📝 Marginal Costing

 📝 Marginal Costing

🧐 Marginal Costing Theoretical Questions and Answers

1. Question: Define Marginal Cost.

Answer:

 Marginal cost is the additional cost incurred by producing one more unit of a product. It typically includes Variable Costs only.

2. Question: What is the fundamental formula for calculating the Contribution?

Answer:

Contribution = Sales Revenue - Variable Cost.

3. Question: State the formula for the Profit/Volume Ratio (P/V Ratio).

Answer:    P/V Ratio = {Contribution} / {Sales})  *100

 {Change in Profit} / (Change in Sales} *100

4. Question: Define the Break-Even Point (BEP) in units.

Answer:

The Break-Even Point in units is the level of output where Total Revenue equals Total Cost, resulting in zero profit or loss.

5. Question: State the formula for calculating the Break-Even Point (BEP) in value (sales).

Answer: BEP (Value) = Fixed Cost / P/V Ratio.

6. Question: What is Contribution Margin?

Answer:

Contribution margin is the excess of sales revenue over variable cost. It is the amount available to first recover Fixed Costs and then earn Profit.

7. Question: How is Marginal Costing different from Absorption Costing regarding inventory valuation?

Answer:

 In Marginal Costing, inventory is valued only at Variable Manufacturing Cost, whereas in Absorption Costing, it is valued at Total Manufacturing Cost (Variable + Fixed).

8. Question: What is a Variable Cost? Give one example.

Answer:

A Variable Cost is a cost that changes in total directly and proportionally with the change in the level of activity or volume of output. Example: Direct Material Cost.

9. Question: What is a Fixed Cost? Give one example.

Answer:

A Fixed Cost is a cost that remains constant in total, irrespective of the changes in the volume of output, within the relevant range and time period. Example: Factory Rent.

10. Question: Define Margin of Safety (MOS).

Answer:

 Margin of Safety is the difference between the Actual Sales or Budgeted Sales and the Break-Even Sales.

11. Question: State the formula for calculating Margin of Safety in value.

Answer:

MOS (Value) = Profit / P/V Ratio.

12. Question: What is a Key Factor or Limiting Factor?

Answer:

 A Key Factor is a factor that restricts or limits the level of activity, such as sales demand, raw material availability, or machine hours.

13. Question: State the basic Marginal Cost Equation.

Answer:

 Sales - Variable Cost = Fixed Cost + Profit

{ OR } S - V = F + P

14. Question: What does a high P/V Ratio indicate?

Answer:

 A high P/V Ratio indicates a higher rate of contribution from sales, which usually means the product is more profitable and the BEP is lower.

15. Question: How do you calculate the sales volume required to earn a Target Profit?

Answer:

 Required Sales (Value) = (Fixed Cost + Target Profit) / P/V Ratio.

16. Question: What is the primary purpose of Marginal Costing in decision-making?

Answer:

 The primary purpose is to help management in short-term decision-making, such as fixing selling prices, deciding on product mix, and accepting or rejecting special orders.

17. Question: Is Semi-Variable Cost included in Marginal Cost? If so, how?

Answer:

 Yes. A semi-variable cost is bifurcated into its Fixed and Variable components. Only the Variable Component is included in Marginal Cost.

18. Question: Define the term Differential Cost.

Answer:

Differential Cost is the difference in total cost (or revenue) between two alternative courses of action.

19. Question: What is the concept of Cost-Volume-Profit (CVP) Analysis?

Answer:

CVP Analysis is the study of the inter-relationships between Cost, Volume, and Profit at various levels of activity.

20. Question: What is the main assumption of Marginal Costing regarding Variable Cost per unit?

Answer:

It is assumed that the Variable Cost per unit remains constant at all levels of activity within the relevant range.

21. Question: Under Marginal Costing, when will closing stock profit be higher than in Absorption Costing?

Answer:

 This will never happen. If closing stock is present, the profit under Marginal Costing will be lower than or equal to (if production = sales) Absorption Costing.

22. Question: How is Fixed Cost treated in a Marginal Costing Profit Statement?

Answer:

Fixed Costs are treated as Period Costs and are charged off completely against the contribution of the period in which they are incurred.

23. Question: What is meant by Cost Indifference Point?

Answer:

 The Cost Indifference Point is the level of activity (units) at which the total cost is the same for two or more alternative options.

24. Question: What is the disadvantage of using only Marginal Cost as the basis for long-term pricing decisions?

Answer:

 In the long run, setting the price based only on Marginal Cost may lead to a loss, as it does not recover the Fixed Costs.

25. Question: How does the P/V Ratio behave when the selling price per unit increases (Variable Cost constant)?

Answer:

 When the selling price per unit increases, the P/V Ratio will increase.

26. Question: If the Margin of Safety is 0, what is the profit?

Answer:

 If the Margin of Safety is 0, it means Actual Sales = BEP Sales, and the Profit is zero.

27. Question: State the term for the maximum extent to which sales may fall before a loss is incurred.

Answer:

This term is the Margin of Safety (MOS).

28. Question: Give two alternative terms for the P/V Ratio.

Answer:

Contribution to Sales Ratio or Marginal Income Ratio.

29. Question: What assumption is made about the selling price in Marginal Costing?

Answer:

The selling price per unit is assumed to remain constant irrespective of the volume of production and sales.

30. Question: How is a loss calculated using the Marginal Costing approach?

Answer:

A Loss occurs when Contribution is less than Fixed Cost.

Loss = Fixed Cost - Contribution.

B. Ten-Mark Questions (10 Questions)

1. Question: Explain the concept of Marginal Costing and outline its main characteristics or features.

Answer:

Concept: Marginal Costing is a technique of cost accounting where only Variable Costs (or Marginal Costs) are charged to products, and Fixed Costs are treated as period costs, written off in the period they are incurred. It distinguishes between fixed and variable costs and focuses on Contribution to aid short-term decision-making.

Characteristics:

• Cost Classification: Costs are strictly separated into Fixed and Variable.
• Inventory Valuation: Stocks of finished goods and work-in-progress are valued at Variable Cost only.
• Fixed Costs Treatment: Fixed Costs are excluded from the cost of production and are treated as period costs.
• Contribution: The basic principle relies on Contribution (Sales - Variable Cost) as the yardstick for profitability.
• Decision Making: It is primarily used for short-term decision-making (e.g., make or buy, special orders, product mix).
1. Question: Discuss the advantages (merits) of using Marginal Costing as a management tool.

Answer:

• Simplicity: It is simple to understand and operate as it avoids the complexities of fixed cost apportionment.
• Pricing Decisions: It helps in fixing selling prices, especially in situations like trade depression or for export orders, by focusing on recovering variable costs and making a contribution.
• Profit Planning: Cost-Volume-Profit (CVP) analysis is easily applied, enabling management to forecast profit at various sales levels.
• Short-Term Decisions: It is invaluable for short-term decisions like Make or Buy, Accept or Reject a Special Order, or determining the most profitable product mix under a limiting factor (based on contribution per key factor).
• Performance Evaluation: It provides a better and stable comparison of operating results between two periods, as fixed costs are not included in stock valuation, preventing profit manipulation through inventory build-up.
• Break-Even Analysis: It facilitates the calculation and graphical representation of the Break-Even Point and Margin of Safety.
2. Question: Explain the limitations (disadvantages) of Marginal Costing.

Answer:

• Classification Difficulty: The segregation of all costs into fixed and variable components is often difficult and arbitrary in practice (e.g., semi-variable costs).
• Ignores Fixed Costs: Excluding fixed costs from the product cost in the long run can be misleading, as all costs are variable in the long run. It may lead to setting prices that fail to recover total costs.
• Stock Valuation: Valuation of inventory only at variable cost understates the true cost of the product and may be unacceptable for financial reporting and tax purposes.
• Assumption of Constant Costs: It rests on the unrealistic assumption that the selling price and variable cost per unit remain constant, which is rarely true in the real world.
• Not Suitable for All Industries: It is less suitable for industries where a major portion of the cost is fixed (e.g., highly automated capital-intensive industries).
• Difficulty in Control: The emphasis on variable costs may lead to less attention being paid to the control of fixed costs.
3. Question: Differentiate between Marginal Costing and Absorption Costing based on key parameters.

Answer:

Marginal Costing vs. Absorption Costing

Parameter	Marginal Costing (Variable Costing)	Absorption Costing (Full Costing)
Product Cost	Includes only variable manufacturing costs (Direct Material, Direct Labour, Variable Overheads).	Includes all manufacturing costs, both variable and fixed (Direct Material, Direct Labour, Variable & Fixed Overheads).
Treatment of Fixed Overheads (FOH)	Treated as Period Costs. They are expensed in full in the Profit & Loss Account in the period they are incurred.	Treated as Product Costs. They are allocated (absorbed) into the cost of each unit produced.
Inventory Valuation	Inventory (Finished Goods & WIP) is valued at Variable Production Cost only.	Inventory is valued at Full Production Cost (Variable Cost + Fixed Overheads absorbed).
Impact on Profit	Profit fluctuates directly with Sales Volume.	Profit fluctuates with Production Volume and Sales Volume.
Profit Difference	Lower Profit when Production > Sales (FOH is fully expensed).	Higher Profit when Production > Sales (A portion of FOH is carried forward in unsold stock).
Key Profit Measure	Contribution Margin (Sales - Variable Costs).	Gross Profit (Sales - Cost of Goods Sold).
External Reporting	Not acceptable for external financial reporting (GAAP/IFRS) or tax purposes.	Required for external financial reporting (GAAP/IFRS) and tax purposes.
Decision Making	Most suitable for short-term decisions (e.g., pricing, make or buy, acceptance of special orders).	More suitable for long-term pricing and strategic planning as it reflects the full cost of capacity.
Cost Per Unit	Remains constant regardless of the volume of production (within the relevant range).	Fluctuates with the volume of production because fixed overheads are spread over a different number of units.

 

5. Question: Elaborate on the concept of Break-Even Analysis and explain the components of a Break-Even Chart.

Answer:

Break-Even Analysis (BEA): It is a specific application of Marginal Costing that determines the level of sales volume (BEP) at which total revenues equal total costs (fixed and variable). It is a vital tool for profit planning, showing the relationship between costs, volume, and profit.

Components of a Break-Even Chart:

• X-Axis (Volume/Activity): Represents the level of activity (units of production/sales, percentage capacity).
• Y-Axis (Cost/Revenue): Represents the monetary value of costs and revenues.
• Fixed Cost Line: A straight line parallel to the X-axis, representing the constant total fixed cost.
• Total Cost Line: Starts from the fixed cost line (at zero volume) and slopes upward, representing the total of fixed and variable costs.
• Sales/Total Revenue Line: Starts from the origin (zero volume, zero revenue) and slopes upward, representing the total sales revenue.
• Break-Even Point (BEP): The point where the Total Revenue Line intersects the Total Cost Line.
• Margin of Safety: The area to the right of the BEP (Profit Zone).
• Area of Loss: The area to the left of the BEP.
5. Question: Explain how Marginal Costing assists management in making the Make or Buy decision.

Answer:

The Make or Buy decision involves determining whether to manufacture a product or component internally (Make) or purchase it from an external supplier (Buy).

Marginal Costing Approach:

1. Relevant Costs: Management compares the Variable Cost (Marginal Cost) of Making the product with the Purchase Price (Cost of Buying).
2. Fixed Costs: Fixed Costs are generally ignored unless the decision to 'Make' or 'Buy' results in a change in the total fixed cost.
3. Decision Rule:
• If Marginal Cost of Making < Purchase Price, the decision should be to Make (since making is cheaper).
• If Marginal Cost of Making > Purchase Price, the decision should be to Buy (since buying is cheaper).
4. Opportunity Cost: The analysis must also consider the Opportunity Cost—the contribution foregone by using the internal resources for this product instead of for another profitable activity. If a limiting factor is involved, the decision must yield the highest contribution per unit of the limiting factor.

7. Question: Discuss the application of Marginal Costing in determining the most profitable product mix under a Key Factor (Limiting Factor).

Answer:

When a business faces a limitation in resources, such as limited machine hours, labour hours, or raw material availability (the Key Factor), the objective is to maximize the overall profit by producing the most profitable combination of products.

Marginal Costing Approach:

1. Calculate Contribution per Unit: Determine the Contribution (Sales - Variable Cost) for each product.
2. Identify the Key Factor: Determine the resource that is scarce or limited.
3. Calculate Contribution per Unit of Key Factor: Divide the Contribution per unit by the quantity of the Key Factor required to produce one unit of that product.
4. Ranking: Rank the products in the descending order of the Contribution per Unit of Key Factor.
5. Optimal Mix: The product with the highest ranking (highest contribution per key factor) should be produced first up to the maximum market demand. The remaining capacity of the key factor is then allocated to the second-ranked product, and so on, until the key factor is exhausted. This ensures the maximum possible total profit.

8. Question: Explain the significance of the P/V Ratio and the Margin of Safety (MOS) in managerial decision-making.

Answer:

P/V Ratio (Profit/Volume Ratio):

• Significance: It measures the relationship between Contribution and Sales. It indicates the rate at which contribution is earned on every rupee of sales.
• Decision-Making: A higher P/V Ratio is always desirable as it means the company can recover its fixed costs and earn profit faster. It is used to:
• Determine BEP: (Fixed Cost / P/V Ratio).
• Calculate Sales for Target Profit: [(Fixed Cost + Target Profit) / P/V Ratio].
• Product Comparison: Helps compare the relative profitability of different products.

Margin of Safety (MOS):

• Significance: It is the cushion between the actual/budgeted sales and the Break-Even Sales. It indicates the maximum drop in sales that a business can sustain before it starts incurring a loss.
• Decision-Making: A higher MOS is desirable as it indicates a healthier and safer business position. It is used to:
• Assess Risk: Low MOS signals a high-risk scenario, prompting management to reduce costs or increase prices/sales.
• Measure Business Health: It is a key indicator of the firm's financial stability and resilience.
• Calculate Profit: MOS (Value) $\times$ P/V Ratio = Profit.
8. Question: How does Marginal Costing assist in setting the selling price under different market conditions?

Answer:

Marginal Costing provides a clear distinction between the minimum price and the desired price, which varies with market conditions:

• Recession/Depression (Minimizing Loss): The price can be set at a level that is equal to or slightly above the Variable Cost. This is the minimum or floor price. Although it yields no profit or even a slight loss, it keeps the business running, utilizes idle capacity, and covers variable costs, thereby minimizing the total loss (since Fixed Costs are unavoidable).
• Special Export Orders/Tender Pricing: For a bulk or one-off special order, the price should be set to cover the Variable Cost and contribute as much as possible towards fixed costs and profit. Any price above the variable cost is acceptable, provided the existing market is not affected.
• Normal Conditions (Maximizing Profit): The price is set to cover the Total Cost (Variable + Fixed) plus a desired profit margin. In this scenario, the full cost (Absorption Cost) is often used as a base, ensuring both fixed costs and a target return are recovered. Marginal Costing still provides the floor price for negotiations.
• Decision to Accept a Special Order: If the price offered is above the Variable Cost and the company has idle capacity, the order should be accepted, as it generates an incremental contribution.
9. Question: Write a detailed note on the concept of Profit Planning using Marginal Costing principles.

Answer:

Profit Planning is the process of setting a profit target and determining the necessary course of action to achieve that target. Marginal Costing, through CVP Analysis, is the primary tool for profit planning.

Key Elements in Profit Planning:

1. Establish P/V Ratio: This ratio indicates the profitability of sales. Management can aim to improve this ratio by increasing selling price, reducing variable costs, or changing the product mix.
2. Determine Break-Even Point (BEP): Knowing the BEP allows management to set sales targets above this crucial level to ensure profitability.
3. Calculate Sales for Target Profit: The key formula {Required Sales} = ({Fixed Cost} + {Target Profit}) / {P/V Ratio} allows management to directly calculate the sales volume needed to achieve a specific profit objective.
4. Decision on Cost Structure: Management can evaluate the impact of changing the cost structure (e.g., investing in new machinery, which increases fixed costs but reduces variable costs) on the BEP and overall profitability.
5. Product Mix Decisions: In a multi-product firm, Marginal Costing guides the promotion of products with a higher contribution margin (or higher contribution per key factor) to maximize the overall total profit.

📋 Section A: Easy Questions (Q. 1-10)

(Focus on Direct Application of Basic Formulas)

Q. 1

Question: Selling Price (SP) 100, Variable Cost (VC) 60. Calculate Contribution per Unit.

Formula: Contribution = SP - VC

Solution: 100 - 60 = 40

Q. 2

Question: Contribution per Unit 50, Sales 5,00,000. Calculate P/V Ratio.

Formula: P/V Ratio = (Total Contribution / Total Sales) x 100

Solution: Assuming 10,000 units sold, Total Contribution is 5,00,000. (5,00,000 / 5,00,000) x 100 = 100%

Q. 3

Question: Fixed Costs (FC) 1,00,000, P/V Ratio 25%. Calculate Break-Even Sales (₹).

Formula: BEP (Sales) = FC / P/V Ratio

Solution: 1,00,000 / 0.25 = 4,00,000

Q. 4

Question: FC 50,000, Contribution per Unit 10. Calculate BEP (Units).

Formula: BEP (Units) = FC / Contribution per Unit

Solution: 50,000 / 10 = 5,000 units

Q. 5

Question: Sales 2,00,000, BEP Sales 1,50,000. Calculate Margin of Safety (MOS) (₹).

Formula: MOS = Actual Sales - BEP Sales

Solution: 2,00,000 - 1,50,000 = 50,000

Q. 6

Question: Contribution 80,000, FC 60,000. Calculate Profit.

Formula: Profit = Contribution - FC

Solution: 80,000 - 60,000 = 20,000

Q. 7

Question: Sales 3,00,000, P/V Ratio 30%. Calculate Total Contribution.

Formula: Contribution = Sales x P/V Ratio

Solution: 3,00,000 x 0.30 = 90,000

Q. 8

Question: Profit 45,000, P/V Ratio 15%. Calculate Margin of Safety (₹).

Formula: MOS (Sales) = Profit / P/V Ratio

Solution: 45,000 / 0.15 = 3,00,000

Q. 9

Question: Variable Cost Ratio 70%. Calculate P/V Ratio.

Formula: P/V Ratio = 100% - VC Ratio

Solution: 100% - 70% = 30%

Q. 10

Question: Contribution per Unit 25, P/V Ratio 50%. Calculate Selling Price (SP) per Unit.

Formula: SP = Contribution / P/V Ratio

Solution: 25 / 0.50 = 50

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🚀 Section B: Medium Questions (Q. 11-30)

(Focus on Multi-step Calculations, Missing Figures, and Two-Period Data)

Q. 11

Question: Sales 5,00,000, VC 3,00,000, FC 1,50,000. Calculate Profit.

Formula: C = S - VC; or

                    Profit = C - FC

Solution: C = 5,00,000 - 3,00,000 = 2,00,000.

                    Profit = 2,00,000 - 1,50,000 = 50,000.

Q. 12

Question: Sales 10,00,000, P/V Ratio 40%. Calculate Variable Costs.

Formula: VC Ratio = 100% - P/V Ratio;

                       VC = Sales x VC Ratio

Solution: VC Ratio = 100% - 40% = 60%.

                    VC = 10,00,000 x 0.60 = 6,00,000.

Q. 13

Question: FC 90,000, Desired Profit 30,000, P/V Ratio 20%. Calculate Sales required (₹).

Formula: Sales = (FC + Desired Profit) / P/V Ratio

Solution: (90,000 + 30,000) / 0.20 = 6,00,000.

Q. 14

Question: Selling Price 50, VC Ratio 60%. If FC is 40,000, find BEP in Units.

Formula: C/Unit = SP x P/V Ratio; BEP = FC / C/Unit

Solution: P/V Ratio = 40%. C/Unit = 50 x 0.40 = 20. BEP = 40,000 / 20 = 2,000 units.

Q. 15

Question: Sales 4,00,000, MOS 1,00,000, FC 60,000. Find P/V Ratio.

Formula: BEP = Sales - MOS;

                     P/V Ratio = FC / BEP

Solution: BEP = 4,00,000 - 1,00,000 = 3,00,000.

                        P/V Ratio = 60,000 / 3,00,000 = 0.20 or 20%.

Q. 16

Question: Year 1: Sales 3,00,000, Profit 30,000. Year 2: Sales 5,00,000, Profit 70,000. Calculate P/V Ratio.

Formula: P/V Ratio = (Change in Profit / Change in Sales) x 100

Solution: (70,000 - 30,000) / (5,00,000 - 3,00,000)

                       = 40,000 / 2,00,000

                        = 0.20 or 20%.

Q. 17

Question: Using the data from Q. 16, calculate Fixed Costs.

Formula: FC = Contribution - Profit

Solution: C1 = 3,00,000 x 0.20 = 60,000.

                         FC = 60,000 - 30,000

                                   = 30,000.

Q. 18

Question: A product's VC is 20. If FC are 60,000, and P/V Ratio is 40%, find the Selling Price (SP).

Formula: P/V Ratio = (C / SP);

                   C = SP - VC

Solution: 0.40 = (SP - 20) / SP.

              0.40 SP = SP - 20.

                        20 = 0.60 SP.

                           SP = 20 / 0.60 = 33.33.

Q. 19

Question: FC 1,00,000. P/V Ratio 35%. Calculate Profit at sales of 5,00,000.

Formula: C = Sales x P/V Ratio;

                   Profit = C - FC

Solution: C at S 5L = 5,00,000 x 0.35 = 1,75,000.  

                  Profit = 1,75,000 - 1,00,000 = 75,000.

Q. 20

Question: Current Sales 4,00,000 (P/V Ratio 30%, FC 90,000). If sales are increased by 1,00,000, find the New Profit.

Formula: Profit_new = Profit_current + (Inc. in Sales x P/V Ratio)

Solution: Current Profit = (4,00,000 x 0.30) - 90,000 = 30,000.

                         Inc. in C = 1,00,000 x 0.30 = 30,000.

                            New Profit = 30,000 + 30,000 = 60,000.

Q. 21

Question: Product A: SP 20, VC 12. Product B: SP 30, VC 20. Sales Mix is 1:1. FC 1,00,000. Calculate Composite BEP (Units).

Formula: WAC/Unit = (C_A + C_B) / 2 units;

                                    BEP = FC / WAC/Unit

Solution: C_A = 8, C_B = 10. WAC/Unit = (8 + 10) / 2 = 9.

                    BEP = 1,00,000 / 9 = 11,111.11 composite units.

Or

Calculation of Composite BEP (Units)

The goal is to determine the total units required (in the 1:1 mix) to cover the total Fixed Costs (FC) of ₹1,00,000.

1. Calculate Contribution per Unit (C/Unit)

• Formula: {Contribution} (C) ={Selling Price} (SP) - {Variable Cost} (VC)
• Product A: ₹20 - ₹12 = ₹8
• Product B: ₹30 - ₹20 = ₹10

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2. Calculate Weighted Average Contribution (WAC) per Unit

Since the sales mix is 1:1 (one unit of A for every one unit of B), the total units in one composite batch is 2.

• Total Contribution in one batch:
• (₹8 \ 1 unit) + (₹10 \ 1 unit) = ₹8 + ₹10 = ₹18
• Formula: {WAC per Unit} ={Total Contribution of the Mix}{Total Units in the Mix}
• WAC per Unit: ₹18 / 2 units = ₹9.00

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3. Calculate Composite BEP (Total Units)

• Formula: {Composite BEP (Units)} ={Total Fixed Costs} (FC)}{WAC per Unit}}
• Calculation: ₹1,00,000 / ₹9.00
• Composite BEP (Total Units): approx 11,111.11 units

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📝 Breakdown of Break-Even Units

To break even, the company must sell 11,111.11 total units maintaining the 1:1 sales ratio:

• BEP Units of Product A: 11,111.11 (1/2) **5,555.56 { units}
• BEP Units of Product B: 11,111.11 (1/2) approx **5,555.56 { units

This combined sale ensures a total contribution of ₹1,00,000, which exactly covers the fixed costs.

 

Q. 22

Question: A component can be made for 18 (VC 14, FC 4) or bought for 16. Advise.

Formula: Compare Marginal Cost (VC) with Purchase Price.

Solution: Marginal Cost to Make = 14. Purchase Price = 16. Decision: Make (Saves 2 per unit).

Q. 23

Question: FC 1,00,000, BEP (Units) 10,000. If SP is 30, what is the Variable Cost per Unit?

Formula: C/Unit = FC / BEP (Units);

                      VC = SP - C/Unit

Solution: C/Unit = 1,00,000 / 10,000 = 10.

                VC = 30 - 10 = 20.

Q. 24

Question: A special order for 5,000 units is offered at 15. Normal SP 25, VC 18. There is idle capacity. Advise.

Formula: Compare Offer Price with Marginal Cost (VC).

Solution: Offer Price 15 is less than Marginal Cost 18. Decision: Reject (Results in a loss of 3 per unit).

Q. 25

Question: Sales 6,00,000, VC 3,60,000. If Fixed Costs increase by 60,000, find the New BEP (₹). (Assume old FC was 1,20,000).

Formula: P/V Ratio = C/S; New FC = Old FC + Inc.;

                               New BEP = New FC / P/V Ratio

Solution: C = 2,40,000. P/V Ratio = 40%.

                        New FC = 1,20,000 + 60,000 = 1,80,000.

                    New BEP = 1,80,000 / 0.40 = 4,50,000.

Q. 26

Question: Sales 8,00,000, Profit 1,00,000, FC 1,40,000. Calculate Variable Cost Ratio.

Formula: C = Profit + FC; P/V Ratio = C / S;

                          VC Ratio = 1 - P/V Ratio

Solution: C = 1,00,000 + 1,40,000 = 2,40,000.

                      P/V Ratio = 2,40,000 / 8,00,000 = 0.30 or 30%.

                             VC Ratio = 100% - 30% = 70%.

Q. 27

Question: Current Sales 3,00,000. P/V Ratio 25%. How much must sales increase to compensate for a 15,000 increase in Fixed Costs?

Formula: Inc. in Sales = Inc. in FC / P/V Ratio

Solution: Inc. in Sales = 15,000 / 0.25 = 60,000.

Q. 28

Question: Selling Price 80, VC 50. FC 75,000. Calculate MOS (Units) if Actual Sales are 3,000 units.

Formula: C/Unit = SP - VC; BEP (Units) = FC / C/Unit;

                      MOS = Actual Units - BEP Units

Solution: C/Unit = 30. BEP = 75,000 / 30 = 2,500 units.

                   MOS = 3,000 - 2,500 = 500 units.

Q. 29

Question: If the P/V Ratio is 40%, and a firm is operating at a MOS of 2,00,000, what is the Profit?

Formula: Profit = MOS x P/V Ratio

Solution: Profit = 2,00,000 x 0.40 = 80,000.

Q. 30

Question: Calculate Shut Down Point (₹): FC 1,00,000, Avoidable Fixed Costs 70,000, P/V Ratio 25%.

Formula: Shut Down Sales = Avoidable FC / P/V Ratio

Solution: Shut Down Sales = 70,000 / 0.25 = 2,80,000.

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🧠 Section C: Hard Questions (Q. 31-50)

(Focus on Limiting Factor, Product Mix Optimisation, Complex Sensitivity Analysis)

Q. 31

Question: Product P: SP 50, VC 30 (2 hrs/unit). Product Q: SP 60, VC 35 (3 hrs/unit). Limiting Factor: Machine Hours (Total 2,00,000 hrs). Find Optimal Product Mix.

Formula: Rank based on Contribution per Limiting Factor (C / Hour).

Solution: 1. C/Unit: P: 20; Q: 25. 2. C/Hr: P: 20/2 = 10 (Rank 1). Q: 25/3 = 8.33 (Rank 2). 3. Optimal Mix: Produce P first. Total units of P = 2,00,000 / 2 = 1,00,000 units of P (0 units of Q).

Q. 32

Question: Product A (SP 40, VC 20) and Product B (SP 50, VC 35). Sales Mix 3:2 (A:B). Total FC 1,00,000. Calculate Composite BEP (₹).

Formula: Comp. P/V Ratio = (Total C / Total S); BEP = FC / Comp. P/V Ratio

Solution: 1. Total S in a Mix: (3x40) + (2x50) = 220. 2. Total C in a Mix: (3x20) + (2x15) = 90. 3. Comp. P/V Ratio: 90 / 220 = 40.91%. 4. Comp. BEP: 1,00,000 / 0.4091 = 2,44,444.

Q. 33

Question: After-tax profit of 42,000 (Tax Rate 40%) is desired. FC 1,50,000. P/V Ratio 30%. Calculate Required Sales (₹).

Formula: Profit_Before Tax = Profit_After Tax / (1 - Tax Rate); Sales = (FC + Desired PBT) / P/V Ratio

Solution: 1. Required PBT: 42,000 / 0.60 = 70,000. 2. Required Sales: (1,50,000 + 70,000) / 0.30 = 7,33,333.

Q. 34

Question: Current BEP is 5,00,000 (P/V Ratio 20%). VC is reduced by 10%. Calculate New BEP (₹).

Formula: FC = BEP x P/V Ratio; New P/V Ratio = 1 - (Old VC Ratio x 0.90)

Solution: 1. FC: 5,00,000 x 0.20 = 1,00,000. 2. New VC Ratio: 80% x 0.90 = 72%. 3. New P/V Ratio: 100% - 72% = 28%. 4. New BEP: 1,00,000 / 0.28 = 3,57,143.

Q. 35

Question: A special order for 1,000 units is offered at 10. Normal SP 18, VC 12. Operating at idle capacity. Advise on the order.

Formula: Compare Offer Price with Marginal Cost (VC).

Solution: Marginal Cost: 12. Offer Price: 10. Price is LESS than Marginal Cost. Incremental Loss = 1,000 x (10 - 12) = -2,000. Decision: Reject the offer.

Q. 36

Question: Product Z sells for 100, VC 70, FC 90,000. If FC is increased by 20% and SP is reduced by 10%, calculate the new BEP (Units).

Formula: Find New FC and New C/Unit; BEP = New FC / New C/Unit

Solution: 1. New FC: 90,000 x 1.20 = 1,08,000. 2. New SP: 100 x 0.90 = 90. 3. New C/Unit: 90 - 70 = 20. 4. New BEP (Units): 1,08,000 / 20 = 5,400 units.

Q. 37

Question: Sales 8,00,000 (at 80% capacity). VC 6,40,000. FC 1,00,000. What profit would be earned at 100% capacity?

Formula: Find P/V Ratio; Calculate Sales and Contribution at 100%.

Solution: 1. P/V Ratio: (8,00,000 - 6,40,000) / 8,00,000 = 20%. 2. Sales at 100%: 8,00,000 / 0.80 = 10,00,000. 3. Contribution at 100%: 10,00,000 x 0.20 = 2,00,000. 4. Profit: 2,00,000 - 1,00,000 = 1,00,000.

Q. 38

Question: SP 40, VC 24. Current sales 5,000 units. FC 40,000. If the SP is increased to 45, and sales drop by 500 units, what is the change in Profit?

Formula: Calculate Profit in both scenarios (Profit = C - FC).

Solution: 1. Current Profit: (5,000x16) - 40,000 = 40,000. 2. New Profit: (4,500 units x (45-24)) - 40,000 = 54,500. 3. Change: 54,500 - 40,000 = 14,500 increase.

Q. 39

Question: Sales 7,00,000, VC 4,20,000. If machinery is bought (depreciation 10,000, a fixed cost), how much additional sales are needed to maintain the current profit?

Formula: P/V Ratio = C/S; Add. Sales = Add. FC / P/V Ratio.

Solution: 1. P/V Ratio: (7,00,000 - 4,20,000) / 7,00,000 = 40%. 2. Add. FC: 10,000. 3. Add. Sales: 10,000 / 0.40 = 25,000.

Q. 40

Question: Minimum Profit of 50,000 per month is required. FC 1,50,000. P/V Ratio 30%. Calculate the minimum monthly sales (₹).

Formula: Sales = (FC + Min. Profit) / P/V Ratio

Solution: (1,50,000 + 50,000) / 0.30 = 6,66,667.

Q. 41

Question: Sales 10,00,000, VC 6,00,000. FC 2,00,000. What is the Profit if the company invests 50,000 more in advertising (FC), increasing sales by 10%?

Formula: New Profit = New C - New FC

Solution: 1. P/V Ratio: 40%. 2. New S: 11,00,000. 3. New C: 11,00,000 x 0.40 = 4,40,000. 4. New FC: 2,00,000 + 50,000 = 2,50,000. 5. New Profit: 4,40,000 - 2,50,000 = 1,90,000.

Q. 42

Question: Firm produces 10,000 units (SP 20, VC 15, FC 40,000). A customer demands 2,000 additional units at 16. Should the firm increase capacity (by 20% increase in FC) to meet the order?

Formula: Compare Incremental C with Incremental FC.

Solution: 1. Incremental C: 2,000 x (16 - 15) = 2,000. 2. Incremental FC: 40,000 x 0.20 = 8,000. 3. Incremental Profit: 2,000 - 8,000 = -6,000 Loss. Decision: Reject.

Q. 43

Question: A multi-product firm has a Comp. P/V Ratio of 30% and BEP of 10,00,000. If the sales mix shifts, lowering the Comp. P/V Ratio to 25%, what is the new BEP (₹)?

Formula: FC = Old BEP x Old P/V Ratio; 

New BEP = FC / New P/V Ratio

Solution: 

1. FC: 10,00,000 x 0.30 = 3,00,000. 

2. New BEP: 3,00,000 / 0.25 = 12,00,000.

Q. 44

Question: Calculate the Sales (₹) required to earn a Profit of 15% on Sales. FC 75,000. P/V Ratio 40%.

Formula: Sales = (FC + Profit) / P/V Ratio 

implies S = (75,000 + 0.15S) / 0.40.

Solution: 0.40 S = 75,000 + 0.15 S. 0.25 S = 75,000.

 S = 75,000 / 0.25 = 3,00,000.

Q. 45

Question: Product K: C/unit 20 (2 units of material/unit). Product L: C/unit 30 (3 units of material/unit). Limiting Factor: Raw Material (Total 4,000 units). Find Optimal Mix.

Formula: Rank based on Contribution per Unit of Limiting Factor.

Solution: 

1. C per Material Unit: K: 20/2 = 10 (Rank 1). L: 30/3 = 10 (Rank 2). 

2. Since there is a tie, any mix order is viable. 

Assume K is produced first: 1,000 units of K (uses 2,000 material units). 

Remaining material: 2,000.

 L units: 2,000 / 3 = 666.67. 

Mix: 1,000 K and 667 L.

Q. 46

Question: Sales 5,00,000, VC 3,50,000. FC 1,00,000. Proposes to outsource (saving all VC and 50% of FC) at a purchase price of 4,00,000. Advise.

Formula: Compare Total Cost (Make) with Total Cost (Buy).

Solution: 

1. Cost to Make: 

3,50,000 + 1,00,000 = 4,50,000. 

2. Cost to Buy: 

Purchase Price 4,00,000 + Unavoidable FC (50,000) = 4,50,000. 

Decision: Indifferent (Costs are equal).

Q. 47

Question: A company makes a profit of 80,000 at a MOS of 50%. If the P/V Ratio is 40%, calculate Total Sales (₹).

Formula: MOS (Sales) = Profit / P/V Ratio; Actual Sales = MOS / MOS Ratio

Solution: 

1. MOS (Sales): 80,000 / 0.40 = 2,00,000. 

2. MOS Ratio: 50%. 3. Total Sales (S): S = 2,00,000 / 0.50 = 4,00,000.

Q. 48

Question: Sales 10,00,000, VC 60%. If a temporary 10% reduction in SP is made to boost sales by 20%, calculate the change in Profit (₹). (Assume FC 2,00,000).

Formula: New Profit = New C - FC

Solution:

 1. Current Profit: 4,00,000 - 2,00,000 = 2,00,000. 

2. New Scenario: New S=12,00,000. New P/V Ratio: 33.33%. 

New C: 12,00,000 x 0.3333 = 4,00,000. 

New Profit: 4,00,000 - 2,00,000 = 2,00,000. 

Change in Profit: 0.

Q. 49

Question: FC 1,50,000. SP 120, VC 80. If the VC per unit increases by 10% and FC decreases by 20%, find the difference in BEP (Units).

Formula: Calculate Old BEP and New BEP.

Solution: 

1. Old BEP: 1,50,000 / (120-80) = 3,750 units. 

2. New BEP: (1,50,000 x 0.80) / (120 - 88) 

= 1,20,000 / 32 = 3,750 units. Difference: 0.

Q. 50

Question: Sales 5,00,000, VC 3,50,000. BEP is 3,00,000. A new product line is introduced (Incremental FC 50,000, expected to generate 2,00,000 sales with a 20% P/V Ratio). Calculate the overall new Profit.

Formula: New Profit = Old Profit + Incremental Profit (or Loss)

Solution:

 1. Old P/V Ratio: 30%. 

2. Old FC: 3,00,000 x 0.30 = 90,000.

 3. Old Profit: 1,50,000 - 90,000 = 60,000.

 4. Incremental Profit: (2,00,000 x 0.20) - 50,000 = -10,000 Loss. 

5. New Profit: 60,000 - 10,000 = 50,000.