Chapter 5: Cost-Volume-Profit (CVP) Analysis
CVP analysis (also called break-even analysis) examines the relationship between costs, volume of output, and profit. It is one of the most powerful and widely used tools in management accounting for planning, decision-making, and profit forecasting. This chapter covers contribution margin, break-even point, margin of safety, profit-volume ratio, and multi-product CVP analysis.
5.1 Key CVP Concepts
| Concept | Formula | Meaning |
|---|---|---|
| Contribution Margin (CM) | Sales - Variable Costs | Amount available to cover fixed costs and generate profit |
| CM per Unit | Selling Price - Variable Cost per Unit | Contribution from each unit sold |
| CM Ratio (P/V Ratio) | CM / Sales × 100 | % of each sales rupee that contributes to fixed costs and profit |
| Break-Even Point (Units) | Fixed Costs / CM per Unit | Units needed to cover all costs (zero profit) |
| Break-Even Point (Sales) | Fixed Costs / CM Ratio | Sales value needed to cover all costs |
| Margin of Safety | Actual Sales - BEP Sales | How far sales can fall before losses begin |
| Target Profit Volume | (Fixed Costs + Target Profit) / CM per Unit | Units needed to achieve desired profit |
5.2 Comprehensive Worked Example
Data: A Nepali furniture company produces chairs. Selling price = NPR 2,000/chair. Variable cost = NPR 1,200/chair. Fixed costs = NPR 4,00,000/year. Current sales = 800 chairs/year.
1. Contribution Margin per unit: 2,000 - 1,200 = NPR 800
2. P/V Ratio: 800/2,000 × 100 = 40%
3. BEP (Units): 4,00,000/800 = 500 chairs
4. BEP (Sales): 4,00,000/0.40 = NPR 10,00,000
5. Margin of Safety: 800 - 500 = 300 chairs or (300/800)×100 = 37.5%
6. Current Profit: (800 × 800) - 4,00,000 = 6,40,000 - 4,00,000 = NPR 2,40,000
7. Target Profit NPR 4,00,000: (4,00,000 + 4,00,000)/800 = 1,000 chairs
5.3 CVP Income Statement (Contribution Format)
| Particulars | Total (NPR) | Per Unit | % |
|---|---|---|---|
| Sales (800 units) | 16,00,000 | 2,000 | 100% |
| Less: Variable Costs | (9,60,000) | (1,200) | 60% |
| Contribution Margin | 6,40,000 | 800 | 40% |
| Less: Fixed Costs | (4,00,000) | ||
| Net Profit | 2,40,000 |
5.4 Applications of CVP Analysis
| Decision | CVP Application | Example |
|---|---|---|
| Pricing | Calculate minimum price to break even | Min price = VC + FC/Expected units |
| Product Mix | Rank products by CM per limiting factor | Allocate capacity to highest CM product |
| Make or Buy | Compare make cost (VC + allocated FC) vs buy price | Outsource if buy price < variable cost of making |
| Accept Special Order | Accept if price > variable cost (when spare capacity exists) | Export order at lower price covers VC and adds profit |
| Add/Drop Product Line | Keep if contribution > avoidable fixed costs | Continue branch if it generates positive contribution |
5.5 Multi-Product CVP Analysis
When a company sells multiple products, the BEP calculation uses a weighted average contribution margin based on the sales mix.
Example: Company sells Product X (SP=100, VC=60, CM=40) and Product Y (SP=150, VC=90, CM=60). Sales mix: X:Y = 3:2. Fixed costs = NPR 3,60,000.
Weighted average CM = (3×40 + 2×60)/(3+2) = (120+120)/5 = NPR 48
BEP (total units) = 3,60,000/48 = 7,500 units
BEP for X = 7,500 × 3/5 = 4,500 units
BEP for Y = 7,500 × 2/5 = 3,000 units
5.6 Assumptions and Limitations
| Assumption | Reality/Limitation |
|---|---|
| Selling price is constant | Price may change with volume (discounts) |
| Costs are linear (purely fixed or variable) | Semi-variable costs exist; step costs |
| Sales mix is constant | Mix changes with market conditions |
| Production = Sales (no inventory change) | Inventory levels fluctuate |
| Single product or constant mix | Companies sell multiple changing products |
5.7 Sensitivity Analysis in CVP
Sensitivity analysis examines how changes in key variables affect profit. This "what-if" analysis helps managers understand which variables have the greatest impact.
Base Case: SP = NPR 2,000, VC = NPR 1,200, FC = NPR 4,00,000, Sales = 800 units
Base Profit = (800 × 800) - 4,00,000 = NPR 2,40,000
| Scenario | Change | New Profit | % Change in Profit |
|---|---|---|---|
| 10% increase in selling price | SP = 2,200 | (800×1000)-400,000 = 4,00,000 | +66.7% |
| 10% increase in variable cost | VC = 1,320 | (800×680)-400,000 = 1,44,000 | -40.0% |
| 10% increase in fixed costs | FC = 4,40,000 | 640,000-440,000 = 2,00,000 | -16.7% |
| 10% increase in volume | Units = 880 | (880×800)-400,000 = 3,04,000 | +26.7% |
| 10% decrease in selling price | SP = 1,800 | (800×600)-400,000 = 80,000 | -66.7% |
Key Insight: Selling price has the greatest impact on profit (±66.7% from just 10% change). Variable cost is second most sensitive. Fixed cost changes have moderate impact. This tells management to protect pricing above all else.
5.8 Operating Leverage and CVP
Operating leverage measures how sensitive profit is to changes in sales volume. It depends on the proportion of fixed costs to variable costs.
Degree of Operating Leverage (DOL) = Contribution / Profit
Two Companies Comparison:
| Item | Company A (High Fixed) | Company B (High Variable) |
|---|---|---|
| Sales (1,000 units @ NPR 100) | 1,00,000 | 1,00,000 |
| Variable Costs | 30,000 (30%) | 70,000 (70%) |
| Contribution | 70,000 | 30,000 |
| Fixed Costs | 50,000 | 10,000 |
| Profit | 20,000 | 20,000 |
| DOL | 70,000/20,000 = 3.5 | 30,000/20,000 = 1.5 |
If sales increase 20%:
Company A profit increase = 20% × 3.5 = 70% → New profit = NPR 34,000
Company B profit increase = 20% × 1.5 = 30% → New profit = NPR 26,000
If sales DECREASE 20%:
Company A profit decrease = 20% × 3.5 = 70% → New profit = NPR 6,000
Company B profit decrease = 20% × 1.5 = 30% → New profit = NPR 14,000
Conclusion: High operating leverage (A) amplifies both gains and losses. Suitable for stable demand businesses. Low leverage (B) is safer during uncertainty. Nepal implication: tourism businesses have high fixed costs (hotel buildings) = high operating leverage = severely impacted by demand drops (COVID-19 showed this clearly).
5.9 CVP Analysis for Service Industry in Nepal
Example: Everest Trekking Agency, Pokhara
Revenue per trek group = NPR 50,000 | Variable cost per group (guides, food, transport) = NPR 30,000 | Annual fixed costs (office, permits, marketing, staff) = NPR 24,00,000
CM per group: 50,000 - 30,000 = NPR 20,000
P/V Ratio: 20,000/50,000 = 40%
BEP (groups): 24,00,000/20,000 = 120 groups/year
BEP (revenue): 24,00,000/0.40 = NPR 60,00,000
If target profit = NPR 12,00,000:
Required groups = (24,00,000 + 12,00,000)/20,000 = 180 groups/year
That's 180/12 = 15 groups per month
Margin of Safety: If actual = 200 groups: MOS = (200-120)/200 = 40% (safe — sales can drop 40% before loss)
During COVID-19 (sales dropped to 30 groups):
Loss = (30 × 20,000) - 24,00,000 = 6,00,000 - 24,00,000 = NPR -18,00,000 loss
This shows how high fixed costs devastate service businesses when demand collapses.
5.10 Break-Even Chart Description
A break-even chart plots total revenue and total cost against output volume. Key elements to include when drawing:
| Element | Position on Chart | Description |
|---|---|---|
| X-axis | Horizontal | Output/Sales volume (units) |
| Y-axis | Vertical | Cost and Revenue (NPR) |
| Fixed Cost Line | Horizontal line at FC level | Parallel to X-axis (doesn't change with volume) |
| Total Cost Line | Starts at FC, slopes upward | FC + VC per unit × volume |
| Total Revenue Line | Starts at origin, slopes upward steeper | SP × volume |
| BEP | Where TR and TC lines intersect | No profit, no loss |
| Profit Area | Above BEP (TR > TC) | Shaded area between TR and TC lines |
| Loss Area | Below BEP (TC > TR) | Shaded area between TC and TR lines |
| Margin of Safety | Distance from BEP to actual sales | Shown as horizontal distance on X-axis |
Exam tip: Always label all elements clearly. Show the BEP point, profit area, loss area, and margin of safety. Use a ruler for straight lines.
Practice Questions
Short Answer:
1. Define contribution margin, P/V ratio, and margin of safety.
2. Derive the break-even formula in units and sales value.
3. How is target profit volume calculated?
4. What are the assumptions of CVP analysis?
5. Explain multi-product BEP analysis.
Long Answer:
6. SP = NPR 500, VC = NPR 300, FC = NPR 6,00,000. Calculate: BEP units, BEP sales, units for NPR 2,00,000 profit, margin of safety if actual sales = 5,000 units. Prepare CVP income statement. (15 marks)
7. A company sells two products: A (SP=200, VC=120) and B (SP=300, VC=180). Mix is 2:3. FC = NPR 12,00,000. Find BEP for each product and total BEP sales. (15 marks)
8. Discuss five applications of CVP analysis in management decision-making with examples. (15 marks)
9. A hotel in Pokhara has FC of NPR 50 lakhs/year. Average room rate NPR 3,000, variable cost NPR 1,000/room-night. Calculate BEP room-nights, revenue at BEP, and rooms needed for NPR 20 lakh profit. (15 marks)
10. Critically evaluate CVP analysis as a decision-making tool. What are its assumptions and limitations? (15 marks)
Exam Tips: ✓ CVP numerical problems are ALWAYS asked — practice extensively ✓ Know all formulas: BEP, CM, P/V ratio, MOS, target profit ✓ Multi-product BEP requires weighted average CM ✓ Draw break-even chart if asked ✓ Always verify: at BEP, profit should equal zero