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• Break-Even Dollars for Faucet Filters = Break-Even Units for Faucet Filters * Selling Price per Faucet

• Break-Even Dollars for Faucet Filters = 6,000 units * $72 = $432,000

• Break-Even Dollars for Pitcher Filters = Break-Even Units for Pitcher Filters * Selling Price per Pitcher

• Break-Even Dollars for Pitcher Filters = 9,000 units * $88 = $792,000

In summary, at the current sales mix, Forever Pure needs to sell 6,000 faucet filters ($432,000) and 9,000 pitcher filters ($792,000) to break even.

Break-Even Point with New Production Equipment

1. Calculate the New Variable Costs:

• New Variable Cost per Faucet Filter = Old Variable Cost – Decrease = $20 – $4 = $16
• New Variable Cost per Pitcher Filter = Old Variable Cost – Decrease = $16 – $8 = $8

2. Calculate the New Contribution Margins:

• New Contribution Margin per Faucet Filter = Selling Price – New Variable Cost = $72 – $16 = $56
• New Contribution Margin per Pitcher Filter = Selling Price – New Variable Cost = $88 – $8 = $80

3. Calculate the New Weighted-Average Contribution Margin per Unit:

• New Weighted-Average Contribution Margin per Unit = (Sales Mix % for Faucet * New Contribution Margin per Faucet) + (Sales Mix % for Pitcher * New Contribution Margin per Pitcher)
• New Weighted-Average Contribution Margin per Unit = (0.40 * $56) + (0.60 * $80)
• New Weighted-Average Contribution Margin per Unit = $22.40 + $48.00 = $70.40

4. Calculate the New Break-Even Point in Total Units:

• New Fixed Costs = Old Fixed Costs + Increase = $960,000 + $166,400 = $1,126,400
• New Break-Even Point in Total Units = New Fixed Costs / New Weighted-Average Contribution Margin per Unit
• New Break-Even Point in Total Units = $1,126,400 / $70.40 = 16,000 units

5. Calculate the New Break-Even Point in Units for Each Type of Filter:

• New Break-Even Units for Faucet Filters = New Break-Even Point in Total Units * Sales Mix % for Faucet

• New Break-Even Units for Faucet Filters = 16,000 units * 0.40 = 6,400 units

• New Break-Even Units for Pitcher Filters = New Break-Even Point in Total Units * Sales Mix % for Pitcher

• New Break-Even Units for Pitcher Filters = 16,000 units * 0.60 = 9,600 units

Assuming the same sales mix, Forever Pure needs to sell 6,400 faucet filters and 9,600 pitcher filters to break even with the new equipment.

Total Sales Level for Indifference

To find the total sales level where Forever Pure would be indifferent between the old and new equipment, we need to find the point where the total profit is the same under both scenarios. Let ‘X’ be the total number of units sold.

Profit under Old Equipment:

Profit = (Weighted-Average Contribution Margin per Unit * Total Units) – Fixed Costs Profit = ($64.00 * X) – $960,000

Profit under New Equipment:

Profit = (New Weighted-Average Contribution Margin per Unit * Total Units) – New Fixed Costs Profit = ($70.40 * X) – $1,126,400

Set the profits equal to each other and solve for X:

$64.00X – $960,000 = $70.40X – $1,126,400 $1,126,400 – $960,000 = $70.40X – $64.00X $166,400 = $6.40X X = $166,400 / $6.40 X = 26,000 total units

Now, calculate the total sales dollars at this level using the weighted-average selling price.

Weighted-Average Selling Price:

• Weighted-Average Selling Price = (Sales Mix % for Faucet * Selling Price per Faucet) + (Sales Mix % for Pitcher * Selling Price per Pitcher)
• Weighted-Average Selling Price = (0.40 * $72) + (0.60 * $88)
• Weighted-Average Selling Price = $28.80 + $52.80 = $81.60

Total Sales Level for Indifference:

• Total Sales Dollars = Total Units * Weighted-Average Selling Price
• Total Sales Dollars = 26,000 units * $81.60 = $2,121,600

Forever Pure would be indifferent between using the old equipment and buying the new production equipment at a total sales level of 26,000 units or $2,121,600.

Decision on Buying New Production Equipment with Expected Sales of 23,000 Units

We need to calculate the profit under both scenarios at a sales level of 23,000 units.

Profit with Old Equipment (23,000 units):

Profit = ($64.00 * 23,000) – $960,000 Profit = $1,472,000 – $960,000 = $512,000

Profit with New Equipment (23,000 units):

Profit = ($70.40 * 23,000) – $1,126,400 Profit = $1,619,200 – $1,126,400 = $492,800

Based on the expected sales of 23,000 units, Forever Pure should NOT buy the new production equipment. The profit is higher ($512,000) with the old equipment compared to the new equipment ($492,800) at this sales volume.

Lessons Learned Concerning Cost-Volume-Profit Analysis and Decision Making

This analysis highlights several important lessons regarding cost-volume-profit (CVP) analysis and decision making:

• Understanding the Sales Mix is Crucial: When a company sells multiple products, the sales mix significantly impacts the break-even point and profitability. Changes in the sales mix will alter the weighted-average contribution margin and, consequently, the number of units needed to cover fixed costs.
• Fixed Costs and Variable Costs Behave Differently: Fixed costs remain constant in total regardless of changes in production or sales volume (within a relevant range), while variable costs change in direct proportion to changes in volume. Understanding this behavior is fundamental to CVP analysis.
• Contribution Margin Drives Profitability: The contribution margin (selling price per unit minus variable cost per unit) represents the amount each sale contributes towards covering fixed costs and generating profit. A higher contribution margin leads to a lower break-even point.
• Capital Investments Impact CVP Relationships: Investing in new equipment can significantly alter the cost structure by changing fixed costs (usually increasing due to depreciation and potentially higher maintenance) and variable costs (often decreasing due to increased efficiency). These changes need to be carefully analyzed to determine the financial impact at different sales levels.
• Break-Even Analysis is a Starting Point, Not the Only Factor: While break-even analysis is essential for understanding the sales volume required to cover costs, it’s not the sole determinant in decision making. Factors like market demand, competitive landscape, strategic goals, and risk assessment also need to be considered.
• Indifference Point Helps Evaluate Investment Decisions: Determining the indifference point (the sales level where two alternatives yield the same profit) is valuable for evaluating investments that change the cost structure. It helps managers understand the sales volume at which the new investment becomes financially advantageous.
• Future Sales Forecasts are Critical: The accuracy of sales forecasts is crucial for making informed decisions based on CVP analysis. In the Forever Pure example, the decision to invest in new equipment hinges on whether the expected sales volume is above or below the indifference point.
• CVP Analysis is a Tool for “What-If” Scenarios: Managers can use CVP analysis to evaluate the potential impact of various changes, such as changes in selling prices, variable costs, fixed costs, or sales mix, on profitability and break-even points. This allows for better planning and proactive decision making.
• Focus on Relevant Costs: When making decisions like investing in new equipment, it’s important to focus on the relevant costs and benefits, which are future costs and revenues that differ between the alternatives. Sunk costs (like the cost of the old equipment) are irrelevant to the decision.

By carefully applying CVP analysis and understanding these key lessons, Forever Pure’s management can make more informed decisions about pricing, production, and capital investments to improve profitability and achieve their business objectives.