Northlake Nordic Centre Inc. has three lines: passes (sales 600,000, CM ratio 0.70), rentals (200,000, 0.55) and café (200,000, 0.40); fixed costs total 427,000. Compute the blended CM ratio (four decimals), break-even in total sales dollars, the break-even sales of passes and of rentals, and break-even in total sales dollars if the mix shifts to 50/25/25 with total sales unchanged (to the cent).
Northlake Nordic Centre Inc. has three lines: passes (sales 600,000, CM ratio 0.70), rentals (200,000, 0.55) and café (200,000, 0.40); fixed costs total 427,000. Compute the blended CM ratio (four decimals), break-even in total sales dollars, the break-even sales of passes and of rentals, and break-even in total sales dollars if the mix shifts to 50/25/25 with total sales unchanged (to the cent).
Answer
Blended contribution margin ratio → 0.61 · Break-even in total sales dollars → 700000 · Break-even sales of day passes → 420000 · Break-even sales of rentals → 140000 · Break-even in total sales dollars if the mix shifts to 50/25/25 → 726808.51
Cells - Blended contribution margin ratio · ±0.0005 - Break-even in total sales dollars · ±0 - Break-even sales of day passes · ±0 - Break-even sales of rentals · ±0 - Break-even in total sales dollars if the mix shifts to 50/25/25 · ±0.5 Mix 60/20/20. Blended = 0.6 × 0.70 + 0.2 × 0.55 + 0.2 × 0.40 = **0.61**. Break-even = 427,000 ÷ 0.61 = **700,000**; passes 60 % = **420,000**, rentals 20 % = **140,000** (café 140,000). Shifted: 0.5 × 0.70 + 0.25 × 0.55 + 0.25 × 0.40 = 0.5875; 427,000 ÷ 0.5875 = **726,808.51**. Excel: `=SUMPRODUCT(mix, ratios)`.
Hermanson Vol 2 ch 21 (the sales-dollar mix — shape adapted); OpenStax Managerial Accounting §3.4 (the composite unit — reference) (concept map J10–J12)