Unit 2: Marginal Costing and CVP Analysis

I. Orientation

Marginal costing is a technique that separates costs into variable and fixed components to show how changes in output and sales affect contribution and profit. Cost-volume-profit (CVP) analysis uses this classification to study the relationship among selling price, sales volume, variable cost, fixed cost, and profit over a specified period.

• Defining principle: Only variable production costs are charged to units of output; fixed costs are treated as period costs and written off against total contribution.
• Cost behaviour:
  • Variable cost changes in total with activity but is assumed constant per unit.
  • Fixed cost remains constant in total within the relevant range but changes per unit as output changes.
• Central measure: Contribution is the amount remaining after variable costs; it first covers fixed costs and then generates profit.
• Core assumptions:
  • Selling price per unit and variable cost per unit remain constant.
  • Total fixed cost remains constant within the relevant range.
  • Production and sales efficiency do not change materially.
  • In multi-product analysis, the sales mix remains constant.
  • Costs and revenues can be identified reliably and expressed linearly.
• Main convention: Inventory is valued at variable production cost, so fixed production overhead is not carried forward in closing inventory.
• Planning horizon: The technique is most useful for short-term decisions where capacity, technology, and total fixed costs are largely predetermined.

II. Foundations of Marginal Costing — Cost Classification and Contribution

A. Concept, nature, and importance of marginal costing

Marginal costing determines product cost using variable costs and evaluates profitability through contribution rather than full cost per unit.

• Concept: Marginal cost is the additional cost arising from producing one more unit; under linear cost assumptions, it equals variable cost per unit.
• Nature:
  • It is a decision-making technique, not an independent system of cost accounting.
  • Costs are classified primarily by behaviour as fixed, variable, or semi-variable.
  • Fixed production overhead is charged fully to the period in which it is incurred.
  • Profit is affected by sales volume rather than production volume when selling price, costs, and sales mix remain unchanged.
• Inventory valuation: Work-in-progress and finished goods include variable production costs but exclude fixed production overhead.
• Importance:
  • It reveals the contribution earned by each product, department, or sales channel.
  • It supports profit planning by connecting volume, cost, price, and target profit.
  • It prevents arbitrary fixed-overhead allocations from distorting short-term decisions.
  • It assists decisions involving spare capacity, limiting factors, special orders, and temporary closure.
• Limitation: The fixed-variable distinction may be difficult because semi-variable costs must be separated and cost behaviour can change outside the relevant range.

B. Marginal costing equation

The marginal costing equation expresses the relationship between sales, variable cost, contribution, fixed cost, and profit.

S - V = C
C - F = P
Therefore: S - V = F + P

• Symbols:
  • S = total sales revenue.
  • V = total variable cost.
  • C = total contribution.
  • F = total fixed cost.
  • P = profit; a negative value represents loss.
• Interpretation: Contribution is applied first toward fixed cost; profit arises only after fixed cost has been recovered.
• Loss position: If C < F, the loss equals F - C; if C = F, profit is zero and the business is at break-even.
• Unit form:

Contribution per unit = Selling price per unit - Variable cost per unit
Total contribution = Contribution per unit × Units sold
Profit = Total contribution - Fixed cost

• Example: If 4,000 units sell for ₹50 each, variable cost is ₹30 per unit, and fixed cost is ₹60,000, contribution is 4,000 × ₹20 = ₹80,000, producing a profit of ₹80,000 - ₹60,000 = ₹20,000.

C. Contribution margin

Contribution margin measures how much sales revenue is available to cover fixed costs and profit after variable costs have been deducted.

• Total contribution:

C = S - V

• C = total contribution.
• S = sales revenue.
• V = total variable cost.

• Unit contribution:

c = s - v

• c = contribution per unit.
• s = selling price per unit.
• v = variable cost per unit.

• Decision relevance: A product with positive contribution helps recover fixed cost even when its full cost shows an accounting loss.
• Incremental analysis: Additional business is normally beneficial when incremental revenue exceeds incremental variable cost and any avoidable incremental fixed cost.
• Constraint qualification: When a scarce resource limits production, total contribution per unit is insufficient; contribution per unit of the limiting factor becomes the relevant measure.

D. Profit/volume (P/V) Ratio

The P/V ratio expresses contribution as a percentage of sales and indicates the rate at which profit changes with sales revenue.

P/V ratio = Contribution ÷ Sales × 100
P/V ratio = Contribution per unit ÷ Selling price per unit × 100

• Meaning: A P/V ratio of 40% means every ₹1 of sales generates ₹0.40 of contribution.
• Profit change:

Change in profit = Change in sales × P/V ratio

• Comparison: A higher P/V ratio generally indicates stronger profitability, provided fixed costs, capacity requirements, risk, and demand are also considered.
• Improvement methods:
  • Increase selling price without causing a disproportionate fall in demand.
  • Reduce variable cost through purchasing, process, or design improvements.
  • Shift sales toward products with higher P/V ratios where no limiting factor applies.
• Caution: The ratio assumes a stable selling price, variable cost rate, and product mix.

III. Cost-Volume-Profit Thresholds — Risk and Profit Planning

A. Break-even point

The break-even point is the sales level at which total revenue equals total cost, making contribution exactly equal to fixed cost and profit equal to zero.

BEP in units = Fixed cost ÷ Contribution per unit
BEP sales value = Fixed cost ÷ P/V ratio

• Symbols and units:
  • BEP = break-even point.
  • Fixed cost is measured in currency per period.
  • Contribution per unit is measured in currency per unit.
  • P/V ratio is used as a decimal in calculations; for example, 30% becomes 0.30.
• Target-profit extension:

Required units = (Fixed cost + Target profit) ÷ Contribution per unit
Required sales = (Fixed cost + Target profit) ÷ P/V ratio

• Example: With fixed cost of ₹90,000, selling price of ₹50, and variable cost of ₹35 per unit, unit contribution is ₹15 and break-even output is ₹90,000 ÷ ₹15 = 6,000 units.
• Interpretation: Sales below 6,000 units produce a loss, while each unit above 6,000 adds ₹15 to profit under the stated assumptions.
• Graphical view: On a break-even chart, the intersection of the total revenue line and total cost line represents break-even.

B. Margin of safety

Margin of safety measures how far actual or budgeted sales exceed break-even sales and therefore indicates exposure to a decline in demand.

Margin of safety = Actual sales - Break-even sales
Margin of safety percentage = Margin of safety ÷ Actual sales × 100

• Profit relationship:

Profit = Margin of safety × P/V ratio
Margin of safety = Profit ÷ P/V ratio

• Interpretation:
  1. High margin: Sales can decline substantially before the organization incurs a loss.
  2. Low margin: Even a small sales decline may eliminate profit, indicating greater operating risk.
• Example: If actual sales are ₹500,000 and break-even sales are ₹350,000, the margin of safety is ₹150,000, or ₹150,000 ÷ ₹500,000 × 100 = 30%.
• Management use: The measure helps assess budget resilience, compare operating risk, and evaluate whether fixed-cost commitments are excessive.

IV. Organizational Decisions — Relevant Cost Applications

A. Applications of marginal costing for decision making in organizations

Marginal costing supports short-term choices by comparing future revenues and costs that differ between alternatives.

• Relevant-cost rule: Include future cash flows that change because of the decision; exclude sunk costs and unavoidable common fixed costs.
• Special-order decisions: With idle capacity, an order below normal price may be accepted if its revenue covers incremental variable costs, special fixed costs, and opportunity cost.
• Pricing decisions: Contribution analysis establishes a short-term minimum price, but long-run prices must also recover fixed costs and provide an adequate return.
• Shutdown decisions: Temporary operation is preferable when contribution exceeds avoidable fixed costs; unavoidable fixed costs continue even after shutdown.
• Discontinuation decisions: A product should not be dropped merely because allocated full cost shows a loss. Dropping it is beneficial only if avoidable fixed-cost savings exceed contribution lost.
• Sell or process further: Joint costs incurred before the split-off point are sunk; further processing is worthwhile when incremental revenue exceeds incremental processing cost.
• Capacity decisions: The value of scarce capacity equals the contribution sacrificed by its next-best use, creating an opportunity cost.
• Limitations: Qualitative factors such as quality, employee effects, supplier reliability, customer relationships, and long-term strategy must accompany the numerical result.

V. Sourcing Choice — Internal Production versus External Supply

A. Make or buy decision

A make-or-buy decision compares the relevant cost of producing a component internally with the relevant cost of purchasing it from an outside supplier.

• Relevant cost of making: Include direct materials, direct labour, variable overhead, avoidable fixed cost, and opportunity cost of capacity used.
• Relevant cost of buying: Include purchase price, transport, inspection, handling, and any other incremental procurement cost.
• Comparison rule:

Make if: Relevant cost of making < Relevant cost of buying
Buy if: Relevant cost of buying < Relevant cost of making

• Unavoidable fixed cost: Existing rent, depreciation, or supervision that continues under either option is irrelevant because it does not differ between alternatives.
• Opportunity cost: If internal capacity could earn contribution from another product, the lost contribution must be added to the cost of making.
• Example: A component has variable manufacturing cost of ₹24, avoidable fixed cost of ₹3, and opportunity cost of ₹4 per unit. Its relevant make cost is ₹31. A supplier price of ₹29 favours buying by ₹2 per unit.
• Qualitative factors: Final judgment should consider supplier reliability, quality control, confidentiality, delivery continuity, workforce implications, and dependence on external vendors.

VI. Output Selection — Optimizing the Sales and Production Mix

A. Product mix decision

A product mix decision determines the combination of products that maximizes total contribution when resources or market demand are limited.

• No limiting factor: When capacity is sufficient, products are generally ranked by contribution per unit, subject to demand and strategic considerations.
• Single limiting factor: Products must be ranked by contribution per unit of the scarce resource.

Contribution per limiting-factor unit
= Contribution per product unit ÷ Scarce resource required per product unit

• Possible constraints: The limiting factor may be machine hours, labour hours, kilograms of material, production space, finance, or maximum market demand.
• Selection procedure:
  1. Calculate contribution per unit for each product.
  2. Identify the scarce resource and each product’s resource requirement.
  3. Calculate contribution per unit of the limiting factor.
  4. Rank products from highest to lowest ratio.
  5. Allocate the resource in rank order, subject to demand and contractual commitments.
• Example: Product A contributes ₹30 and uses 3 machine hours, yielding ₹10 per machine hour. Product B contributes ₹24 and uses 2 hours, yielding ₹12 per machine hour. With machine hours scarce, B receives priority despite its lower contribution per product unit.
• Multiple constraints: Where several resources are simultaneously scarce, simple ranking may not produce the optimum mix; linear programming is then more appropriate.
• Decision boundary: Customer continuity, minimum product ranges, technical dependencies, and long-term market effects may justify a mix that differs from the short-term numerical optimum.