Marginal Costing – CA Inter Cost and Management Accounting Study Material is designed strictly as per the latest syllabus and exam pattern.
Marginal Costing – CA Inter Costing Study Material
Marginal Costing:
It is a costing system where products or services and inventories are valued at variable costs only. It does not consider fixed costs.
- Total Contribution (C) = Sales Revenue (S) – Total Variable Cost (V)
Contribution per unit = Sales price per unit – Variable cost per unit
- Profit = Contribution – Fixed Cost
- Marginal Cost Equation = S – V = C = F ± P
S = Selling price per unit, V = Variable cost per unit, C = Contribution, F = Fixed Cost
Profit Volume (P/V) Ratio: It shows the proportion of sales available to cover fixed costs and profit.
P/V Ratio = \(\frac{\text { Contribution }}{\text { Sales }}\) × 100 OR \(\frac{\text { Change in Contribution or profit }}{\text { Change in Sales }}\) × 100 OR \(\frac{\text { Fixed Cost }}{\text { Breakeven Sales }}\) × 100
Sales = \(\frac{\text { Contribution }}{\text { PV Ratio }}\)
Fixed cost = Break-even sales × P/V Ratio
Break-even point: It is the point where neither profits nor losses have been made.
BEP (in units) = \(\frac{\text { Fixed Cost }}{\text { Contribution per unit }}\)
BEP (in ₹) = \(\frac{\text { Fixed Cost }}{\text { PV Ratio }}\) OR Total Sales – Margin of Safety Sales
Cash Break-even point: When break-even point is calculated only with those fixed costs which arc payable in cash. Depreciation and other- non-cash fixed costs are excluded from fixed costs.
= \(\frac{\text { Cash Fixed Costs }}{\text { Contribution per unit }}\)
Multi-product break even analysis; Break-even point needs adjustm ents when more than one product is manufactured by using a common fixed costs. Composite Contribution is calculated by taking weights for the products. VVdghty = sales:mix quantity or sales mix values,
BEP = \(\frac{\text { Common Fixed Cost }}{\text { Composite Contribution per unit }}\)
Margin of Safety = \(\frac{\text { Profit }}{\text { PV Ratio }}\) or Total sales – Break-even sales
Margin of Safety ratio = \(\) x 100
2. Absorption Costing: A method of costing in which all costs, both variable | and fixed are charged to operations, process or product.
Theory Questions
Question 1.
What are the characteristics of marginal costing? [ICAI Module]
Answer:
- All elements of cost are classified into fixed and variable components. Semi-variable costs are also analyzed into fixed and variable elements.
- The marginal or variable costs are treated as the cost of product.
- The value of finished goods and work-in-progress is also comprised only of marginal costs. Variable selling and distribution are excluded for valuing these inventories. Fixed costs are not considered for valuation of closing stock of finished goods and closing WIP.
- Fixed costs are treated as period costs and are charged to profit and loss account for the period for which they are incurred.
- Prices are determined with reference to marginal costs and contribution margin.
- Profitability of departments and products is determined with reference to their contribution margin.
Question 2.
State the advantages of marginal costing. [CA Inter May 2001, 6 Marks]
Answer:
1. Simplified Pricing Policy: The marginal cost remains constant per unit of output whereas the fixed cost remains constant in total. This help in making firm decisions on pricing policy.
2. Proper recovery of Overheads: Overheads are recovered in costing on the basis of pre-determined rates. If fixed overheads are included on the basis of pre-determined rates, there will be under-recovery or over-recovery of. This creates the problem of treatment of such under or over-recovery of overheads. Marginal costing avoids such under or over-recovery of overheads.
3. Shows Realistic Profit: Under the marginal costing, the stock of finished goods and WIP are carried on marginal cost basis and the fixed expenses are written off to profit and loss account as period cost. This shows the true profit of the period.
4. How much to produce: Marginal costing helps in the preparation of break-even analysis which shows the effect of increasing or decreasing production activity on the profitability of the company.
5. More control over expenditure: Segregation of expenses as fixed and variable helps the management to exercise control over expenditure. The management can compare the actual variable expenses with the budgeted variable expenses and take corrective action through analysis of variances.
6. Helps in Decision Making: Marginal costing helps the management in taking a number of business decisions like make or buy, discontinuance of particular product, replacement of machines, etc.
Question 3.
What are the limitations of marginal costing? [CA Inter May 2019, May 2001, 5 Marks]
Answer:
(i) Difficulty in classifying fixed and variable elements:
It is difficult to classify exactly the expenses into fixed and variable category. Most of the expenses are neither totally variable nor wholly fixed. For example, various amenities provided to workers may have no relation either to volume of production or time factor.
(ii) Dependence on key factors:
Contribution of a product itself is not a guide for optimum profitability unless it is linked with the key factor.
(iii) Scope for Low Profitability:
Sales staff may mistake marginal cost for total cost and sell at a price; which will result in loss or low profits. Hence, sales staff should be cautioned while giving marginal cost.
(iv) Faulty valuation:
Overheads of fixed nature cannot altogether be excluded particularly in large contracts, while valuing the work-in-progress. In order to show the correct position fixed overheads have to be included in work-in-progress.
(v) Unpredictable nature of Cost:
Some of the assumptions regarding the behaviour of various costs are not necessarily true in a realistic situation. For example, the assumption that fixed cost will remain static throughout is not correct. Fixed cost may change from one period to another. Also, the variable costs do not remain constant per unit of output. There may be changes in the prices of raw materials, wage rates etc. after a certain level of output has been reached.
(vi) Marginal costing ignores time factor and investment:
The marginal cost of two jobs may be the same but the time taken for their completion and the cost of machines used may differ. The true cost of a job which takes longer time and uses costlier machine would be higher. This fact is not disclosed by marginal costing.
(vii) Understating of W-I-P:
Under marginal costing stocks and work-in-progress are understated.
Question 4.
Discuss basic assumptions of Cost Volume Profit analysis. [CA Inter May 2012, May 2003, 4 Marks]
Answer:
Assumptions of CVP Analysis:
- Changes in the levels of revenues and costs arise only because of changes in the number of products (or service) units produced and sold.
- Total cost can be separated into two components: Fixed and variable
- Graphically, the behaviour of total revenues and total cost are linear in relation to output level within a relevant range.
- Selling price, variable cost per unit and total fixed costs are known and constant.
- The proportion of different products when multiple products are sold will remain constant as the level of total units sold changes.
- All revenues and costs can be added, sub-traded and compared without taking into account the time value of money.
Question 5.
Explain and illustrate cash break-even chart. [CA Inter May 2008, May 2001, 3 Marks]
Answer:
When break-even point is calculated only with those fixed costs which are payable in cash, such a break-even point is known as cash break-even point. This means that depreciation and other non-cash fixed costs are excluded from the fixed costs in computing cash break-even point. It is computed as under:
Cash BEP (Units) = \(\frac{\text { Cash Fixed Costs }}{\text { Contribution per unit }}\)
Hence for example suppose insurance has been paid on 1st January, 2016 till 31st December, 2020 then this fixed cost will not be considered as a cash fixed cost for the period 1st January, 2018 to 31st December, 2020.
Question 6.
What is Margin of Safety? What does a large Margin of Safety indicates? How can you calculate Margin of Safety? [CA Inter July2021,5Marks]
Answer:
The margin of safety can be defined as the difference between the expected level of sale and the break-even sales. Large margin of safety indicates the high chances of making profits. The Margin of Safety can also be calculated by identifying the difference between the projected sales and break-even sales in units multiplied by sale price per unit.
Margin of Safety (in units) = \(\frac{\text { Profit }}{\text { Contribution per unit }}\)
Margin of Safety (in ₹) = \(\frac{\text { Profit }}{\text { Profit Volume Ratio }}\)
Question 7.
Write short note on Angle of Incidence. [CA Inter May 2012, 2 Marks]
Answer:
Angle of Incidence is formed by the intersection of sales line and total cost line at the break-even point. This angle shows the rate at which profits are being earned once the break-even point has been reached. The wider the angle the greater is the rate of earning profits. A large angle of incidence with a high margin of safety indicates extremely favourable position.
Question 8.
Differentiate between “Marginal and Absorption Costing”. [CA Inter Nov. 2001, Nov. 2020, 5 Marks]
Answer:
Difference between Marginal costing and Absorption costing
| Marginal costing |
Absorption costing |
| (i) Only variable costs are considered for product costing and inventory valuation. |
Both fixed and variable costs are considered for product costing and inventory valuation. |
| (ii) Fixed costs are regarded as period costs. The Profitability of different products is judged by their P/V ratio. |
Fixed costs are charged to the cost of production. Each product bears a reasonable share of fixed cost and thus the profitability of a product is influenced by the apportionment of fixed costs. |
| (iii) Cost data presented highlight the total contribution of each product. |
Cost data are presented in conventional pattern. Net profit of each product is determined after subtracting fixed cost along with their variable costs. |
| (iv) The difference in the magnitude of opening stock and closing stock does not affect the unit cost of production. |
The difference in the magnitude of opening stock and closing stock affects the unit cost of production due to the impact of related fixed cost. |
| (v) In case of marginal costing the cost per unit remains the same, irrespective of the production as it is valued at variable cost. |
In case of absorption costing the cost per unit reduces, as the production increases as it is fixed cost which reduces, whereas, the variable cost remains the same per unit. |
Practical Questions
Question 1.
Product Z has a profit-volume ratio of 28%. Fixed operating costs directly attributable to product Z during the quarter will be ₹ 2,80,000.
Calculate the sales revenue required to achieve a quarterly profit of ₹ 70,000. [CA Inter May 2009, 3 Marks]
Answer:
Computation of sales revenue:
P/V ratio = 28%
Quarterly fixed Cost = ₹ 2,80,000
Desired Profit = ₹ 70,000
Sales revenue required to achieve desired profit
Total contribution = Fixed Cost + Desired Profit
= ₹ 2,80,000 + ₹ 70,000
= ₹ 3,50,000 28%
= ₹ 12,50,000
Total sales revenue = \(\frac{\text { Total contribution }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{₹ 3,50,000}{28 \%}\)
= ₹ 12,50,000
Question 2.
Following information are available for the years 2020 and 2021 of PIX Limited:
| Years |
2020 |
2021 |
| Sales |
₹ 32,00,000 |
₹ 57,00,000 |
| Profit/ (Loss) |
(₹ 3,00,000) |
₹ 7, 00,000 |
Calculate:
(i) P/V ratio
(ii) Total fixed cost
(iii) Sales required to earn a Profit of ₹ 12,00,000 [CA Inter Nov. 2016, May 2010, 5 Marks]
Answer:
(i) P/V Ratio
(ii) Total fixed cost = Total contribution – Profit
= (Sales × P/V ratio) – Profit
= (₹ 57,00,000 × 40%) – ₹ 7,00,000
= ₹ 22,80,000 – ₹ 7,00,000
= ₹ 15,80,000
(iii) Total contribution = \(=\frac{\text { Total contribution }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\)
= ₹ 69,50,000
Question 3.
PQR Ltd. has furnished the following data for the two years:
|
2019-20 |
2020-21 |
| Sales |
₹ |
? |
| Profit/Volume Ratio (P/V ratio) |
50% |
37.5% |
| Margin of Safety sales as a % of total sales |
40% |
21.875% |
There has been substantial savings in the fixed cost in the year 2020-21 due to the restructuring process. The company could maintain its sales quantity level of 2019-20 in 2020-21 by reducing selling price.
You are required to calculate the following:
(i) Sales for 2020-21 in Value,
(ii) Break-even sales for 2020-21 in Value,
(iii) Fixed cost for 2020-21 in Value. [ICAI Module]
Answer:
Total Variable cost in 2019-20 = Sales – P/V Ratio
= ₹ 8,00,000 – 50% = ₹ 4,00,000
In 2020-21, sales quantity has not changed. Thus, variable cost in 2020-21 will remain the same i.e. ₹ 4,00,000.
P/V ratio (2020-21) = 37.50%
Thus, Variable cost ratio = 10096 – 37.596 = 62.5%
(i) Thus, sales in 2020-21 = \(\frac{4,00,000}{62.5 \%}\) = ₹ 6,40,000
In 2020-21, Break-even sales = 100% – 21.875% (Margin of safety) = 78.125%
(ii) Break-even sales in 2020-21:
In 2020-21, Break-even sales = 10096 – 21.87% – 6 (Margin of safety) = 78.125%
= 6,40,000 × 78.1259c = ₹ 5,00,000
(iii) Fixed cost in 2020-21 = B.E. sales × P/V ratio
= ₹ 5,00,000 × 37.5096 = ₹ 1,87,500.
Question 4.
Following information is available for the 1st and 2nd quarter of the year 2020-21 of ABC Ltd:
|
Production (in units) |
Semi-variable cost (₹) |
| Quarter I |
36,000 |
2,80,000 |
| Quarter II |
42,000 |
3,10,000 |
You are required to segregate the semi-variable cost and calculate:
(a) Variable cost per unit;
(b) Total fixed cost. [CA Inter May 2009, 2 Marks]
Answer:
|
Production (in units) |
Semi-variable cost (₹) |
| Quarter I |
36,000 |
2,80,000 |
| Quarter II |
42,000 |
3,10,000 |
Variable Cost per Unit = \(\frac{\text { Change in Semi Variable Cost }}{\text { Change in Production }}\)
= \(\frac{₹ 30,000}{6000 \text { units }}\) = ₹ 5perunit
Total Fixed Cost = Semi Variable Cost – (Production × Variable Cost per Unit)
= ₹ 2,80,000 – (36,000 units × ₹ 5 per unit)
= ₹ 2,80,000 – ₹ 1,80,000
= ₹ 1,00,000
Question 5.
PQ Ltd. reports the following cost structure at two capacity levels;
|
(100% capacity) 2,000 units |
(75% capacity) 1,590 units |
| Production overhead I |
₹ 3 per unit |
₹ 4 per unit |
| Production overhead II |
₹ 2 per unit |
₹ 2 per unit |
If the selling price, reduced by direct material and labour is ₹ 8 per unit, what would be its break-even point? [CA Inter Nov. 2008, 3 Marks]
Answer:
Computation of Break-even point in units:
|
2,000 units |
1,500 units |
Production Overhead I:
Fixed Cost (₹) |
6,000
(2,000 unit × ₹ 3 per unit) |
6,000
(1,500 unit × ₹ 4 per unit) |
| Selling price – Material and labour (₹) (A) |
8 |
8 |
| Production Overhead II (Variable Overhead) (B) |
2 |
2 |
| Contribution per unit (A)-(B) |
6 |
. 6 |
Break-even point = \(\frac{\text { Fixed cost }}{\text { Contribution per unit }}=\frac{6,000}{6}\) = 1,000 units
Question 6.
A Company sells two products, J and K. The sales mix is 4 units of J and 3 units of K. The contribution margins per unit are ₹ 40 for J and ₹ 20 for K. Fixed costs are ₹ 6,16,000 per month. Compute the break-even point. [CA Inter Nov. 2009, 2 Marks]
Answer:
Let 4a = No. of units of J
Then, 3a = No. of units of K
Units Break-even point of Product J = 4 × 2,800 = 11,200 units
Break-even point of Product K = 3 × 2,800 = 8,400 units
Question 7.
PVC Ltd. sold 55,000 units of its product at ₹ 375 per unit. Variable costs are ₹ 175 per unit (manufacturing costs of ₹ 140 and selling cost ₹ 35 per unit). Fixed costs are incurred uniformly throughout the year and amount to ₹ 65,00,000 (including depreciation of ₹ 15,00,000). There is no beginning or ending inventories.
Required:
(i) Compute break even sales level quantity and cash break-even sales level quantity.
(ii) Compute the P/V ratio.
(iii) Compute the number of units that must be sold to earn an income (EBIT) of ₹ 5,00,000.
(iv) Compute the sales level achieve an after-tax income (PAT) of ? 5,00,000, assume 40% corporate tax rate. [CA Inter Nov. 2019, RTPJ
Answer:
Contribution per unit = ₹ 375 – ₹ 175 = ₹ 200
(iii) No. of units that must be sold to earn an Income (EBIT) of ₹ 2,50,000
= \(\frac{\text { Fixed cost }+ \text { Desired EBIT }}{\text { Contribution margin per unit }}\)
= \(\frac{₹ 65,00,000+₹ 5,00,000}{₹ 200}\)
= 35,000 units
(iv) After Tax Income (PAT) = ₹ 5,00,000
Tax rate = 40%
Desired level of Profit before tax = ₹ 5,00,000/60 × 100 = ₹ 8,33,333/-
= \(\frac{₹ 65,00,000+₹ 8,33,333}{53.33 \%}\)
= \(\frac{₹ 65,00,000+₹ 8,33,333}{53.33 \%}\)
= ₹ 1,37,50,859/-
Question 8.
MNP Ltd. sold 2,75,000 units of its product at ₹ 37.50 per unit. Variable costs are ₹ 17.50 per unit (manufacturing costs of ₹ 14 and selling cost ₹ 3.50 per unit). Fixed costs are incurred uniformly throughout the year and amount to ₹ 35,00,000 (including depreciation of ₹ 15,00,000). There is no beginning or ending inventories.
Required:
(i) Estimate break-even sales level quantity and cash break-even sales level quantity.
(it) Estimate the P/V ratio.
(iii) Estimate the number of units that must be sold to earn an income (EBIT) of ₹ 2,50,000.
(iv) Estimate the sales level achieve an after-tax income (PAT) of ₹ 2,50,000, Assume 40% corporate Income Tax rate. [CA Inter Nov. 2010, 8 Marks]
Answer:
Contribution per unit = ₹ 37.50 – ₹ 17.50 = ₹ 20
(i) Break-even Sales Quantity
(iii) No. of units that must be sold to earn an Income (EBIT) of ₹ 2,50,000
= \(\frac{\text { Fixed cost }+ \text { Desired EBIT }}{\text { Contribution margin per unit }}\)
= \(\frac{₹ 35,00,000+₹ 2,50,000}{₹ 20}\)
= 1,87,500 units
(iv) After Tax Income (PAT) = ₹ 2, 50,000
Tax rate = 40%
Desired level of Profit before tax = ₹ 2,50,000/60 × 100 = ₹ 4,1.6,667/-
Estimate Sales Level = \(\frac{\text { Fixed Cost }+ \text { Desired Profit }}{\mathrm{P} / \text { V ratio }}\)
= \(\frac{₹ 35,00,000+₹ 4,16,667}{53.33 \%}\)
= ₹ 73,43,750 /-
Question 9.
The P/V Ratio of Delta Ltd. is 50% and margin of safety is 40%, The company sold 500 units for ₹ 5,00,000. You are required to calculate:
(i) Break-even point, and
(ii) Sales in units to earn a profit of 10% on sales [CA Inter Nov. 2011, 5 Marks]
Answer:
(i) P/V Ratio = 50%
Margin of Safety = 40%
Calculation of Break Even Point (BEP)
Margin of Safety Ratio = \(\frac{(\text { Sales }- \text { BEP }) \times 100}{\text { Sales }}\)
40 = \(\frac{5,00,000-\mathrm{BEP}}{5,00,000}\) × 100
BEP = ₹ 3,00,000
BEP Per Unit = 3,00,000/1000 = 300 Units
(ii) Sales in units to earn a profit of 10 % on sales
Let the sales be x
Profit = 10% of x ie. 0.1x.
Sales = \(\frac{\text { Fixed Cost }+ \text { Desired Profit }}{\text { P/V ratio }}\)
x = \(\frac{1,50,000+0.1 \mathrm{x}}{50 \%}\)
or x = ₹ 3,75,000
Sales (in units) = 3,75,000/1,000
= 375 Units
Working Notes:
1. Selling Price = ₹ 5,00,000/₹ 500
= ₹ 1,000 per unit
2. Variable cost per unit = Selling Price – (Selling Price × P/V Ratio)
= 1,000 – (1,000 × 50%)
= ₹ 500
3. Profit at present level of sales
Margin of Safety = 40% of Total sales
= 40% of ₹ 5,00,000 = ₹ 2,00,000
Profit = Margin of Safety × P/V Ratio
= ₹ 2,00,000 × 50%
= ₹ 1,00,000
4. Fixed Cost = (Sales × P/V Ratio) – Profit
= (5,00,000 × 50%) – 1,00,000
= ₹ 1,50,000
Question 10.
Omega Ltd. manufactures a product, currently utilising 75% capacity with a turnover of ₹ 99,00,000 at ₹ 275 per unit. The cost data is as under:
| Direct Material per unit |
96 |
| Direct wages per unit |
42 |
| Variable overhead per unit |
18 |
| Semi- variable overheads |
7,32,000 |
| P/V ratio |
40% |
Fixed overhead cost is ₹ 28,81,000 upto 80% level of activity, beyond this level an additional ₹ 2,38,500 will be incurred.
Required:
(i) Break even point in units and activity level at Break even point.
(ii) Number of units to be sold to earn profit of ₹ 25 per unit. [Inter CA May 2019. 5 Marks]
Answer:
Contribution per unit = ₹ 275 × 40% = ₹ 110
Total Variable cost per unit = ₹ 275 – ₹ 1 10 = ₹ 165
Semi-variable cost per unit:
= Total variable cost – (Direct Material + Direct wages + Variable Overheads)
= ₹ 165 – (96 + 42 + 18)
= ₹ 9 per unit
Total fixed cost:
= Fixed cost part of semi-variable cost + Fixed overheads
= (Semi variable overheads at 75% level – Variable cost part) + Fixed Over heads
=[₹ 7,32,000 – (₹ 9 × 36,000 units)] + ₹ 28,81,000 – ₹ 4,08,000 + ₹ 28,81,000
= ₹ 32,89,000
(i) Calculation of Break-even point
BEP (in units) = \(\frac{\text { Total fixed cost }}{\text { Contribution per unit }}=\frac{₹ 32,89,000}{₹ 110}\) = 29,900 units
Activity level = \(\frac{29,900}{48,000}\) × 100 = 62.29%
(ii) Number of units to be sold to earn profit of ₹ 25 per unit:
No.of units = \(\frac{\text { Total fixed cost at } 75 \% \text { level }}{\text { Contribution per unit }- \text { Desired profit per unit }}\)
= \(\frac{₹ 32,89,000}{₹ 110-₹ 25}\) = 38,694 units
Activity level = \(\frac{38,694}{48,000}\) × 100 = 80.61%
This is more than 80% capacity level, hence fixed overheads would increase by ₹ 2,38,500 and so the Break-even point.
BEP = \(\frac{\text { Total fixed cost beyond } 80 \% \text { level }}{\text { Contribution per unit }- \text { Desired profit per unit }}\)
= \(\frac{₹ 32,89,000+₹ 2,38,500}{₹ 110-₹ 25}\) = 41,500 units
Question 11.
ABC Limited started its operations in the year 2019 with a total production capacity of 2,00,000 units. The following information, for two years, are made available to you:
|
Year 2019 |
Year 2020 |
| Sales (units) |
80,000 |
1,20,000 |
| Total Cost (₹) |
34,40,000 |
45,60,000 |
There has been no change in the cost structure and selling price and it is anticipated that it will remain unchanged in the year 2021 also.
Selling price is ₹ 40 per unit.
Calculate:
(i) Variable cost per unit.
(ii) Profit Volume Ratio.
(iii) Break-Even Point (in units)
(iv) Profit if the firm operates at 75% of the capacity. [CA Inter May 2015, May 2013, 5 Marks]
Answer:
(iii) Fixed Cost = Total Cost in 2019 – Total Variable Cost in 2019
= ₹ 34,40,000 – (₹ 28 × 80,000 units)
= ₹ 34,40,000 – ₹ 22,40,000
= ₹ 12,00,000
Break Even Point (in units) = \(\frac{\text { Fixed cost }}{\text { Contribution per unit }}\)
= \(\frac{\text { Fixed cost }}{\text { Contribution per unit }}\) = 1,00,000 units
(iv) Profit if the firm operates at 75% of the capacity:
Number of units to be produced and sold = 2,00,000 units × 75%
= 1,50,000 units
Profit = Total contribution – Fixed Cost
= (₹ 12 × 1,50,000 units) – ₹ 12,00,000
= ₹ 18,00,000 – ₹ 12,00,000
= ₹ 6,00,000
Question 12.
A company gives the following information:
| Margin of Safety |
₹ 3,75,000 |
| Total Cost |
₹ 3,87,500 |
| Margin of Safety (Qty.) |
15,000 units |
| Break Even Sales in Units |
5,000 units |
You are required to calculate:
(i) Selling price per unit
(ii) Profit
(iii) Profit/Volume Ratio
(iv) Break-even Sales (in Rupees)
(v) Fixed Cost [CA Inter Nov. 2019. Nov. 2015, 5 Marks]
Answer:
(i) Selling Price per unit = \(\frac{\text { Margin of Safety in Rupee value }}{\text { Margin of Safety in Quantity }}\)
= \(\frac{₹ 3,75,000}{15,000 \text { units }}\) = ₹ 25
(ii) Profit = Sales Value – Total Cost
= [Selling price per unit × (BEP units + MoS units)] – Total Cost
= [₹ 25 × (5,000 + 15,000) units] – ₹ 3,87,500
= ₹ 5,00,000 – ₹ 3,87,500
= ₹ 1,12,500
(iv) Break-even Sales (in ₹)
= BEP units × Selling Price per unit
= 5,000 units × ₹ 25 = ₹ 1,25,000
(v) Fixed Cost = Break-even Sales (in ₹) × P/V Ratio
= ₹ 1,25,000 × 30%
= ₹ 37,500
Question 13.
When volume is 4,000 units; average cost is ₹ 3.75 per unit. When volume is 5,000 units, average cost is ₹ 3.50 per unit. The Break-Even point is 6,000 units.
Calculate:
(i) Variable Cost per unit
(ii) Fixed Cost and
(iii) Profit Volume Ratio. [CA Inter Nov. 2019, 5 Marks]
Answer:
Question 14.
During a particular period ABC Ltd. has furnished the following data: Sales ₹ 10,00,000
Contribution to sales ratio 37% and Margin of safety is 25% of sales.
A decrease in selling price and decrease in the fixed cost could change the “contribution to sales ratio” to 30% and “margin of safety” to 40% of the revised sales. Calculate:
(i) Revised Fixed Cost;
(ii) Revised Sales; and
(iii) New Break-Even Point. [CA Inter Jan. 2021, 5 Marks]
Answer:
Contribution to sales ratio (P/V ratio) = 37%
Variable cost ratio = 100% – 37% = 63%
Variable cost = ₹ 10,00,000 × 63% = ₹ 6,30,000
After decrease in selling price and fixed cost, sales quantity has not changed. Thus, variable cost is ₹ 6,30,000.
Revised Contribution to sales =30%
Thus, Variable cost ratio = 100% – 30% = 70%
Revised, Break-even sales ratio = 100% – 40% (revised Margin of safety) = 60
(i) Revised fixed cost = Revised break even sales × Revised contribution to sales ratio
= (₹ 9,00,000 × 60%) × 30%
= 5,40,000 × 30%
= ₹ 1,62,000
(ii) Revised sales = ₹ 6,30,000/70%
= ₹ 9,00,000
(iii) Revised Break-even point = Revised sales × Revised break-even sales ratio
= ₹ 9,00,000 × 60%
= ₹ 5,40,000
Question 15.
AZ company has prepared its budget for the production of 2,00,000 units. The variable cost per unit is ₹ 16 and fixed cost is ₹ 4 per unit. The company fixes its selling price to fetch a profit of 20% on total cost.
You are required to calculate:
(i) Present break-even sales (in ₹ and in quantity).
(ii) Present profit-volume ratio.
(iii) Revised break-even sales in ₹ and the revised profit-volume ratio, if it reduces its selling price by 10%.
(iv) What would be revised sales in quantity and the amount, if a company desires a profit increase of 20% more than the budgeted profit and selling price is reduced by 10% as above in point (iii). [CA Inter Dec. 2021, 10 Marks]
Answer:
Total Cost = Variable cost + Fixed Cost = ₹ 16 + ₹ 4 = ₹ 20 per unit
Total Fixed Cost = 2,00,000 units × ₹ 4 per unit = ₹ 8,00,000
Profit = 2096 on total cost = ₹ 20 × 20% = ₹ 4 per unit
Selling Price = Total Cost + Profit = ₹ 20 + ₹ 4 = ₹ 24 per unit
Contribution = Selling Price – Variable cost = ₹ 24 – ₹ 16 = ₹ 8 per unit
(i) Present Break-even Sales (Quantity) = \(\frac{\text { Fixed Cost }}{\text { Contribution per unit }}\)
= \(\frac{₹ 8,00,000}{₹ 8}\) = 1,00,000
Present Break-even Sales (₹) = 1,00,000 units × ₹ 24 = ₹ 24,00,000
(ii) Present P/V ratio = \(\frac{\text { Contribution per unit }}{\text { Selling price per unit }}\) × 100
= \(\frac{₹ 8}{₹ 24}\) × 100 = 33.33%
(iii) Revised S.P ₹ 24 – 10% = ₹ 21.60 per unit
Revised Contribution = ₹ 21.60 – ₹ 16 = ₹ 5.60 per unit
Revised P/V Ratio \(\frac{₹ 5.60}{₹ 21.60}\) × 100 = 25.926%
Revised Break-even Sales (₹) = \(\frac{\text { Fixed Cost }}{\text { Revised P/V Ratio }}\)
= \(\frac{₹ 8,00,000}{25.926 \%}\)
= ₹ 30,85,705
(iv) Present Profit = ₹ 4 × 2,00,000 units = ₹ 8,00,000
Desired Profit = ₹ 8,00,000 + 20% = ₹ 9,60,000
Sales Required (units) = \(\frac{\text { Total Fixed Cost }+ \text { Desired Profit }}{\text { Contribution per unit }}\)
= \(\frac{₹ 8,00,000+₹ 9,60,000}{₹ 5.60}\)
= 3,14,286 units
Sales Required (₹) = 3,14,286 units × ₹ 21.60
= ₹ 67,88,578
Question 16.
A company produces single product which sells for ₹ 20 per unit. Variable cost is ₹ 15 per unit and Fixed overhead for the year is ₹ 6,30,000.
Required:
(a) Calculate sales value needed to earn a profit of 10% on sales.
(b) Calculate sales price per unit to bring BEP down to 1,20,000 units
(c) Calculate margin of safety sales if profit is ₹ 60,000. [CA Inter Nov. 2007, 3 Marks]
Answer:
(a) Suppose sales units are x then Sales revenue = 20x
Total contribution = (₹ 20 – ₹ 15) x = 5x
Total profit = (20 × 10%) x = 2x
P/V ratio = \(\frac{\text { Total contribution } \times 100}{\text { Sales revenue }}=\frac{5 x}{20 x}\) × 100 = 25%
Total contribution = Total fixed cost + Total profit
5x = 6,30,000 + 2x
3x = 6,30,000
∴ x = 6,30,000/3 = 2,10,000 units
Sales value = 2,10,000 × 20 = ₹ 42,00,000
(b) Sales price to down BEP = 1,20,000 units
Contribution per unit = \(\frac{\text { Total fixed cost }}{\text { Break Even Point }}\)
= \(\frac{₹ 6,30,000}{1,20,000 \text { units }}\)
= ₹ 5.25
Sales price = Variable cost per unit + Contribution per unit
= ₹ 15 + ₹ 5.25
= ₹ 20.25
(c) Margin of Safety Sales = \(\frac{\text { Profit }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{₹ 60,000}{25 \%}\)
= ₹ 2,40,000
Question 17.
A company has fixed cost of ₹ 90,000, Sales ₹ 3,00,000 and Profit of ₹ 60,000.
Required:
(i) Sales volume it’ in Ihe next period, the company suffered a loss of ₹ 30,000.
(ii) What is the margin of safety for a profit of ₹ 90,000? [CA Inter May 2008, 3 Marks]
Answer:
Total contribution = Total fixed cost + Total profit
= ₹ 90,000 + ₹ 60,000
= ₹ 1,50,000
Question 18.
SHA Limited provides the following trading results:
| Year |
Sale |
Profit |
| 2019-20 |
₹ 25,00,000 |
10% of sale |
| 2020-21 |
₹ 20,00,000 |
8% of sale |
You are required to calculate:
(i) Fixed Cost
(ii) Break Even Point
(iii) Amount of profit, if sale is ₹ 30,00,000
(iv) Sale, when desired profit is ₹ 4,75,000
(v) Margin of Safety at a profit of ₹ 2,70,000 [CA Inter May 2014, 5 Marks]
Answer:
Profit in year 2019-20 = ₹ 25,00,000 × 10% = ₹ 2,50,000
Profit in year 2020-21 = ₹ 20,00,000 × 8% = ₹ 1,60,000
So, P/V Ratio = \(\frac{\text { Change in profit (loss) } \times 100}{\text { Change in sales }}\)
= \(\frac{(₹ 2,50,000-₹ 1,60,000) \times 100}{(₹ 25,00,000-₹ 20,00,000)}\)
= \(\frac{₹ 90,000 \times 100}{₹ 5,00,000}\) = 18%
(i) Fixed Cost = Contribution (in year 2019-20) – Profit (in year 2019-20)
= (Sales × P/V Ratio) – ₹ 2,50,000
= (₹ 25,00,000 × 18%) – ₹ 2,50,000
= ₹ 4,50,000 – ₹ 2,50,000
= ₹ 2,00,000
(ii) Break-even Point (in Sales) = \(\frac{\text { Fixed Cost }}{\text { P V Ratio }}\)
= \(\frac{\text { Fixed Cost }}{\text { P V Ratio }}\) = ₹ 11,11,111 (Approx)
(iii) Calculation of profit, if sale is ₹ 30,00,000
Profit = Contribution – Fixed Cost
= (Sales × P/V Ratio) – Fixed Cost
= (₹ 30,00,000 × 18%) – ₹ 2,00,000
= ₹ 5,40,000 – ₹ 2,00,000 = ₹ 3,40,000
So profit is ₹ 3,40,000, if Sale is ₹ 30,00,000.
(iv) Calculation of Sale, when desired Profit is ₹ 4,75,000
Contribution Required = Desired Profit + Fixed Cost
= ₹ 4,75,000 + ₹ 2,00,000
= ₹ 6,75,000
Sales = \(\frac{\text { Contribution }}{\mathrm{P} / \mathrm{V} \text { Ratio }}\)
= \(\frac{\text { Contribution }}{\mathrm{P} / \mathrm{V} \text { Ratio }}\) = ₹ 37,50,000
Sales is ₹ 37,50,000 when desired profit is ₹ 4,75,000.
(v) Margin of Safety = \(\frac{\text { Profit }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{2,70,000}{18 \%}\) = ₹ 15,00,000
So Margin of Safety is ₹ 15,00,000 at a profit of ₹ 2,70,000
Question 19.
A company has introduced a new product and marketed 20,000 units. Variable cost of the product is ₹ 20 per units and fixed overheads are ₹ 3,20,000.
You are required to:
(i) Calculate selling price per unit to earn a profit of 10% on sales value, – BEP and Margin of Safety?
(if) If the selling price is reduced by the company by 10%, demand is expected to increase by 5,000 units, then what will be its impact on Profit, BEP and Margin of Safety?
(iii) Calculate Margin of Safety if profit is ₹ 64,000 [CA Inter Nov. 2016, 8 Marks]
Answer:
(i) Let ‘X’ be the selling price per unit:
Sales value = Variable Cost + Fixed Cost + Profit
20,000 units × X = (₹ 20 × 20,000 units) + ₹ 3,20,000 + (10% of 20,000 units × X)
Therefore, Selling price per unit = ₹ 40
Contribution per unit = Selling price per unit – variable cost per unit
= ₹ 40 – ₹ 20 = ₹ 20
P/V ratio = \(\frac{\text { Contribution per unit }}{\text { Selling price per unit }}\) × 100 = \(\frac{₹ 20}{₹ 40}\) × 100 = 50%
= (₹ 40 × 20,000 units) – (₹ 20 × 20,000 units) – 3,20,000
Break-even Point (in units) = ₹ 80,000
= \(\frac{\text { Fixed Overheads }}{\text { Contribution per unit }}\)
= \(\frac{₹ 3,20,000}{₹ 20}\)
= 16,000 units
Break – even point (in value) = \(\frac{\text { Fixed Overheads }}{\text { P / V Ratio }}\)
= \(\frac{₹ 3,20,000}{50 \%}\)
= ₹ 6,40,000
Margin of Safety = Total sales value – Break-even sale
= (₹ 40 × 20,000) – ₹ 6,40,000
= ₹ 1,60,000
(ii) Profitability Statement
|
₹ |
| Sales Value (7 36 X 25,000 units) |
9,00,000 |
| Variable Cost (7 20 X 25,000 units) |
(5,00,000) |
| Contribution |
4,00,000 |
| Fixed overheads |
(3,20,000) |
| Profit |
80,000 |
Impact on Profit:
Though there is no impact on the total profit amount but the rate of profit is decreased from 10% to 8.89% (80,000/9,00,000 × 100).
Break-even Point (in units) = \(\frac{\text { Fixed Overheads }}{\text { Contribution per unit }}\)
= \(\frac{₹ 3,20,000}{₹ 36-₹ 20}\)
= 20,000 units
Break-even point (in value) = Selling price per unit × BEP
= ₹ 36 × 20,000 units
= ₹ 7,20,000
Impact on Break-even point (BEP):
The Break-even point is increased by 4,000 units (20,000 units – 16,000 units) or by 7 80,000 (7 7,20,000 – 7 6,40,000).
Impact on Margin of Safety = Total sales value – Break-even sale
= ₹ 9,00,000 – ₹ 7,20,000
= ₹ 1,80,000
Margin of safety is increased by ₹ 20,000 (₹ 1,80,000 – ₹ 160,000) or 1,000 units (5,000 units – 4,000 units)
(iii) Margin of Safety when, profit is ₹ 64,000:
= \(\frac{\text { Profit }}{\mathrm{P} / \mathrm{V} \text { ratio }}=\frac{₹ 64,000}{50 \%} .\) = ₹ 1,28,000
Question 20.
Following figures have been extracted from the books of M/s. RST Private Limited:
| Financial Year’ |
Sales |
Profit/Loss |
| 2019-20 |
4,00,000 |
15,000 (loss) |
| 2020-21 |
5,00,000 |
15,000 (profit) |
You are required to calculate:
(i) Profit Volume Ratio
(ii) Fixed Costs
(iii) Break Even Point
(iv) Sales required to earn a profit of 45,000.
(v) Margin of Safety in Financial Year 2020-21. [CA Inter May 2018, 5 Marks]
Answer:
| Year |
Sales |
Profit/Loss |
| 2019-20 |
₹ 4,00,000 |
₹ (15,ooo) |
| 2020-21 |
₹ 5,00,000 |
₹ 15,000 |
| Difference |
₹ 1,00,000 |
₹ 30,000 |
(i) Profit Volume Ratio:
P/V Ratio = \(\frac{\text { Change in profit }(\text { loss }) \times 100}{\text { Change in sales }}\)
= \(\frac{₹ 30,000 \times 100}{₹ 1,00,000}\)
= 30%
(ii) Fixed Costs:
|
₹ |
| Contribution in 2019-20 (₹ 4,00,000 × 30%) |
1,20,000 |
| Add: Loss in 2019-20 |
15,000 |
| Fixed Cost |
1,35,000 |
(iii) Break Even Point:
Break Even Point = \(\frac{\text { Fixed Cost }}{\mathrm{P} / \mathrm{V} \text { Ratio }}\)
= \(\frac{₹ 1,35,000}{30 \%}\)
= ₹ 4,50,000
(iv) Sales required to earn a profit of ₹ 45,000
Total contribution = Total fixed cost + Total profit
= ₹ 1,35,000 + ₹ 45,000
= ₹ 1,80,000
Sales revenue = \(\frac{\text { Total contribution }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{₹ 1,80,000}{30 \%}\)
= ₹ 6,00,000
(v) Margin of Safety = \(\frac{\text { Profit }}{P / \text { V ratio }}\)
= \(\frac{15,000}{30 \%}\) = ₹ 50,000
So Margin of Safety is ₹ 50,000 at a profit of ₹ 15,000
Question 21.
MFN Limited started its operation in 2019 with the total production capacity of 2,00,000 units. The following data for two years is made available to you:
|
2019 |
2020 |
| Sales units |
80,000 |
1,20,000 |
| Total Cost (₹) |
34,40,000 |
45,60,000 |
There has been no change in the cost structure and selling price and it is expected to continue in 2021 as well. Selling price is ₹ 40 per unit.
You are required to calculate:
(i) Break-Even Point (in units)
(ii) Profit at 75% of the total capacity in 2021 [CA Inter May 2013, 5 Marks]
Answer:
(i) Break-even point:
Variable cost per unit = \(\frac{\text { Change in total cost }}{\text { Change in unts }}\)
= \(\frac{₹ 45,60,000-₹ 34,40,000}{1,20,000-80,000}\)
= ₹ 28 per unit
Total Fixed Cost = ₹ 45,60,000 – (1,20,000 × ₹ 28)
= ₹ 12, 00, 000
Break-even point in units = \(\frac{\text { Fixed cost }}{\text { Contribution per unit }}=\frac{₹ 12,00,000}{₹ 40-₹ 28}\)
= 1,00,000 units
(ii) Profit at 75% of the total capacity:
Capacity at 75% = 2,00,000 units × 75% = 1,50,000 units
Contribution per unit ₹ 12
Contribution (₹) 1,50,000 × ₹ 12 = ₹ 18,00,000
Fixed Cost = ₹ 12,00,000
Profit = Contribution – Fixed Cost = ₹ 18,00,000 – 12,00,000
= ₹ 6,00,000
Question 22.
A manufacturing company is producing a product ‘A’ which is sold in the market at ₹ 45 per unit. The company has the capacity to produce 40,000 units per year. The budget for the year 2020-21 projects a sale of 30,000 units.
The costs of each unit are expected as under:
|
₹ |
| Materials |
12 |
| Wages |
9 |
| Overheads |
6 |
Margin of safety is ₹ 4,12,500.
You are required to:
(i) Calculate fixed cost and break-even point.
(ii) Calculate the volume of sales to earn profit of 20% on sales.
(iii) If management is willing to invest ₹ 10,00.000 with an expected return of 20%, calculate units to be sold to earn this profit.
(iv) Management expects additional sales if the selling price is reduced to ₹ 44. Calculate units to be sold to achieve the same profit as desired in above (iii). [CA Inter Nov 2018, 10 Marks]
Answer:
Contribution per unit = Selling price per unit – Variable cost per unit
= ₹ 45 – (₹ 12 + ₹ 9 + ₹ 6)
= ₹ 18
P/V ratio = \(\frac{\text { Contribution per unit }}{\text { Selling price per unit }}\) × 100
= \(\frac{₹ 18}{₹ 45}\) × 100 = 40%
Margin of Safety = \(\frac{\text { Profit }}{\mathrm{P} / \mathrm{V} \text { Ratio }}\)
4, 12 , 500 = \(\frac{\text { Profit }}{40 \%}\)
Profit = 4,12,500 × 40%
= 1,65,000
(i) Fixed Cost
Profit = Total contribution – Fixed Cost
Profit = (Sales × P/V Ratio) – Fixed Cost
1,65,000 = [(30,000 × 45) × 40%] – Fixed Cost
Fixed Cost = ₹ 5,40,000 – ₹ 1,65,000
= ₹ 3,75,000
Break-even Point = Total Sales – Margin of Safety
= (30,000 × ₹ 45) – ₹ 4,12,500
= ₹ 13,50,000 – ₹ 4,12,500
= ₹ 9,37,500
(ii) Volume of sales to earn profit of 20% on sales:
Let sales volume be ‘S’ units. Therefore, total sales value will be 45S and Contribution will be 18S
Contribution = Fixed Cost + Desired Profit
18S = 3,75,000 + (20% of 45S)
18S = 3,75,000 + 9S = 3,75,000
9S = 3,75,000
So, S = \(\frac{3,75,000}{9}\) = 41666.67 Units
Volume of sales = Contribution per unit × Selling price per unit
= 41666.67 Units × 45
= ₹ 18,75,000
So, ₹ 18,75,000 sales are required to earn profit on 20% of sales
(iii) Calculation of No. of units to be sold to earn 20% return on investment
Contribution = Fixed Cost + Desired Profit
18S = 3,75,000 + Return on Investment
18S = 3,75,000 + 2,00,000 (ie. ₹ 10,00,000 × 20%)
S = \(\frac{5,75,000}{18 \text { Units }}\) = 31,945 Units (approx.)
So, 31,945 Units to be sold to earn a return of ₹ 2,00,000.
(iv) When selling price reduced to ₹ 44 per unit to earn same profits as above
Revised Contribution = Fixed Cost + Desired Profit
(₹ 44 – ₹ 27)S = 3,75,000 + 2, 00,000
17S = 5,75,000
S = \(\frac{5,75,000}{17 \text { Units }}\) = 33,824 units (approx.)
Additional Sales to be sold to achieve the same profit is 33,824 Units.
Question 23.
A company is producing an identical product in two factories. The following are the details in respect of both factories:
|
Factory X |
Factory Y |
| Selling price per unit (₹) |
50 |
50 |
| Variable cost per unit (₹) |
40 |
35 |
| Fixed cost (₹) |
2.00.000 |
3,00,000 |
| Depreciation included in above fixed cost (₹) |
40,000 |
30,000 |
| Sales in units |
30,000 |
20,000 |
| Production capacity (units) |
40,000 |
30,000 |
You are required to determine:
(i) Break Even Point (BEP) each factory individually.
(ii) Cash break even point for each factory individually.
(iii) BEP for company as a whole, assuming the present product mix is in sales ratio,
(iv) Consequence on profit and BEP if product mix is changed to 2:3 and total demand remain same. [CA Inter May 2018, 8 Marks]
Answer:
(iv) New Sales Mix
Factory X = 50,000 × \(\frac{2}{5}\) = 20,000 units
Factory Y = 50,000 × \(\frac{3}{5}\) = 30,000 units
Calculation of Composite contribution = 10 × \(\frac{2}{5}\) + 15 × \(\frac{3}{5}\)
= 4 + 9 = ₹ 13
Consequence on profit
|
Existing Mix |
New Mix |
| Contribution |
6,00,000
(50,000 × 12) |
6,50,000
(50,000 × 13) |
| Less: Fixed Cost |
5,00,000 |
5,00,000 |
| Profit |
1,00,000 |
1,50,000 |
∴ Increase in profit = ₹ 1,50,000 – ₹ 1,00,000
= ₹ 50,000
Consequence on BEP
New BEP as a whole = \(\frac{\text { Complete Fixed Cost }}{\text { Composite Contribution }}\)
= \(\frac{5,00,000}{13}\)
= 38,462 units
So, BEP Reduced by 3,205 units (41,667 – 38,462)
Question 24.
Zed Limited sells its product at ₹ 30 per unit. During the quarter ending, it produced and sold 16,000 units and suffered a loss of ₹ 10 per unit. If the volume of sales is raised to 40,000 units, it can earn a profit of ₹ 8 per unit.
You are required to calculate:
(i) Break Even Point in Rupees.
(ii) Profit if the sale volume is 50,000 units.
(iii) Minimum level of production where the company needs not to close the production if unavoidable fixed cost is ₹ 1,50,000 [CA Inter Nov 2014, 5 Marks]
Answer:
| Units sold |
Sales value (₹) |
Profit/(loss) (₹) |
| 16,000 units |
4,80,000 (₹ 30 × 16,000 units) |
(1,60,000) (₹ 10 × 16,000 units) |
| 40,000 units |
12,00,000 (₹ 30 × 40,000 units) |
3,20,000 (₹ 8 × 40,000 units) |
Total Contribution in case of 40,000 units = Sales Value × P/V Ratio
= ₹ 12,00,000 × 66.67
= ₹ 8,00,000
So, Fixed cost = Contribution – Profit
= ₹ 8,00,000 – ₹ 3,20,000
= ₹ 4,80,000
(i). Break-even Point in Rupees = \(\frac{\text { FIXed cost }}{\text { Contribution per unit }}\)
= \(\frac{4,80,000}{66.67 \%}\)
= ₹ 7,20,000
(ii) If sales volume is 50,000 units, then profit = (Sales Value × P/V Ratio) – Fixed Cost
= (50,000 units × ₹ 30 × 66.67%) – ₹ 4,80,000
= ₹ 5,20,000
(iii) Minimum level of production where the company needs not to close the production, if unavoidable fixed cost is ₹ 1,50,000:
= 16,500 units.
At production level of ≥ 16,500 units, company needs not to close the production.
Question 25.
A company-manufactures radios, which are sold at ₹ 1,600 per unit. The total cost is composed of 30% for direct materials, 40% for direct w ages and 30% and in wage rates by 10% is expected in the forthcoming year, as a result of which the profit at current selling price may decrease by 40% of the present profit per unit. You are required to prepare a statement showing current and future profit at present Selling Price. How much Selling Price should be increased to maintain the present rate of profit? [CA Inter May 2001, 4 Marks]
Answer:
Let X be the cost, Y be the profit and ₹ 1,600 selling price per unit of radio manufactured by a company.
Hence,
X + Y = 1,600 ………….(i)
Statement of present and future cost of a radio
An increase in material price and wage rates resulted into a decrease in current profit by 40 per cent at present selling price; therefore we have:
1.13X + 0.6 Y= 1,600 …………(ii)
On solving (i) and (ii) we get:
X = ₹ 1,207.55
Y = ₹ 392.45
Current profit ₹ 392.45 or 32.5% of cost Future profit ₹ 235.47
Question 26.
M.K. Ltd. manufactures and sells a single product X whose selling price is ₹ 40 per unit and the variable cost is ₹ 16 per unit.
(i) If the Fixed Costs for this year are ₹ 4,80,000 and the annual sales are at 60% margin of safety, calculate the rate of net return on sales, assuming an income tax level of 40%.
(ii) For the next year, it is proposed to add another product line Y whose selling price would be ₹ 50 per unit and the variable cost ₹ 10 per unit. The total fixed costs are estimated at ₹ 6,66,600. The sales mix values of X : Y would be 7 : 3. Determine at what level of sales next year, would M.K. Ltd. break even? Give separately for both X and Y the break-even sales in rupee and quantities. [ICAIModule]
Answer:
(i) Contribution per unit = Selling price – Variable cost
= ₹40 – ₹ 16 = ₹ 24
Break-even Point = \(\frac{₹ 4,80,000}{₹ 24}\) = 20, 000 units
Margin of Safety = 60%
Therefore, break even sales will be 40%.
Total Sales = \(\frac{\text { Break-even Sales }}{40 \%}=\frac{20,000 \text { units }}{40 \%}\) = 50,000 units
|
₹ |
| Sales Value (50,000 units x ? 40) |
20,00,000 |
| Less: Variable Cost (50,000 units x ? 16) |
8,00,000 |
| Contribution |
12,00,000 |
| Less: Fixed Cost |
4,80,000 |
| Profit |
7,20,000 |
| Less: Income Tax @ 40% |
2,88,000 |
|
4,32,000 |
Rate of Net Return on Sales = 21.6%(\(\frac{₹ 4,32,000}{₹ 20,00,000}\) × 100)
(ii) Computation of Break even sales of product X and product Y
|
X(₹) |
Y (₹) |
| Selling Price |
40 |
50 |
| Less: Variable Cost |
16 |
10 |
| Contribution per unit |
24 |
40 |
Weighted Contribution = \(\frac{24 \times 7+40 \times 3}{10}\) = ₹ 28.8 per unit
Total Break-even Point = \(\frac{\text { Total Fixed Cost }}{\text { Weighted Cost }}=\frac{6,66,600}{28.80}\) = 23,145.80 units
Break-even Point
X = \(\frac{7}{10}\) × 23,145.80 = 16,202 units
or 16,202 × ₹ 40 = ₹ 6,48,080
Y = \(\frac{3}{10}\) × 23,145.80 = 6,944 units or 6,944 × 50 = 3,47,200
Question 27.
A company has three factories situated in North, East and South with its Head Office in Mumbai. The Management has received the following summary report on the operations of each factory for a period:
Calculate the following for each factory and for the company as a whole for the period:
(i) Fixed Cost
(ii) Break-even Sales [CA Inter RTP Nov., 2021]
Answer:
Computation of Profit Volume (P/V) Ratio (₹ in ’000)
(i) Computation of Fixed Costs (₹ in ’000)
(ii) Computation of Break-Even Sales
Question 28.
Mega Company has just completed its first year of operations. The unit costs on a normal costing basis are as under:
|
₹ |
| Direct material 4 kg @ ₹ 4 |
16.0 |
| Direct labour 3 hrs @ ₹ 18 |
54.00 |
| Variable overhead 3 hrs @ ₹ 4 |
12.00 |
| Fixed overhead 3 hrs @ ₹ 6 |
18.00 |
| Selling and administrative costs: |
100.00 |
| Variable |
₹ 20 per unit |
| Fixed During the year the company has the following activity: |
₹ 7,60,000 |
| Units produced |
24,000 |
| Units sold |
21,500 |
| Unit selling price |
₹ 168 |
| Direct labour hours worked |
72,000 |
Actual fixed overhead was ₹ 48,000 less than the budgeted fixed overhead. Budgeted variable overhead was ₹ 20,000 less than the actual variable overhead. The company used an expected actual activity level of 72,000 direct labour hours to compute the pre-determine overhead rates.
Required:
(i) Compute the unit cost and total income under:
(a) Absorption costing
(b) Marginal costing
(ii) Under or over absorption of overhead.
(iii) Reconcile the difference between the total income under absorption and marginal costing. [CA Inter .You 2009. 13 Marks]
Answer:
(i) Computation of Unit Cost & Total Income
| Unit Cost |
Absorption Costing (₹) |
Marginal Costing (₹) |
| Direct Material |
16.00 |
16.00 |
| Direct Labour |
54.00 |
54.00 |
| Variable Overhead (₹ 12 + ₹ 20,000/24,000) |
12.83 |
12.83 |
| Fixed Overhead |
18.00 |
– |
| Unit Cost |
100.83 |
82.83 |
Income Statement
(ii) Under or over absorption of overhead:
(iii) Reconciliation of Profit:
Difference in Profit = ₹ 3,02,083 – ₹ 2,57,083
= ₹ 45,000
This is due to Fixed Factory Overhead being included in Closing Stock in Absorption Costing and not in Marginal Costing.
Therefore, Difference in Profit
= Fixed Overhead Rate (Production – Sale) = ₹ 18 (24,000 -21,500)
= ₹ 45,000
Working Note: Calculation of Cost of Goods Sold
Question 29.
A dairy product company manufacturing baby food with a shelf life of one year furnishes the following information:
(i) On 1st January, 2021, the company has an opening stock of 20,000 packets whose variable cost is ₹ 180 per packet.
(ii) In 2020, production was 1,20,000 packets and the expected production in 2021 is 1,50,000 packets. Expected sales for 2021 is 1,60,000 packets.
(iii) In 2020, fixed cost per unit was ₹ 60 and it is expected to increase by 10% in 2021. The variable cost is expected to increase by 25%. Selling price for 2021 has been fixed at ₹ 300 per packet.
You are required to calculate the Break-even volume in units for 2021. [CA Inter May 2016, 5 Marks]
Answer:
Calculation of Break-even Point (in units):
Since, shelf life of the product is one year only, hence, opening stock is to be sold first.
|
₹ |
| Total Contribution required to recover total fixed cost in 2021 and to reach break-even volume. |
79,20,000 |
| Less: Contribution from opening stock (20,000 units × (₹ 300 – ₹ 180)} |
24,00,000 |
| Balance Contribution to be recovered |
55,20,000 |
Units to be produced to get balance contribution
= \(\frac{\text { Balance Contribution to be recovered }}{\text { Contribution per unit }}\)
= \(\frac{₹ 55,20,000}{(₹ 300-₹ 225)}\)
= 73,600 packets.
Break-even volume in units for 2021
|
Packets |
| From 2021 production |
73,600 |
| Add: Opening stock from 2020 |
20,000 |
|
93,600 |
Working Notes:
|
2020 (₹) |
2021 (₹) |
| Fixed Cost |
72,00,000 (₹ 60 × 1,20,000 units) |
79,20,000 (110% of ₹ 72,00,000) |
| Variable Cost |
180 |
225 (125% of ₹ 180) |
Question 30.
A company, with 90% Capacity utilization, is manufacturing a product and makes a sale of ₹ 9,45,000 at ₹ 30 per unit. The cost data is as under:
| Materials |
₹ 9.00 per unit |
| Labour |
₹ 7.00 per unit |
Semi variable cost (including variable cost of ₹ 4.25 per unit) ₹ 2,10,000.
Fixed cost is ₹ 94,500 upto 90% level of output (capacity). Beyond this, an additional amount of ₹ 15,000 will be incurred.
You are required to calculate:
(i) Level of output at break-even point
(ii) Number of units to be sold to earn a net income of 10% of sales
(iii) Level of output needed to earn a profit of ₹ 1,41,375 [CA Inter Nov. 2017, 8 Marks]
Answer:
No. of units at 90% capacity utilization = \(\frac{\text { Sales Value }}{\text { Selling price per unit }}\)
= \(\frac{₹ 9,45,000}{₹ 30}\) = 31,500 units
Calculation of Contribution per unit:
|
₹ |
| Material |
9.00 |
| Labour cost |
7.00 |
| Variable overheads |
4.25 |
| Total Variable Cost |
20.25 |
| Selling price |
30.00 |
| Contribution per unit (Selling price – Variable Cost) |
9.75 |
Calculation of Total Fixed Cost
|
₹ |
| Semi-variable cost |
2,10,000 |
| Less: Variable cost (31,500 units × ₹ 4.25) |
1,33,875 |
| Fixed Cost |
76,125 |
| Add: Fixed cost upto 90% level |
94,500 |
| Total Fixed Cost |
1,70,625 |
(i) Break-even point = \(\frac{\text { Total Fixed Cost }}{\text { Contribution per unit }}\)
= \(\frac{₹ 1,70,625}{₹ 9.75}\)
= 17,500 Units
At 17,500 units, output level is 50% (17,500/31,500 × 90%). This means that at 50% activities level, this company reaches at BEP.
(ii) Number of units to be sold to earn a net income of 10% of sales
10% of sales = 10% of ₹ 30 = ₹ 3 per unit profit.
Let us assume ‘S’ is the No. of units to be sold, hence profit will be 3S
Sales (Units) = \(\frac{\text { Fixed Cost }+ \text { Profit }}{\text { Contribution per unit }}\)
S = \(\frac{₹ 1,70,625+3 S}{₹ 9.75}\)
9.75 S = ₹ 1,70,625 + 3S
S = \(\frac{₹ 1,70,625}{6.75}\) = 25,278 units.
(iii) Level of output needed to earn a profit of ₹ 1,41,375
Sales (units) = \(\frac{₹ 1,70,625+₹ 1,41,375}{₹ 9.75}\) = 32,000 units
32,000 units is beyond 90% activity level. In such case, the fixed cost will be increased by ₹ 15,000 to ₹ 3,27,000.
Then, S = \(\frac{₹ 3,27,000}{₹ 9.75}\) = 33,538 units i.e. 33,538/35,000 × 100 = 95.82% activity level.
Question 31.
J Ltd. manufactures a Product-Y. Analysis of income statement indicated a profit of ₹ 250 lakhs on a sales volume of 5,00,000 units. Fixed costs are ₹ 1,000 lakhs which appears to be high. Existing selling price is ₹ 680 per unit. The company is considering revising the profit target to ₹ 700 lakhs.
You are required to compute:
(i) Break-even point at existing levels in units and in rupees.
(ii) The number of units required to be sold to earn the target profit.
(iii) Profit with 10% increase in selling price and drop in sales volume by 10%.
(iv) Volume to be achieved to earn target profit at the revised selling price as calculated in (ii) above, if a reduction of 10% in the variable costs and ₹ 170 lakhs in the fixed cost is envisaged. [CA Inter Nov. 2020, RTP]
Answer:
Sales Volume 5,00,000 Units
Computation of existing contribution
|
Per unit (₹) |
Total (₹ In lakhs) |
| Sales (A) |
680 |
3,400 |
| Fixed Cost |
200 |
1 ,000 |
| Profit |
50 |
250 |
| Contribution (B) |
250 |
1,250 |
| Variable Cost [(A) – (B)] |
430 |
2,150 |
(i) Break even sales (units) = \(\frac{\text { Cixed Cost }}{\text { Contribution per unit }}\)
= \(\frac{₹ 10,00,00,000}{₹ 250}\)
= 4,00,000 units
Break even sales (₹) = 4,00,000 units × ₹ 680
= ₹ 2,720 lakhs
(ii) Number of units sold to achieve a target profit of ₹ 700 lakhs:
Desired Contribution = Fixed Cost + Target Profit
= ₹ 1,000 lakhs + 700 lakhs
= ₹ 1,700 lakhs
Number of units to be sold = \(=\frac{\text { Desired Contribution }}{\text { Contribution per unit }}=\frac{₹ 17,00,00,000}{₹ 250}\)
= 6,80,000 units
(iii) Profit if selling price is increased by 10% and sales volume drops by 10%:
Existing Selling Price per unit = ₹ 680
= ₹ 680 × 110% – ₹ 748
= 5,00,000 units
= 5,00,000 units – (10% of 5,00,000)
= 4,50,000 units
Statement of Profit at sales volume of 4,50,000 units @ 748 per unit
(iv) Volume to be achieved to earn target profit of ₹ 700 lakhs with revised selling price and reduction of 10% in variable costs and ₹ 170 lakhs in fixed cost:
Revised selling price per unit = ₹ 748
Variable costs per unit existing = ₹ 430
Revised Variable Costs = ₹ 430 – (10% of 430)
= ₹ 430 – ₹ 43
= ₹ 387
Total Fixed Cost (existing) = ₹ 1,000 lakhs
Reduction in fixed cost = ₹ 170 lakhs
Revised fixed cost = ₹ 1,000 lakhs – ₹ 170 lakhs
= ₹ 830 lakhs
Revised Contribution (unit) = ₹ 748 – 1387 = ₹ 361
Desired Contribution = Revised Fixed Cost + Target Profit
= ₹ 830 lakhs + ₹ 700 lakhs
= ₹ 1,530 lakhs
No.of units to be sold = \(\frac{\text { Desired Contribution }}{\text { Contribution per unit }}\)
= \(\frac{₹ 15,30,00,000}{₹ 361}\) = 4,23,823 units
Question 32.
The following information was obtained from the records of a manufacturing unit:
|
₹ |
₹ |
| Sales 80,000 units @ ₹ 25 |
|
20,00,000 |
| Material consumed |
8,00,000 |
|
| Variable Overheads |
2,00,000 |
|
| Labour Charges |
4,00,000 |
|
| Fixed Overheads |
3,60,000 |
17,60,000 |
| Net Profit |
|
2,40,000 |
Calculate:
(i) The number of units by selling which the company will neither lose nor gain anything.
(ii) The sales needed to earn a profit of 20% on sales.
(iii) The extra units which should be sold to obtain the present profit if it is proposed to reduce the selling price by 20% and 25%.
(iv) The selling price to be fixed to bring down its Break-even Point to 10,000 units under present conditions. [CA Inter May 2017, 8 Marks]
Answer:
(i) The number of units to be sold for neither loss nor gain i.e. Break-even units:
= \(\frac{\text { Fixed Overheads }}{\text { Contribution per unit }}=\frac{₹ 3,60,000}{₹ 7.50}\) = 48,000 units
(ii) The sales needed to earn a profit of 20% on sales:
Let desired total sales be X.
Desired Sales = \(\frac{\text { Fixed Cost }+ \text { Desired Profit }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
X = \(\frac{₹ 3,60,000+0.2 \mathrm{X}}{30 \%}\)
or, 0.30X = 3,60,000
or, 0.10X = 3,60,000
or, X = ₹ 36,00,000
No. of units to be sold = \(\frac{36,00,000}{25}\) = 1,44,000 units
(iii) Calculation of extra units to be sold to earn present profit of ₹ 2,40,000 under the following proposed selling price:
(iv) Sales price to bring down BEP to 10,000 units:
B.E.P (Units) = \(\frac{\text { Fixed Cost }}{\text { Contribution per unit }}\)
Or Contribution per unit = \(\frac{₹ 3,60,000}{10,000 \text { units }}\) = ₹ 36
So, Sales Price (per unit) = Variable Cost + Contribution
= ₹ 17.5 + ₹ 36 = ₹ 53.50
Workings:
Variable cost per unit = \(\frac{₹ 8,00,000+₹ 2,00,000+₹ 4,00,000}{80,000 \text { units }}\) = ₹ 17.50
Contribution per unit = ₹ 25 – ₹ 17.50 = ₹ 7.50
P/V Ratio = \(\frac{\text { Contribution per unit }}{\text { Selling price per unit }}\) × 100 = \(\frac{7.50}{25}\) × 100 = 30%
Question 33.
LR Ltd. is considering two alternative methods to manufacture a new product it intends to market. The two methods have a maximum output of 50,000 units each and produce identical items with a selling price of ₹ 25 each. The costs are:
|
Method 1
Semi-Automatic (₹) |
Method 2
Fully-Automatic (₹) |
| Variable cost per unit |
15 |
10 |
| Fixed costs |
1,00,000 |
3,00,000 |
You are required to calculate:
(1) Cost Indifference Point in units. Interpret your results.
(2) The Break-even Point of each method in terms of units.
Answer:
Question 34.
M/s Gaurav Private Limited is manufacturing and selling two products: ‘BLACK’ and ‘WHITE’ at selling price of ₹ 20 and ₹ 30 respectively.
The following sales strategy has been outlined for the financial year 2020-21:
(i) Sales planned for the year will be ₹ 81,00,000 in the case of ‘BLACK’ and ₹ 54,00,000 in the case of ‘WHITE’.
(ii) The selling price of ‘BLACK’ will be reduced by 10% and that of ‘WHITE’ by 20%.
(iii) Break-even is planned at 70% of the total sales of each product.
(iv) Profit for the year to be maintained at ₹ 8,26,200 in the case of ‘BLACK’ and ₹ 7,45,200 in the case of ‘WHITE’. This would be possible by- reducing the present annual fixed cost of ₹ 42,00,000 allocated as ₹ 22,00,000 to ‘BLACK’ and ₹ 20,00,000 to ‘WHITE’.
You are required to calculate:
1. Number of units to be sold of ‘BLACK’ and ‘WHITE’ to Break even
during the financial year 2020-21.
2. Amount of reduction in fixed cost product-wise to achieve desired profit mentioned at (iv) above. [CA Inter May 2019, 3 Marks]
Answer:
(i) Statement showing Break Even Sales
(ii) Statement Showing Fixed Cost Reduction
Question 35.
PH Gems Ltd. is manufacturing ready made suits. It has annual production capacity of 2,000 pieces. The Cost Accountant has presented following information for the year to the management:
|
₹ |
₹ |
| Sales 1,500 pieces @ ₹ 1,800 per piece |
|
27,00,000 |
| Direct Material |
5,94,200 |
|
| Direct Labour |
4,42,600 |
|
| Overheads (40% Fixed) |
11,97,000 |
22,33,800 |
| Net Profit |
|
4,66,300 |
Evaluate following options:
(i) If selling price is increased by ₹ 200, the sales will come down to 60% of the total annual capacity. Should the company increase its selling price?
(ii) The company can earn a profit of 20% on sales if the company provides TIEPIN with ready-made suit. The cost of each TIEPIN is ₹ 18. Calculate the sales to earn a profit of 20% on sales. [CA Inter May 2018, 10 Marks]
Answer:
(i) Evaluation of Option (i)
Selling Price = ₹ 1800 + ₹ 200 = ₹ 2,000
Sales = 2000 × 60° = 1200 Pieces
Yes, the company should increase its selling price. As at sales of 1,500 pieces it can earn profit of ₹ 310.8 per unit and at sales of 1,200 pieces it can earn profit of ₹ 431 per unit.
(ii) Evaluation of Option (ii)
Sales required to earn a profit of 20%
Sales = \(\frac{₹ 4,78,800+0.20 \text { sales }}{34.00 \%}\)
0.34 Sales = ₹ 4,78,000 + 0.20 sales
Sales = ₹ 34,20,000 or 1,900 units (₹ 34,20,000/1800)
To earn profit 20% on sales of readymade suit (along with TIEPIN) company has to sold 1,900 units i.e. 95% of the full capacity. This sales level of 1,900 units is justified only if variable cost is constant. Any upside in variable cost would impact profitability, to achieve the desired profitability. Production has to be increased but the scope is limited to 5% only.
Question 36.
PJ Ltd. manufactures hockey sticks. It sells the products at ₹ 500 each and makes a profit of ₹ 125 on each stick. The Company is producing 5,000 sticks annually by using 50% of its machinery capacity.
The cost of each stick is as under:
| Direct Material |
₹ 150 |
| Direct Wages |
₹ 50 |
| Works Overhead |
₹ 125 (50% fixed) |
| Selling Expenses |
₹ 50 (25% variable) |
The anticipation for the next year is that cost will go up as under:
| Fixed Charges |
10% |
| Direct Wages |
20% |
| Direct Material |
5% |
There will not be any change in selling price.
There is an additional order for 2,000 sticks in the next year.
Calculate the lowest price that can be quoted so that the Company can earn the same profit as it has earned in the current year? [CA Inlet Nor. 2019, 10 Marks]
Answer:
Selling Price = ₹ 500
Profit = ₹ 125
No. of Sticks = 5,000
Let lowest price quoted be K
Now, Sales = Target Profit + Variable Cost + Fixed Cost
(5,000 × 500) + (2,000 × K) = (5,000 units × ₹ 125) + (7,000 units × ₹ 292.50)
25,00,000 + 2,000K = 6,25,000 + 20,47,500 + 5,50,000
= ₹ 361.25
So, Lowest Price that can be quoted to earn the profit of ₹ 6,25,000 (same as current year) is ₹ 361.25.
Question 37.
A Ltd. manufacture and sales Its. product R-9. .The following figures have been collected from cost records of last year for the product R-9:
| Elements of Cost |
Variable Cost portion |
Fixed Cost |
| Direct Material |
30% of Cost of Goods Sold |
– |
| Direct Labour |
15% of Cost of Goods Sold |
– |
| Factory Overhead |
10% of Cos? of Goods Sold |
₹ 2,30,000 |
| Administration Overhead |
2% of Cost of Goods Sold |
₹ 71,000 |
| Selling & Distribution Overhead |
4% of Cost of Sales |
₹ 68,000 |
Last Year 5,000 units were sold at ₹ 185 per unit. From the given, determine the followings:
(i) Break-even Sales (in ₹)
(ii) Profit earned during last year
(iii) Margin of safety (in %)
(iv) Profit if the sales were 10% less than the actual sales (Assume that Administration Overhead is related with production activity) [CA Inter RTF May 203,0]
Answer:
(i) Break-Even Sales
= \(\frac{\text { Fixed cost }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{₹ 3,69,000}{53.41 \%}\)
= ₹ 6,90,882
(ii) Profit earned during the last year
= (Sales – Total Variable Costs) – Total Fixed Costs
= (₹ 9,25,000 – ₹ 4,31,000) – ₹ 3,69,000
= ₹ 1,25,000
(iii) Margin of Safety (%)
= \(\frac{\text { Sales }- \text { Break-even sales }}{\text { Sales }}\) × 100
= \(\frac{₹ 9,25,000-₹ 6,90,882}{₹ 9,25,000}\) × 100
= 25.3196
(iv) Profit if the sales were 10% less than the actual sales:
Profit = 90% of (₹ 9,25,000 – ₹ 4,31,000) – ₹ 3,69,000
= ₹ 4,44,600 – ₹ 3,69,000
= ₹ 75,600
Working Notes:
1. Calculation of Cost of Goods Sold (COGS):
COGS = Direct Material + Direct Labour + Factory Overhead + Administration Overhead
COGS = [0.3 COGS + 0.15 COGS + (0.10 COGS + ₹ 2,30,000) + (0.02 COGS + ₹ 71,000)]
COGS = 0.57 COGS + ₹ 3,01,000
COGS = \(\frac{₹ 3,01,000}{0.43}\) = ₹ 7,00,000
2. Calculation of Cost of Sales (COS):
COS = COGS + Selling & Distribution Overhead
COS = COGS + (0.04 COS + ₹ 68,000)
COS = ₹ 7,00,000 + (0.04 COS + ₹ 68,000)
COS = \(\frac{₹ 7,68,000}{0.96}\) = ₹ 8,00,000
Calculation of Variable Costs:
| Direct Material |
(0.30 × ₹ 7,00,000) |
₹ 2,10,000 |
| Direct Labour |
(0.15 × ₹ 7,00,000) |
₹ 1,05,000 |
| Factory Overhead |
(0.10 × ₹ 7,00,000) |
₹ 70,000 |
| Administration OH |
(0.02 × ₹ 7,00,000) |
₹ 14,000 |
| Selling & Distribution OH |
(0.04 × ₹ 8,00,000) |
₹ 32,000 |
|
|
₹ 4,31,000 |
4. Calculation of total Fixed Costs:
| Factory Overhead |
₹ 2,30,000 |
| Administration OH |
₹ 71,000 |
| Selling & Distribution OH |
₹ 68,000 |
|
₹ 3,69,000 |
5. Calculation of P/V Ratio:
P/V Ratio = \(\frac{\text { Contribution }}{\text { Sales }}\) × 100
= \(\frac{\text { Sales Variable Costs }}{\text { Sales }}\) × 100
= \(\frac{(₹ 185 \times 5,000 \text { units })-4,31,000}{₹ 185 \times 5,000 \text { units }}\) × 100
= 53.41%
Question 38.
The following figures are related to LM Limited for the year ending 31st March, 2021:
Sales – 24,000 units @ ₹ 200 per unit;
P/V Ratio 25% and Break-even Point 50% of sales.
You are required to calculate:
(i) Fixed cost for the year
(ii) Profit earned for the year
(iii) Units to be sold to earn a target net profit of ₹ 11,00,000 for a year.
(iv) Number of units to be sold to earn a net income of 25% on cost.
(v) Selling price per unit if Break-even Point is to be brought down by 4,000 units. [CA Inter Nov. 2012, 8 Marks]
Answer:
Break even point (in units) = 50% of sales = 12,000 units
Break even point (in sales value) = 12,000 units × ₹ 200 = ₹ 24,00,000
(i) Break even sales = \(\frac{\text { Fixed Cost }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
or 24,00,000 = \(\frac{\text { Fixed cost }}{25 \%}\)
or Fixed Cost = ₹ 24,00,000 × 2596 = ₹ 6,00,000
So Fixed Cost for the year is ₹ 6,00,000
(ii) Contribution for the year = Total Sales × P/V Ratio
= (24,000 units × ₹ 200) × 2596 = ₹ 12,00,000
Profit for the year = Contribution – Fixed Cost
= ₹ 12,00,000 – ₹ 6,00,000
= ₹ 6,00,000
(iii) Target net profit is ₹ 11,00,000
Contribution per unit = 25% of ₹ 200 = ₹ 50 per unit
No.of units to be sold = \(\frac{\text { Fixed Cost }+ \text { Desired Profit }}{\text { Contribution per unit }}\)
= \(\frac{₹ 6,00,000+₹ 11,00,000}{₹ 50}\) = 34,000 units
(iv) Let desired total sales be X, then desired profit is 25% on Cost or 20% on Sales i.e. 0.2X
Fixed Cost + Desired Profit
Desired Sales = \(\frac{\text { Fixed Cost }+ \text { Desired Profit }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
X = \(\frac{₹ 6,00,000+0.2 \mathrm{X}}{25 \%}\)
or, 0.25 X = 6,00,000 + 0.2X
or, 0.05 X = 6,00,000
or, X = ₹ 1,20,00,000
No. of units to be sold – \(\frac{1,20,00,000}{200}\) = 60,000 units
(v) If Break even point is to be brought down by 4,000 units, then Breakeven point will be 12,000 units – 4000 units = 8000 units .
B.E.P (Units) = \(\frac{\text { Fixed Cost }}{\text { Contribution per unit }}\)
Or, Contribution per unit = \(\frac{6,00,000}{8,000 \text { unit }}\) = ₹ 75
So, Sales Price (per unit) = Variable Cost + Contribution
= ₹ 150 + ₹ 75 = ₹ 225
Question 39.
Two manufacturing companies A and B are planning to merge. The details are as follows:
|
A |
B |
| Capacity utilisation (%) |
90 |
60 |
| Sales (₹) |
63,00,000 |
48,00,000 |
| Variable Cost (₹) |
39,60,000 |
22,50,000 |
| Fixed Cost (₹) |
13,00,000 |
15,00,000 |
Assuming that the proposal is implemented, calculate:
(i) Break-Even sales of the merged plant and the capacity utilization at that stage,
(ii) Profitability of the merged plant at 80% capacity utilization
(iii) Sales Turnover of the merged plant to earn a profit of ₹ 60,00,000.
(iv) When the merged plant is working at a capacity to earn a profit of ₹ 60,00,000, what percentage of increase in selling price is required to sustain an increase of 5% in fixed overheads. [CA Inter January 2021, 10 Marks]
Answer:
P/V ratio of merged plant = \(\frac{\text { Contribution }}{\text { sales }}\) × 100
= \(\frac{₹ 68,50,000}{1,50,00,000}\) × 100
= 45.67%
(i) Break-even sales of merged plant = \(\frac{\text { Fixed cost }}{\mathrm{P} / \mathrm{V} \text { ratio }}\)
= \(\frac{28,00,000}{45.67 \%}\)
= ₹ 61,30,939.34 (approx.)
(ii) Profitability of the merged plant at 80% capacity utilisation
= (₹ 1,50,00,000 × 80%) × P/V ratio – fixed cost
= ₹ 1,20,00,000 × 45.67% – ₹ 28,00,000
= ₹ 26,80,400
(iii) Sales to earn a profit of ₹ 60,00,000
Desired sales = \(\frac{\text { Fixed Cost }+ \text { desired profit }}{\text { P / V Ratio }}\)
= \(\frac{₹ 28,00,000+₹ 60,00,000}{45.67 \%}\)
= ₹ 1,92,68,666 (approx.)
(iv) Increase in fixed cost = ₹ 28,00,000 × 5% = ₹ 1,40,000
Therefore, percentage increase in sales price
= \(\frac{₹ 1,40,000}{₹ 1,92,68,666}\) × 100 = 0.726% (approx)
Question 40.
XYZ Ltd. is engaged in the manufacturing of toys. It can produce 4,20,000 toys at its 70% capacity on per annum basis. Company is in the process of determining sales price for the financial year 2020-21. It has provided the following information:
| Direct Material |
₹ 60 per unit |
| Direct Labour |
₹ 30 per unit |
| Indirect Overheads |
|
| Fixed |
₹ 65,50,000 per annum |
| Variable |
₹ 15 per unit |
| Semi-variable |
₹ 5,00,000 per annum up to 60% capacity and ₹ 50,000 for every 5% increase in capacity or part thereof up to 80% capacity and thereafter ₹ 75,000 for every 10% increase in capacity or part thereof |
Company desires to earn a profit of ₹ 25,00,000 for the year. Company has planned that the factory will operate at 50% of capacity for first six months of the year and at 75% of capacity for further three months and for the balance three months, factory will operate at full capacity.
You are required to:
(1) Determine the average selling price at which each of the toys should be sold to earn the desired profit.
(2) Given the above scenario, advise whether company should accept an offer to sell each Toy at:
(a) 1130 per Toy
(b) ₹ 129 per Toy (CA Inter January 2021, 10 MarksJ
Answer:
(1) Statement of Cost
* ₹ 5,00,000 + [3 times (from 60% to 75%) × 50,000] = ₹ 6,50,000
** ₹ 6,50,000 + [1 time (from 75% to 80%) × 50,000] + [2 times (from 80% to 100%) × 75,000] = ₹ 8,50,000
(2) Company Should accept the offer as it is above its targeted sales price of ₹ 128.45 per toy.
Question 41.
PQR Ltd. manufactures medals for winners of athletic events and other contests. Its manufacturing plant has the capacity to produce 10,000 medals each month. The company has current production and sales level of 7,500 medals per month. The current domestic market price of the medal is ₹ 150,
The cost data for the month of August 2021 is as under:
|
₹ |
| Variable costs: |
|
| Direct materials |
2,62,500 |
| Direct labour cost |
3,00,000 |
| Overhead |
75,000 |
| Fixed manufacturing costs |
2,75,000 |
| Fixed marketing costs |
1,75,000 |
|
10,87,500 |
PQR Ltd, has received a special one-time only order for 2,500 medals at ₹ 120 per medal.
Required:
(i) Should PQR Ltd, accept the special order? Why? Explain briefly.
(ii) Suppose the plant capacity was 9,000 medals instead of 10,000 medals each month. The special order must be taken either in full or rejected totally. Analyse whether PQR Ltd. should accept the special order or not. [ICAI Module]
Answer:
(z) Since, the offered price (₹ 120) for the additional demand of 2,500 medals is more than the variable cost per unit (₹ 85), the order will be accepted.
Increase in profit by accepting order = (₹ 120 – ₹ 85) × 2,500 medals
= ₹ 87,500
(ii) If the plant capacity is 9,000 medals, then by accepting special order of 2,500 medals, the company has to lose contribution on 1,000 medals from existing customers.
By accepting the special order at ₹ 120 per unit, the total profit of the company is increased by ₹ 22,500 (₹ 60,000 – ₹ 37,500) hence the order may be accepted, however, other qualitative factors may also be taken care-off.
Question 42.
A company using a continuous manufacturing operation achieves an output of 3 kg per hour. The selling price is ₹ 450 per kg. The raw material cost ₹ 3 25 per kg. of output and the direct labour and variable overheads amount to ₹ 316 per kg. of output. The company has provided an expenditure of ₹ 640 on maintenance and ₹ 6,400 on breakdown repairs per month in its budget. Breakdowns averaging 300 hours per month occur due to mechanical faults. These could be reduced or eliminated, if additional maintenance on the following scale were undertaken:
| Breakdown Hours |
Maintenance Costs (₹) |
Repair Costs (₹) |
| 0 |
20,480 |
0 |
| 60 |
10,240 |
1,920 |
| 120 |
5,120 |
2,560 |
| 180 |
2,560 |
3.840 |
| 240 |
1,280 |
5,120 |
| 300 |
640 |
6,400 |
Using the incremental cost and incremental revenue concept, you are required to:
(i) Determine the optimum level upto which breakdown can be reduced to increase production.
(ii) Calculate the additional profits obtainable at that level as compared to the present situation. [CA Inter May 2003, 7 Marks]
Answer:
Contribution per hour :
Contribution per kg = Selling price per kg – Variable cost per kg
= ₹ 450 – (₹ 125 material cost + ₹ 316 direct labour and overheads)
= ₹ 450 – ₹ 441
= ₹ 9
Contribution per hour = 3 kg. × Contribution per kg.
= 3 kg. × ₹ 9
= ₹ 27
(i) Optimum level upto which breakdown can be reduced to increase production
Optimal level upto which breakdown can be reduced to increase production:
Saving of 180 hours and breakdown of 120.
(ii) Additional profit at optimum level as compared to present position:
₹ 340 + ₹ 1,620 + ₹ 2,260 = ₹ 4,220
Question 43.
OPR Ltd. purchases crude vegetable oil. It does refining of the same. The refining process results in four products at the split-off point – S, P, N and A. Product ‘A’ is fully processed at the split-off point. Product S, P and N can be individually further refined into SK, PM and NL respectively. The join cost of purchasing the crude vegetable oil and processing it were ₹ 40,000 other details are as follows:
| Product |
Further processing cost (₹) |
Sales at split-off point (₹) |
Sales after further processing (₹) |
| S |
80,000 |
20,000 |
1,20.000 |
| P |
32,000 |
12,000 |
40,000 |
| N |
36,000 |
28,000 |
48.000 |
| A |
– |
20,000 |
– |
You are required to identify the products which can be further processed for maximizing profits and make suitable suggestions. a [CA Inter July 2021, 5 Marks]
Answer:
Statement showing further processing decisions
Since the Incremental Revenue from Product S exceeds the Incremental Cost of further processing, Product S should be processed further and Products P and N should be sold at split off point.
Question 44.
The profit for the year of R.J. Ltd. works out to 12.5% of the capital employed and the relevant figures are as under:
| Sales |
₹ 5,00,000 |
| Direct Materials |
₹ 2,50,000 |
| Direct Labour |
₹ 1,00,000 |
| Variable Overheads |
₹40,000 |
| Capital Employed |
₹ 4,00,000 |
The new Sales Manager who has joined the company recently estimates for next year a profit of about 23% on capital employed, provided the volume of sales is increased by 10% and simultaneously there is an increase in Selling Price of 4% and an overall cost reduction in all the elements of cost by 2%.
Required:
Find out by computing in detail the cost and profit for next year, whether the proposal of Sales Manager can be adopted. [ICAIModule]
Answer:
Present profit = Capital employed ₹ 12.5% = ₹ 4,00,000 × 12.5% = ₹ 50,000
Variable Costs = Direct Materials + Direct Labour + Variable o/h
= ₹ 2,50,000 + ₹ 1,00,000 + ₹ 40,000 = ₹ 3,90,000
Sales = Variable Costs + Fixed Cost + Profit
₹ 5,00,000 = ₹ 3,90,000 + Fixed Cost + ₹ 50,000
Fixed Cost = ₹ 60,000
Statement Showing “Cost and Profit for the Next Year”
Profit on Capital Employed = (\(\frac{₹ 92,780}{₹ 4,00,000}\) × 100) = 23.19%
Since the Profit of ₹ 92,780 is more than 23% of capital employed, the proposal of the Sales Manager can be adopted.
Question 45.
Moon Ltd. produces products ‘X’, ‘Y’ and ‘27 and has decided to analyse its production mix in respect of these three products – ‘X’, ‘Y’ and ‘Z’
You have the following information:
|
X |
Y |
Z |
| Direct Materials ₹ (per unit) |
160 |
120 |
80 |
| Variable Overheads ₹ (per unit) |
8 |
20 |
129 |
Direct labour:
From the current budget, further details are as below :
There is a constraint on supply of labour in Department-A and its manpower cannot be increased beyond its present level.
Required:
(i) Identify the best possible product mix of Moon Ltd.
(ii) Calculate the total contribution from the best possible product mix. [CA Inter Nov 2020, 5 Marks]
Answer:
(i) Statement Showing “Calculation of Contribution/ unit”
(ii) Statement Showing Total Contribution from best mix
Existing Hours = 10,000 × 6 hrs. + 12,000 × 10 hrs. + 20,000 × 5 hrs.
= 2,80,000 hrs.
Allocation of Hours on the basis of ranking:
Question 46.
Mohit Limited manufactures three different products and the following information has been collected from the books of account:
The company has currently under discussion, a proposal to discontinue the manufacture of Product U and replace it with Product M, when the following results are anticipated:
Required:
(i) Compute the PV ratio, total contribution, profit and Break-even sales for the existing product mix.
(ii) Compute the PV ratio, total contribution, profit and Break even sales for the proposed product mix. [CA Inter RTP, May 2021]
Answer:
(i) Computation of PV ratio, contribution and break-even sales for existing product mix
(ii) Computation of PV ratio, contribution and break-even sale for proposed product mix
Question 47.
X Ltd. supplies spare parts to an air craft company Y Ltd. The production capacity of X Ltd. facilitates production of any one spare part for a particular period of time. The following are the cost and other information for the production of the two different spare parts A and B:
|
Part A |
Part B |
| Per unit Alloy usage |
1.6 kgs. |
1.6 kgs. |
| Machine Time: Machine P |
0.6 hrs |
0.25 hrs. |
| Machine Time: Machine Q |
0.5 hrs. |
0.55 hrs. |
| Target Price (₹) |
145 |
115 |
Total hours available Machine P 4,000 hours
Machine Q 4,500 hours
Alloy available is 13,000 kgs. @ ₹ 12.50 per kg.
Variable overheads per machine hours
Machine P: ₹ 80
Machine Q: ₹ 100
Required:
(i) Identify the spare part which will optimize contribution at the offered price.
(ii) If Y Ltd. reduces target price by 10% and offers ₹ 60 per hour of unutilized machine hour, calculate the total contribution from the spare part identified above? [ICAI Module]
Answer:
(i) Computation of maximum number of parts that can be manufactured
Computation of Total Contribution at maximum number of parts
(ii) Total Contribution from Spare part A when target price reduced by 10% and unutilised machine hour can be utilised (5 ₹ 60 per hour)
|
Part A |
| Parts to be manufactured numbers |
6,666 |
| Machine P hours used |
4,000 |
| Machine Q hours used |
3,333 |
| Underutilized Machine Hours (4,500 hrs. – 3,333 hrs.) |
1,167 |
| Compensation for unutilized machine hours (1,167 hrs. × ₹ 60) |
70,020 |
