Question

Alliance Enterprises is considering extensively modifying their manufacturing equipment. The modifications will result in less wastage of materials, which will reduce variable manufacturing costs and introduce changes to the production process that will improve product quality. This will allow Alliance to increase the selling price of the product. Annual fixed costs are expected to increase to $660,000 if the modifications are made. Expected fixed and variable costs as well as the selling prices are shown below:

Cost Item	Existing Equipment			Modified Equipment
Selling price per unit	$	18		$	20
Variable cost per unit		14			14
Fixed costs		320,000			660,000

Required:

1.	Determine the break-even point in units for the two machines.

    

2.	Determine the sales level in units at which the modified equipment will achieve a 10% target profit-to-sales ratio (ignore taxes).

       

3.	Determine the sales level in units at which the modified equipment will achieve $151,200 in after-tax operating income. Assume a tax rate of 30%.

      

4.	Determine the sales level at which profits will be the same for either the existing or modified equipment.

      

Answer 1

1) Calculation of break even units for two machines is shown as follows:-

Break even point in units = Total Fixed cost/Contribution per unit

Contribution per unit for existing equipment = Selling price per unit - variable cost per unit

= $18 - $14 = $4 per unit

Total Fixed cost for existing equipment = $320,000

Break even point in units for existing equipment = $320,000/$4 per unit = 80,000 units

Contribution per unit for modified equipment = Selling price per unit - variable cost per unit

= $20 - $14 = $6 per unit

Total Fixed cost for modified equipment = $660,000

Break even point in units for modified equipment = $660,000/$6 per unit = 110,000 units

2) Let the required sales level in units equal to X. (for modified equipment)

Required profit per unit = Selling price per unit*10% = $20*10% = $2 per unit

Total Contribution - Fixed cost = Total Profit

(Contribution per unit*units sold) - Fixed cost = (Profit per unit*units sold)

($6 per unit*X) - $660,000 = ($2*X)

6X - 2X = $660,000

4X = $660,000

X = $660,000/4 = 165,000 units

Therefore the required sales level in units at which the modified equipment will achieve a 10% target profit-to-sales ratio is 165,000 units.

3) Required after tax operating income = $151,200

Tax rate = 30%

Operating income before tax = $151,200/(1-0.30) = $151,200/0.70 = $216,000

Sales level (in units) = (Fixed cost+Operating Income before tax)/contribution per unit

= ($660,000+$216,000)/$6 per unit

= $876,000/$6 per unit = 146,000 units

Therefore at the level of 146,000 units, the modified equipment will achieve $151,200 in after-tax operating income.

4) Sales level at which profits will be same for either the existing or modified equipment is calculated as follows:-

Let the required sales level equal to Y.

Profit is equal to contribution minu fixed cost

Profit in existing equipment = Profit in modified equipment

(Total Contribution - Fixed cost) = (Total Contribution - Fixed cost)

($4 per unit*Y) - $320,000 = ($6 per unit*Y) - $660,000

$660,000 - $320,000 = 6Y - 4Y

2Y = $340,000

Y = $340,000/2 = 170,000 units

Therefore at the sales level of 170,000 units, profits will be the same for either the existing or modified equipment.