Question

Sockerville machine shop fabricates polished steel casings. They currently sell 27,000 casings at a selling price of $70. They have the following cost structure:

Variable costs per unit	$45
Fixed costs	$210,000

Answer and Show Work:

1. What is the breakeven point in units?

Break-even point in units:

2. Suppose that if they decrease their price to $65, they could increase sales to 32,000 units. What would the change in profit be if they decrease their price to $65?

Change in profit if price is $65 (be sure to say whether profit increases or decreases):

3. What is the minimum price that Sockerville would be willing to charge in order to achieve an increase in sales to 32,000 units (round to the nearest cent)?

Minimum price for increase to 32,000 units:

4. Suppose that Sockerville can purchase a machine that would increase fixed costs to $300,000 and decrease unit variable costs to $30 per unit. At what level of production and sales would Sockerville be indifferent between the old machine and the new machine?

Level of production and sales (in units):

Answer 1

Solution a:

Break-even point in units = Fixed costs / Contribution margin per unit = $210,000 / ($70 - $45) = 8400 units

Solution b:

Current profit = (27000*$25) - $210,000 = $465,000

If selling price reduced to $65 then revised contribution margin per unit = $65 - $45 = $20 per unit

If sales increased to 32000 units then new profit = (32000*$20) - $210,000 = $430,000

Change in profit = $430,000 - $465,000 = $35,000 decrease

Solution c:

Required contribution margin on 32000 units = $465,000 + $210,000 = $675,000

Required contribution margin per unit = $675,000 / 32000 = $21.09 per unit

Minimum price for increase to 32,000 units = Required contribution margin per unit + Variable cost per unit

= $21.09 + $45 = $66.09 per unit

Solution d:

Let at X level production Sockerville be indifferent between the old machine and the new machine.

Therefore profit under both situation will be the same.

Contribution margin per unit from new machine = $70 - $30 = $40 per unit

Now

($25X - $210,000) = ($40X - $300,000)

15X = $90,000

X = 6000 units

Therefore at production level of 6000 units, Sockerville be indifferent between the old machine and the new machine