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Management Accounting · Marginal Costing (Management Accounting)

CVP Analysis and P/V Ratio for CMA Intermediate

Updated 10 October 2026 · Fact-checked

CVP analysis studies how cost, sales volume and profit move together. Contribution is sales minus variable cost. P/V ratio is contribution ÷ sales × 100. Break-even sales = fixed cost ÷ P/V ratio. Margin of safety is actual sales minus break-even sales. Find the P/V ratio first, then solve for sales or profit.

Understand Cost-Volume-Profit (CVP) Analysis and P/V Ratio

Cost-Volume-Profit (CVP) analysis shows how profit changes when sales volume, selling price or cost changes. It rests on marginal costing, which splits cost into variable cost and fixed cost.

Contribution is sales minus variable cost. It first pays for fixed cost. Once fixed cost is covered, every further rupee of contribution is profit. So Profit = Contribution − Fixed cost.

The P/V ratio (profit-volume ratio, also called contribution to sales ratio) tells you how much of each rupee of sales becomes contribution. A P/V ratio of 40% means ₹0.40 of every ₹1 of sales is contribution. As long as selling price and variable cost per unit stay constant, the ratio is the same at every sales level. That is why you can use it to find profit, sales or break-even directly.

The break-even point is the sales level where contribution equals fixed cost and profit is nil. The margin of safety is how far actual sales are above break-even. A larger margin means the business can lose more sales before it makes a loss.

CVP assumes a single product or a constant sales mix, fixed cost constant within the relevant range, and variable cost per unit constant. State these if the question asks for limitations.

Key rules to remember

Contribution
Contribution = Sales − Variable cost = Fixed cost + Profit
Per unit: Contribution per unit = Selling price per unit − Variable cost per unit.
P/V ratio
P/V ratio = Contribution ÷ Sales × 100
Also = Change in profit ÷ Change in sales × 100, when fixed cost is unchanged and price and variable cost per unit are constant.
Variable cost ratio
Variable cost ratio = Variable cost ÷ Sales × 100 = 100% − P/V ratio
Use this to move between the two ratios.
Break-even sales (value)
BEP (₹) = Fixed cost ÷ P/V ratio
Break-even units = Fixed cost ÷ Contribution per unit.
Sales for a target profit
Required sales (₹) = (Fixed cost + Target profit) ÷ P/V ratio
Units = (Fixed cost + Target profit) ÷ Contribution per unit.
Margin of safety
MoS (₹) = Actual sales − Break-even sales = Profit ÷ P/V ratio
MoS ratio = MoS ÷ Actual sales × 100.
Profit from margin of safety
Profit = Margin of safety × P/V ratio
Above break-even, only contribution counts, since fixed cost is already recovered.

How to solve Cost-Volume-Profit (CVP) Analysis and P/V Ratio questions

Use this order for most CVP questions. It keeps the working short and avoids unit and value mix-ups.

  1. 1List the data: sales, variable cost, fixed cost, profit. Mark which are totals and which are per unit.
  2. 2Find contribution: Sales − Variable cost, or Fixed cost + Profit if variable cost is not given.
  3. 3Compute the P/V ratio = Contribution ÷ Sales × 100. If two periods are given, use change in profit ÷ change in sales.
  4. 4Find break-even sales = Fixed cost ÷ P/V ratio. Convert to units if asked.
  5. 5Find margin of safety = Actual sales − Break-even sales, or Profit ÷ P/V ratio. Express as a percentage of sales if asked.
  6. 6For a changed situation (new price, cost or target profit), recompute contribution or P/V ratio first, then reapply the formulas.
  7. 7Show each formula and substitution, then write the final answer with units (₹ or units) and a one-line interpretation.

Quickest way: P/V ratio shortcut using profit and margin of safety

When to use it: Use when the question gives sales, profit and fixed cost, or two periods of data, and asks for break-even, margin of safety or profit at a new sales level.

  1. Get the P/V ratio from one quick line: Contribution ÷ Sales, or Δ Profit ÷ Δ Sales.
  2. Break-even = Fixed cost ÷ P/V ratio.
  3. Profit at any sales level = Sales × P/V ratio − Fixed cost.
  4. Margin of safety = Profit ÷ P/V ratio.
  5. Check: contribution at break-even must equal fixed cost.

Common mistakes in Cost-Volume-Profit (CVP) Analysis and P/V Ratio

  • Using total cost instead of variable cost to find contribution.

    Students see 'cost' in the question and subtract all of it from sales.

    Fix: Subtract only variable cost. Fixed cost is deducted from contribution to get profit.

  • Using Δ profit ÷ Δ sales when fixed cost has changed.

    The shortcut is memorised without its condition.

    Fix: Use it only when fixed cost is the same in both periods and price and variable cost per unit are constant. Otherwise compute contribution directly.

  • Dividing fixed cost by the P/V ratio in percent form without converting.

    Mixing 40 with 0.40 gives answers 100 times too large.

    Fix: Write the ratio as a fraction or decimal (40% = 0.40) before dividing.

  • Writing margin of safety as actual sales minus break-even units, mixing value and units.

    Break-even is calculated in units but sales are in rupees.

    Fix: Convert both to the same unit first. State the unit in the answer.

  • Adding a rise in fixed cost to variable cost when a question changes costs.

    Students treat every increase as a change in the P/V ratio.

    Fix: A fixed cost change alters break-even and profit but not the P/V ratio. Only price or variable cost changes alter it.

  • Writing only the answer with no formula or interpretation.

    Students rush in written questions worth 14 marks.

    Fix: Write the formula, the substitution and the result on separate lines. Add a line such as 'the firm can lose 25% of sales before incurring a loss'.

Worked examples

Example 1

A company sells 20,000 units at ₹50 per unit. Variable cost is ₹30 per unit and fixed cost is ₹3,00,000. Calculate (a) contribution per unit and P/V ratio, (b) break-even sales in units and rupees, (c) margin of safety and profit.

Show the solution
  1. Contribution per unit = 50 − 30 = ₹20.
  2. P/V ratio = 20 ÷ 50 × 100 = 40%.
  3. Break-even units = 3,00,000 ÷ 20 = 15,000 units.
  4. Break-even sales = 15,000 × 50 = ₹7,50,000. Check: 3,00,000 ÷ 0.40 = ₹7,50,000.
  5. Actual sales = 20,000 × 50 = ₹10,00,000.
  6. Margin of safety = 10,00,000 − 7,50,000 = ₹2,50,000, which is 5,000 units. MoS ratio = 2,50,000 ÷ 10,00,000 × 100 = 25%.
  7. Profit = MoS × P/V ratio = 2,50,000 × 0.40 = ₹1,00,000. Check: total contribution 20,000 × 20 = 4,00,000, less fixed cost 3,00,000 = ₹1,00,000.

Answer: Contribution per unit ₹20; P/V ratio 40%; break-even 15,000 units or ₹7,50,000; margin of safety ₹2,50,000 (25% of sales); profit ₹1,00,000.

Example 2

A firm had sales of ₹8,00,000 and profit of ₹60,000 in one year. In the next year sales were ₹10,00,000 and profit was ₹1,00,000. Fixed cost is the same in both years. Find (a) P/V ratio, (b) fixed cost, (c) break-even sales, (d) sales needed for a profit of ₹1,60,000.

Show the solution
  1. Change in profit = 1,00,000 − 60,000 = ₹40,000.
  2. Change in sales = 10,00,000 − 8,00,000 = ₹2,00,000.
  3. P/V ratio = 40,000 ÷ 2,00,000 × 100 = 20%.
  4. Contribution in year 1 = 8,00,000 × 0.20 = ₹1,60,000.
  5. Fixed cost = Contribution − Profit = 1,60,000 − 60,000 = ₹1,00,000. Check with year 2: 10,00,000 × 0.20 = 2,00,000; less 1,00,000 = ₹1,00,000 profit.
  6. Break-even sales = 1,00,000 ÷ 0.20 = ₹5,00,000.
  7. Sales for profit ₹1,60,000 = (1,00,000 + 1,60,000) ÷ 0.20 = 2,60,000 ÷ 0.20 = ₹13,00,000.

Answer: P/V ratio 20%; fixed cost ₹1,00,000; break-even sales ₹5,00,000; sales required for ₹1,60,000 profit is ₹13,00,000.

Exam tips

  • In MCQs, work in the P/V ratio form. Most answers need only one division after you find the ratio.
  • Check which items are given. If only sales and profit for two periods appear, the question is hinting at the Δ profit ÷ Δ sales method.
  • Use the identity Profit = MoS × P/V ratio to check or shortcut margin of safety questions.
  • In written answers, set out a short marginal cost statement (sales, variable cost, contribution, fixed cost, profit) before the ratios. It earns step marks even if a later figure is wrong.
  • Read the last line of the question. Some ask for margin of safety in units, some in rupees and some as a percentage.

Practice questions from Marginal Costing (Management Accounting)

Cost-Volume-Profit (CVP) Analysis and P/V Ratio in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Cost-Volume-Profit (CVP) Analysis and P/V Ratio: frequently asked questions

What is the P/V ratio and why is it useful?

The P/V ratio is contribution as a percentage of sales. It is useful because it stays constant when price and variable cost per unit are constant. You can use it to find break-even sales, profit at any sales level and margin of safety without recalculating costs.

How do I calculate margin of safety?

Margin of safety is actual sales minus break-even sales. You can also compute it as profit ÷ P/V ratio. Divide by actual sales to express it as a percentage.

Does a change in fixed cost change the P/V ratio?

No. The P/V ratio depends only on selling price and variable cost. A change in fixed cost changes the break-even point and profit, but not the ratio.

Is contribution the same as profit?

No. Contribution is sales minus variable cost. Profit is contribution minus fixed cost. The two are equal only when fixed cost is zero.