A blended CM ratio; the composite unit; a mix shift moves break-even
◈ 7 cardsCompute a multi-product break-even by the blended CM ratio (sales-dollar mix), split it back to products, show the same answer by composite unit, and explain why a shift in mix changes break-even at constant total sales.
Three lines, one break-even
Northlake Nordic Centre Inc. does not sell only day passes. Widen the picture to three lines, each with its own contribution margin ratio:
| Line | Sales | Mix (by dollars) | CM ratio |
|---|---|---|---|
| Day and season passes | 600,000 | 60 % | 0.70 |
| Rentals | 200,000 | 20 % | 0.55 |
| Café | 200,000 | 20 % | 0.40 |
| Total | 1,000,000 | 100 % |
Total fixed costs across the business are 427,000. There is no single unit any more — a skier-day, a rental and a sandwich are not one thing — so break-even is found in dollars, using a blended CM ratio weighted by each line's share of sales dollars:
The unweighted mean of the three ratios, 0.55, is wrong — passes are three-fifths of the business and their 0.70 must count for three-fifths. Then:
split back to the lines in the mix: passes 60 % = 420,000, rentals 140,000, café 140,000. The split is part of the answer: a break-even of 700,000 is only true at this mix, and the marker wants to see that you know it. In Excel the blended ratio is =SUMPRODUCT(mix, ratios).
The mix shifts
Suppose the café and the rental shop grow faster than the passes, so that the mix becomes 50 / 25 / 25 — with total sales unchanged at 1,000,000. The blended ratio falls:
and break-even rises to 427,000 ÷ 0.5875 = 726,808.51. Nothing changed in the total, in any price, in any cost — only the proportion of the sales dollars that come from the low-ratio lines, and that alone moved break-even up by 26,809. A business that drifts toward its lower-margin products needs more sales to stay whole, which is why a case will give you the mix in two years and ask what happened.
The composite unit
When the products do have units and sell in a fixed proportion, the same answer comes from a composite unit — a bundle in the sales-mix ratio. Bramble Lane Outfitters Ltd. sells three headlamps (CM 22 each) for every pair of trail shoes (CM 40). One bundle contributes 3 × 22 + 1 × 40 = 106. With fixed costs of 53,000, the store breaks even at 53,000 ÷ 106 = 500 bundles — 1,500 headlamps and 500 pairs of shoes. The blended-ratio route on the same data gives the same dollar figure; the two methods are one method with the unit chosen differently, and a case that asks for units wants the composite.