Part A:
- Break-even point:

To calculate the break-even point, we need to find the number of lawn ornaments Wilson needs to sell in order to cover the fixed costs.

Break-even point (in units) = Fixed costs / Contribution margin per unit

Contribution margin per unit = Selling price per unit – Variable cost per unit

Contribution margin per unit = $25.00 – $15.00 = $10.00

Fixed costs = $100,000

Break-even point (in units) = $100,000 / $10.00 = 10,000 units

Therefore, Wilson needs to sell 10,000 lawn ornaments to break even.

- Profit of $150,000:

To calculate the sales required to generate a profit of $150,000, we need to consider the contribution margin.

Profit = (Sales – Variable costs) – Fixed costs

Profit = ($150,000 + Fixed costs) / Contribution margin per unit

Sales = ($150,000 + $100,000) / $10.00 = $250,000

Therefore, Wilson needs to make $250,000 in sales to generate a profit of $150,000.

- Contribution margin income statement:

Sales Revenue: $25.00 * 25,000 = $625,000

Variable Costs: $15.00 * 25,000 = $375,000

Contribution Margin: $625,000 – $375,000 = $250,000

Fixed Costs: $100,000

Profit: Contribution Margin – Fixed Costs = $250,000 – $100,000 = $150,000

Contribution Margin Income Statement:

Sales Revenue: $625,000

Variable Costs: $375,000

Contribution Margin: $250,000

Fixed Costs: $100,000

Profit: $150,000

- Margin of safety:

Margin of Safety (in dollars) = Actual Sales – Break-even Sales

Actual Sales = Sales at 25,000 units = $25.00 * 25,000 = $625,000

Margin of Safety (in dollars) = $625,000 – ($25.00 * 10,000) = $375,000

Therefore, the margin of safety is $375,000.

- Purchase of the machine:

To determine whether the company should pursue the purchase of the machine, we need to calculate the impact on contribution margin.

New Variable Cost per ornament = $15.00 – $7.50 = $7.50

New Fixed Costs = $100,000 + $50,000 = $150,000

Contribution margin per unit = Selling price per unit – Variable cost per unit

Contribution margin per unit = $25.00 – $7.50 = $17.50

New Break-even point (in units) = $150,000 / $17.50 = 8,571.43 units

The break-even point decreases from 10,000 units to 8,571.43 units if the company purchases the machine.

Since the break-even point decreases and the company’s fixed costs increase, it indicates that the purchase of the machine would be beneficial. The company should pursue the purchase of the machine.

Part B:

- Weighted average contribution margin per unit:

To calculate the weighted average contribution margin per unit, we need to consider the proportion of small and large ornaments sold.

Weighted average contribution margin per unit = (Contribution margin per unit for small ornaments * Proportion of small ornaments) + (Contribution margin per unit for large ornaments * Proportion of large ornaments)

Contribution margin per unit for small ornaments = $8.00 – $4.00 = $4.00

Contribution margin per unit for large ornaments = $20.00 – $8.00 = $12.00

Proportion of small ornaments = 3 / (3 + 1) = 0.75

Proportion of large ornaments = 1 / (3 + 1) = 0.25

Weighted average contribution margin per unit = ($4.00 * 0.75) + ($12.00 * 0.25) = $3.00 + $3.00 = $6.00

Therefore, the weighted average contribution margin per unit for Bearcat Paws is $6.00.

- Break-even point in units:

To calculate the break-even point in units, we need to consider the fixed costs and the weighted average contribution margin per unit.

Break-even point (in units) = Fixed costs / Weighted average contribution margin per unit

Break-even point (in units) = $75,000 / $6.00 = 12,500 units

Therefore, the break-even point for Bearcat Paws is 12,500 units.

- Number of small and large ornaments at the break-even point:

To determine the number of small and large ornaments needed at the break-even point, we need to consider the proportion of small and large ornaments.

Number of small ornaments = Proportion of small ornaments * Break-even point

Number of large ornaments = Proportion of large ornaments * Break-even point

Number of small ornaments = 0.75 * 12,500 = 9,375 ornaments

Number of large ornaments = 0.25 * 12,500 = 3,125 ornaments

Therefore, at the break-even point, Bearcat Paws needs to produce 9,375 small ornaments and 3,125 large ornaments.