Final Answer:
The relative sales mix between the two products is 20% for Power Lite and 80% for Total. The weighted-average contribution margin per unit across both products is $132. The break-even point in total number of units is 627 units. Kidd must sell 127 units of Power Lite and 500 units of Total to break even. The margin of safety, based on combined sales, is $107,600.
Step-by-step explanation:
To determine the relative sales mix, divide the budgeted sales for each product by the total budgeted sales. For Power Lite, $80,000 / $368,000 = 0.217, or 21.7%. For Total, $288,000 / $368,000 = 0.783, or 78.3%. Thus, the sales mix is 21.7% for Power Lite and 78.3% for Total.
The weighted-average contribution margin per unit is found by considering the contribution margin per unit for each product and their respective sales mix. Multiply the contribution margin per unit of Power Lite ($180) by its sales mix (0.217), and do the same for Total ($120 * 0.783). Then sum these values: ($180 * 0.217) + ($120 * 0.783) = $39.06 + $93.96 = $132. This weighted-average contribution margin represents the average contribution per unit across both products.
The break-even point in total number of units is calculated by dividing the total fixed costs ($66,000) by the weighted-average contribution margin per unit ($132), resulting in 500 units. To determine how many units of each product Kidd must sell to break even, use the sales mix percentages. For Power Lite, 500 units * 0.217 = 127 units. For Total, 500 units * 0.783 = 393 units. Therefore, Kidd must sell 127 units of Power Lite and 393 units of Total to break even.
Finally, to find the margin of safety based on combined sales, subtract the break-even sales revenue ($368,000) from the actual budgeted sales revenue ($475,600). The margin of safety is $475,600 - $368,000 = $107,600. This indicates how much sales can decline before the company reaches the break-even point.