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Stylewise Printing Company currently leases its only copy machine for \(\$ 1,000\) a month. The company is considering replacing this leasing agreement with a new contract that is entirely commission based. Under the new agreement Stylewise would pay a commission for its printing at a rate of \(\$ 10\) for every 500 pages printed. The company currently charges \(\$ 0.15\) per page to its customers. The paper used in printing costs the company \(\$ .03\) per page and other variable costs, including hourly labor amount to \(\$ .04\) per page. 1\. What is the company's breakeven point under the current leasing agreement? What is it under the new commission based agreement? 2\. For what range of sales levels will Stylewise prefer (a) the fixed lease agreement (b) the commission agreement? 3\. Do this question only if you have covered the chapter appendix in your class. Stylewise estimates that the company is equally likely to sell 20,\(000 ; 40,000 ; 60,000 ; 80,000 ;\) or 100,000 pages of print. Using infor mation from the original problem, prepare a table that shows the expected profit at each sales level under the fixed leasing agreement and under the commission based agreement. What is the expected value of each agreement? Which agreement should Stylewise choose?

Step by step solution

01

Calculate Revenue and Costs

First, calculate the revenue and costs. For each printed page, the revenue is \(\\( 0.15\) per page, while the cost is \(\\) 0.03 + \\( 0.04 = \\) 0.07\) per page. This includes paper cost and other variable costs. Thus, the profit per page is \(\\( 0.15 - \\) 0.07 = \$ 0.08\).

02

Breakeven Point under Leasing Agreement

Under the current leasing agreement, Stylewise pays a fixed cost of \(\$ 1,000\) monthly. To find the breakeven point where costs equal revenues, divide the fixed cost by the profit per page: \( \frac{1000}{0.08} = 12,500 \) pages. Hence, they must print 12,500 pages to break even.

03

Breakeven Point under Commission Agreement

In the commission agreement, the company pays \(\\( 10\) for every 500 pages, which is \(\\) 0.02\) per page. Combine this with the \(\\( 0.07\) cost, making total cost \(\\) 0.09\) per page. Therefore, profit per page is \(\\( 0.15 - \\) 0.09 = \$ 0.06\). Breakeven is \( \frac{0}{0.06} = 0 \) pages, since the only costs are variable, they are always covered by the revenue.

04

Sales Level Preferences

For the fixed lease agreement to be cheaper, Stylewise should print fewer than 12,500 pages. For more than 12,500 pages, the commission agreement is better due to lower costs per page.

05

Expected Profit Calculation

Calculate profits for each sales level. For each level, subtract total costs from total revenue and then calculate the average profit for both agreements.

06

Decision Based on Expected Values

Calculate expected values by multiplying profits at each sales level by their probabilities and summing them. The agreement with the higher expected value is preferred.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fixed Costs

Fixed costs are expenses that remain constant regardless of the level of production or sales. In the context of Stylewise Printing Company, the fixed cost is the $1,000 monthly lease for their copy machine. Fixed costs are incurred independently of how many pages are printed.
These costs are typically long-term and do not fluctuate with the output level.
For companies, it is crucial to carefully analyze fixed costs to ensure they are sustainable and within budget. Fixed costs create a financial obligation that can affect the company’s cash flow if sales do not cover them. It is important to achieve a sales volume that covers these fixed costs, which leads us to the breakeven analysis.

Variable Costs

Variable costs vary directly with the volume of production. For Stylewise Printing Company, variable costs include the cost of paper and hourly labor, amounting to $0.07 per page. Under the new commission-based agreement, this cost increases by an additional $0.02 per page for the commission, making it $0.09.
Variable costs increase as production increases, and decrease as production decreases.
Businesses need to monitor and control variable costs because they directly impact profitability. By keeping these costs in check, companies can maintain favorable profit margins. When making business decisions such as changing a leasing agreement, companies must consider both variable and fixed costs to determine their impacts on overall costs and profitability.

Profit Margin

Profit margin is a measure of how much profit a company makes for each dollar of revenue. For Stylewise Printing Company, the profit margin is calculated based on the difference between revenue per page ($0.15) and total costs per page. Under the leasing agreement, with costs at $0.07 per page, the profit margin is $0.08 per page. Under the commission-based agreement, the margin decreases slightly to $0.06 per page.
The profit margin reflects the efficiency in controlling costs while generating revenue.
A higher profit margin indicates better control of costs and higher profitability. Companies should strive for higher profit margins as they indicate better cost management and financial health. When comparing different business strategies, such as choosing between leasing and commission agreements, analyzing profit margins can reveal which option is more favorable financially.

Cost-Volume-Profit Analysis

Cost-Volume-Profit (CVP) analysis is a method that helps businesses understand the relationship between costs, sales volume, and profit. It's a crucial tool for decision-making. For Stylewise Printing Company, CVP analysis can help determine the breakeven point - the sales level at which total revenue equals total costs.
This analysis shows that under the leasing agreement, the breakeven point is 12,500 pages. However, under the commission agreement, since all costs are variable and directly covered by revenue, the company technically breaks even immediately.
CVP analysis provides insight into the impact of changes in costs, sales volume, and pricing. It can help identify at what sales levels each agreement is more profitable. By using CVP analysis, businesses like Stylewise can strategically plan their operations and pricing to maximize profits at different sales levels, ensuring financial stability and growth.