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1.
Calculate the break-even point in sales units for the overall Product E for the current year.
1.
Explanation of Solution
Sales mix: It refers to the relative distribution of the total sales among the number of products sold by a company. In other words, it is expressed as a percentage of units sold for each product with respect to the total units sold for all the products.
Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations. The formula to calculate the break-even point in sales units is as follows:
Break-even point in Sales(units) =Fixed CostsContribution Margin per unit
Determine the break-even point in sales units for the overall Product E.
Fixed cost =$2,498,600
Contribution margin per unit =$620 per unit (3)
Break-even point in Sales(units) for Product E] =Fixed CostsContribution Margin per unit=$2,498,600$620=4,030 units
Note: For break-even analysis, the Product-Laptops and Product-Tablets are considered as the components of one overall company’s Product E.
Working note (1):
Determine the selling price per unit of Product E.
Selling price per unit of Product E] =(Selling price per unit of Laptops× sales mix of Laptops)+(Selling price per unit of Tablets× sales mix of Tablets)=($1,600 per unit×40%)+($850 per unit×60%)=$640 per unit+$510 per unit=$1,150 per unit
Working note (2):
Determine the variable cost per unit of Product E.
Variable cost per unit of Product E] =(Variable cost per unit of Laptops× sales mix of Laptops)+(Variable cost per unit of Tablets× sales mix of Tablets)=($800 per unit×40%)+($350 per unit×60%)=$320 per unit+$210 per unit=$530 per unit
Working note (3):
Determine the unit contribution margin of Product E.
Unit Contribution Margin of Product E] =(Selling price per unit)−(Variable cost per unit)=$1,150 per unit(1)−$530 per unit(2)=$620 per unit
Therefore, the break-even point in sales units for the overall Product E for the current year is 4,030 units.
2.
Calculate the break-even sales (units) for Product-Laptops and Product-Tablets.
2.
Explanation of Solution
Determine the break-even point in sales units:
For Product-Laptops
Break-even point in sales units for Product E =4,030 units (refer Part a)
Sales Mix for Product Laptops =40%
Break-even point in Sales(units) for Product Laptops] =(Break-even point in Sales(units) for Product E)×(Sales mix forProduct Laptops)=4,030 units×40%=1,612 units
For Product-Tablets
Break-even point in sales units for Product E =4,030 units (refer Part a)
Sales Mix for Product Tablets =60%
Break-even point in Sales(units) for Product Tablets] =(Break-even point in Sales(units) for Product E)×(Sales mix forProduct Tablets)=4,030 units×60%=2,418 units
Therefore, the break-even point in sales units for the Product Laptops is 1,612 units and for the Product Tablets are 2,418 units.
3.
Compare the break-even point with that in Part (1).
3.
Explanation of Solution
The break-even point calculated in (1) with a sales mix of 50% laptops and 50% tablets is 3,844 units. It is less than the break-even point of 4,030 units calculated in Part 1.
The reason for the difference is the sales mix which is allocated at a higher percentage to the laptops (50%) and tablets (50%) in the present case. It resulted in the higher contribution margin per unit of $650 per unit than in Part 1 ($620 per unit). Thus, it decreases the break-even point of sales (units) in the present case.
Working note (4):
Determine the break-even point in sales units for the overall Product E.
Fixed cost =$2,498,600
Contribution margin per unit =$620 per unit (7)
Break-even point in Sales(units) for Product E] =Fixed CostsContribution Margin per unit=$2,498,600$650=3,844 units
Note: For break-even analysis, the Product-Laptops and Product-Tablets are considered as the components of one overall company’s Product E.
Working note (5):
Determine the selling price per unit of Product E.
Selling price per unit of Product E] =(Selling price per unit of Laptops× sales mix of Laptops)+(Selling price per unit of Tablets× sales mix of Tablets)=($1,600 per unit×50%)+($850 per unit×50%)=$800 per unit+$425 per unit=$1,225 per unit
Working note (6):
Determine the variable cost per unit of Product E.
Variable cost per unit of Product E] =(Variable cost per unit of Laptops× sales mix of Laptops)+(Variable cost per unit of Tablets× sales mix of Tablets)=($800 per unit×50%)+($350 per unit×50%)=$400 per unit+$175 per unit=$575 per unit
Working note (7):
Determine the unit contribution margin of Product E.
Unit Contribution Margin of Product E] =(Selling price per unit)−(Variable cost per unit)=$1,225 per unit(5)−$575 per unit(6)=$650 per unit
Working note (8):
Determine the break-even point in sales units:
For Product-Laptops:
Break-even point in sales units for Product E =3,844 units (4)
Sales Mix for Product Laptops =50%
Break-even point in Sales(units) for Product Laptops] =(Break-even point in Sales(units) for Product E)×(Sales mix forProduct Laptops)=3,844 units×50%=1,922 units
Working note (9):
For Product-Tablets:
Break-even point in sales units for Product E =3,844 units (4)
Sales Mix for Product Tablets =50%
Break-even point in Sales(units) for Product Tablets] =(Break-even point in Sales(units) for Product E)×(Sales mix forProduct Tablets)=3,844 units×50%=1,922 units
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Chapter 6 Solutions
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