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 $300,000 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		140,000			300,000

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 $75,600 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. Computation of Break even point (in units) for the two machines:

Since,

Break even point (in units) = Fixed Costs / Contribution margin per unit

Cost Item	Existing Equipment	Modified Equipment
Selling price per unit	$18	$20
Less: Variable cost per unit	$14	$14
Contribution Margin per unit (A)	$4	$6
Fixed costs (B)	$140,000	$300,000
Break even point (in units) (B/A)	35,000	50,000

2. Computation of sales level (in units) at which the modified equipment will achieve a 10% target profit-to-sales ratio:

We know that,

Target/Desired Sales (in units) = (Fixed Costs + Target Profit) / Contribution per unit

Let us assume Sales level in units be 'x'.

Therefore, total sales = $20*x = $20x

Profit to Sales Ratio = 10%

Target Profit = 10% of $20x = $2x

Substituting the values, we get

x =(300,000 + 2x) / 6

Solving,we get x = 75,000 units

Therefore, Sales level in units = 75,000 units

Verification:

Sales (75,000 * $20) $1,500,000

Less: Variable costs (75,000 * $14) $1,050,000

Contribution margin $450,000

Less: Fixed costs $300,000

Profit $150,000

Profit to sales ratio = Profit / Sales * 100

= 150,000 / 1,500,000 * 100 = 10%

Hence, verified.

3. Computation of sales level (in units) at which the modified equipment will achieve $75,600 in after tax operating income:

Given, After tax operating income = $75,600

Rate of tax = 30%

Profit before tax = Profit after tax / ( 1 - Tax rate)

= 75,600 / ( 1 - 0.3)

= 75,600 / 0.7

= $108,000

Now, Desired Sales (units) =(Fixed costs + Target Profit before tax) / Contribution per unit

Desired Sales (units) = ( 300,000 + 108,000) / 6

Desired Sales (units) = 68,000 units

4. Computation of sales level at which profits under both existing and modified equipment will be same:

Here, we have to compute Indifference Point where firm has same profit under both alternatives.

Sales level = Difference in fixed costs / Difference in Contribution per unit

Sales level = (300,000 - 140,000) /(6 - 4)

Sales level = 80,000 units

Verification:

Particulars	Existing (Amount in $)	Modified (Amount in $)
Sales	1,440,000	1,600,000
Less: Variable cost	1,120,000	1,120,000
Contribution margin	320,000	480,000
Less: Fixed costs	140,000	300,000
Profit	180,000	180,000

Hence, verified.