Answer:
A) Contribution margin : Product X: $8; Product Y: $12
B)The expected net income: $18,000
C) Break-even point in units for each product is Product X 19,500 units, Product Y 6,500 units.
D) Break-even point in units for each product is Product X 14,625 units, Product Y 9,750 units.
Explanation:
A) Contribution margin for each product:
Product X = Selling price of X - Variable cost of X = 46 - 38 = $8
Product Y = Selling price of Y - Variable cost of Y = 36 - 24 = $12
B) The expected net income:
Expected net income = Contribution margin of product X x Units of Product X sold + Contribution margin of product Y x Units of Product Y sold - Fixed cost = 8 x 21,000 + 12 x 7,000 - 234,000 = $18,000
C) The break-even point in units for each product assuming the sales mix is 3 units of Product X for every 1 unit of Product Y:
Denote a is the number of Y BEP (in units) => 3a is the number of X in BEP (in units)
We have 3a x 8 + a x 12 = 234,000 <=> 36a = 234,000 <=> a = $6,500 <=> 3a = 19,500
Thus, break-even point in units for each product is Product X 19,500 units, Product Y 6,500 units.
D) The break-even point in units for each product assuming the sales mix is 3 units of Product X for every 2 units of Product Y:
Denote b is the number of Y BEP (in units) => 3b/2 is the number of X in BEP (in units)
We have 3b/2 x 8 + b x 12 = 234,000 <=> 24b = 234,000 <=> b = $9,750 <=> 3b/2 = 14,625
Thus, break-even point in units for each product is Product X 14,625 units, Product Y 9,750 units.
