Cost Accounting · Marginal Costing

Multi-Product Break-Even and Sales Mix Analysis

Updated 10 October 2026 · Fact-checked

Multi-product break-even finds the sales at which total contribution from all products equals fixed cost. Compute each product's contribution, add them, divide by total sales for the weighted average P/V ratio, then divide fixed cost by it. Split the answer by sales mix. If the mix changes, recompute the ratio.

Understand Multi-Product Break-Even and Sales Mix Analysis

A single-product break-even point is easy: fixed cost divided by contribution per unit. Most firms sell several products, and fixed costs such as rent and salaries are shared by all of them. So you cannot find one break-even point per product unless you know how the fixed cost is split. Instead, you find one composite break-even point for the whole business.

The key idea is the sales mix, the proportion in which products are sold. Each product earns a different P/V ratio. A mix with more high-P/V products gives a higher overall P/V ratio, a lower break-even point and a higher profit. The overall ratio is the weighted average P/V ratio, with sales value as the weights.

So the break-even sales of the firm depend on the mix. If the mix changes, the composite P/V ratio changes, and the break-even point changes with it. Questions often ask you to compare two mixes and recommend the better one. The better mix is the one with the higher composite P/V ratio, provided total sales are the same.

Two related ideas appear in the same chapter. The indifference point is the sales level at which two alternatives (for example two machines or two cost structures) give the same profit. The shutdown point is the sales level below which it is better to stop operations than to continue, because contribution no longer covers the fixed costs that would be saved by stopping.

Key rules to remember

Contribution per unit: Contribution per unit = Selling price per unit − Variable cost per unit; Use variable cost of all kinds: material, labour, variable overheads and variable selling cost.
P/V ratio of a product: P/V ratio = Contribution ÷ Sales × 100; Use totals or per-unit values, but be consistent.
Weighted average (composite) P/V ratio: Composite P/V ratio = Total contribution of all products ÷ Total sales of all products; Equals Σ (P/V ratio of each product × its share in sales value). Weights must be sales value shares, not unit shares.
Composite break-even sales: Break-even sales (₹) = Total fixed cost ÷ Composite P/V ratio; Valid only for the sales mix assumed in the question.
Break-even sales of each product: Product break-even sales = Composite break-even sales × Product's share in sales value; This assumes the mix stays constant.
Break-even in units (bundle method): Bundles to break even = Fixed cost ÷ Contribution per bundle; units of a product = bundles × units of it in one bundle; Use when the mix is given in units, for example 3 units of A to 2 units of B.
Margin of safety and profit: Margin of safety = Actual sales − Break-even sales; Profit = Margin of safety × Composite P/V ratio; Also, Profit = Total contribution − Fixed cost.
Indifference point: Indifference sales = Difference in fixed costs ÷ Difference in P/V ratios; in units = Difference in fixed costs ÷ Difference in contribution per unit; The alternative with higher fixed cost and higher P/V ratio is better above this point; the other is better below it.
Shutdown point: Shutdown sales = Avoidable fixed cost ÷ P/V ratio; in units = Avoidable fixed cost ÷ Contribution per unit; Only fixed costs that would be saved on shutdown count. Unavoidable fixed costs continue anyway.

How to solve Multi-Product Break-Even and Sales Mix Analysis questions

Use this order for any multi-product, sales mix, indifference or shutdown question.

1Write the data for each product in one table: selling price, variable cost, contribution per unit and the sales mix. Convert a unit mix to sales value if the question asks for value.
2Find the contribution and the P/V ratio of each product.
3Compute the composite P/V ratio as total contribution ÷ total sales. Do this by taking a convenient base, such as ₹100 of sales or one bundle of units.
4Find composite break-even sales as fixed cost ÷ composite P/V ratio. Divide it among products in the sales mix to get each product's break-even sales.
5For profit or margin of safety, use Profit = Total contribution − Fixed cost, and cross-check with Margin of safety × composite P/V ratio.
6If a new mix is given, repeat steps 2 to 5 with the new weights and compare. State which mix is better and why.
7For indifference points, equate the profit of the two alternatives or use the difference formula. For shutdown points, identify avoidable fixed cost first and divide by P/V ratio or contribution per unit.
8Close with a one-line interpretation: what the figure means and what the manager should do.

Quickest way: Base of ₹100 sales or one bundle

When to use it: Use when the mix is given as percentages of sales or as a ratio of units and you need the composite P/V ratio fast.

If the mix is in value, take total sales as ₹100 and split it by the mix. Contribution of each = share × its P/V ratio. Add up to get the composite P/V ratio directly.
If the mix is in units, build one bundle (for example 3 of A and 2 of B). Compute contribution and sales of the bundle.
Break-even bundles = fixed cost ÷ contribution per bundle. Multiply by units in the bundle for each product.
For indifference, divide the fixed cost difference by the P/V difference. Test one sales figure on each side to confirm which alternative wins.
Cross-check profit in two ways before writing the final answer.

Common mistakes in Multi-Product Break-Even and Sales Mix Analysis

Averaging the P/V ratios simply, for example (40% + 25%) ÷ 2.
Students forget that products contribute different amounts of sales.
Fix: Always weight by sales value share, or divide total contribution by total sales.
Using the unit mix as the weights for P/V ratio.
The question gives the mix in units, and students apply it to ratios.
Fix: Convert units to sales value first, or use the bundle method with contribution per bundle.
Reusing the old break-even point after the sales mix changes.
Students treat break-even as a fixed number for the firm.
Fix: Recompute the composite P/V ratio for each mix and then the break-even sales.
Using total fixed cost for the shutdown point.
Students confuse shutdown with break-even.
Fix: Use only the avoidable fixed cost. Unavoidable fixed cost is a loss whether or not you operate.
Wrong choice between alternatives near the indifference point.
Students find the point but do not say which alternative is better on each side.
Fix: The alternative with the higher P/V ratio (and higher fixed cost) is better above the point; the other is better below it. Verify with a test value.
Allocating the shared fixed cost to products before finding break-even.
Students want a break-even point for each product and split the fixed cost arbitrarily.
Fix: Find the composite break-even point first, then divide it by the sales mix, unless the question gives specific fixed costs.

Worked examples

Example 1

Sundaram Foods sells two products, A and B, in the value ratio 60:40. Total sales are ₹10,00,000. P/V ratio of A is 40% and of B is 25%. Fixed cost is ₹1,02,000. Find (a) the composite P/V ratio, (b) break-even sales of each product, (c) profit, and (d) profit and break-even sales if the mix changes to 40:60 with the same total sales.

Show the solution

Sales: A = ₹6,00,000; B = ₹4,00,000.
Contribution: A = 40% × 6,00,000 = ₹2,40,000; B = 25% × 4,00,000 = ₹1,00,000. Total = ₹3,40,000.
(a) Composite P/V ratio = 3,40,000 ÷ 10,00,000 = 34%.
(b) Break-even sales = 1,02,000 ÷ 0.34 = ₹3,00,000. A = 60% × 3,00,000 = ₹1,80,000; B = 40% × 3,00,000 = ₹1,20,000.
(c) Profit = 3,40,000 − 1,02,000 = ₹2,38,000. Check: margin of safety = 10,00,000 − 3,00,000 = ₹7,00,000; × 34% = ₹2,38,000.
(d) New mix 40:60 gives A sales ₹4,00,000 and B sales ₹6,00,000. A contribution = 40% × 4,00,000 = ₹1,60,000; B contribution = 25% × 6,00,000 = ₹1,50,000. Total = ₹3,10,000.
New composite P/V ratio = 3,10,000 ÷ 10,00,000 = 31%. New profit = 3,10,000 − 1,02,000 = ₹2,08,000.
New break-even sales = 1,02,000 ÷ 0.31 = ₹3,29,032 (approx.).
Interpretation: the 40:60 mix has a lower composite P/V ratio, so break-even rises and profit falls by ₹30,000. The 60:40 mix is better.

Answer: (a) 34%. (b) A ₹1,80,000 and B ₹1,20,000, total ₹3,00,000. (c) Profit ₹2,38,000. (d) Composite P/V ratio 31%, profit ₹2,08,000, break-even sales about ₹3,29,032. The original 60:40 mix is better.

Example 2

Kaveri Plastics can use Machine X or Machine Y. Machine X has fixed cost ₹4,00,000 and variable cost 60% of sales. Machine Y has fixed cost ₹7,00,000 and variable cost 45% of sales. (a) Find the indifference point. (b) Which machine is better at sales of ₹16,00,000 and ₹25,00,000? (c) For Machine Y, ₹2,20,000 of its fixed cost is avoidable if operations stop. Find the shutdown sales.

Show the solution

P/V ratio: X = 100% − 60% = 40%; Y = 100% − 45% = 55%.
(a) Indifference sales = (7,00,000 − 4,00,000) ÷ (55% − 40%) = 3,00,000 ÷ 0.15 = ₹20,00,000.
Check: X profit = 40% × 20,00,000 − 4,00,000 = 8,00,000 − 4,00,000 = ₹4,00,000. Y profit = 55% × 20,00,000 − 7,00,000 = 11,00,000 − 7,00,000 = ₹4,00,000. Equal.
(b) At ₹16,00,000: X = 6,40,000 − 4,00,000 = ₹2,40,000; Y = 8,80,000 − 7,00,000 = ₹1,80,000. X is better.
At ₹25,00,000: X = 10,00,000 − 4,00,000 = ₹6,00,000; Y = 13,75,000 − 7,00,000 = ₹6,75,000. Y is better.
(c) Shutdown sales for Y = Avoidable fixed cost ÷ P/V ratio = 2,20,000 ÷ 0.55 = ₹4,00,000.
Meaning: below sales of ₹4,00,000, Y's contribution is less than the ₹2,20,000 fixed cost that stopping would save, so shutting down is better.

Answer: (a) Indifference point ₹20,00,000. (b) Machine X at ₹16,00,000; Machine Y at ₹25,00,000. (c) Shutdown sales of Machine Y ₹4,00,000.

Exam tips

In the MCQ section, most questions here ask for composite P/V ratio, break-even sales or the indifference point. Use the ₹100 base and finish in under two minutes. Check that the four options differ before guessing.
In written answers, show a table of product data first, then the composite ratio, then break-even. Step marks are given for each of these lines.
If a question gives a new mix, always compare the two composite P/V ratios and write a recommendation. Interpretation earns marks.
For shutdown questions, separate avoidable and unavoidable fixed costs in a small list before calculating. Do not use total fixed cost.
Write the formula before substituting numbers, and round only the final answer to the nearest rupee.

Practice questions from Marginal Costing

Multi-Product Break-Even and Sales Mix Analysis in other exams

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

Multi-Product Break-Even and Sales Mix Analysis: frequently asked questions

How do you calculate break-even point for multiple products?

Find total contribution and total sales at the given mix, and divide to get the composite P/V ratio. Then divide total fixed cost by this ratio. Split the result among products in the sales mix.

What is the indifference point in cost volume profit analysis?

It is the sales level at which two alternatives give the same profit, for example two machines with different fixed costs and P/V ratios. Compute it as the difference in fixed costs divided by the difference in P/V ratios. Above it the higher fixed cost option wins if it has the higher P/V ratio.

What is the shutdown point in marginal costing?

It is the sales level at which contribution just equals the fixed cost that would be saved by stopping operations. Below it, shutting down is better. Use only avoidable fixed cost: shutdown sales = avoidable fixed cost ÷ P/V ratio.

Why does the break-even point change when the sales mix changes?

Each product has a different P/V ratio, so changing the mix changes the weighted average P/V ratio. A lower composite ratio means each rupee of sales covers less fixed cost, so break-even sales rise.