Chester has negotiated a new labor contract for the next round that will affect the cost for their product Cat. Labor costs will go from $2.90 to $3.40 per unit. Assume all period and variable costs as reported on Chester's Income Statement remain the same. If Chester were to pass on half the new labor costs to their customers, how many units of product Cat would need to be sold next round to break even on the product

if Chester were to pass on half the new labor costs to their customers, the number of unit that Cat would need to be sold next round to break even on the product will be 2,379 units.

We are not given some information, so we will assume that "Selling price per unit = $54, Current total variable cost = $24.50, Total Fixed Costs = $69,000"

The new variable cost will increase by:

= ($3.40 - $2.90)/2

= $0.50 / 2

= $0.25

The new variable costs will be:

= Current total variable cost + Increment cost

= $24.50 + $0.25

= $24.75

The contribution margin per unit will be:

= Selling price per unit - New variable costs

= $54 - $24.75

= $29.25

The old break-even units is:

= Old fixed cost / Contribution margin per unit

= $69,000/$29.50

= 2,339 units

The new fixed costs will be:

= Total Fixed Costs + (Increment cost* Old break-even units)

= $69,000 + ($0.25 * 2,339)

= $69,000 + $585

= $69,585

The new break-even units will be

= Fixed cost / Contribution margin per unit

= $69,585 / $29.25

= 2,379 units.

Therefore, if Chester were to pass on half the new labor costs to their customers, the number of unit that Cat would need to be sold next round to break even on the product will be 2,379 units.

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Question Completion:

Assume the following:

Selling price per unit = $54

Current total variable cost = $24.50

Total Fixed Costs = $69,000

Chester

To break-even on product Cat, Chester needs to sell 2,379 units instead of 2,339 units.

Explanation:

a) Calculations:

New variable cost will increase by ($3.40 - $2.90)/2 = $0.25

New variable costs will be = $24.75 ($24.50 + $0.25)

Contribution margin per unit = $29.25 ($54 - $24.75)

New fixed costs = $69,000 + ($0.25 * 2,339) = $69,585

Old break-even units = $69,000/$29.50 = 2,339 units

New break-even units = Fixed cost/contribution margin per unit

= $69,585/$29.25

= 2,379 units

b) Chester's break-even point in units is calculated by using the break-even formula: Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or $69,585/$29.25.  The variable cost per unit includes only the cost that will be passed to customers.  This means that half of the labor cost is regarded as variable, while the other half is taken is fixed cost.