Question

CollegePak Company produced and sold 86,000 backpacks during the year just ended at an average price of $46 per unit. Variable manufacturing costs were $20.00 per unit, and variable marketing costs were $6.68 per unit sold. Fixed costs amounted to $556,000 for manufacturing and $228,800 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.) Required:Compute CollegePak’s break-even point in sales dollars for the year. (Do not round intermediate calculations. Round your final answer up to the nearest whole dollar.)Compute the number of sales units required to earn a net income of $620,000 during the year. (Do not round intermediate calculations. Round your final answer up to nearest whole number.)CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm’s break-even point in sales dollars for the coming year. (Do not round intermediate calculations. Round your final answer up to the nearest wh

Answer 1

To find the profit-maximizing quantity for AAA Aquarium Co., total revenue, marginal revenue, total cost, and marginal cost must be calculated and compared. This allows the firm to see at what point marginal cost equals marginal revenue, indicating no further profits can be made with additional production.

Step-by-step explanation:

The AAA Aquarium Co. aims to determine the profit-maximizing quantity of aquariums to produce and sell. To do this, we will calculate several key financial metrics: total revenue, marginal revenue, total cost, and marginal cost for each output level from one to five units. These calculations are integral to understanding how changes in production levels affect profitability.

For each additional aquarium produced and sold, both total and marginal revenues will increase by the sales price of $20. However, total costs will escalate at a variable rate depending on how many units are produced due to increasing variable costs. By comparing marginal revenue and marginal cost, we can pinpoint the output level at which they are equal - this is the profit-maximizing quantity as additional production would no longer increase profit.

A table is constructed to illustrate these financials for output levels one through five, and diagrams are used to visually represent the total revenue and total cost curves, as well as the marginal revenue and marginal cost curves. These will clearly show the intersection point where profit maximization occurs.

Answer 2

Part 1

$1,868,571

Part 2

72,713 units

Part 3

$ 2,065,263

Step-by-step explanation:

Break even point is the point where a firm makes neither a profit nor a loss.

Break even point (sales dollars) = Fixed Costs ÷ Contribution Margin Ratio

Where,

Contribution Margin Ratio = Contribution ÷ Sales

= (Sales - Variable Costs) ÷ Sales

= ($46.00 - $20.00 - $6.68) ÷ $46.00

= 0.42

Therefore,

Break even point (sales dollars) = ($556,000 + $228,800) ÷ 0.42

= $ 1,868,571.429

= $1,868,571

Units to achieve a target profit = Fixed Costs + Target Profit ÷ Contribution per unit

Where,

Contribution per unit = Sales per unit - Variable Costs per unit

= $46.00 - $20.00 - $6.68

= $19.32

Therefore,

Units to achieve a target profit = ($556,000 + $228,800 + $620,000) ÷ $19.32

= 72,712.21532

= 72,713

After 10% increase in variable manufacturing costs.

Variable manufacturing costs = ($20.00 × 1,10)

= $22

Contribution Margin Ratio will be = (Sales - Variable Costs) ÷ Sales

= ($46.00 - $22 - $6.68) ÷ $46.00

= 0.37652

= 0.38

Break even point (sales dollars) = ($556,000 + $228,800) ÷ 0.38

= $ 2,065,263.15

= $ 2,065,263