Question

1. A small business company is considering updating the current production line. There are two plans. For plan A, the fixed cost will be $42,000 and the variable cost will be $29 per unit after the update. For plan B, the fixed costs will be $44,000 and the variable cost will be $28 per unit after the update. Please answer the following questions:
(a) Suppose the selling price is $50, what is the break-even volume for each plan? Which plan has a lower break-even volume?

(b) Suppose the selling price is $50. Also, the company aims to achieve a profit of $21,000 after the update. What selling volume will be required to achieve the profit for each plan? Which plan has a lower volume?

Answer 1

Answer- 1 (a)

Break- even point (units) = Fixed cost / (Selling price per unit - variable cost per unit)

For A, Break- even point = 42000/(50-29) = 42000/21= 2000.

For B, Break-even point = 44000/(50-28) = 44000/22= 2000.

Both the plant have same volume of break-even point.

Answer- 1 (b)

Profit = {(Selling price × number of units) - [Fixed cost + (variable cost× number of units)]}

For plant A-  

u = number of units.

21000 ={(50× u) -[42000 +(29×u)]}

21000= {50u-[42000+29u]}

21000= 50u -42000-29u

21000 + 42000 = 50u-29u

63000= 21u

63000/21= u

3000= u

Plant A needs to sell 3000 units to achieve 21000 dollar profit.

For Plant B -

Z = number of units

21000 = {(50 ×z) - [44000 + (28 × z)]}

21000 = {50z - [44000+ 28z]}

21000= 50z -44000 - 28z

21000+44000 = 50z-28z

65000 = 22z

z= 65000/22= 2954.59 units or 2955 units

Plant A needs more units to achieve 21000 dollar profit.

Plant B has the lower volume (2955).