91Ó°ÊÓ

The Doral Company manufactures and sells pens. Currently, 5,000,000 units are sold per year at \(\$ 0.50\) per unit. Fixed costs are \(\$ 900,000\) per year. Variable costs are \(\$ 0.30\) per unit. Consider each case separately: 1a. What is the current annual operating income? b. What is the present breakeven point in revenues? Compute the new operating income for each of the following changes: 2\. A \(\$ 0.04\) per unit increase in variable costs 3\. \(A \cdot 10 \%\) increase in fixed costs and a \(10 \%\) increase in units sold 4\. \(A 20 \%\) decrease in fixed costs, a \(20 \%\) decrease in selling price, a \(10 \%\) decrease in variable cost per unit, and a \(40 \%\) increase in units sold Compute the new breakeven point in units for each of the following changes: 5\. \(A \cdot 10 \%\) increase in fixed costs 6\. \(A \cdot 10 \%\) increase in selling price and a \(\$ 20,000\) increase in fixed costs.

Step by step solution

01

Calculate Current Annual Operating Income

The current annual operating income is the difference between total revenue and total costs. Start by calculating the total revenue: \(5,000,000 \times 0.50 = \\( 2,500,000\). Calculate the total variable cost: \(5,000,000 \times 0.30 = \\) 1,500,000\). The total cost is the sum of the fixed costs and total variable costs, \(900,000 + 1,500,000 = \\( 2,400,000\). Therefore, operating income is \(2,500,000 - 2,400,000 = \\) 100,000\).

02

Calculate Present Breakeven Point in Revenue

To find the breakeven point in revenues, we need to know when the total revenue equals the total costs. The breakeven volume in units is calculated as \( \frac{900,000}{0.50 - 0.30} = 4,500,000\) units. Therefore, breakeven point in revenue is \(4,500,000 \times 0.50 = \$ 2,250,000\).

03

Compute New Operating Income for Change 2

If variable costs increase by \(\\(0.04\) per unit, they become \(\\) 0.34\) per unit. New total variable costs are \(5,000,000 \times 0.34 = \\( 1,700,000\). New total costs are now \(1,700,000 + 900,000 = \\) 2,600,000\). New operating income is \(2,500,000 - 2,600,000 = -\$ 100,000\).

04

Compute New Operating Income for Change 3

With a \(10\%\) increase in fixed costs, they become \(900,000 \times 1.10 = \\( 990,000\). With a \(10\%\) increase in units sold, the sales volume becomes \(5,000,000 \times 1.10 = 5,500,000\) units. Total revenue is now \(5,500,000 \times 0.50 = \\) 2,750,000\) and variable costs are \(5,500,000 \times 0.30 = \\( 1,650,000\). Total costs are \(990,000 + 1,650,000 = \\) 2,640,000\). Thus the new operating income is \(2,750,000 - 2,640,000 = \$ 110,000\).

05

Compute New Operating Income for Change 4

With a \(20\%\) decrease in fixed costs, they become \(900,000 \times 0.80 = \\( 720,000\). A \(20\%\) decrease in selling price changes it from \(0.50\) to \(0.40\) and a \(10\%\) decrease in variable cost changes it to \(0.30 \times 0.90 = \\) 0.27\). Sales units increase by \(40\%\) to \(5,000,000 \times 1.40 = 7,000,000\). Total revenue now is \(7,000,000 \times 0.40 = \\( 2,800,000\) and variable costs are \(7,000,000 \times 0.27 = \\) 1,890,000\). Total costs are \(720,000 + 1,890,000 = \\( 2,610,000\). New operating income becomes \(2,800,000 - 2,610,000 = \\) 190,000\).

06

New Breakeven Point in Units for Change 5

For a \(10\%\) increase in fixed costs, they are \(990,000\) and selling price remains \(0.50\) and variable cost \(0.30\). Breakeven units are \(\frac{990,000}{0.50 - 0.30} = 4,950,000\) units.

07

New Breakeven Point in Units for Change 6

With a \(10\%\) increase in selling price, it changes to \(0.55\) and fixed costs increase by \$ 20,000 making them \(920,000\). Variable costs remain \(0.30\). Breakeven units now are \(\frac{920,000}{0.55 - 0.30} \approx 3,680,000\) units.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Cost Accounting

Cost accounting is a process that helps businesses understand their costs to make better financial decisions. It's concerned with controlling and managing costs connected to making a product or providing a service. In cost accounting, you focus on determining how much it costs to produce each unit of a product. This information helps in setting prices and planning future operations. Key elements include recording, analyzing, and reporting all related costs.
Typically, costs are divided into fixed and variable costs, allowing for more granular insights. By understanding these, a business can find its break-even point, which is where total revenue equals total costs.

• Helps businesses plan budgets
• Aids in setting product prices strategically
• Supports decision-making processes by providing input on cost efficiency

Cost accounting is essential for profitability analysis, offering a detailed view of where and how a company incurs costs.

Variable Costs

Variable costs change with the level of production. They are directly linked to the output level, meaning as production increases, variable costs will increase and vice versa. For Doral Company, the variable cost for manufacturing pens is $0.30 per unit. Therefore, if they produce more pens, the total variable cost will rise proportionally.
Variable costs include costs like materials and production supplies. They are an essential part of cost analysis as they fluctuate based on how much is produced.

• Calculation: Variable cost per unit x Number of units produced = Total variable cost
• Examples: Raw materials, packaging, direct labor
• Impact on pricing and profitability, as variable costs affect margins

Adjusting variable costs can significantly impact production strategies and business profitability.

Fixed Costs

Fixed costs remain constant regardless of the production level. These are expenses that do not change even when the output changes. For instance, Doral Company has fixed costs of $900,000 annually. Regardless of whether they sell zero pens or millions, this cost remains unchanged.
These costs include items such as rent, salaries, and insurance. It's crucial for businesses to cover their fixed costs to ensure survival.

• Characteristics: Unchanging with production volume
• Includes expenses like lease payments, utilities, and salaries
• Important for calculating the breakeven point, as fixed costs must be covered by revenue for a business to be profitable

Understanding and managing fixed costs is vital for effective financial planning and long-term sustainability.

Operating Income

Operating income is a measure of a company's profitability from ordinary operations, excluding any other income or expenses not related to the core business activities. It's calculated as the difference between total revenue and total operating costs, which include both fixed and variable costs.
For Doral Company, the operating income is determined by subtracting total costs from total revenue. Initially, it was $100,000, with total revenue of $2,500,000 and total costs of $2,400,000.

• A key indicator of operational efficiency
• Does not include taxes or interest expenses
• Helps assess whether primary business activities are profitable

Monitoring operating income lets a business understand the financial health of its core operations and make necessary adjustments to improve profitability.