Question

Tiago makes three models of camera lens. Its product mix and contribution margin per unit follow:

Percentage of Unit sales Contribution Margin per unit

Lens A 38 % $ 34

Lens B 31% $ 26

Lens C 31% $39

Suppose the product mix has shifted to 43/29/28. Required:

1. Determine the new weighted-average contribution margin per unit. (Round your intermediate calculation to 2 decimal places. Round your answer to 2 decimal places.)

2. Determine the number of units of each product that Tiago must sell to break even if fixed costs are $192,000. (Round intermediate calculations to nearest whole number. Round your answers up to the next whole number.)

3. Determine how many units of each product must be sold to generate a profit of $78,000. (Round intermediate calculations to nearest whole number. Round your answers up to the next whole number.)

Answer 1

1.

Weighted average Contribution margin per unit = (Lens A contribution margin per unit * product mix) + (Lens B contribution margin per unit * product mix) + (Lens C contribution margin per unit * product mix)

= (34 * 43%) + (26 * 29%) + (39 * 28%)

= 14.62 + 7.54 + 10.92

= 33.08

2.

Total number of units to be sold to breakeven = Fixed costs / Weighted average Contribution margin per unit

= 192,000 / 33.08

= 5,804

Number of units of Lens A that Tiago must sell to breakeven = 5,804 * 43% = 2,496

Number of units of Lens B that Tiago must sell to breakeven = 5,804 * 29% = 1,683

Number of units of Lens C that Tiago must sell to breakeven = 5,804 * 28% = 1,625

3.

Total number of units to be sold to generate desired profit = (Fixed costs + desired profit) / Weighted average Contribution margin per unit

= (192,000 + 78,000) / 33.08

= 8,162

Number of units of Lens A that Tiago must sell to attain desired profit = 8,162 * 43% = 3,510

Number of units of Lens B that Tiago must sell to attain desired profit = 8,162 * 29% = 2,367

Number of units of Lens C that Tiago must sell to attain desired profit = 8,162 * 28% = 2,285