Question

1.            The All Natural Food Market is a merchandiser of organic food items. The company is considering the possibility of selling pomegranates that would sell for $0.59 each.   Pomegranates can be acquired in unlimited quantities for $0.43 each.   There are no additional variable costs associated with acquiring and selling pomegranates since labor is on a salaried basis.   However, in order to acquire pomegranates at this price, All Natural Food Market must pay $3,000 per year for membership in an International co-op.

a.            How many pomegranates would All Natural Food Market need to sell annually to justify joining the co-op (break-even)?

b.            What would be the total revenue at the break-even point?

c.             How many pomegranates would the company need to sell to earn a profit of $5,000?

d.            If pomegranates cost were $0.51 instead of $0.43, how many pomegranates would need to be sold to earn the same $5,000?

e.            If the Market considers the possibility of diversifying its products by also selling mangos that would sell for $0.34 each, with a cost of $0.24 each, and anticipates a sales mix of 50% of each fruit, how many of each fruit would the Market need to sell to break-even? (use the initial assumptions for the pomegranate information and fixed costs)

Answer 1

Solution a:

Selling price of pomegranates = $0.59

Variable cost of pomegranates = $0.43

Contribuiton per pomegranates = $0.59 - $0.43 = $0.16

Annual membership fee of International Coop (Fixed cost) = $3,000

Nos of pomegranates to sold to justify joining the coop = $3,000 / $0.16 = 18750 pomegranates

Solution b:

Total revenue at breakeven point = Breakeven point * selling price per unit = 18750 * $0.59 = $11,062.50

Solution c:

Required profit = $5,000

Required contribution = $5,000 + $3,000 = $8,000

nos of pomegranates to be sold to earn desired profit = Desired contribution / Contribution per unit = $8,000 / 0.16 = 50000 pomegranates

Solution d:

If pomegranates cost is $0.51, then revise contribution per unit = $0.59 - $0.51 = $0.08

Nos of pomegranates to sold to earn profit of $5,000 = $8,000 / 0.08 = 100000 pomegranates

Solution e:

Selling price of mango = $0.34

Variable cost of mango = $0.24

Contribution per mango = $0.34 - $0.24 = $0.10

Contributon per pomegranates = $0.16

Sales mix = 50% each fruit

Weighted average contribution margin per unit = $0.10 * 50% + $0.16 * 50% = $0.13 per fruit

Nos of fruit to be sold to breakeven = Fixed cost / Weighted average contribution per fruit = $3,000 / $0.13 = 23077 fruits

Nos of mango to be sold = 23077*50% = 11538.50

Nos of pomegranates to be sold = 23077*50% = 11538.50