Question

Consider the following:           

Product  Sales Price  Variable Production Cost  Allocated fixed manufacturing overhead

X  $40  12  36363.64     

Y  $60  30  29090.91     

Z  $92  55  14545.45     

The sales ratio for X:Y:Z is  10:8:4        

Total current sales (units)  16000        

Additionally, average cost data for two levels of sales volume are as follows:

Sales Volume (units) 10,000  30000     

Administration Expense (per unit) $18 6     

Sales & Marketing (per unit) $12 12     

Other Operating Expense $2.40 1.8     

ABC company is subject to a 40% income tax rate.      

X company's current margin of safety is:

How many units of Product Y does ABC need to sell to earn a after-tax income of $48,000: ?  

Answer 1

Answer

Step:1 - Identification of Type of cost (Variable, Fixed, Mixed)

Sales Volume	10000	30000	Cost type
Administration Expense	$18	$6	Fixed
Sales & Marketing	$12	$12	Variable
Other Operating Expense	$2.40	$1.80	Mixed

a) Administration Expense is fixed expense because total cost remain the same and per unit amount is changes.(10000 x $18 = $180,000 or 30000 x $6 = $180,000)

b) Sales & Marketing is variable expense because variable cost changes with the change in the volume and per unit cost remain same.

c) For Mixed cost, Variable cost and fixed cost needs to be seperated using High-Low Method.

Total Operating cost at 10000 = 10000 x $2.40 = $24,000

Total Operating cost at 10000 = 30000 x $1.80 = $54,000

Variable Cost per unit = (Highest activity cost−Lowest Activity Cost​ ) / Highest activity units − Lowest Activity Units

Variable Cost per unit = ($54,000 - $24,000) / 30000 - 10000

Variable Cost per unit = $30,000 / 20000 = $1.50 per unit

​Fixed Cost = Highest activity cost − (Variable Cost × Highest activity units)

​Fixed Cost = $54,000 - ($1.5 x 30000)

​Fixed Cost = $9,000

So,

Variable Other Operating Expense = $1.5 per unit

Fixed Other Operating Expense = $9,000

Step:2- Calculation of Total Fixed Cost

	Particulars	Amount
A	Allocated fixed Manufacturing overhead
	X	$36,363.64
	Y	$29,090.91
	Z	$14,545.45
	Total	$80,000.00
B	Administration Expense	$1,80,000.00
C	Fixed Other Operating Expense	$9,000.00
	Total Fixed Cost(A+B+C)	$2,69,000.00

Step:3 - Calculation of Breakeven Point

	X	Y	Z	Total
Sales price	$40.00	$60.00	$92.00
Variable Production cost	$12.00	$30.00	$55.00
Variable Sales & Marketing	$12.00	$12.00	$12.00
Variable Other Operating Expense	$1.50	$1.50	$1.50
Total Variable Cost per unit	$25.50	$43.50	$68.50
Contribution margin per unit	$14.50	$16.50	$23.50
Multiply by Sales Mix	10.00	8.00	4.00	22.00
Weighted Average Contribution margin per unit	$6.59 [$14.50 x (10/22)]	$6.00 [$16.50 x (8/22)]	$4.27 [$23.50 x (4/22)]	$16.86

  

Break-Even Point in units= Total Fixed Cost /  Weighted Average Contribution margin per unit

Break-Even Point in units = $269,000 / $16.86

Break-Even Point in units = 15,955 Units

Step : 4 - Calculation of Margin of Safety

Margin of Safety = Total Sales - Break even sales

Product	Sales Mix	Sales Unit	Break even units	Sales Price	Actual Sales	Break Even Sales
X	10	7273	7252	$40	$2,90,920	$2,90,080
Y	8	5818	5802	$60	$3,49,080	$3,48,120
Z	4	2909	2901	$92	$2,67,628	$2,66,892
Total	22	16000	15955		$9,07,628	$9,05,092

Margin of Safety = $907,628 - $905092= $2536

Step:5 - Calculation of Units to sold to earn after tax profit of $48,000

Target Sales in Unit = (Total Fixed Cost + Net Income Before Tax) / Weighted Average Contribution margin per unit

= ($269,000 + 48000/1-40%) / $16.86

= ($269,000 + $80,000) / $16.86

Target Sales in Unit = 20700 units

Multiply above units with sales mix 10:8:4

X = 20695 x 10/22 = 9409 units

Y = 20695 x 8/22 = 7527 units

Z = 20695 x 4/22 = 3764 units

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