Marginal costing and break-even analysis: contribution, P/V ratio, BEP and margin of safety

1. Marginal cost and marginal costing

Marginal cost is the amount by which total cost changes when output is increased or decreased by one unit. In practice it equals variable cost: direct material, direct labour, direct expenses and variable overheads. Marginal costing is the technique of ascertaining marginal cost and the effect on profit of changes in volume or type of output, by separating fixed and variable costs. Fixed costs are treated as period costs and written off against contribution; they are not carried in stock.

2. The marginal cost statement

3. The formulas

1. Contribution = Sales − Variable cost = Fixed cost + Profit.
2. P/V ratio = Contribution / Sales × 100; from two periods, = Change in profit / Change in sales × 100.
3. Break-even point (sales) = Fixed cost / P/V ratio; in units = Fixed cost / Contribution per unit.
4. Sales for a desired profit = (Fixed cost + Desired profit) / P/V ratio.
5. Margin of safety = Actual sales − BEP sales = Profit / P/V ratio.

At the break-even point total revenue equals total cost and there is neither profit nor loss; contribution exactly covers fixed cost. The break-even chart plots fixed cost as a horizontal line, total cost rising from it, and sales rising from the origin; the point where sales and total cost lines cross is the BEP, and the angle between them is the angle of incidence (wider angle, higher rate of profit). The margin of safety measures how far sales can fall before losses begin; a low margin means high fixed cost or a low P/V ratio.

4. Solved: two-year data (January 2026, B.Com)

Sales 2,00,000 and profit 30,000 in 2005; sales 2,50,000 and profit 50,000 in 2006; selling price Rs. 10.

• P/V ratio = (50,000 − 30,000) / (2,50,000 − 2,00,000) = 20,000 / 50,000 = 40%.
• Fixed cost = Contribution − Profit = 2,00,000 × 40% − 30,000 = 50,000.
• BEP = 50,000 / 40% = Rs. 1,25,000, i.e. 12,500 units.
• Sales for profit of 60,000 = (50,000 + 60,000) / 40% = Rs. 2,75,000.
• Profit at sales of 2,00,000 = 2,00,000 × 40% − 50,000 = Rs. 30,000 (as given for 2005, which is the check).

January 2025 (B.Com). Sales 1,40,000 / profit 15,000 and 1,60,000 / 20,000. P/V ratio = 5,000 / 20,000 = 25%; fixed cost = 35,000 − 15,000 = 20,000; BEP = 80,000; sales for profit of 40,000 = 60,000 / 25% = 2,40,000; profit at sales of 1,20,000 = 30,000 − 20,000 = 10,000.

5. Solved: BEP and margin of safety (January 2026, B.Com, 100 marks)

Fixed cost 72,000; variable cost 1,20,000; sales 2,40,000; units 80,000.

• Contribution = 1,20,000; P/V ratio = 50%. Price Rs. 3, variable cost Rs. 1.50, contribution Rs. 1.50 a unit.
• BEP = 72,000 / 50% = Rs. 1,44,000, or 72,000 / 1.50 = 48,000 units.
• Margin of safety = 2,40,000 − 1,44,000 = Rs. 96,000 (32,000 units, 40% of sales).
• Check: profit = 1,20,000 − 72,000 = 48,000 = margin of safety × P/V ratio (96,000 × 50%).

6. Importance of marginal costing

1. Pricing: the floor price in a slump or for a special order is marginal cost; any price above it adds contribution.
2. Make or buy: buy only if the outside price is below the marginal cost of making.
3. Product mix and key factor: rank products by contribution per unit of the limiting factor (machine hours, material).
4. Shut down or continue: continue while contribution covers avoidable fixed costs.
5. Profit planning through BEP and sales for target profit.
6. Cost control: variable costs are controllable by the line manager; fixed costs by top management.
7. Stock valuation is free of arbitrary fixed overhead apportionment.

Limitations. Splitting semi-variable costs is hard; fixed costs change in the long run; stock valued at marginal cost is not accepted for financial statements (Ind AS 2 requires fixed production overheads to be absorbed on normal capacity); and ignoring fixed costs in pricing can lead to losses over time.

How this is examined

The problem is the 10-mark or 6-mark Unit V question in the B.Com paper, alternating with the flexible budget; in the 100-mark paper it is part of Q. 9. Write each formula before substituting, and close with a check (profit = margin of safety × P/V ratio). For the essay, define, give the statement format and list the uses.