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Homework answers / question archive / Alliance Enterprises is considering extensively modifying their manufacturing equipment
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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 $870,000 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 | 420,000 | 870,000 | ||||
Determine the break-even point in units for the two machines
Determine the sales level in units at which the modified equipment will achieve a 10% target profit-to-sales ratio (ignore taxes)
Determine the sales level in units at which the modified equipment will achieve $88,200 in after-tax operating income. Assume a tax rate of 30%.
| Determine the sales level at which profits will be the same for either the existing or modified equipment |
a) Existing Equipment: Selling Price per unit = $18 | Variable cost per unit = $14 | Fixed Costs = $420,000
Contribution margin per unit = (Selling price per unit - Variable cost per unit) = 18 - 14 = $4
BEP or Break-even Point is the point where, Contribution margin per unit * Units Sold = Fixed costs
Therefore, BEP in units = Fixed costs / Contribution margin per unit = 420,000 / 4
Hence, Break-even Point for Existing Equipment in units = 105,000 units
Modified Equipment: Selling Price per unit = $20 | Variable cost per unit = $14 | Fixed Costs = $870,000
Contribution margin per unit = (Selling price per unit - Variable cost per unit) = 20 - 14 = $6
BEP in units = Fixed costs / Contribution margin per unit = 870,000 / 6
Hence, Break-even Point for Modfied Equipment in units = 145,000 units
b) Target Profit to Sales ratio = 10%
Modified Equipment: Selling Price per unit = $20 | Variable cost per unit = $14 | Fixed Costs = $870,000
Contribution Margin per unit = 20 - 14 = $6
Profit = Contribution margin per unit * Units sold - Fixed costs
Sales = Selling price per unit * Units sold
Profit / Sales = (CM per unit * Units sold) / (SP per unit * Units sold) - Fixed costs / (SP per unit * Units sold)
Profit / Sales = CM per unit / SP per unit - Fixed costs / (SP per unit * Units sold)
Putting values and solving the equation for Units sold
=> 10% = 6 / 20 - 870,000 / (20 * Level of Sales in units)
=> 870,000 / (20 * Level of Sales in units) = 30% - 10%
=> Level of Sales in units = 870,000 / (20 * 20%)
Hence, Level of Sales in units for Modified equipment to achieve 10% Profit to Sales ratio = 217,500 units
c) Target After tax Operating income = $88,200 | Tax rate = 30%
After-tax Operating Income = Operating Income * (1 - Tax rate)
Operating Income = After-tax Operating Income / (1 - Tax rate)
Putting values, Operating Income = 88,200 / (1 - 30%) = 88,200 / 70%
Target Operating Income = $126,000
We know, Operating Income = Contribution margin per unit * Units sold - Fixed costs
Unit sales for Target Operating Income = (Target Operating Income + Fixed costs) / Contribution margin per unit
Modified Equipment: Contribution Margin per unit = $6 | Fixed Costs = $870,000
Putting Values, Unit sales for Target Operating Income = (126,000 + 870,000) / 6 = 996,000 / 6
Hence, Unit Sales for Modified equipment to achieve Target after tax Operating Income = 166,000 units
d) Let Unit sales at which Profits are same for both Existing and Modified equipment be X units
Existing Equipment: Contribution margin per unit = $4 | Fixed Costs = $420,000
Existing Equipment's Profit = Contribution margin per unit * X units - Fixed costs = 4 * X - 420,000
Modified Equipment: Contribution Margin per unit = $6 | Fixed Costs = $870,000
Modified Equipment's Profit = Contribution margin per unit * X units - Fixed costs = 6 * X - 870,000
Now we will equalize Profits of both Existing and Modified equipment and solve for X units
=> Existing Equipment's Profit = Modified Equipment's Profit
=> 4 * X - 420,000 = 6 * X - 870,000
=> 870,000 - 420,000 = 6X - 4X
=> 450,000 = 2X
=> X = 450,000 / 2
Hence, Sales level where Profits of both equipments are same = 225,000 units
