a) Manufacturing company which produces and sales three products. The income statement of the company has been presented below: Particulars Product A Product B Product C Total : : : : : Production…

a) Differential Income Statement to Analyze Dropping Product B

To determine whether the company should drop Product B, we must analyze the differential income (change in profit) that would occur if Product B is discontinued. The key considerations are:

1. Loss of Contribution Margin from Product B: If Product B is dropped, the company loses its contribution margin of Rs. 50,000.
2. Avoidable Fixed Costs: The depreciation and allocated fixed costs associated with Product B can be saved if it is discontinued.
   • Depreciation: Rs. 40,000 (avoidable)
   • Allocated fixed cost: Rs. 15,000 (avoidable)
   • Total avoidable fixed costs: Rs. 55,000
3. Impact on Other Products: Dropping Product B reduces sales of other products by 10%.
   • Sales reduction for Products A and C:
     • Product A: 10% of Rs. 200,000 = Rs. 20,000
     • Product C: 10% of Rs. 100,000 = Rs. 10,000
   • Variable cost reduction:
     • Product A: 10% of Rs. 100,000 = Rs. 10,000
     • Product C: 10% of Rs. 50,000 = Rs. 5,000
   • Net effect on contribution margin:
     • Product A: Rs. 20,000 (lost revenue) - Rs. 10,000 (saved variable cost) = Rs. 10,000 loss
     • Product C: Rs. 10,000 (lost revenue) - Rs. 5,000 (saved variable cost) = Rs. 5,000 loss
     • Total loss in contribution margin: Rs. 15,000

Differential Income Statement

Conclusion

• Current net income: Rs. 65,000
• Net income if Product B is dropped: Rs. 55,000
• Difference: -Rs. 10,000

Recommendation: The company should not drop Product B because discontinuing it would reduce overall net income by Rs. 10,000.

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b) Semi-Variable Costs: Definition and Examples

Definition

Semi-variable costs (also called mixed costs) are costs that contain both fixed and variable components. They remain constant up to a certain level of activity but increase in steps or proportional increments beyond that point.

Key Characteristics

1. Fixed Component: Does not change with production volume within a certain range.
2. Variable Component: Increases as production or sales volume increases beyond a threshold.
3. Step-wise Behavior: Costs remain constant for a range of activity but jump at certain intervals.

Examples of Semi-Variable Costs

Mathematical Representation

The semi-variable cost can be expressed as: $$\text{Semi-Variable Cost}=\text{Fixed Cost}+(\text{Variable Cost per Unit}\times \text{Number of Units})$$ Example: If a company’s electricity bill is Rs. 500 (fixed) + Rs. 5 per kWh, then:

• At 100 kWh: Rs. 500 + (5 × 100) = Rs. 1,000
• At 200 kWh: Rs. 500 + (5 × 200) = Rs. 1,500

Importance in Cost Analysis

1. Cost-Volume-Profit (CVP) Analysis: Helps in predicting costs at different activity levels.
2. Budgeting and Forecasting: Useful for setting realistic budgets.
3. Pricing Decisions: Helps in determining the break-even point and profit margins.
4. Cost Control: Identifies areas where cost-saving measures can be applied.

How to Separate Fixed and Variable Components?

Methods include:

• High-Low Method: Uses the highest and lowest activity levels to separate costs.
• Least Squares Regression: Provides a more accurate separation by analyzing historical data.
• Scatter Graph Method: Plots cost vs. activity and identifies the fixed and variable portions.

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