Question

Break-Even Units: Units for Target Profit

Jay-Zee Company makes an in-car navigation system. Next year, Jay-Zee plans to sell 18,000 units at a price of $340 each. Product costs include:

Direct materials	$71.00
Direct labor	$41.00
Variable overhead	$10.00
Total fixed factory overhead	$608,500

Variable selling expense is a commission of 5 percent of price; fixed selling and administrative expenses total $95,000.

Required:

1. Calculate the sales commission per unit sold. If required, round your answers to the nearest dollar. Use rounded answers in subsequent computations.
$ per unit

Calculate the contribution margin per unit.
$ per unit

2. How many units must Jay-Zee Company sell to break even? Round your answer to the nearest whole number.
units

Prepare an income statement for the calculated number of units. If an amount is zero, enter "0". Do NOT round Break-even units and, if required, round your answer to the nearest dollar.

Jay-Zee Company
Income Statement
	$
	$
	$

3. Calculate the number of units Jay-Zee Company must sell to achieve target operating income (profit) of $364,212. Round your answer to the nearest whole number.
units

4. What if the Jay-Zee Company wanted to achieve a target operating income of $351,750? Would the number of units needed increase or decrease compared to your answer in Requirement 3? Round your answer to the nearest whole number.

Compute the number of units needed for the new target operating income.
units

Answer 1

Required 1 :

Calculate the Sales Commission per unit sold :

Sales Commission per unit sold = Selling price per unit * 5 % of selling price per unit

Sales Commission per unit sold = $ 340 Per Unit * 5 %

Sales Commission per unit sold = $ 17 Per Unit

Calculate the Contribution margin per Unit :
Particulars	$ Per Unit	$ Per Unit
Sales Per unit		$ 340
Less: Variable cost per unit :
Direct Materials	$ 71
Direct Labor	$ 41
Variable Overhead	$ 10
Variable Selling Price (Above calculated)	$ 17
Total Variable Cost per Unit		($139)
Contribution Margin Per Unit		$ 201

Required 2 :

Break even point (in units ) = Total Fixed Expenses / Contribution Margin per unit

Total Fixed Expenses = Fixed Factory Overhead + Fixed Selling and Administrative Expense

Total Fixed Expenses = $ 608,500 + $ 95,000

Total Fixed Expenses = $ 703,500

Contribution margin per unit = $ 201 per Unit (Above Calculated )

Break even point (in units ) = Total Fixed Expenses / Contribution Margin per unit

Break even point (in units ) = $703,500 / $201 per unit

Break even point (in units ) = 3,500 units

So, Number of units must sell to Break Even = 3,500 Units

Prepare Income Statement :
Particulars	Amount($)	Amount($)
Sales (18,000 units *$340 )		$ 6,120,000
Less: Variable costs
Direct Materials (18,000 units *$71)	$ 1,278,000
Direct Labor (18,000 units *$41)	$ 738,000
Variable Overhead (18,000 units *$10 )	$ 180,000
Variable Selling Price (18,000 units*$17)	$ 306,000
Total Variable Costs		($2,502,000)
Contribution Margin		$ 3,618,000
Less: Fixed Expenses
Fixed Factory Overhead	$ 608,500
Fixed selling and administrative expenses	$ 95,000
Total Fixed Expenses		($703,500)
Net Income		$ 2,914,500

Required 3 :

Number of units must sell to achieve target Operating Income = ( Total Fixed Expenses + Target Operating Income)/ Contribution Margin per unit

Number of units must sell to achieve target Operating Income = ( $703,500 + $364,212)/ $ 201 per unit

Number of units must sell to achieve target Operating Income = $ 1,067,712 / $ 201 per unit

Number of units must sell to achieve target Operating Income = 5,312 units

Required 4 :

Number of units must sell to achieve target Operating Income = ( Total Fixed Expenses + Target Operating Income)/ Contribution Margin per unit

Number of units must sell to achieve target Operating Income = ( $703,500 + $351,750)/ $ 201 per unit

Number of units must sell to achieve target Operating Income = $ 1,055,250/ $ 201 per unit

Number of units must sell to achieve target Operating Income = 5,250 units

So, Number of units needed decreased by 62 units {5,312 units - 5,250 units }