Marginal Costing and CVP Analysis: P/V Ratio, Break-even Point and Profit Planning

Overview

Cost-Volume-Profit (CVP) analysis studies the relationship between:

• cost (fixed and variable),
• volume (units/sales), and
• profit.

Marginal costing is the technique that supports CVP analysis. The central idea is contribution:

[ \text{Contribution} = \text{Sales} - \text{Variable Cost} ]

Contribution first covers fixed cost, and the balance becomes profit.

[ \text{Profit} = \text{Contribution} - \text{Fixed Cost} ]

This topic is very scoring because formulas are standard and questions are mostly calculation + interpretation.

Meaning of marginal costing

Marginal costing is a technique of cost control and decision-making in which:

• variable costs are charged to cost units (products), and
• fixed costs are treated as period costs and written off against profit of the period.

The marginal cost of a unit is essentially its variable cost (variable material + variable labour + variable overhead).

Key assumptions of marginal costing (important)

Most CVP formulas work under these assumptions:

• selling price per unit is constant (within the relevant range)
• variable cost per unit is constant
• total fixed cost is constant (within the relevant range)
• volume is the only factor affecting costs/revenue
• production = sales (or inventory changes are ignored) in basic problems
• product mix is constant in multi-product cases

In exams, write 3–4 assumptions if asked.

Contribution: meaning and formulas

Contribution shows how much sales “contributes” towards fixed cost and profit.

Formulas:

• Contribution (total) = Sales − Variable cost
• Contribution per unit = Selling price per unit − Variable cost per unit
• Profit = Contribution − Fixed cost

Sometimes “C/S ratio” is used for P/V ratio.

P/V ratio: meaning and interpretation

P/V ratio (Profit-Volume ratio) measures contribution as a proportion of sales.

[ \text{P/V ratio} = \frac{\text{Contribution}}{\text{Sales}} \times 100 ]

Interpretation:

• Higher P/V ratio means higher contribution per rupee of sales.
• It improves when selling price increases or variable cost decreases.

Useful shortcut:

• If you know P/V ratio, then Contribution = Sales × P/V ratio.

Break-even point (BEP): meaning and formulas

Break-even point is the sales level at which profit is zero (no profit, no loss).

At BEP: Contribution = Fixed cost.

Common formulas:

1. BEP (units): [ \text{BEP (units)} = \frac{\text{Fixed cost}}{\text{Contribution per unit}} ]

2. BEP (sales value): [ \text{BEP (₹)} = \frac{\text{Fixed cost}}{\text{P/V ratio}} ]

(Use P/V ratio in decimal form, e.g., 40% = 0.40.)

Margin of safety (MOS)

Margin of safety indicates how much sales can fall before the firm reaches break-even.

[ \text{MOS} = \text{Actual sales} - \text{BEP sales} ]

[ \text{MOS%} = \frac{\text{MOS}}{\text{Actual sales}} \times 100 ]

Higher MOS means safer position (lower risk of loss).

Profit-volume relationship (simple chart idea)

• At low sales: contribution is not enough to cover fixed cost → loss.
• At BEP: total contribution = fixed cost → profit = 0.
• Above BEP: contribution exceeds fixed cost → profit increases linearly.

A simple visual:

Profit
  ^
  |           /
  |          /
  |         /
  |________/____________> Sales
          BEP

Worked example 1: contribution, PV ratio, BEP and MOS

Given:

• Selling price per unit (SP) = ₹100
• Variable cost per unit (VC) = ₹60
• Fixed cost (FC) = ₹20,000
• Actual sales = 500 units

Step 1: Contribution per unit Contribution/unit = SP − VC = 100 − 60 = ₹40

Step 2: P/V ratio P/V ratio = Contribution / Sales

Contribution per unit = ₹40, Sales per unit = ₹100 So P/V ratio = 40/100 = 0.40 or 40%

Step 3: Break-even point (units) BEP (units) = FC / Contribution per unit = 20,000 / 40 = 500 units

Step 4: Actual profit at 500 units Sales = 500 × 100 = ₹50,000 Variable cost = 500 × 60 = ₹30,000 Contribution = 20,000 Profit = Contribution − FC = 20,000 − 20,000 = ₹0 (break-even)

Step 5: Margin of safety Actual sales (units) = 500 BEP sales (units) = 500 MOS = 500 − 500 = 0 units MOS% = 0/500 × 100 = 0%

Interpretation: Company is exactly at break-even; any fall in sales will cause loss.

Worked example 2: sales required for target profit

Using the same data (SP ₹100, VC ₹60, FC ₹20,000). Find sales required for profit of ₹10,000.

Step 1: Required contribution Required contribution = Fixed cost + Target profit = 20,000 + 10,000 = ₹30,000

Step 2: Sales in units Sales (units) = Required contribution / Contribution per unit = 30,000 / 40 = 750 units

Step 3 (optional): Sales value Sales value = 750 × 100 = ₹75,000

Impact of changes (what happens if price/cost/fixed cost changes)

Key idea: BEP depends on fixed cost and contribution per unit.

Limitations of marginal costing

• Assumptions may not hold (price and costs may change).
• Difficult to separate semi-variable costs accurately.
• Ignores inventory valuation issues in detailed financial reporting.
• In multi-product cases, constant sales mix assumption may not be realistic.

Flow: quick steps to solve CVP problems

Common exam mistakes

• Using P/V ratio as 40 instead of 0.40 in formulas.
• Confusing profit on cost vs profit on sales (in other topics).
• Not writing contribution equation (Profit = Contribution − Fixed cost).
• Rounding too early; keep decimals and round at the end.

Key Terms

• Marginal cost: variable cost of a unit.
• Contribution: sales minus variable cost.
• P/V ratio: contribution as % of sales.
• BEP: level of sales where profit is zero.
• MOS: excess of actual sales over BEP sales.

Quick Recap (1-minute revision)

• Contribution = Sales − Variable cost.
• Profit = Contribution − Fixed cost.
• P/V ratio = Contribution/Sales.
• BEP (units) = Fixed cost / Contribution per unit.
• MOS = Actual sales − BEP sales.