

Illustration 16.6 (Optimizing product mix—More than one limiting factor)

The following cost data are extracted from a company:

	Product “x”	Product “y”
Sales (per unit)	Rs. 200	240
Consumption of material	4 kgs	6 kgs
Material cost	Rs. 20	Rs. 30
Direct wages cost	Rs. 30	Rs. 20
Direct expenses	Rs. 10	Rs. 15
Machine hours used	3	2
Overhead expenses:
Fixed	Rs. 10	Rs. 20
Variable	Rs. 30	Rs. 40
Direct wage per hour is Rs. 10

I: Comment on the profitability of each product if both use the same raw material when:

1. Total sales potential in units is limited.
2. Total sales potential in value is limited.
3. Raw material is in short supply.
4. Production capacity (in terms of machine hours) is the limiting factor.

II: Assuming that raw material is the key factor, availability of which is 25,000 kgs and the maximum sales potential of each product being 4,000 units, find out the product mix which will yield the maximum profit.

 

[I.C.W.A.I. (Adapted and Modified)]

Solution

NOTE:

1. In these illustrations, there are more than one key factor.
2. First, the profitability for each product has to be computed (i.e., contribution per unit).
3. Based on the value of contribution, the profitability for each product taking in the key factors separately has to be ascertained and has to be ranked.
4. Finally, the maximum profit-yielding product mix has to be ascertained.

STAGE I: Statement showing profitability

Particulars	Product
	X	Y
Step 1: Sale price (given)	Rs.	Rs.
	200	240
Step 2: Less: Marginal cost:	Rs.	Rs.
(i) Direct material	20	30
(ii) Direct wages	30	20
(iii) Direct expenses	10	15
(iv) Variable overheads	30	40
Step 3: 2 (i) + (ii) + (iii) + (iv)	90	105
Step 4: Contribution per unit (Step 1 – Step 3) (Sales price – Marginal cost)	110	135

STAGE II: When total sales potential in units is limited:

In this case, the demand in terms of units is a limiting factor.

Hence, profitability = contribution per unit.

Contribution per unit is worked out in Stage I.

∴Profitability = Rs. 110 (for x) & Rs. 135 (for y).

    Ranking = II Rank (x) and I Rank (y).

STAGE III: When total sales potential in value is limited:

Hence, the demand in terms of value is a limiting factor.

Hence,

Stage IV: When raw material is in short supply, the raw material is a limiting factor.

Hence,

STAGE V: When production capacity (in terms of machine hours) is the limiting factor:

STAGE VI: Calculation of product mix which will yield the maximum profit:

• When “raw material” is the limiting factor, we find that product x appears (Rs. 27.50/kg) to be more profitable than product y (Rs. 22.50/kg).
• To utilize the available raw material in an optimum way, one should prefer to produce product “x”.
• But demand being another key factor, the production of “x” has to be limited to 4,000 units (given).
• Under these circumstances, the allocation of raw materials has to be made as follows:
  1. Raw materials available = 25,000 kgs (given)
  2. Less: Allocation of raw materials to product:

     “x” being ranked first (4000 units × 4 kgs) = 16,000 kgs

  3. Balance quantity available for product “y”
  4. 
  5. Hence, the product mix which will yield a maximum profit is 4,000 units of product “x” and 1,500 units of product “y”.
  6. Calculation of total profit:

		Rs.
(a) Contribution by Product “x”: (4000 units × Rs. 110)		= 4,40,000
(b) Contribution by Product “y”: (1500 units × Rs. 135)		= 2,02,500
Total contribution (both the products)		= 6,42,500
(c) Less: Fixed costs	Rs.
(i) Product x: (4000 units × Rs. 10)	40,000
(ii) Product y: (1500 units × Rs. 20)	30,000	70,000
Total maximum profit		= 5,72,500

16.9.3 Make or Buy Decisions

Quite often the management of a manufacturing company will face the problem whether a component or a product should be purchased from an outside source (suppliers) or manufactured by the company itself. Marginal-cost analysis renders a helping hand to arrive at a proper and suitable solution in solving such a problem. Besides this, we have to consider the following two situations.

Situation 1: The company may have unused capacity which may be utilized for making component parts or products or needed similar items. In such situation, the marginal cost of manufacturing the required component parts have to be compared with the prices quoted by outside sources (suppliers). If the purchase price is lower than the marginal cost, the wise decision would be to buy them from outside. If marginal costs are lower than the purchase price, the decision to manufacture the components in the firm itself will be wise. For this, the fixed costs are to be excluded on the assumption as they are incurred already and the manufacture would involve only the variable cost. At this juncture, it is important to take into consideration the limiting factor, if it exists.

Situation 2: When there is no unutilized capacity, the circumstances drive to manufacture the components in the company itself. The problem of putting aside the other work and the loss of contribution from such displaced work will have to be taken into account. If the purchase price is higher than the marginal cost of production + traceable fixed costs + loss of contribution (as mentioned above), then the decision to manufacture them will result in an increased profit.

Under the following circumstances, it is better to make instead of buy the components from the outside vendors, even if the marginal contribution is less or zero:

1. The design or process may be a trade secret which the management may not like to pass on to external people.
2. To ensure a normal and reliable supply of the components, and to facilitate a smooth normal production function, it is always better to make the components in the factory itself.
3. Making the components in the factory itself would ensure a better control on the deliveries of stock.
4. Relying on outsource purchase depends mainly on one more factor—transport, which may often result in delay in deliveries.
5. It depends on the management policy also.

But, under the following circumstances, buying a product or components or materials from outside sources is preferred:

1. When the companies lack specialized techniques to manufacture them.
2. When proper men and equipment are not available
3. When the market trends for the components which are to be manufactured are seasonal or cyclical
4. when the return on the additional capital employed is not favourable.

Illustration 16.7

A lap-top manufacturing company finds that it costs to the make one component, the same is available in the market at Rs. 50 each, with assurance of uninterrupted supply.

The breakdown of cost is as follows:

	Rs.
Materials	20.00 each
Labour	17.50 each
Variable overheads	7.50 each
	45.00
Depreciation and other fixed cost	15.00 each
	60.00 each

You are required to decide:

1. Whether the company should make or buy the component.
2. If another vendor from the outside would offer the component at Rs. 44.00 each?

Solution

Step 1: First, the marginal cost of the component per unit has to be computed as follows:

 

		Rs.
(i)	Materials	20.00
(ii)	Labour	17.50
(iii)	Variable overheads	7.50
	∴ Marginal cost	= 45.00

Decision:

1. 1. The purchase cost of the above component is Rs. 50 (given).
   2. The marginal cost is Rs. 45.00 (Ref. Step 1).
   3. As the marginal cost is less than the purchase cost by Rs. 5 per unit (Rs. 50 – Rs. 45), it will be profitable to manufacture the component in the factory itself subject to the condition that the company has unused capacity with skilled labour.
2. As the purchase cost of the above component is Re. 1 per unit less than the marginal cost (Rs. 45 – Rs. 44), the decision to buy the component from another vendor from the outside sources will result in an increased profitability.

Illustration 16.8 Make or buy decision (with key factors)

Following is the data relating to bought-out prices and costs of production of the undernoted items:

You are required to prepare a suitable statement showing which items should be purchased from outside by assigning ranks in the order of preference for buying, by assuming:

1. There is no constraint or key factor.
2. Machine hours is a key factor.
3. Labour hours is a key factor.

Solution

1. First the difference between the purchase price per unit and the marginal cost of production per unit (or excess) has to be calculated.
2. Then, based on this, the key factor – per machine hour is to be calculated.
3. Finally, taking the labour hour as a constraint factor, per labour hour has to be computed.
4. Based on these results, the ranking is assigned and tabulated as follows:

Statement showing make or buy analysis:

Decision: Purchase price of item “B” is lower than its marginal cost, where as the purchase price of items A and C is higher than their marginal cost. Hence, it is profitable to purchase the item “B”, irrespective of the limiting factors.

16.9.4 Opportunity Cost*

When there is no idle (unused) capacity and at the same time the component part is manufactured in (instead of buying) the factory by replacing the other work, the loss of contribution from the displaced work has to be considered along with the marginal cost of production. The contribution so lost or foregone is called “opportunity cost”. The loss of contribution has to be determined with reference to the limiting factor.

*This concept is explained in detail in the chapter: Differential Cost Analysis.

Illustration 16.9

A company produces a variety of products each having a number of component parts. Product B takes 10 hours to process on a machine working to its full capacity. B has a selling price of Rs. 100 and a marginal cost of Rs. 50. AA’ – a component part (used for product A), could be made on the same machine in 2 hours for a marginal cost of Rs. 15. The suppliers’ price is Rs. 20. Should one make or buy the component AA’? Assume that the machine hour is the limiting factor.

Solution

First the opportunity cost, that is, the contribution lost per unit has to be determined.

	Rs.
Step 1 → Selling price per unit for Product B	= 100
Step 2 → Marginal cost/unit for Product B	= 50

Step 8 → This cost to make the component part AA’ – (product of A), that is, Rs. 25 is higher than that of the supplier’s price of Rs. 20.

Step 9 → Decision: Hence, it would be more profi table to buy AA’ than make the same.

Important Note

The loss of contribution or opportunity cost must be added to the marginal cost of the component which has to displace the regular work.

16.9.5 Profit Planning

Marginal-costing technique is also used in planning the profit level of the business. To put in other words, profit planning is the planning of future operation (level of activity planning) to attain a maximum profit or to maintain a desired level of profit. Following are some of the ways to improve the profit level of the business:

1. by increasing volume.
2. by increasing selling price
3. by decreasing variable costs.
4. by decreasing fixed costs.

Marginal costing focuses mainly on the contribution margin. Consequently, in this chapter problems are solved by applying marginal-costing technique only. The contribution-ratio technique (ratio of marginal contribution to sales) also plays a vital role in determining the profit performance of a business. The techniques of applying ratios especially P-V ratio is discussed in the next chapter captioned, “Break-even and Cost–volume–profit analysis”. Now, the contribution concept is applied in making the decision to ensure a profit level.

Illustration 16.10

A company has a capacity of producing 50,000 units of a certain product in a month. The sales department reports that the following schedule of sale prices is possible:

Volume of Production	Selling Price Per Unit
	Re
60%	0.95
70%	0.90
80%	0.85
90%	0.75
100%	0.60

The variable cost of manufacture between these levels is Re 0.20 per unit and the fixed cost is Rs 15,000. At which volume of production will the profit be the maximum?

 

[B.Com (Madras University) – Modified]

Solution

Decision: Based on the results, the contribution at 80% level of activity is maximum. As fixed cost remains constant, profit is maximum at 80% level of production.

Illustration 16.11

The following date relates to a manufacturing company:

Plant capacity: 2,00,000 units per annum

Present utilization = 50%

Actuals for the year are:

 

Selling price	Rs. 40 per unit
Materials cost	Rs. 15 per unit
Variable manufacturing costs	Rs. 9 per unit
Fixed costs	Rs. 18 lakhs

In order to improve the capacity utilization, the following proposals are being considered:

1. Reduce the selling price by 15%.
2. Spend additionally Rs. 2,00,000 on sales promotion How many units should be made and sold in order to earn a profit of Rs. 5,00,000 per year?

Solution

 

Step 1 →	Revised selling price (Rs. 40 less 15%) (40−6)	= Rs. 34/unit
Step 2 →	Variable costs:
	(i) Material cost	= Rs. 15
	(ii) Variable manufacturing Cost/Unit	= Rs.  9
Step 3 →	Total variable cost ((i) + (ii)	= Rs. 24/unit
Step 4 →	Contribution (Step 1 - Step 3)	= Rs. 10/unit
Step 5 →	Total contribution required:
	(i) Fixed costs	= Rs. 18,00,000
	(ii) Additional Sales Promotion Expenses	= Rs. 2,00,000
	(iii) Profit to be earned	= Rs. 5,00,000
	Add: (i) + (ii) + (iii)	= Rs. 25,00,000
Step 6 →	Total number of units to be made and sold to earn contribution of Rs.25,00,000
	Substituting the figures, we get
		= 2,50,000 units per annum.

Illustration 16.12

A Gel pen (advanced technique) manufacturer makes an average profit of Rs. 2.80 per piece on a selling price of Rs. 15.10 by producing and selling 50,000 pieces or 50% of the potential capacity. His cost of sales is: (per unit)

 

	Direct material	Rs. 3.80
	Direct wages	Rs. 1.40
	Works overhead	Rs. 6.40 (50% fixed)
	Sales overhead	Rs. 0.90 (30% variable)

During the current year, the manufacturer anticipates that his fixed charges will increase by 10% and rates of direct material and direct labour will increase by 7% and 9%, respectively. He has no option of increasing the selling price. Under this situation, he obtains an offer of an order equal to 20% of his capacity. This customer is a special customer.

What minimum price will you recommend for acceptance to ensure an overall profit of Rs. 1,81,000?

Solution

Step 8 → Marginal cost of additional units:

            20% capacity of 20,000 units × Rs. 9.062 (Ref: Step 3) = Rs. 1,81,240.

Step 9 → Increased contribution required

                        = Rs. 1,81,000 − Rs. 93,165.

                                    ↓                         ↓

                        (Given in question) (Refer: Step: 7)

                        = Rs. 87,835.

Step 10 → Total sales price expected for additional 20,000 pieces

 

Step 11 → Sales priceper piece or unit

Decision:	* This price Rs. 13. 45 is lesser than the selling price Rs. 15.10.
	* Such lower price is acceptable subject to the following conditions:
	1. If markets belong to special markets category.
	2. If customers belong to a special category (like government)
	3. If unutilized (idle) capacity of the plant exits.
	* This price cannot be acceptable to other type of customers.

16.9.6 Shut-Down Decisions

The decision on the closure of a department or discontinuance of a product or a section of a business can be made by applying marginal-costing technique. This technique helps in deciding the profitability of a product. It shows the contribution of each product towards fixed cost and profit. As discussed earlier, now one can be able to understand that if a product or a department should not be shutdown where the contribution exceeds the fixed costs. That is, greater the contribution, the higher the profits would be. On the other hand, if the contribution is less, that is, the profits are less or loss, in such cases, the decision to shut down would be wise. At this juncture, it is important to take into account the factor of fixed costs. If a portion of fixed costs can be avoided by closing down temporarily, such product or department should be shut down as the avoidable fixed cost is more than the contribution. To put in a nutshell, the products giving the highest contribution can be chosen and those giving the least contribution can be closed or discontinued. The amount of fixed costs which is essential for just maintaining the section or unit of business should also be taken into consideration.

Illustration 16.13

X ltd—a public limited company—has a chain of marketing centres across the country to sell its own products. The directors of the company are confronted with the problem—whether to continue business at Kanpur and Nagpur or to close these units and letting out the premises at an annual rental of Rs. 6,000 for Kanpur and Rs. 8,000 for Nagpur, which have been offered by A Ltd and B Ltd who are engaged in the same type of business as that of X Ltd. There is no connection between A Ltd and B Ltd and the acceptance of offer of one company does not necessarily involve the acceptance of the other.

The condensed P&L A/c of the two marketing centres for the year ended 31 December 2009 is shown as follows:

The average stock at the cost of the two marketing centres is:

            Kanpur: Rs. 30,000.

            Nagpur: Rs. 50,000.

If business at either marketing unit is continued, the trading results are expected to remain the same in the year 2009. The company can invest its surplus funds to yield an interest at 5% per annum. It is unlikely that there will be any saving in the head-office-administration costs expecting a reduction in the audit fee and a saving in the travelling expenses of the head office staff at Rs. 200 per marketing unit per annum.

Should, in your opinion as a cost accountant, either or both of the premises be let out at the rents offered. Give reasons for your recommendations.

Solution

 

NOTE:	*First, the present position has to be determined.
	*Then, the proposed position has to be determined.
	* Finally, based on the analysis of these two different situations, the net benefi t has to be determined. Based on this, the fi nal decision may be taken.

STAGE I: Analysis of the present position

Particulars	Kanpur Centre Rs.	Nagpur Centre Rs.
Step 1 → (i) Net profit	3,380	4,610
Step 2 → (ii) Share of head-offi ce-administration cost absorbed	4,500	5,500
Step 3 → (iii) Benefit [(i) + (ii) Step 1 + Step 2]	7,880	10,110

STAGE II: Analysis of the proposed position

Particulars	Kanpur Centre Rs.	Nagpur Centre Rs.
Step 1 → (i) Off ered rent by others	6,000	8,000
Step 2 → (ii) Saving in head-offi ce audit & travelling fees	200	200
Step 3 → (iii) Amount if not invested in stocks, will be an additional capital; and thereby the interest earned @ 5% pa.	1,500 (Rs. 30000 × 5/100)	2,500 (Rs. 50000 × 5/100)
Step 4 → Benefit [Add : Step 1 + Step 2 + Step 3]	7,700	10,700

STAGE III: Net benefit/loss if continued with the present situation             180              –590

STAGE IV: Decision: It is profitable to run Kanpur centre and let out Nagpur centre.

16.9.7 Change in Selling Price

The management often faces one important problem: the effect on profit of a change in the sales price. Generally, to attract a wider market, the price reduction is contemplated. In such cases, it would be essential to determine the effect of such proposals. The marginal-costing technique will be helpful in ascertaining the effect of such a proposal.

Illustration 16.14

The directors of Goodluck Ltd are considering the results of the profit and loss statement for the year that ended on 31 December 2009. The extract is as follows:

	Rs.	Rs.
Sales		15,00,000
Direct materials	4,50,000
Direct wages	3,00,000
Variable overheads	1,20,000
Fixed overheads	4,40,000	13,10,000
Profit		1,90,000

16.9.7.1 Effect of Change in Selling Price

The budgeted capacity of the company is Rs. 20,00,000, but the key factor is sales demand. The sales manager is proposing that in order to utilize the existing capacity, the selling price of the only product manufactured by the company should be reduced by 5%.

You are required to prepare a forecast statement which should show the effect of the proposed reduction in the selling price and to include any changes in the costs expected during the year 2010.

The following additional information is provided:

1. Sales forecast: Rs. 19,00,000.
2. Direct material prices are expected to increase by 2%.
3. Direct wages are expected to increase by 5% per unit.
4. Variable overhead costs are expected to increase by 5% per unit.
5. Fixed overheads will increase by Rs. 20,000.

[B.Com. (Madras University) – Adapted]

Solution

The following factors have to be calculated to prepare a statement showing the effect of change in the selling price:

STAGE I: Increase in sales has to be determined first:

STAGE I:

	Rs.
Step 1 → Sales forecast (after 5% reduction)	= 19,00,000
Step 2 → Add: Reduction in the selling price	= 1,00,000
Step 3 → Sales before the price reduction	= 20,00,000
Step 4 → Less: Sales last year	= 15,00,000
Step 5 → Increase in sales	= 5,00,000

NOTE: This increase in sales can be expressed in percentage as:

STAGE II: This percentage increase has to be taken into account in adjusting the increase in costs.

	Rs.	Rs.
Step 1 → For direct materials:
(i) Last year’s (2009) value:	4,50,000
(ii) Add: (due to increase in volume)	1,50,000
	6,00,000
(iii) Add: 2% increase (2010)	= 12,000	6,12,000
Step 2 → For direct wages:
(i) Last year’s value	= 3,00,000
(ii) Add :	1,00,000
	4,00,000
(iii) Add: 5% increase (2010)	= 20,000	4,20,000
Step 3 → For variable overheads:
(i) Last year’s (2009) value	= 1,20,000
(ii) Add :	40,000
	1,60,000
(iii) 5% increase in rate	8,000	1,68,000

STAGE III: Statement showing the effect of change in the selling price

 

Step 1 → Sales		Rs. 19,00,000
Step 2 → Add: Variable costs:	Rs.
(i) Direct materials: (Ref: Stage II Step 1)	6,12,000
(ii) Direct wages:	4,20,000
(Ref: Stage II Step 2)
(iii) Variable overheads: (Ref: Stage II Step 3)	1,68,000	12,00,000
Step 3 → Contribution (Step 1 − Step 2)		7,00,000
Step 4 → Less: Fixed costs (Rs. 4,40,000 + Rs. 20,000)		4,60,000
Step 5 → PROFIT		2,40,000

 

Result:	The profit forecast for the coming year 2010 is still Rs. 50,000 (Rs. 2,40,000 – Rs. 1,90,000) higher than that of last year 2009, despite the costs having been increased and the selling price has been reduced.
Reason:	Increased volume of sales at the reduced sales price has resulted in an increased contribution. This increased contribution is more than sufficient to cover the increase in both costs, that is, fixed cost and variable cost.

16.9.8 Product Pricing—Fixation of Selling Prices

The management is often confronted with the problem of product pricing. In multiproduct pricing, the management should decide whether each product is priced competitively so that the contribution by each product may be sufficient enough to recover the fixed cost and profit. Product pricing is essential: (i) under normal circumstances; (ii) in times of competition; (iii) during a period of depression; (iv) in accepting additional orders in case of utilizing unused capacity; and (v) in exporting. The technique of marginal costing can be helpful in arriving at a proper decision to fix prices.

Price under normal circumstances for a longer period should be based on the total costs. It is also based on marginal costs—the underlying principle is that price should be equal to the marginal costs PLUS a certain amount. The amount that should be added will depend on (i) demand and supply; (ii) competition; (iii) nature and variety of products; (iv) policy of pricing; and (v) other related factors.

Pricing for a short period may not be a problem. We have to just see if the contribution is sufficient for the recovery of fixed cost and profit.

But pricing in certain specific situations, as described in the following, should be considered with great care:

1. When a new product is introduced into the market.
2. When a cut-throat competition prevails in the market.
3. When an existing product is to be popularized.
4. When future market forecasts are adverse.
5. When foreign market has to be undertaken.
6. When retrenchment of employees cannot be possible but production has to be maintained.
7. When the sale of one product can push up the sales of other products of the same company.
8. When the goods become obsolete or out of fashion.
9. Unutilized capacity of the plant may be utilized.
10. When to offer quotations at lower rates.

16.9.8.1 (a) Pricing in Depression

Illustration 16.15

X Ltd is found to be working below the normal capacity due to recession. The directors have been approached by another company with an enquiry for a special purpose job. The costing department estimated the following in respect of that job:

 

	Direct materials – Rs. 1,00,000.
	Direct labour – 5000 hours @ Rs. 3 = 15,000.
Overhead costs: Normal recovery rates:
	Variable = Re 1 per hour.
	Fixed = Rs. 1.50 per hour.

You are required to advise the company on the minimum prices to be charged.

Solution

Marginal costs will have to be determined as follows.

 

		Rs.
(i)	Direct materials	= 1,00,000
(ii)	Add: Direct labour	= 15,000
(iii)	Add: Variable overhead @ Re 1 per hour for 5000 hours	= 5,000
(iv)	Total marginal costs	= 1,20,000

The floor price, the absolute minimum price should be Rs. 1,20,000. That is, a total of marginal costs. At this level, it will not make any contribution. Hence, a certain portion of fixed costs must be added to the marginal costs to accept the job with profit. In this case, the fixed overhead is found to be Rs 7,500 (5000 hours × Rs. 1.50 per hour).

Thus, this technique assists in pricing a product.

16.9.8.2 (b) Acceptance of Additional Orders, Exporting Additional Markets

While accepting the export order, the following should be taken into account:

1. It should not have any adverse effect on the price that is already existing in the home market.
2. In case the order is accepted, one should think about the possibility of rejecting an order with high contribution during that period of execution of the order.
3. The interest on incremental working capital should not be lower than the contribution factor from the export order.
4. It should be seen that those products which are exported would not be revered to home market again.
5. In case the customer is not a foreign one (i.e. local customer), the price reduction is not at all advisable as it will affect normal markets.

Illustration 16.16

X Ltd. having a capacity of 1,50,000 units per year produces 1,00,000 units which are consumed in the home market at Rs. 20 per unit. The cost sheet (per unit) on the basis of this output is as follows:

Materials	Rs.
Labour	6.00
Fixed factory expenses	4.00
Variable factory expenses	1.50
Office expenses	1.00
Selling expenses	1.00
Fixed	0.50
Variable	1.00
Total cost	15.00

A foreign customer who is interested in the product is willing to buy 50,000 units at a price of Rs.14 per unit.

Do you advise to accept the order? Support your decision with a suitable cost data. What will be your advice if (i) the new customer is not a foreign one and (2) if the price offered is Rs. 11.50 per unit.

Solution

First contribution and then profit are to be determined which are depicted in the following statement of profitability:

 

Decision:

1. Export order can be accepted as it increases the total profit by Rs. 1,00,000. But it is subject to certain considerations as explained earlier. Further, if the customer is not a foreign one, the price reduction must not be allowed, as it will affect the normal market prices.
2. The marginal cost per unit has to be determined:

Statement showing marginal cost per unit

Particulars	Amount Rs.
Direct materials	6.00
Direct labour	4.00
Variable factory expenses	1.00
Variable selling expenses	1.00
Marginal cost per unit	12.00

Decision: Such order should not be accepted. Because the price offered by the buyer is less than the marginal cost.

16.9.9 Decision on Manufacturing Methods

The problem whether to use a machine or produce by hand labour or use any combination of machine and labour can be best solved by the usage of marginal-costing technique. To decide the best production method, the relative contribution from each method acts as the basis for selection. The method of manufacture which will give the greatest contribution, has to be selected on the basis of selection of method, but the key factor should not be lost sight of. In case the time taken on production is mentioned, the time factor must be taken into account while deciding on the selection of manufacturing methods.

Illustration 16.17

Product LM can be produced by machine A or machine B. Machine A can produce 15 units of LM per hour and B takes 25 units per hour. The total machine hours available are 7,500 hours per annum. From the following comparative costs and selling price, you are required to determine the profitable method of manufacture:

	Per Unit of Machine A Rs.	Product LM – Machine B Rs.
Direct materials	30	30
Direct labour	15	20
Overhead:
Variable	17	22
Fixed	8	8
Total costs	70	80
Selling price	75	75

Solution

Contribution has to be determined by preparing a profitability statement as follows:

 

Particulars	Machine A	Product LM – Machine B
Machine hours per annum	7,500	7,500
Output per hour	15 units	25 units
Per unit – contribution is to be computed	Rs.	Rs.
Step 1: Direct materials	30	30
Step 2: Direct labour	15	20
Step 3: Overhead: Variable	17	22
Step 4: Marginal costs (Add: Step 1 + Step 2 + Step 3)	62	72
Step 5: Selling price	75	75
Step 6: CONTRIBUTION (Step 5 – Step 4)	13	3
Step 7: Contribution per hour	195	75
	(Rs. 13 × 15 unit)	(Rs. 3 × 25 units)
Step 8: Annual contribution	Rs. 14,62,500	Rs. 5,62,500

Hence, the production in Machine A, Rs. 9,00,000 is more profitable (Rs. 14,62,500 – Rs. 5,62,000) by producing in Machine A.

16.9.10 Maintaining a Desired Level of Profit

A company has to face the problem of cutting prices for various reasons such as competition, government regulations and unforeseen compelling situations. If the selling price is reduced, automatically it will result in a reduced contribution which, in turn, affects the level of profit. In order to maintain the level of profits, the volume of sales has to be increased. The marginal-costing techniques will be helpful in determining the desired volume of sales.

Illustration 16.18

RB Ltd manufactures and markets a single consumer product. The following information is available:

	Rs.
Materials	10
Conversion costs (variable)	7
Dealer’s margin	3
Selling price	30
Fixed cost	Rs. 4,00,000
Present sale	75,000 units
Capacity utilization	60%

There is severe competition and extra efforts are needed to sell. Suggestions have been made for increasing sales:

1. By reducing sales price by 10%.
2. By increasing dealers’ margin by 25% over the existing rate.

Solution

STAGE I: First, the present marginal cost per unit is to be determined as follows:

 

	Rs.
Step 1: Materials	10
Step 2: Add: Conversion costs	7
Step 3: Add: Dealer’s margin	3
Step 4: Marginal cost (Step 1 + 2 + 3)

Step 5: Contribution per unit = Selling price − Marginal cost

                                     = Rs. 30 − Rs. 20 = Rs. 10.

Step 6: Total contribution = No of units × Contribution

                           = 75,000 × Rs. 10 = Rs. 7,50,000.

Step 7: Profit = Total contribution – Fixed cost

                      = Rs. 7,50,000 – Rs. 4,00,000 (given)

                      = Rs. 3,50,000.

STAGE II: If sales prices are reduced by 10%,

Step 1: New sales price = (Rs. 30 − 10% of Rs. 30) = Rs. 30 − Rs. 3

                                      = Rs. 27.

Step 2: New dealer’s margin

                     10% of Rs. 27 = Rs. 2.70.

Step 3: Variable costs = Direct material + Conversion cost + Dealer’s margin

                   = Rs. 10 + Rs. 7 + Rs. 2.70 = Rs. 19.70

Step 4: Contribution/unit = Rs. 27 − Rs. 19.70

                                       = Rs. 7.30.

Step 5:

[NOTE: Since the fixed costs remain unchanged, the present level of profit can be maintained by keeping the total contribution at the present level, that is, Rs. 7,50,000.]

STAGE III: If dealer’s margin is increased by 25%,

 

Step 1: New dealer’s margin	= Rs. 3 + 25% of Rs. 3
	= Rs. 3 + Rs. 0.75 = Rs. 3.75.
Step 2: New variable cost	= Rs. 10 + Rs. 7+ Rs. 3.75 = Rs. 20.75.

Step 3: Contribution = Rs. 30 − Rs. 20.75 = Rs. 9.25.

Step 4:

Recommendation

The second proposal (i.e., increase the dealer’s margin by 25%) is recommended. Reason is

1. Contribution per unit is higher by Rs. 1.95 (Rs. 9.25 − Rs. 7.30).
2. Sales (in units) are lower by 21,659 units (1,02,740 − 81,081).

In total, lower sales efforts and less finance will be the resultant factors to implement the second proposal.

16.9.11 Production and Market-Expansion Decisions

Maximum use or absorption of fixed costs will be the ultimate aim of any business. The installed capacity of an entity can be utilized maximum by planning the production as well as the market expansion. Such decisions may be guided by the marginal-costing technique. The amount of additional contribution to be earned by extra production and increase in volume of sales (after deducting fixed costs) will determine whether to venture it or not. If contribution is higher, such expansion decisions are more profitable.

16.9.12 Offering Quotations

Suppose, if a company is not operating at its fullest capacity, the remaining unutilized capacity can be put into usage by way of offering quotations and undertaking extra production. In such situations, the company can quote any amount above the marginal cost. Such decisions will result in profit to the company.

To put in a nutshell, the computation of contribution is the sole main criteria to take any decision on many of the areas as discussed so far. Needless to mention that the marginal-costing technique plays a vital role.

16.10 SPECIAL CIRCUMSTANCES IN WHICH THE SELLING PRICE AT OR BELOW THE MARGINAL COST IS JUSTIFIED

Generally, if the selling price is below the marginal cost, loss will be more than the fixed costs, as the variable expenses will not be covered entirely. Every effort has to be made to fix the selling price at a price which is at least equal to the marginal cost or preferably above the marginal cost. If the price is below the marginal cost, it is wise to discontinue the production. But in some circumstances, fixing the price below the marginal cost is justified, which are explained as follows:

Introduction of a new product: When a new product is introduced in the market, the selling price is fixed below the marginal cost in order to make the new product more popular. This is done with a notion that the sale will increase in due course and the cost of production will decline.

To maintain production: In some cases, the production level has to be kept at a minimum (optimum) to keep the employees engaged. Plant and machinery may depreciate more quickly when kept idle than when being used. Exploration of foreign market: Sometimes, the government allows import quota against foreign exchange earned. Profit may be more in such cases.

To prevent the loss of future orders: If a firm’s products are in short supply, other firms or other products take its place. At such a later stage, it is not possible to recover the lost markets.

Stock of huge inventory (materials): When a firm has already purchased large quantities of materials, it is advisable to convert them into finished products. Selling them at a price lower than the marginal cost occurs.

Disposal of perishable goods: When goods are of perishable nature, it is better to sell such goods at whatever price they can be realized. Leaving them unattended, nothing can be realized if they are totally perished.

Elimination of competitors: When there is a strong competition in the market, selling at or below the marginal cost is justified. The aim is to eliminate the competition from the weaker rivals.

Sale of complementary product: When sales of one product at a price below the marginal cost will push up the sales of an other product (which is profitable), this can be justified.

Market trend: If the prices have fallen throughout the market, and a loss has already occurred due to market behaviour, it is advisable to reduce prices below the marginal cost.

PROFESSIONAL COURSES – (INTER LEVEL)

Illustration 16.19

The following data relate to a company which makes and sells computers and accessories:

	May	June
Sales (units)	2,500	5,000
Production (units)	5,000	2,500
Selling price per unit	200 (Rs.)	200 (Rs.)
Variable production cost per unit	100	100
Fixed production overhead incurred	1,00,000	1,00,000
Fixed production overhead cost per unit, being the	20	20
predetermined overhead absorption rate
Selling, distribution and administration cost (all fixed)	50,000	50,000

You are required to present comparative profit statements using: (1) absorption costing and (2) marginal costing

 

[I.C.W.A. – Inter – Modified]

Solution

1. Under absorption costing, the first unit cost of production has to be determined.

   	May Rs./Unit	June Rs./Unit
   Step 1: Variable production cost	100	100
   Step 2: Add: Fixed production overhead absorption rate	20	20
   Step 3: Unit cost of production (1 + 2)	120	120

2. Closing stock of May will become the opening stock of June.
3. Closing stock, under absorption costing, has to be valued at a variable production cost PLUS fixed production overhead (absorbed rate).

Profit and loss statement under absorption costing is as follows:

 

Production	May	June
	Production – 5,500 Units Sales – 2,500 Units Rs.	Production – 2500 Units Sales – 5,000 Units Rs.
Step 1: Sales value	5,00,000 (2500 × Rs. 200)	10,00,000 (5000 × Rs. 200)
Step 2: Less: Cost of goods sold
(i) Opening stock	NIL	3,00,000 (2500 × Rs. 120)
(ii) Cost of production	6,00,000 (5,000 × Rs. 120)	3,00,000 (2500 × Rs. 120)
Step 3: Add: Adjustment for underapplied volume variance	–	50,000 (2500 × Rs. 20)
Step 4: Less: Closing stock	3,00,000 (2500 × Rs. 120) 3,00,000	NIL 6,50,000
Step 5: GROSS PROFIT	2,00,000	3,50,000
Step 6: Less: Selling, distribution & administration overhead	50,000	50,000
Step 7: NET PROFIT (Step 5 − Step 6)	1,50,000	3,00,000

Profit and loss statement under marginal costing is as follows:

	May Rs.	June Rs.
Under absorption costing	1,50,000	3,00,000
Under marginal costing	1,00,000	3,50,000

Illustration 16.20

A firm can produce three different products from the same raw material using the same production facilities. The requisite labour is available at Rs. 4 per hour for all products. The supply of raw material which is imported at Rs. 4 per kg is limited to 10,400 kg for the budget period. The variable overheads are Rs. 2.80 per hour. The fixed overheads are Rs. 25,000. The selling commission is 10% on sales.

1. From the following information, you are required to suggest the most suitable sales mix, which will maximize the firm’s profits. Also determine the profit that will be earned at that level:
   
2. Assume, in the above situation, an additional 4,500 kg of raw material is made available for production, should the firm go in for further production if it will result in additional fixed overheads of Rs. 10,000 and a 25% increase in the rates per hour for labour and variable overheads.

[C.A. (Inter) – Modified]

Solution

* First, the contribution per unit for all the three products have to be determined. Based on the contribution, the order of ranking has to be assigned.

*Then, as per suggested sales mix—the profit has to be ascertained.

*Finally, we have to find out whether the use of additional raw materials will increase the profits (by determining the additional contribution).

STAGE I: Determination of Contribution – Statement

STAGE II: Statement of profit as per suggested sales mix

Total contribution:	58,072
Less: Fixed overheads:	25,000
∴ Profit	33,072

STAGE III:

(b) In case the additional 4,500 kg of raw materials are available for production, it will be utilized to produce 3000 additional units of product C. (∴ 4500 kg ÷ 1.5 kg – raw material required per unit = 3000 units). The additional profit due to the use of this material will be as follows:

	Rs.	Rs.
Step 1: Contribution for 3000 units @ Rs. 6 − 30 per unit		18,900
Step 2: Less:
(i) Increase in labour cost for 3000 units @ Rs. 1.50 (25 % of Rs. 6.00)	4,500
(ii) Increase in variable overhead (3000 units × Rs. 1.05) (25% of Rs. 4.20)	3,150	7,650
Step 4: Additional contribution (Step 1 − Step 2 (i) & (ii)		11,250
Step 5: Less additional fixed costs		10,000
Step 6: ∴Additional profit (Step 4 − Step 5)		1,250

Decision: The additional use of 4500 kg of material increases the profit by Rs. 1,250. It is advisable to go into the production of additional 3,000 units of product “C”.

Illustration 16.21

A manufacturing company produces and sells products P, Q and R. It has an available inactive-hour capacity of one-lakh hours, interchangeable among the three products. Presently, the company produces and sells 20,000 units of P and 15,000 units each of Q and R. The unit-selling price of the three products are Rs. 25, Rs. 32 and Rs. 42 for P, Q and R, respectively. With this price structure and the aforesaid sales mix, the company is incurring loss. The total expenditure exclusive of fixed charges (presently, Rs. 5 per unit) is Rs. 13.75 lakhs. The unit cost ratio among the products P, Q and R is 4: 6: 7. Since the company desires to improve its profitability without changing its cost and price structures, it has been considering the following three mixes so as to be within its total available capacity.

You are required to compute the quantum of loss now incurred and advise the most profitable mix which could be considered by the company.

 

[I.C.W.A. – Inter]

Solution

STAGE I: First variable cost per unit has to be determined.

STAGE II: Under present position, the quantum of loss has to be ascertained.

Result:

1. Product Mix I incurs a loss of Rs. 25,000.
2. Product Mix II incurs neither profit nor loss.
3. Product Mix III incurs a profit of Rs. 15,000.

Decision: The management is advised to choose Product Mix III to earn profit.

Illustration 16.22

 

The cost per unit of three products X,Y and Z of a company are given as follows:

Production arrangements are such that if one product is given up, the production of the others can be raised by 50%. The directors propose that Z should be given up because the contribution from the product is the lowest. Present suitable analysis of the data indicates whether the proposal should be accepted.

 

[I.C.W.A. – Modified]

Solution

First, the contribution per unit for the products will be determined.

 

NOTE 1:	Product X gives the maximum contribution per unit. No limiting factor is given in the problem. As such the company naturally opts to maximize the production of product X.
NOTE 2:	In the problem, there is a restrictive condition. If one product is given up, the production of others can by raised by 50%.
NOTE 3:	This restrictive condition has to be taken into account and an analysis has to be carried out as follows:

 

Result:

1. The discontinuance of Product X gives the lowest incremental contribution (i.e., Rs. 1,26,000).
2. Discontinuance of Product Z results in sub-optimal decision.
3. Management is advised to discontinue product X in order to optimize the company’s profit and reject the proposal to discontinue the product X.

Illustration 16.23

Bhagya Ltd is producing a software equipment from five components, three of which are made by using general-purpose machines and two by manual labour. The data for the manufacture of the equipment are as follows:

The marketing department of the company anticipates a 45% increase in demand during the next period. General-purpose machinery used to manufacture A, B and C which are already working to the maximum capacity of 9,504 hours and there is no possibility of increasing this capacity during the next period. But labour is available for making components D and E and also for assembly according to the demand. The management is considering the purchase of one of the components A, B or C from the market to meet the increase in demand. These components are available in the market at the following prices:

	Rs.
Component A	100
Component B	300
Component C	200

Required:

1. Profit made by the company from the current operations.
2. If the company buys any one of the components A, B or C, what is the extent of additional capacity that can be created?
3. Assuming a 50% increase in demand during the next period, which component should be bought from the market?
4. The increase in profit, if any, if the component suggested in C is purchased from the market.
5. Which component should be purchased and in what quantity if production is increased by 55%?

[I.C.W.A. – Inter – Modified]

Solution

NOTE 1: *First, the number of units manufactured by equipments has to be determined:

No. of unitsof product manufactured

*Profit/loss made by the company from current operations has to be computed.

STAGE I: Statement showing profit/loss from current operations

Particulars		Amount Rs.
Step 1: Sales value		79,200
132 units × Rs. 600 (Ref: Note: 1): (given)
Step 2: Less: Marginal cost of sales:
(i) Component cost	Rs.
[132 units × Rs. 160 (given)]	Rs. 21,120
(ii) Assembly cost
[132 units × Rs. 40 (given)]	Rs. 5,280	26,400
Step 3: CONTRIBUTION (Step 1 − Step 2)		52,800
Step 4: Less: Fixed cost [(132 units × Rs. 316 (given)]		41,712
Step 5: PROFIT (Step 3 − Step 4)		11,088

STAGE II:

NOTE: If the company buys any one of the components from the market.

Situation 1: If the company purchases the component A, then the machine hours needed for its manufacture can be freed for manufacturing the other components B and C.

Situation 2: If the component B is purchased, then the machine hours needed for its manufacture, can be freed for manufacturing the other components A and C.

Situation 3: Similarly, if the component C is purchased, then the machine hours needed for its manufacture can be freed for manufacturing the other components A and B.

In each of the situation described earlier, the machine hours required per unit has to be determined. This is shown as follows:

STAGE III:

• The management anticipates a 45% increase in demand.
• The management cannot meet such a demand by purchasing the component A. Reason is: A creates only 38.63% of additional capacity (Ref: Analysis above).
• Accordingly, the management is left with two options only, that is, buy either the component B or C.
• Savings per machine hour has to be computed to select the option.

Particulars	Component B Rs.	Component C Rs.
Step 1: Purchasing price per unit (given)	300	200
Step 2: Marginal cost of production/unit (given)	54	58
Step 3: Savings from manufacture (Step 1 − Step 2)	246	142
Step 4: Machine hours required (given in question)	28	24
Step 5: Savings per machine hour (Step 3 ÷ Step 4)
	Rs. 8.78	Rs. 5.92

Decision: If surplus capacity exists, it is not advisable to buy either B or C from outside.

Reason: Purchase prices are relatively much higher than the marginal costs.

• But here, no surplus capacity exists. Hence, no other way to buy any one component even.
• The management may be advised to buy the Component C.

Reason: It generates least savings through manufacture (per unit of limiting factor).

STAGE IV: Finally, an increase in profit/loss from buying component C has to be determined as follows:

 

Particulars	Rs.	Amount Rs.
Step 1: Sales value: (198 units × Rs. 600) (132 + 50% 132 + 66 = 198 units)		1,18,800
Step 2: Less: Marginal cost of sales:
(i) Component cost (198 units × Rs. 102)	20,196
(ii) Assembly cost (198 units × Rs. 40)	7,920
(iii) Purchase price of “C” (198 units × 200)	39,600	67,716
Step 3: CONTRIBUTION (Step 1 − Step 2)		51,084
Step 4: Less: Fixed costs (132 units) × Rs. 316		41,712
Step 5: PROFIT (Step 3 − Step 4)		9,372
Step 6: Decrease in profit		Rs. 11,088 – Rs. 9,372 = Rs. 1716

STAGE V: From the results obtained (Ref: Stage IV), buying the component “B” is the only solution. Hence, in case the production capacity is increased by 55%, the buying components A and C will not be achieving a 55% growth in production. Hence, the total requirement – component ‘B’ should be purchased.

Illustration 16.24

 

A company manufactures a single product in its factory utilizing 60% of its capacity. The price and cost details are given as follows:

	Rs.
Sales (6,000 units)	2,70,000
Direct materials	48,000
Direct labour	60,000
Direct expenses	9,000
Fixed overhead:
Factory	1,00,000
Administration	10,500
Selling X distribution	12,500

An analysis of the fixed overhead reveals that 12.5% of factory overheads and 20% of selling and distribution overheads are variable with production and sales. But administration overheads are wholly fixed. Since the existing product could not achieve the budgeted level for two consecutive years, the company decides to introduce a new product with marginal investment but largely using present plant and machinery. The cost estimates of the new product are as follows:

Cost Elements	Rs./Unit
Direct materials	8.00
Direct labour	7.50
Direct expenses	0.75
Variable factory overheads	1.00
Variable selling and distribution overheads	0.75

It is expected that 2,000 units of the new product can be sold at a price of Rs. 30 per unit. The fixed factory overheads are expected to increase by 10% while fixed selling and distribution expenses will go up by Rs. 6,250 annually. Administration overheads remain unchanged. However, there will be an increase of working capital to the extent of Rs. 37,500 which would take the total project cost to Rs. 4,37,500.

The company considers that 20% pre-tax and interest return on investment are the minimum acceptable things to justify any new instrument.

Required:

1. Should the new product be introduced?
2. Given the data above and making any assumptions that you would consider appropriate, are there any further observations or recommendations you wish to make?

Solution

NOTE 1: In this problem, the return on investment is a new factor. It is computed applying the formula:

NOTE 2: Variable overheads pertaining to the existing products are determined as follows: Rs.

 

	Rs.
1.Variable factory overheads: (12.51% of Rs. 1,00,000)	= 12,500
Add 2:Variable selling and distribution overheads (20% of Rs. 12,500)	= 2,500
	15,000

NOTE 3: Increase in fixed overheads due to the introduction of a new product is determined as:

 

1: Increase in fixed overheads:	Rs.
Total fixed factory overheads	= Total fixed overhead – Variable overhead.
	= Rs. 1,00,000 – Rs. 12,500
	= Rs. 87,500
10% of Rs. 87,500	= 8,750
2: Increase in fixed selling and distribution overheads (given)	= 6,250

STAGE I: *A comparative statement showing the estimated profit and loss of the existing product as well as that of the new product has to be prepared.

* From the net profit (to be) ascertained, the return on investment is to be computed

 

[Before transferring the figures, the students are asked to refer the notes explained at the commencement of the solution. The overhead figures may mislead at times]

 

Results:

• The new product contributes a profit of Rs. 9,000 and the return on investment is also 24%, a 4% higher than the company’s investment criterion.
• It also contributes to the recovery of fixed costs.
• Therefore, it is advisable to introduce the new product.

However, to answer the second question some more analysis has to be undertaken as follows:

Results:

1. The overall contribution as a percentage of sales has declined from 51.11% to 49.09% after the introduction of a new product.
2. But, incidentally, the net profit as a percentage of sales has risen to 15% from 11.11%.

   Reasons:

   1. Variable cost as a percentage of sales has increased.
   2. The incidence of fixed costs has fallen.
   3. Direct wages and factory overheads are high.
3. Currently, the return on investment is 7.5% only. But it has prescribed a minimum return on investment as 20%.

Advice:

1. Fixed costs and working capital have to be reduced judiciously.
2. Constant vigil and a thorough probe into those elements of cost using industrial engineering and business process re-engineering techniques are necessary in order to reduce direct wages and factory overheads.

Absorption Costing: A principle by which the fixed as well as the variable costs are charged to cost units and the total overheads are absorbed according to the activity level.

Limitations of Absorption Costing: (a) the changes in volume of stock will affect the profit; (b) the arbitrary apportionment of overheads will distort the production costs; (c) all costs are not charged to P&L A/c of the period in which they are incurred; (d) fails to provide basis for decisions; and (e) costs are not segregated into fixed and variable.

Marginal Costing: The principle whereby the marginal costs of cost units are ascertained. Only variable costs are charged to cost units, the fixed cost attributable to a relevant period being written off in full against the contribution for that period.

Contribution represents the excess of sales price over the marginal costs of such sales.

Differences Between Absorption Costing and Marginal Costing: Differences exist in (i) charging cost to products; (ii) methods of approach; (iii) stock valuation; (iv) treatment of changes in volume of stock over periods; and (v) net-operating profit.

Special Features of Marginal Costing: (a) Segregation of costs into fixed and variable; (b) only variable costs—as product costs; (c) fixed costs to be treated as a period cost; (d) stocks are valued at marginal cost (e) emphasis is on the contribution margin; and (f) pricing at a marginal cost.

Advantages of Marginal Costing: (1) fixed costs are treated as period cost; (2) product costs approximate differential costs; (3) eliminates fluctuations in profit; (4) contribution is shown in books of accounts; and (5) a better control over fixed costs exists.

Limitations of Marginal Costing: (1) inventory is under-valued; (2) calculation of variable costs for all levels is difficult; (3) if the demand is seasonal, monthly profits vary; (4) only internal-report circumstances in which selling at or below marginal costing, which again are: (i) to maintain production continuity; (ii) to retain skilled labour; (iii) to avoid loss of future orders; (iv) to eliminate competition; (v) to introduce a new product; (vi) to dispose off perishable products; (vii) to accept export orders; and (9) to boost the sales of complementary products.

Managerial Applications of Marginal Costing: Marginal costing is useful in taking decisions with respect to (1) optimize the product mix; (2) make or buy decisions; (3) alternative methods of production; (4) shut-down decisions; (5) product pricing; (6) profit planning; (7) production and expansion; and (7) cost control.

Application of marginal-costing technique to decide on the earlier-explained factors is again described by way of illustrations. (Refer: Illustration No 4 to Illustration No. 18).

Absorption Costing: A principle (or method) of costing whereby the fixed as well as the variable costs are allotted to cost units and the total overheads are absorbed to the activity level. It includes production, administrative and other costs.

Contribution: Excess of sales value over marginal cost of such sales.

Direct Costing: A principle whereby all costs that are directly related are charged to products, processes, operations or services, of which they form an integral part.

Marginal Cost: The variable cost of one unit of a product or a service, which is a cost that would be avoided if the unit was not provided or the service not provided.

Marginal Costing: The principle whereby the marginal costs of the cost units are ascertained. Only variable costs are charged to cost units and the fixed cost that is attributable to a relevant period is being written off in full against the contribution for that period.

Key Factor: The factor that limits the production and/or sales when the resources are scarce and selection of a profitable product must be on the basis of contribution per unit of key factor. It is also known as the limiting factor. Higher the contribution per unit of key factor, the more profitable is the product.

 

Bhabatosh Banerjee; ‘The cost Accounting’; The World Press Private Ltd., Calcutta

Manash Dutta; ‘Cost Accounting: Principles and Practice’; Pearson Education, New Delhi

Charles T. Horngreen, Srikant M. Datar, George Foster., “Cost Accounting – A Managerial Emphasis – Pearson Education., New Delhi.

1. Contribution = Sales value − Marginal cost

                                                (Variable cost)

   [∵ Marginal cost and variable cost are synonyms]

2. Sales value = Variable cost + Fixed cost + Profit.
3. Sales value – Variable cost = Fixed cost + Profit.
4. Contribution = Fixed cost + Profit.
5. Profit = Contribution – Fixed cost.
6. Profitability = Contribution per unit. (No key factor.)
7. Profi tability =
8. When key factor is given specifically: Profitability =
   1. when raw material is a key factor
      
   2. when labour hours is a key factor
      
   3. When machine hours is a key factor
      

   (Instead of machine hours, key factor may be stated as “capacity time” required.)

9. Differences between the profits as per absorption costing and marginal costing: Fixed overheads per unit × change in inventory units.

QUESTION BANK

 

I. State whether the following statements are true or false

1. Under marginal-costing method, costs are segregated into fixed and variable parts.
2. Variable cost per unit are not fixed at all levels of output.
3. Fixed costs cannot be controlled.
4. Marginal costing is not a method but a technique.
5. To compute the value of stocks of WIP of finished goods, both fixed and variable costs are taken into account under this technique.
6. Under marginal-costing technique, fixed costs are charged off to revenue fully during the period in which they are incurred but not taken into account for valuing inventories.
7. Marginal costing combines the techniques of cost recording and cost reporting.
8. The role of contribution is negligible in fixing prices under marginal-costing technique.
9. The unit cost of a product means the average variable cost of manufacturing the product.
10. Contribution is the difference between sales and profit.
11. The excess of fixed assets over contribution is loss.
12. When selling price is at cost, then contribution = fixed cost.
13. Under marginal costing, fixed factory overhead is included in the inventory.
14. Fixed costs are written off against the contribution during that period in which they are incurred.
15. Basic marginal equation is: Sales – Marginal costs = Fixed costs – Profit.
16. Under all situations, the profit shown by marginal costing and the profits shown by absorption costing may be the same.
17. In absorption costing, the effects of sales and production are combined whereas in marginal costing the emphasis is on sales only.
18. Under marginal-costing technique, variable costs act as an effective tool in studying the relationship between cost, price and volume.
19. Selling below the marginal cost is never advised, whatever may be the situation.
20. Segregation of semi-variable costs into their fixed and variable parts cannot be possible.

Answers:

 

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

 

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

1. Under marginal-costing method, cost per unit is ascertained only on the basis of _____.
2. _____ costs are not taken into account under marginal costing.
3. Marginal costing is known as _____.
4. Marginal costing is a technique to study the relationship between _____ and the volume of output.
5. Marginal costing and _____ costing are interchangeable terms.
6. Contribution is the difference between sales and _____ cost of sales.
7. Under marginal-costing technique, profit is determined by deducting fixed costs from the total _____.
8. Under marginal-costing technique, costs are separated into _____ and _____ elements.
9. Marginal costing combines the technique of cost recording and cost _____.
10. The unit cost of a product means the average _____ of manufacturing the product.
11. The excess of contribution over fixed costs is _____.
12. When selling price equals the cost, contribution = _____.
13. Under marginal costing, fixed costs will be a _____ amount.
14. Direct materials, direct labour and direct expenses are all called as _____ costs.
15. The straight-line equation used in segregating the semi-variable costs into their fixed and variable elements is

    Y = _____ + C.

16. Under _____ technique, both fixed and variable costs are charged to product costs.
17. Profits shown by marginal costing and profits shown by absorption costing will not be _____ at all conditions.
18. Basic marginal equation is: Sales – marginal costs = _____.
19. Whereas in the above equation Contribution = _____ + Profit.
20. If the sale price of a product is Rs. 10 and the variable cost is Rs. 7.50, then the contribution will be _____.
21. Under absorption costing, profit is the difference between the sales and _____.
22. Period costs are nothing but _____.
23. Key factor is also known as _____.
24. Selling of a new product, which is to be introduced in the market, at or below _____ is justified.
25. Key factor is important in determining the _____ of products.

Answers:

1. Variable cost
2. Fixed
3. Variable costing
4. Profit
5. Direct
6. Marginal (or) variable
7. Contribution
8. Variable cost and fixed cost
9. Reporting
10. Variable cost
11. Profit
12. Fixed cost
13. Constant
14. Direct
15. Mix
16. Absorption costing
17. Same
18. Contribution
19. Fixed cost
20. Rs. 2.50
21. Cost of goods sold
22. Fixed overhead
23. Limiting
24. Marginal cost
25. Profitability

III. Multiple choice questions choose the correct answer:

1. Marginal cost represents:
   1. variable cost
   2. variable overhead
   3. fixed cost
   4. semi-variable cost
2. Marginal costing is:
   1. a method of costing
   2. a technique of costing
   3. a system of costing
   4. a stage in accounting process
3. Contribution is the difference between:
   1. sales and profit
   2. sales and fixed cost
   3. sales and variable cost
   4. fixed cost and variable cost
4. The prime objective of marginal costing is to:
   1. make decisions and control costs
   2. prepare final accounts
   3. make reports to statutory authorities
   4. predict profit
5. Under marginal-costing technique, the prices are based on:
   1. fixed costs
   2. variable costs
   3. variable costs and contribution
   4. fixed costs and contribution
6. Marginal-costing technique combines the technique of
   1. standard costing and budgetary control
   2. contract costing and operating costing
   3. job costing and break-even analysis
   4. cost recording and cost reporting
7. In marginal costing, the cost of production includes
   1. prime cost and variable overhead
   2. direct cost and indirect cost
   3. prime cost and fixed overhead
   4. none of these
8. Period costs are:
   1. variable costs
   2. costs that occur at regular periods
   3. fixed overhead
   4. total costs that occur at a specified period
9. Key factor is important:
   1. in making key decisions
   2. in ascertaining the profitability
   3. in segregating semi-variable costs
   4. none of these
10. The main difference between marginal costing and absorption costing lies in the treatment of
    1. direct cost
    2. fixed overhead
    3. variable overhead
    4. semi-variable overheads

Answers:

 

1. a	2. b	3. c	4. a	5. c
6. d	7. a	8. c	9. b	10. c

1. Define marginal costing.
2. How will you classify expenses? Give two examples of each.
3. Define the economic concept of marginal cost.
4. How do the accountants view marginal cost.
5. Write down the equation relating to contribution if the
   1. selling price is at profit;
   2. selling price is at cost; and
   3. selling price is at loss.
6. Define absorption costing.
7. What is the main difference between marginal costing and absorption costing?
8. Give the basic marginal (cost) equation.
9. Whether the profit shown by marginal and absorption costing will differ? Give reason for your answer
10. What are direct costs?
11. How will you treat the opening stock and closing stock under marginal-costing and absorption-costing methods?
12. Write down the formula to ascertain the differences between the profits shown by absorption costing and marginal costing?
13. Name the various methods by which you split semi-variable costs into its fixed and variable elements?
14. Write down the straight-line equation that is used to segregate semi-variable costs?
15. What do you mean by differential costing?
16. Distinguish between marginal costing and differential costing.
17. What do you mean by “key factor”?
18. Write a short note on: the least-square method of segregation of fixed and variable costs.
19. Enumerate any two circumstances under which you will permit to fix price which is less than the marginal cost of the product.
20. Name the important decision-making areas where marginal-costing technique is used.
21. What are the ways by which you will improve the profit performance of a business?
22. What are the factors to be considered relating to make or buy decisions?
23. Write the equation to determine the sales volume required at a desired level of profit?
24. What is contribution? How is it related to profit?
25. Explain how you will select a suitable “product mix” by using marginal-costing technique?

1. Define marginal costing. Elucidate its salient features.
2. Explain with suitable examples the accounting treatment of variable costs and fixed costs in marginal costing.
3. Distinguish between marginal costing and absorption costing.
4. “Absorption costing obscures the total amount of fixed costs whereas variable costing highlights it”—Comment.
5. Explain clearly what you understand by segregation of semi-variable costs into fixed and variable elements.
6. Describe briefly the various methods that are in use to segregate semi-variable costs.
   1. “Changes in fixed costs are much more significant to a company than changes in variable cost”—Discuss.
   2. What is meant by period costs and product costs and how are they treated in the conventional method of cost accounting and marginal costing.
7. “The choice between using absorption costing and marginal costing is determined by certain factors”.

   What are they? What are the advantages and disadvantages of using marginal costing?

8. What are the important areas of management decisions opened up by the application of marginal-costing technique? Explain.
9. “One of the main objections to the contribution approach to costing is that it ignores fixed costs”. Discuss and explain the advantages of contribution approach.
10. Explain the circumstances when selling at or below the marginal cost may be justified.
11. Explain how the marginal-costing technique will be applied in the decision-making process of the management with illustrations.
12. 1. Discuss the role of cost in product/sales-mix decisions.
    2. State the relative economics of “make vs. buy” decision in management control.
13. “Marginal costing rewards sales whereas absorption costing rewards production” – Comment.

1. From the following data, prepare statements of cost according to both absorption costing as well as marginal-costing techniques:

 

	Rs.
Sales	6,000
Direct material	2,400
Direct labour	1,600
Factory overheads:
Fixed:	1,200
Variable	400
Administrative overheads:
Fixed:	200
Selling overheads:
Fixed:	400
Variable:	200

[Ans:

1. Under absorption costing technique: Profit: Rs. 3,200
2. Under marginal-costing technique: Profit: Rs. 3,200]

   [Reason for no variation is due to the absence of stock.]

2. From the following data, prepare statements of cost according to both absorption costing as well as marginal-costing methods:

 

Normal volume of production	:	1,950 units/month
Sale price per unit	:	Rs. 8
Variable cost per unit	:	Rs. 4
Fixed cost per unit	:	Rs. 2

Selling and distribution costs have been omitted.

The opening stock: 450 units and the closing stock is 150 units.

 

[Ans:	profit under absorption-costing method: Rs. 3,900
	Profit under marginal-costing method: Rs. 4,500
	Reason for variation is due to opening and closing stock.]

3. X Ltd. commenced production on 1 January 2010. During the first three months ending on 31 March 2010, the company produced 10,000 units, selling 8,000 units out of these at the rate of Rs. 10 per unit. The total costs were as follows:

 

	Rs.
Materials	30,000
Labour	40,000
Variable production overheads:	15,000
Fixed production overheads	10,000
Administration & selling expenses	7,500

Ascertain the profit under absorption costing and marginal-costing systems.

 

[Ans:	Profit under absorption costing: Rs. 10,500
	Profit under marginal costing: Rs. 12,500

4. From the following data, compare contribution, profit and P/V ratio:

 

	Rs.
Selling price per unit	50
Materials per unit	10
Wages per unit	5
Fixed overheads per unit	17.50
Variable overheads per unit	7.50

[Ans: Contribution per unit: Rs. 27.50

             Profit per unit: Rs. 10.00]

5. Comment on the relative profitability of the two products X and Y from the following data:

	Product X Rs.	Product Y Rs.
Materials	20	15
Direct labour	10	20
Fixed overheads	30	15
Variable overheads	20	10
Output per quarter	500 units	400 units

	X	Y
	Rs.	Rs.
[Ans: Contribution/unit	50	55
Profit per unit	20	40
Total profit	10,000	16,000]

6. A company manufactures two products M and N. The following data is taken from the costing records:

	Product M (Per Unit) Rs.	Product N (Per Unit) Rs.
Selling price	100	200
Material (Rs. 10/kg)	20	80
Labour (Rs. 5/hr)	25	50
Variable overhead	15	20

Comment on the profitability of each product when:

1. the raw-material is in short supply
2. the production capacity is limited.

		M	N
		Rs.	Rs.
[Ans:	(a) Contribution per unit	40	50
	(b) Contribution per kg of raw material	20	12.50
	(c) Contribution per hour	8	5

Comment:

1. When raw material is in short supply, the contribution per kg of product M is higher than N.
2. When production capacity is limited, the contribution per hour of product M is higher than N.

Under both the conditions, product M is more profitable]

7. A toy-manufacturing company is at present operating at 80% capacity level, the production being 1,500 units pa. The following relevant figures are obtained from the company’s budgets at different capacity utilization levels:

	Capacity 80%	Utilization Level 100%
Sales	Rs. 2,00,000	Rs. 2,50,000
Variable overheads	20,000	25,000
Semi-variable overhead	10,500	11,100
Fixed overhead	40,000	47,000
Output (in units)	1,500	1,875

The management expects a profit margin of 10%. You are required to compare the differential cost of producing additional 375 units by increasing the capacity utilization level to 100%.

 

[I.C.W.A. (Inter) Modified]

[Ans: Rs. 36,850]

8. The following are the maintenance costs incurred in a machine shop for six months with corresponding machine hours:

Month	Machine Hours	Maintenance Cost Rs.
July	4,000	600
August	4,400	640
September	3,400	540
October	4,800	680
November	3,600	560
December	3,800	580
	24,000	3,600

You are required to segregate the maintenance cost which is semi-variable into fixed and variable elements by using Range method.

[Ans: Fixed cost: Rs. 200; Variable cost: Re 0.10, per machine hour]

9. From the following data, which product would you recommend to be manufactured in a factory, time being the key factor?

	Per Unit of Product A	Per Unit of Product B
Direct material	24	14
Direct labour @ Re 1. per hour)	2	3
Variable overhead @ Rs. 2. per hour	4	6
Selling price	100	110
Standard time to produce	2 hrs	3 hrs

[B.Com – University of Madras]

[Ans: Contribution per hour for Product A is Rs. 35; for Product B is Rs. 29 per hour. Hence Product A is recommended]

10. The following particulars are extracted from the records of a company:

	Product X	Product Y
Sales per unit	Rs. 200	Rs. 240
Consumption of material	2 kgs	3 kgs
Material cost	Rs. 20	Rs. 30
Direct wages cost	Rs. 30	Rs. 20
Direct expenses	Rs. 10	Rs. 12
Machine hours used	3	2
Overhead expenses:
Fixed	Rs. 10	Rs. 20
Variable	Rs. 30	Rs. 40
Direct wage per hour is Rs. 10.

1. Comment on the profitability of each product (both use the same raw material) when
   1. Total sales potential in units is limited.
   2. Total sales potential in value is limited.
   3. Raw material is in short supply.
   4. Production capacity (in terms of machine hours) is the key factor.
2. Assuming raw material is the key factor, availability of which is 20,000 kgs and the maximum sales potential of each product being 7,000 units, find the product mix which will yield the maximum profit.

[Ans:

 

		Product X	Product Y
		(Contribution per unit)
(A)	(i) When sales potential in units is a key factor, profi tability = (Ranking)	Rs. 110	Rs. 138
		(II)	(I)
(ii)	When sales potential in terms of value is a key factor, Profi tability =	Rs. 1.10	1.15
		(II)	(I)
(iii)	When raw material is a key factor, Profi tability =	Rs. 55/kg	Rs. 46/kg
		(I)	(II)
(iv)	When machine hours is a key factor, Profi tability =	Rs. 36.66/hour	Rs. 69/hour
		(II)	(I)

  (B) Product mix               X-7,000 units

          and                         Y-2,000 units

          Total profit:         Rs. 9,36,000]

Make or Buy Decision:

11. You are given the following data relating to bought-out prices and the cost of production of undernoted items. Prepare a suitable statement showing which items should be purchased from outside giving ranks in order of preference for buying, assuming (a) there is no constraint or key factor; (b) machine hours is a key factor; and (c) labour hours is a key factor.

[Ans:

Purchase price of item B is lower than its marginal cost. Hence, irrespective of the situation, it is always profitable to purchase (Buy) that item.]

12. A lathe machine takes 3 hours to machine and complete a component for its product. It has a selling price of Rs. 50 and a variable cost of Rs. 20. Another component needed for the same product can be manufactured in the factory. It is also available from the local market at Rs. 32. The above machine could manufacture the component within 2½ hours and has a marginal cost of Rs. 10. You are required to advise the firm whether the component should be manufactured within the factory or purchased from the market?

[Ans: It is advisable to buy the second component instead of manufacturing it in the factory, because the total cost of a component will be Rs. 35, but it is available in the market at Rs. 32.

Hint: Component cost will be Rs. 25]

13. The cost per unit of the three products X, Y and Z are given as follows:

Production arrangements are such that if one product is given up, the production of others can be raised by 50%. The directors propose that the product Z should be given up because the contribution from the product is the lowest. Present suitable analysis of data indicating whether the proposal should be accepted.

 

[I.C.W.A. – Modified]

[Ans:	Hint: Contribution per unit for Products: X: Rs. 48; Y: Rs. 40; and Z: Rs. 32.
	Incremental contribution: (i) if product X is discontinued (–Rs. 2,52,000); (ii) if Product Y is discontinued (Rs. 1,68,000); and (iii) if Product Z is discontinued (Rs. 84,000).

Comment: It is advisable to discontinue Product X, as it generates lowest incremental contribution, that is, (− Rs. 2,52,000). Reject the proposal to discontinue the Product X.]

14. An engineering company has received a one-off export order for its sole product that would require the use of half of the factory’s total capacity, which is estimated at Rs. 2 lakh units per annum. The condition of that export order is that it has to be accepted in full and acceptance of part quantity is not allowed.

The factory is currently operating at 60% level to meet the demand of its domestic customers. As against the current price of Rs. 12 per unit., the export offer is Rs. 9.40 per unit, which is less than the total cost of current production. The cost break-down is given as follows:

 

		Rs. per unit
	Direct material	5
	Direct labour	2
	Variable expenses	1
	Fixed overhead	2
	Total cost	10

The company has the following options:

1. Accept the export order and cut-back domestic sales as necessary.
2. Remove the capacity constraint by installing necessary balancing equipment and also by working overtime to meet both domestic and export demand. This will increase the fixed overheads by Rs. 15,000 annually and the additional cost for the overtime work will amount to Rs. 40,000 for the year.
3. Appoint a sub-contractor to manufacture the additional requirement and meet the domestic and export requirement in full by supplying raw materials, paying a conversion charge of Rs. 4 per unit and appointing a supervisor at a salary of Rs. 3,000 per month for checking the quality of the product and controlling operations at the manufacturing unit.
4. Refuse the order.

Required:

1. A statement of costs and profits under each of the above four options.
2. Your recommendation, with reasons, as to which of these options the company should decide upon.

[I.C.W.A. – Modified]

[Ans:

Comment: Proposal B is the best choice as it generates a maximum profit of Rs. 3,25,000.

Proposal C may be implemented.

Proposal A is not recommended as it requires expansion programme.]

15. ABC Ltd manufactures and sells sole products for Rs. 50 per unit and has a variable cost per unit of Rs. 20. The accounts of the company for the year 2009 are expected to reveal a profit of Rs. 7,00,000 after charging fixed costs of Rs. 5,00,000.

Market-sensitivity tests suggest the following responses to price charges:

Alternatives	Selling price reduced by	Quantity sold increased by
A	5%	10%
B	7%	20%
C	10%	25%

Evaluate these alternatives and state which alternative, on to be profitability consideration, should be adopted for the forthcoming year, assuming the cost structure to be unchanged from 2009.

[Ans: Total contribution for:

	Alternative	A:	Rs. 12,10,000
	Alternative	B:	Rs. 12,72,000
	Alternative	C:	Rs. 12,50,000
	Alternative (B) should be preferable to others, as the total contribution is higher, i.e., Rs. 12,72,000.]

16. The cost per unit of three products A, B and C are given as follows:

Production arrangements are such that if one product is given up, the production of others can be raised by 50%. The directors propose that product C should be given up because the contribution from the product is the lowest. Present suitable analysis of the data indicating whether the proposal should be accepted.

 

[B.Com (Hons) Modified]

[Ans:	The proposal for the discontinuance of the product C should be accepted.
	Hint: Present profit: Rs. 3,46,000; Total fixed cost: Rs. 1,22,000; and Proposed profit: Rs. 3,88,000.]

17. XYZ Ltd has drawn up the following budget for the year 2009–10:

 

	Rs.
Raw materials	40,000
Labour and other variable costs	12,000
Fixed manufacturing overheads	14,000
Packing & Variable distribution cost	8,000
Fixed overheads including selling	6,000
	80,000
Sales revenue @ 10 per unit	1,00,000
Budgeted profit	20,000

1. The General Manager suggests to reduce the selling price by 5% and expects to achieve an additional volume of 5%. A more-intensive manufacturing programme will involve additional costs of Rs. 5,000 for production planning. It will also be necessary to open an additional sales office at the cost of Rs. 10,000 per annum.
2. The Sales Manager, on the other hand, suggests to increase the selling price by 10% which is estimated to reduce the sales volume by 10%. At the same time, saving in manufacturing overheads and general overheads of Rs. 5,000 and Rs. 10,000, per annum, respectively, is expected on this reduced volume. Which of these two proposals would you accept and why? Show the complete working.

[B.Com (Hons) – Delhi University – Modified]

[Ans: profit as per the proposal of Sales Manager (B) is much higher with 19,500 whereas the proposal of General Manager (A) is lower only. Hence, the proposal of Sales Manager should be accepted.

18. A company has three branches and their summarized accounting particulars for a period are given as follows:

Central Office at (Mumbai) expenses:

Rs. 3,10,000 apportioned to branches on the basis of sales 25% of sales is taken as the Gross profit.

Based on the above information, prepare a comparative profit and loss statement for the different branches. Offer your views on the contemplated closure of the branch which shows a loss assuming that in the event of closure of a branch, the Central Office expenses:

1. ill remain unaffected.
2. Can be reduced by 30%

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

[Ans: Branch profit/loss:

Chennai: Rs. 15,000; Cuttack: – Rs. 2,000;

Jaipur: Rs. 44,000; and Total: Rs. 57,000.]

1. Closure of Cuttack branch will result in a loss of contribution by Rs. 78,000. Central Office expenses being constant, the overall profit will come down by Rs. 78,000.

   Contribution from Chennai and Jaipur: Rs. 2,89,000.

   Less : Central Office expenses: Rs. 3,10,000

   Net profit: Rs. (−21,000)

   Hence, the branch at Cuttack should not be closed down.

    

2. Contribution from other two branches: Rs. 2,89,000.

   Less: 30% Less (Rs. 3,10,000 – 93,000): Rs. 2,17,000

   Net profit Rs. 72,000

   Based on this proposal, the closing down of the branch at Cuttack will increase the profit by Rs. 72,000.]

   (Export order: Accept or Reject)

19. ABC Ltd. has been operating at 70% capacity and the following particulars relate to the present level of activity:

 

Units	3,500
Direct materials	Rs. 10, 500
Direct labour	Rs. 5,250
Variable overhead	200% of direct labour
Fixed overhead	Rs. 14,000
Sales	Rs. 47,250

ABC Ltd received an export order for 1,000 units of its product at Rs. 10 per unit. The export order will entail an extra expenditure in the form of special packing at Re 0.50 per unit. Is the export order worth?

 

[B.Com – University of Madras – Adapted]

[Ans: Yes. The export order is worth trying.]

             (Product Mix)

20. A company produces three products. The cost data are as follows:

Fixed overheads is Rs. 4,00,000 per annum. The budget was prepared at a time when the market was sluggish. The budgeted quantities and selling prices are as follows:

Later, the market improved and the sales quantities could be increased by 20% for Product A and 25% for Products B and C. The sales manager confirmed that the increased quantities could be achieved at the prices originally budgeted. The production manager stated that the output cannot be increased beyond the budgeted level due to limitation of direct labour hours in Department 3.

Required:

1. Prepare a statement of budgeted profitability.
2. Statement of optimal product mix.
3. Calculate the optimal profits.

[Ans:	(1) Rs. 3,99,550.
	(2) A: 11,700 units; B: 9,750 units; and C: 5,292 units
	(3) Optimal profi ts: Rs. 4,06,430.]
	(Profit fluctuation)

21. From the following figures, you are required to prepare cost and profit statements for the months of November and December 2009 under marginal-costing and absorption-costing methods:

 

Normal sales:	50,000 units
Selling price:	Rs. 6.25 each
November 2009:	120% of normal capacity production; Sales 40,000 units
December 2009:	84% of normal capacity production; Sales 60,000 units.
Manufacturing cost:
Direct materials:	Re 1 per unit
Direct labour:	Re 1.50 per unit
Manufacturing overhead:	Rs. 70,000 (of which, Rs. 25,000 are variable)
Selling expenses:
Commission:	Re 0.25 per Unit
Fixed selling expenses:	Rs. 12,500
Administrative expenses:	Rs. 10,000
Research & Development expenses:	Rs. 2,000

[Ans:

1. Net profit under marginal costing:

   November: Rs. 51,500; December: Rs. 1,10,500.

2. Net profit under absorption costing:

   November: Rs. 68,500; December: Rs. 94,300.]

22. A firm is considering two alternative prices for its new product which is expected to be marketed very soon. The sales department wants the price to be Rs. 20 per unit whereas the top management wants that the price be fixed at Rs. 22 per unit. To resolve the issue, data were collected from the Market Research and the Production Department. The data are as follows:

1. Expected sales distribution per annum if the price is Rs. 20 per unit:

   Sales in Units	Probability
   5000	.20
   5500	.50
   6000	.30

2. Expected sales distribution per annum if the price is Rs. 22 per unit:

   Sales in Units	Probability
   4,500	.10
   5,000	.40
   5,500	.50

3. Estimated costs for production up to 6,500 units:

   Variable cost Per unit	Probability
   Rs. 10	.30
   Rs. 11	.70

Fixed costs are likely to be around Rs. 35,000 per annum. Which price the firm should choose? Show your workings nearly.

 

[M.Com., Annamalai University]

[Ans: When the selling price is Rs. 20, the expected value of contribution is Rs. 51,615 and when the selling price is Rs. 22, the expected value of contribution is Rs. 58,760. Hence, the firm should choose Rs. 22 as the selling price per unit.

Hint:

1. Calculate the combined probability for Rs. 20 and then for Rs. 22.
2. Determine the contribution per unit under both Rs. 20 and Rs. 22 level.
3. Based on these, calculate the expected value of contribution.]

23. From the following data, you are required to recommend the most profitable product mix, presuming that the direct labour hours available are only 700:

	Product X	Product Y
Contribution per unit	Rs. 30	Rs. 20
Direct Labour per unit	10 hrs	5 hrs

The maximum production possible for each of the products X and Y is 100 units. Fixed overheads are Rs. 2,000.

 

[Ans:	Product X	– 20 units
	Product Y	– 100 units
	Net profit	– Rs. 600]
	(Sales-Mix)

24. During the year 2000, a manufacturing company has produced and sold three products: P: 10,000 units; Q: 7,000 units; and R: 5,000 units. The following further information is available:

Fixed cost = Rs. 1,75,000 (total).

The list prices of the products are subject to a uniform trade discount of 10%.

Due to shortage of labour, the available working hours for the next year are estimated to be only 90,000 hours. Suggest a suitable sales mix for the next year 2010:

1. When there is enough demand for all the products.
2. When the potential demand is 9,000 units for P, 5,000 units for Q and 6,000 units for R.

[M.com., University of Madras – Modified]

[Ans:

1. Contribution per hour for product P: Rs. 3.20;

   Q: Rs. 3; and R: Rs. 8. Product R’s contribution is the highest of all the three. The order of preference would be:

    

   First:	Product R
   Second:	Product P
   Third:	Product Q

2. Sales mix: Product R demands units:	6,000
   Product P demands units:	9,000
   Product Q demands units:	2,500
   Total units:	17,500.]

25. The Modern Software Company, Bangalore, finds that while it costs Rs. 67.50 each to make a component of Pen-Drive, the same is available in the market at Rs. 57.50 each with the assurance of a continued supply. The break-down of cost is as follows:

Rs / Each
Materials	27.50
Labour	17.50
Other variable costs	5.00
Fixed cost	12.50

1. Should you make or buy?
2. What would be your decision if the supplier offered at Rs. 45.50 each?

[Ans: (a) Make (b) Buy]

26. A company engaged in plantation activities has 200 hectares of virgin land which can be used for growing jointly or individually tea, coffee and cardamom. The yield per hectare of the different types of crops and their selling prices per kg are as follows:

	Yield (kgs)	Selling Price Rs./kg
Tea	2,000	20
Coffee	500	40
Cardamom	100	25

The relevant cost data are given as follows:

1. Variable cost per kg:
   
2. Fixed cost per annum:

   	Rs.
   Cultivation and growing cost	10,00,000
   Administrative cost	2,00,000
   Land revenue	50,000
   Repairs and maintenance	2,50,000
   Other costs	3,00,000
   	18,00,000

The policy of the company is to produce and sell all the three kinds of products and the maximum and minimum area to be cultivated per product is as follows:

	Maximum Area	Minimum Area
	(hectares)	(hectares)
Tea	160	120
Coffee	50	30
Cardamom	30	10

You are required to calculate the priority of production, the most-profitable product mix, and the maximum profit which can be achieved.

 

[C.S. (Inter)]

[Ans: Priority of production:

             1. Coffee

             2. Tea

             3. Cardamom

             Maximum profit that can be achieved:

             Rs. 6,55,000.]