Question

Paddleboard Incorporated builds three products: River, Lake, and Ocean. Information for these three products is shown below: River Lake Ocean Total Selling price per unit $310 $260 $270 Variable cost per unit $150 $125 Expected unit sales (annual) 2,000 4,000 20,000 Sales mix 10% 20% 100% Total annual fixed costs are $760,000. Assume the sal les mix remains the same at all levels of sales. (1) a. How many products in total must be sold to break b. How many units of each product must be sold to break even? (2) a. How many products in total must be sold to earn an annual profit of $1.280,000? b. How many units of each product must be sold to cam an annual profit of $1.280,000? SHOW YOUR WORK HTML Editor BIVA-A- IE 3

Answer 1

Answer-1(a):

Break even point = Total fixed cost ÷ (Weighted Avg. Selling Price - Weighted Avg. Variable Expense)

                           = $760,000 / ($297* - $162.50**)

                          = $760,000 / $134.50

                          = 5651 units

*Weighted average selling price:
= ($310 × 70%) + ($260 × 10%) + ($270 × 20%)
= $217 + $26 + $54
= $297

**Weighted average variable expense:
= ($175 × 70%) + ($150 × 10%) + ($125 × 20%)
= $122.50 + $15 + $25
= $162.50

Hence, 5,651 units in total must be sold to break even.

Answer-1(b)

Calculation of the number of units of each product to be sold:

Product River (5,651 × 70%): 3,962 units (adjusted to get exact figure)
Product Lake (5,651 × 10%): 565 units
Product Ocean (5,651 × 20%): 1,124 units (adjusted to get exact figure)
Total:3,962 units + 565 units + 1,124 units = 5,651 units

Answer-2(a)

The company needs to cover $760,000 of fixed expenses plus earn $1,280,000 of profit .

In essence the company needs to cover the equivalent of $2,040,000 of fixed expenses

The amount of sales necessary to give the owner a profit of $1,280,000 is determined by this break-even point formula:

= Fixed expense / Contribution margin

= $2,040,000 / $134.50 = 15,167 units in total

Answer-2(b)

Calculation of the number of units of each product to be sold to achieve desired net income of $1,280,000:

Product River (15,167 × 70%): 10,612 units (adjusted to get exact figure)
Product Lake (15,167 × 10%): 1,517 units
Product Ocean (15,167 × 20%): 3,038 units (adjusted to get exact figure)
Total:10,612 units + 1,517 units + 3,038 units = 15,167 units