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	$175	$150	$125
Expected unit sales (annual)	14,000	2,000	4,000	20,000
Sales mix	70%	10%	20%	100%

Total annual fixed costs are $760,000. Assume the sales mix remains the same at all levels of sales.

(1) a. How many products in total must be sold to break even?
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 earn an annual profit of $1,280,000?

SHOW YOUR WORK

Answer 1

Answer-1-a)- Units sold to break-even = Fixed costs/ Weighted average contribution margin per unit

= $760000/$134.50 per unit

= 5651 units

b)-Units of each product sold at break-even – River = 5651 units*70%= 3956 units

Lake = 5651 units*10%= 565 units

Ocean = 5651 units*20%= 1130 units

Contribution margin per unit = Selling price per unit-Variable cost per unit

River = $310 per unit-$175 per unit = $135 per unit

Lake = $260 per unit-$150 per unit = $110 per unit

Ocean = $270 per unit-$125 per unit = $145 per unit

Weighted average contribution margin per unit =Contribution margin per unit* Sales mix percentage

= ($135 per unit*70%)+($110 per unit*10%)+($145 per unit*20%)

= $94.5 per unit+$11 per unit+$29 per unit

= $134.5 per unit

Answer-2-a)-Units sold to achieve target profit =(Fixed costs+ Target profit)/ Weighted average contribution margin per unit

= ($760000+$1280000)/ $134.5 per unit

= 15167 units

b)-Units of each product sold to achieve target profit – River = 15167 units*70%= 10617 units

Lake = 15167 units*10%= 1517 units

Ocean = 15167 units*20%= 3033 units