|
Answer (C) is correct.
The solutions approach is to divide the total fixed costs by the weighted average unit contribution margin. The total fixed costs are $27,000,000 ($5,000,000 + $12,000,000 + $10,000,000). The total sales for the three products would be $10,000,000, $35,000,000, and $24,000,000, or a total of $69,000,000. The unit contribution margins are $600, $2,000, and $4,000. Multiply these unit margins by the budgeted sales to get the total contribution margin from each product: $600 × 10,000 units = $6,000,000 for Product 1. For Product 2, multiply the $2,000 margin by 7,000 units to get $14,000,000, and for Product 3, multiply the 4,000 margin times the 3,000 units to get $12,000,000. Adding the three contribution margins together, you get a total budgeted CM of $32,000,000. If the question had asked for an allocation based on physical quantity, which it did not, the next step would have been to divide the $32,000,000 total CM by the 20,000 total units to get an average CM of $1,600 per unit. Next, divide the $27,000,000 of fixed costs by the $1,600 unit CM to arrive at a breakeven point of 16,875. However, based on weighted sales, divide the $10,000,000 of Product 1 sales by the total sales of $69,000,000 to find that Product 1 makes up 14.4927% of total sales. Product 2 makes up 50.724638%, while Product 3 composes 34.782609% of total sales. Multiply these percentages by the respective unit contribution margins to get the composite unit CM: ($600 × .144927) + ($2,000 × .507246) + ($4,000 × .3478926) = $2,492.7536. Divide the $27,000,000 of fixed costs by $2,492.7536 to get 10,830 units. |