How many lawn ornaments does Wilson need to sell in order to break even? Determine the dollar amount of sales that Wilson needs to make to generate a profit of $150,000. Prepare a contribution margin income statement for the year assuming that Wilson sold 25,000 lawn ornaments. Calculate the margin of safety in dollars assuming the company expects sales consistent with selling 25,000 lawn ornaments. The company is considering purchasing a machine to automate the production of lawn ornaments.Fixed costs will increase by $50,000 and variable costs will decrease by $7.50 per lawn ornament.Should the company pursue the purchase of the machine?Show calculations to support your decision.

QUESTION

Part A

Wilson Company sells lawn ornaments (rocks) with university athletic logos.The selling price of each lawn ornament is $25.00.The variable costs associated with each lawn ornament are $15.00 and the fixed costs for the company are $100,000 per year.Ignore income taxes.

Required

• How many lawn ornaments does Wilson need to sell in order to break even?
• Determine the dollar amount of sales that Wilson needs to make to generate a profit of $150,000.
• Prepare a contribution margin income statement for the year assuming that Wilson sold 25,000 lawn ornaments.
• Calculate the margin of safety in dollars assuming the company expects sales consistent with selling 25,000 lawn ornaments.
• The company is considering purchasing a machine to automate the production of lawn ornaments.Fixed costs will increase by $50,000 and variable costs will decrease by $7.50 per lawn ornament.Should the company pursue the purchase of the machine?Show calculations to support your decision.

Part B

Bearcat Paws produces two sizes of Christmas Ornaments.The selling prices and variable costs are as follows:

The company sells three small Christmas ornaments for every large Christmas ornament.

The contribution margin income statement for the year ended December 31, 2015 follows:

Required

• Calculate the weighted average contribution margin per unit for Bearcat Paws.
• Determine the break-even point in units.
• Determine the number small and the number of large ornaments that would need to be produced at the break-even point.

• ANSWER

• Part A:
  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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:

  1. 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.

  2. 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.

  3. 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.