Question

Sales (19,500 units at $30 per unit) $585,000 Variable expenses 409,500 Contribution margin 175,500 Fixed expenses 180,000 Net operating loss $(4,500) By automating certain operations, the company could reduce variable costs by $3 per unit. However, fixed costs would increase by $72,000 each month.Compute the new CM ratio and the new break-even point in both units and dollars.Assume that the company expects to sell 26,000 units next month. Prepare two contribution format income statements, one assuming that operations are not automated and one assuming that they are.

Answer 1

To find the new CM ratio, calculate the new fixed cost and variable cost per unit using the given information. Then, calculate the new contribution margin and the new break-even point in units and dollars.

Step-by-step explanation:

To determine the new CM ratio, we first need to calculate the new variable cost per unit and the new fixed cost. By automating certain operations, the company can reduce variable costs by $3 per unit, so the new variable cost per unit would be $30 - $3 = $27. However, fixed costs would increase by $72,000 per month, so the new fixed cost would be $180,000 + $72,000 = $252,000.

The new CM ratio is calculated by dividing the new contribution margin by the new sales. The new contribution margin would be the revenue minus the new variable costs, which is $(27,000 - 585,000) = $(177,000 - 409,500) = $166,500. The new sales would be 26,000 units multiplied by the new selling price of $30, which is $780,000.

To calculate the new break-even point in units and dollars, we can use the formula: Break-even point (in units) = fixed costs / CM ratio, and Break-even point (in dollars) = break-even point (in units) multiplied by the selling price per unit.

Answer 2

Automated

Sales (19,500 units at $30 per unit) $585,000 $585,000

Variable expenses 409,500 351,000

Contribution margin 175,500 234,000

Fixed expenses 180,000 252,000

Net operating loss $(4,500) $( 18,000)

New Cm ratio= Contribution Margin/ Sales Revenue

= $ 234,000 $ 585,000 = 0.4

Break-even point in dollars= Fixed Costs/ 1- (variable Cost/ Sales)

= 252,000/ 1- (351,000/ 585,000)

= 252,000/ 1-0.6

= 252,000/0.4= $ 630,000

The resulting $ 630,000 is the break even point at which neither a loss nor a profit is incurred.This can be checked as follows.

Sales $ 630,000

Variable Costs ( 60 % $ 630,000) $ 378,000

Contribution Margin $ 252,000

Less Fixed Expense $ 252,000

Profit 0

Break even point in units = Fixed Costs/ Contribution Margin in units

= $ 252,000/ (30-18)

=$ 252,000/ $ 12= 21,000 units

Two Contribution format Income Statements:

Automated

Sales (26,000 units at $30 per unit) $780,000 $780,000

Variable expenses 546,000 468,000

Contribution margin 234,000 312,000

Fixed expenses 180,000 252,000

Net operating Profit $ 54,000 $ 60,000

Working:

Variable Costs per unit = $ 409500/19500= $ 21

After reduction variable costs = $ 21- $3= $ 18