## Cost-Volume-Profit (CVP) Analysis
### What is CVP Analysis?
A managerial tool that examines the relationship between cost, selling price, and volume to understand how changes in these variables affect profit.
Three key variables: Cost · Volume · Profit
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### Assumptions of CVP Analysis
| Assumption | Detail |
|---|---|
| Revenue & cost drivers | Changes arise solely from variation in units produced/sold |
| Total cost structure | Fixed costs remain constant; variable costs fluctuate with output |
| Linear behaviour | Both total revenue and total cost are linear within the relevant range |
| Known constants | Selling price/unit, variable cost/unit, and total fixed costs are known and constant |
| Product mix | Single product, or constant proportions if multiple products |
| Time value of money | Excluded from the analysis |
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### Importance of CVP Analysis
Provides answers to:
1. How do costs behave relative to volume?
2. At what output level does the business break even?
3. How sensitive is profit to changes in output?
4. What profit results from a projected sales volume?
5. What quantity is needed to achieve a target profit?
CVP explains the impact of changes in:
- Selling prices
- Volume of sales
- Variable cost per unit
- Total fixed costs
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### P/V Ratio (Profit-Volume Ratio)
$$\text{P/V Ratio} = \frac{\text{Contribution}}{\text{Sales}} = \frac{\text{Sales} - \text{Variable Cost}}{\text{Sales}}$$
The P/V ratio changes only when the relationship between contribution and sales changes.
| Situation | Effect on P/V Ratio | Reason |
|---|---|---|
| Increase in physical sales volume | No change | Volume doesn't affect the ratio |
| Increase in fixed cost | No change | Fixed costs not in the P/V formula |
| Decrease in variable cost per unit | Increases | Contribution rises, sales unchanged |
| Decrease in contribution margin | Decreases | Numerator falls |
| Increase in selling price per unit | Increases | Contribution and sales both rise, but contribution rises proportionally more |
| Decrease in fixed cost | No change | Fixed costs not in the P/V formula |
| 10% increase in both SP and VC | No change | Contribution/Sales ratio stays constant |
| 10% increase in SP, 10% decrease in volume | Increases | Volume doesn't affect P/V; higher SP improves ratio |
| 50% increase in VC, 50% decrease in fixed cost | Decreases | Higher VC reduces contribution |
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### Angle of Incidence
The angle formed at the break-even point where the sales line and total cost line intersect.
- Shows the rate at which profit is earned after BEP is crossed.
- Wider angle → higher rate of profit earning.
- A large angle of incidence + high margin of safety = extremely favourable position.
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### Methods of Break-Even Analysis
1. Algebraic computations — formula-based
2. Graphic presentations — break-even charts and P/V charts
Biggest advantage of P/V Chart: Clearly depicts the effect on profit and BEP of any change in variables.
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### Limitations of Break-Even Analysis
1. Unrealistic assumptions — linear cost and revenue behaviour rarely holds
2. Non-linear costs in practice — costs may be step-fixed or curvilinear
3. Constant stock assumption — ignores inventory fluctuations
4. Ignores external influences — inflation, competition not captured
5. Single cost driver — only activity level considered; other cost drivers ignored
6. Point-in-time analysis — business conditions are dynamic
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### Framework for Decision Making Using CVP
| Step | Action |
|---|---|
| Step 1: Problem Identification | Identify the goal and the problem area |
| Step 2: Options Identification | List all possible courses of action |
| Step 3: Evaluation | Assess each option on financial (profit, ROI) and non-financial criteria (ethics, customer satisfaction) |
| Step 4: Selection | Choose and implement the best option |