Alliance Enterprises is considering extensively modifying th

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 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: process that will improve product quality. This will allow Alliance to increase the Existing Equipment Modified Equipment Selling price per unit Variable cost per unit Fixed costs 18 14 140,000 300,000 Required 1. Determine the break-even point in units for the two machines units equipment units 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%.

Solution

1. Determine the Break even point in units for the two machines

Answer = Break- even point = Fixed cost / Contribution

Existing Equipment

Contribution = Sales - variable cost

= $ 18 - $14

= $4

Break -even point = 140000 / 4 = 35000 units

Modified Equipment

Contribution = Sales - variable cost

= $ 20 - $14

= $6

Break -even point = 300000 / 6 = 50000 units

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

Answer = Profit to sales ratio = 10%

Let sales level in units = X

Profit = 0.10X

Profit = Sales - Variable cost - Fixed cost

0.10X*20 = (20-14)* X - 300000

300000 = 6X - 2X

X = 75000 Units

3. Determine the sales level in units at which the modified equipment will achieve $75600 in after tax operating income. Assuming a tax rate of 30%.

Answer = Let sales level in units = x

Profit = Sales - Variable cost - Fixed cost - Tax

$75600 = (6X - 300000 ) - 30% of net profit

75600 = 0.70 *(6X - 300000)

108000 + 300000 = 6 X

408000 = 6 X

X = 68000

4. Sales Level at which profits will be same for either the existing or modified equipment = Indifference point

Let sales level = X

(18 - 14)X - 140000 = (20-14)X - 300000

4X - 6X = 140000 - 300000

2X = 160000

X = 80000

At 80000 units profit of either equipment will be same