Problem 7 - Accounting

Question

Shatner Inc. has decided to use the high-low method to estimate the total cost and the fixed and variable cost components of the total cost. The data for various levels of production are as follows: \begin{tabular}{cc} Units Produced & Total Costs \\ \hline 7,500 & \(\$ 600,000\) \\ 12,500 & 725,000 \\ 20,000 & 800,000 \end{tabular} a. Determine the variable cost per unit and the fixed cost. b. Based on part (a), estimate the total cost for 10,000 units of production.

Step-by-Step Solution

Answer

Variable cost per unit is \(\$16\); Fixed cost is \(\$480,000\). Estimated cost for 10,000 units is \(\$640,000\).

Step 1: Identify High and Low Activity Points

First, let's identify the points with the highest and lowest levels of production. The lowest units produced is 7,500 with a total cost of \( \\(600,000 \), and the highest units produced is 20,000 with a total cost of \( \\)800,000 \). We will use these points to apply the high-low method.

Step 2: Calculate Variable Cost per Unit

The variable cost per unit is calculated by the change in total cost divided by the change in the number of units produced: \[\text{Variable Cost per Unit} = \frac{800,000 - 600,000}{20,000 - 7,500} = \frac{200,000}{12,500} = \$16 \text{ per unit}\]

Step 3: Calculate Total Fixed Cost

Now, use the variable cost per unit to find the total fixed cost. Using the low point, calculate as follows: \[\text{Total Fixed Cost} = 600,000 - (7,500 \times 16) = 600,000 - 120,000 = 480,000 \]

Step 4: Estimate Total Cost for 10,000 Units

Using the values calculated, estimate the total cost for producing 10,000 units. \[\text{Total Cost} = (10,000 \times 16) + 480,000 = 160,000 + 480,000 = 640,000\]

Key Concepts

Understanding Variable Costs

Variable costs are expenses that change in direct proportion to the level of production activity in a company. For each additional unit produced, the variable costs increase by a consistent amount per unit. These costs are directly tied to the production output.

Here are some key characteristics of variable costs:

• Proportionality: They rise or fall directly with production volume. If you double the number of units produced, your total variable costs will also double.
• Unit Consistency: The cost per unit remains constant, regardless of how many units are produced.
• Examples: Some examples include raw materials, direct labor (if labor is paid per unit produced), and sales commissions.

In our original exercise, we calculated the variable cost per unit using the high-low method. This method gives us a reliable estimate when data points are linear and consistent. By dividing the change in total costs by the change in units, we determine that each unit costs $16 to produce.

Understanding these costs is essential for budgeting and identifying how changes in production levels impact overall expenses.

Exploring Fixed Costs

Fixed costs are expenses that do not change with the level of production or sales volume. These costs remain constant over a period, regardless of how many units a company produces or sells. Understanding fixed costs is critical to effectively manage the financial health of a business.

Key aspects of fixed costs include:

• Stability: Fixed costs remain constant whether the business is booming or facing a downturn. They need to be covered to continue operations.
• Unchanged Per Unit: While total fixed costs remain the same, the fixed cost per unit decreases as production increases, because the costs are spread over more units.
• Examples: Common examples are rent, salaries of permanent staff, depreciation on equipment, and insurance premiums.

In our exercise, after calculating the variable cost, we found the total fixed cost to be $480,000. This calculation was made using the equation for total cost at the low activity level, which allows us to isolate fixed costs by subtracting total variable costs.

Accounting for fixed costs accurately ensures that businesses cover all their expenses and understand how changes in output might affect profits.

Cost Estimation Using the High-Low Method

The high-low method is a cost estimation technique used to separate mixed costs into fixed and variable components. This method is particularly useful when you have a set of data representing different levels of production or business activity and you want to predict future costs.

Here's how the high-low method works:

• Select Data Points: Identify the periods with the highest and lowest levels of activity. These data points will provide the basis for your calculations.
• Calculate Variable Costs: Subtract the total cost of the low activity level from the high activity level to find the change in cost, then divide by the change in activity to find the variable cost per unit.
• Determine Fixed Costs: Use the variable cost to find the fixed cost by substituting into the total cost equation for either the high or low activity level.
• Estimate Future Costs: With the fixed and variable costs identified, you can predict the total cost for any level of production by using the equation: \[\text{Total Cost} = (\text{Variable Cost per Unit} \times \text{Number of Units}) + \text{Total Fixed Costs}\]

In our example, after determining the variable and fixed costs, we accurately estimated the total cost for producing any number of units. For 10,000 units, the estimated total cost was calculated to be $640,000.

The high-low method provides a simple, yet effective way to estimate costs and plan for future production needs.