91Ó°ÊÓ

Total and unit cost, decision making. Gayle's Glassworks makes glass flanges for scientific use. Materials cost \(\$ 1\) per flange, and the glass blowers are paid a wage rate of \(\$ 28\) per hour. A glass blower blows 10 flanges per hour. Fixed manufacturing costs for flanges are \(\$ 28,000\) per period. Period (nonmanufacturing) costs associated with flanges are \(\$ 10,000\) per period and are fixed. 1\. Graph the fixed, variable, and total manufacturing cost for flanges, using units (number of flanges) on the \(x\) -axis. 2\. Assume Gayle's Glassworks manufactures and sells 5,000 flanges this period. Its competitor, Flora's Flasks, sells flanges for \(\$ 10\) each. Can Gayle sell below Flora's price and still make a profit on the flanges? 3\. How would your answer to requirement 2 differ if Gayle's Glassworks made and sold 10,000 flanges this period? Why? What does this indicate about the use of unit cost in decision making?

Step by step solution

01

Calculate the fixed and variable costs per flange

First, we need to determine the fixed costs and variable costs per flange. Fixed costs do not change with the number of units produced, while variable costs do. In this case, the fixed costs include both fixed manufacturing costs and fixed nonmanufacturing costs. Fixed costs per period = \(28,000 + 10,000 = \$38,000\) Now, we will calculate the variable cost per flange, which includes material costs and labor costs. Since a glass blower makes 10 flanges per hour and is paid $28 per hour, the labor cost per flange is: Labor cost per flange = \(28 \div 10 = \$2.80\) Now, we can add the material cost to find the total variable cost: Variable cost per flange = \(1 + 2.80 = \$3.80\)

02

Graph the fixed, variable, and total manufacturing costs

Now that we have calculated the fixed and variable costs per flange, we can graph these costs against the number of flanges (x-axis). The fixed cost line will be horizontal since it doesn't change with the number of units produced. The variable cost line will have a slope because as the number of units produced increases, the total variable cost will also increase. The slope will be equal to the variable cost per flange ($3.80). Finally, the total cost line can be found by adding the fixed cost and the total variable cost. The total cost line will have the same slope as the variable cost line but will be shifted upwards by the fixed cost amount ($38,000).

03

Determine if Gayle's Glassworks can sell below Flora's price and still make a profit

Assuming Gayle's Glassworks manufactures and sells 5,000 flanges, we need to calculate their total cost and revenue to determine if they can sell below Flora's price of $10 and still make a profit. Total Cost = Fixed Cost + (Variable Cost per Flange × Number of Flanges) Total Cost = \(38,000 + (3.80 × 5,000) = \$57,000\) Given that Flora's price is \(10 per flange, if Gayle's Glassworks wants to sell below Flora's price, they need to find a price that will yield a total revenue greater than their total cost. Let's assume Gayle's price is \)p$. Total Revenue = \(p × 5,000\) For profit, Total Revenue > Total Cost, so: \(5,000p > 57,000\) Solving for p, we get: \(p > 11.40\) To summarize, Gayle's Glassworks cannot sell below Flora's price of $10 and still make a profit when producing and selling 5,000 flanges.

04

Analyze the situation if Gayle's Glassworks made and sold 10,000 flanges

If Gayle's Glassworks manufactured and sold 10,000 flanges, we need to recalculate their total cost and analyze how the selling price would change to make a profit. Total Cost = Fixed Cost + (Variable Cost per Flange × Number of Flanges) Total Cost = \(38,000 + (3.80 × 10,000) = \$76,000\) Now, we will use the same equation as earlier to determine the minimum price Gayle's Glassworks can sell their flanges to make a profit: Total Revenue = \(p × 10,000\) For profit, Total Revenue > Total Cost, so: \(10,000p > 76,000\) Solving for p, we get: \(p > 7.60\) In this case, when producing 10,000 flanges, Gayle's Glassworks can sell at a price below Flora's price ($10) and still make a profit. This indicates that unit cost plays a significant role in decision making. As the production volume increases, the fixed cost per unit decreases, which allows the company to sell products at a lower price while still remaining profitable.

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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 those expenses that do not change regardless of how many units a company produces. They are incurred even if production is zero. In the context of Gayle's Glassworks, fixed costs include both the fixed manufacturing and nonmanufacturing costs, which total $38,000 per period. These costs are essential in understanding the breakeven point and overall cost structure of a business.

For Gayle's Glassworks:

• Fixed Manufacturing Costs: $28,000
• Fixed Nonmanufacturing Costs: $10,000
• Total Fixed Costs: $38,000

Fixed costs are represented as a horizontal line on a cost graph because they do not vary with the number of flanges produced. Making accurate assessments of fixed costs is crucial for long-term planning since they are unavoidable regardless of production levels.

Variable Costs

Variable costs, in contrast to fixed costs, fluctuate with production volume. For Gayle's Glassworks, these include the costs of materials and labor directly associated with the production of each glass flange. Understanding variable costs is key to determining the total cost of production and managing budgeting effectively.

Here is a breakdown for Gayle's Glassworks:

• Material Cost per Flange: $1
• Labor Cost per Flange: $2.80 (calculated by $28/hour for 10 flanges)
• Total Variable Cost per Flange: $3.80

On a cost graph, the variable cost line slopes upwards, reflecting the increase in total costs as more units are produced. Knowing the variable cost per unit aids in price setting and profit calculation, ensuring that each sale covers its associated variable costs.

Break-even Analysis

Break-even analysis is a financial calculation used to determine the sales volume at which total costs equal total revenue. At this point, a business neither makes a profit nor suffers a loss. For Gayle's Glassworks, a break-even analysis can help in evaluating the feasibility of selling prices relative to both fixed and variable costs.

To calculate break-even, use the formula:\[\text{Sales Volume at Break-even} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}\]For example, if the selling price per flange needed to cover costs is above Flora's price of $10, Gayle's needs to consider whether reaching that volume is realistic given the market environment.

A decrease in fixed costs or variable costs, or an increase in unit selling price, will lower the break-even point, making higher profitability easier to achieve at lower sales volumes.

Unit Cost Analysis

Unit cost analysis is crucial in establishing the per-unit expenses associated with production. It helps businesses determine the minimum selling price at which they can sell their products and still cover their costs. For Gayle's Glassworks, calculating the unit cost involves adding together the variable and fixed costs per unit.

For each flange at a production volume of 10,000:

• Fixed Cost Per Unit: \(\frac{38,000}{10,000} = \\(3.80\)
• Variable Cost Per Unit: \)3.80
• Total Unit Cost: $7.60 per flange

Unit cost analysis indicates that as production increases, the fixed cost per unit decreases, allowing for a lower viable selling price while maintaining profitability. It is a powerful tool for strategic pricing and cost management, ensuring businesses set competitive prices without sacrificing margins.

Understanding the interplay between fixed and variable costs, along with break-even and unit cost analysis, provides a strong foundation for making informed business decisions regarding pricing and production.