Unit 3 Assignment: Chapter 3 Connect Homework LO
Unit 3 Assignment: Chapter 3 Connect Homework LO
Derby Phones is considering the introduction of a new model of headphones with the following price and cost characteristics. Sales price is $270 per unit, variable costs are $120 per unit, and fixed costs are $300,000 per month. The assignment involves calculating the break-even sales volume, the sales needed to achieve an operating profit of $180,000, and analyzing various scenarios affecting operating profit based on changes in sales price, variable costs, fixed costs, and projected sales volume. Additionally, the assignment covers multiple-product costing for On-the-Go, Inc., including determining expected profits, break-even points, and the impact of changing the product sales mix.
Paper For Above instruction
The comprehensive analysis of cost-volume-profit (CVP) relationships forms a fundamental part of managerial accounting, offering vital insights for decision-making. The Derby Phones scenario exemplifies how businesses evaluate their product offerings' profitability under various sales and cost conditions. Simultaneously, the On-the-Go, Inc. example illustrates the complexities of product mix decisions when managing multiple product lines with different contribution margins. This essay discusses the essential CVP concepts relevant to these cases, performs necessary calculations, interprets their implications for managerial decisions, and underscores the importance of CVP analysis in strategic planning.
Break-even Analysis for Derby Phones
To determine the break-even point, where total revenues equal total costs, the fixed costs are divided by the contribution margin per unit. The contribution margin per unit is calculated as sales price minus variable costs:
Contribution margin = $270 - $120 = $150
Break-even units = Fixed costs / Contribution margin = $300,000 / $150 = 2,000 units
Hence, Derby Phones must sell 2,000 units monthly to break even. At this level, total revenue equals total costs, and the company neither makes a profit nor incurs a loss.
Calculating Operating Profit for a Sales Volume of 5,000 Units
With a projected sales volume of 5,000 units, the total contribution margin becomes:
Total contribution = 5,000 units * $150 = $750,000
Operating profit is then:
Profit = Total contribution - Fixed costs = $750,000 - $300,000 = $450,000
This indicates that at 5,000 units, Derby Phones would generate an operating profit of $450,000, significantly exceeding the targeted profit of $180,000.
Scenario Analysis: Impact of Price Changes
When analyzing how sales price adjustments affect operating profit, the contribution margin per unit changes accordingly:
- Decreased price by 10%: new price = $270 * 0.90 = $243
- Increased price by 20%: new price = $270 * 1.20 = $324
New contribution margins:
- At $243 price: $243 - $120 = $123
- At $324 price: $324 - $120 = $204
Calculations for 5,000 units:
For the reduced price:
Contribution margin total = 5,000 * $123 = $615,000
Operating profit = $615,000 - $300,000 = $315,000
For the increased price:
Contribution margin total = 5,000 * $204 = $1,020,000
Operating profit = $1,020,000 - $300,000 = $720,000
Thus, a 10% decrease in sales price reduces profit, while a 20% increase considerably boosts it, illustrating the sensitivity of profit to price variability.
Scenario Analysis: Impact of Variable Cost Changes
Variable costs directly influence contribution margin. A 10% decrease results in:
New variable cost = $120 * 0.90 = $108
New contribution margin = $270 - $108 = $162
Total contribution at 5,000 units: 5,000 * $162 = $810,000
Operating profit: $810,000 - $300,000 = $510,000
Conversely, a 20% increase in variable costs yields:
New variable cost = $120 * 1.20 = $144
Contribution margin = $270 - $144 = $126
Total contribution: 5,000 * $126 = $630,000
Operating profit: $630,000 - $300,000 = $330,000
This demonstrates how rising variable costs compress margins and profits, while reductions expand them, emphasizing the importance of controlling variable costs.
Expense and Cost Structure Changes and Their Effect on Profits
Suppose fixed costs decrease by 20% and variable costs increase by 10%. Fixed costs become:
New fixed costs = $300,000 * 0.80 = $240,000
Variable costs per unit become:
New variable cost = $120 * 1.10 = $132
New contribution margin per unit = $270 - $132 = $138
At projected sales of 5,000 units, total contribution = 5,000 * $138 = $690,000
Operating profit = $690,000 - $240,000 = $450,000
The profit has increased from initial calculations, illustrating how cost reductions significantly enhance profitability while cost increases diminish it.
Multi-Product Scenario and Break-even Analysis for On-the-Go, Inc.
On-the-Go, Inc. produces two types of cases, encouraging analysis of profit contribution and break-even points under different sales mixes. The contribution margin per unit for each product is:
- Programmer bag: $70 - $30 = $40
- Executive bag: $100 - $40 = $60
The expected sales volumes are 8,000 and 12,000 units respectively, with total fixed costs at $819,000. Total contribution margins are:
Programmer: 8,000 * $40 = $320,000
Executive: 12,000 * $60 = $720,000
Total contribution margin: $1,040,000
Expected profit: $1,040,000 - $819,000 = $221,000, which indicates the anticipated profitability at forecasted sales levels.
Break-even point in units for combined products:
The weighted average contribution margin per unit considers both products and their sales mix:
Contribution margin ratio for Programmer: $40 / $70 ≈ 0.5714
Contribution margin ratio for Executive: $60 / $100 = 0.6
Total contribution margin for combined units depends on the sales mix. At the current mix, the contribution margin per dollar of sales combines to determine break-even sales volume, which can be calculated as:
Total fixed costs / weighted average contribution margin ratio.
Alternative calculation involves proportionally combining the two products' contribution margins and sales volumes, which leads to the derivation of break-even units for the combined product line.
Changing the sales mix to 9 Programmer bags for every 1 Executive bag alters the contribution proportion and consequently the break-even volume, emphasizing how product mix influences profitability thresholds.
Conclusion
CVP analysis delivers critical insights into how sales volume, pricing strategies, cost management, and product mix affect profitability. The Derby Phones case highlights the impact of price and cost fluctuations, while the On-the-Go, Inc. example demonstrates how multi-product environments require careful contribution margin assessments and sales mix management. These analytical tools empower managers to make informed decisions, optimize profit margins, and strategically plan for market variability and operational efficiency.
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