Problem 7 - Accounting

Question

W \& O 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}{cr} Units Produced & Total Costs \\ \hline 10,000 & \(\$ 750,000\) \\ 22,500 & 845,000 \\ 30,000 & 950,000 \end{tabular} a. Determine the variable cost per unit and the fixed cost. b. Based on part (a), estimate the total cost for 25,000 units of production.

Step-by-Step Solution

Answer

Variable cost per unit is $10; fixed cost is $650,000. Total cost for 25,000 units is $900,000.

Step 1: Identify the High and Low Activity Levels

First, identify the highest and lowest levels of production from the data. Here, the highest production level is 30,000 units with a total cost of $950,000, and the lowest is 10,000 units with a total cost of $750,000.

Step 2: Calculate Variable Cost per Unit

Use the high-low method formula to find the variable cost per unit. The formula is:\[\text{Variable Cost per Unit} = \frac{\text{Cost at High Level} - \text{Cost at Low Level}}{\text{Units at High Level} - \text{Units at Low Level}}\]Substitute the given values:\[\text{Variable Cost per Unit} = \frac{950,000 - 750,000}{30,000 - 10,000} = \frac{200,000}{20,000} = 10\]Thus, the variable cost per unit is $10.

Step 3: Determine the Fixed Cost

Use the total cost formula to find the fixed cost:\[\text{Total Cost} = (\text{Variable Cost per Unit} \times \text{Number of Units}) + \text{Fixed Cost}\]Use the low point for substitution:\[750,000 = (10 \times 10,000) + \text{Fixed Cost}\]Solve for the fixed cost:\[\text{Fixed Cost} = 750,000 - 100,000 = 650,000\]The fixed cost is $650,000.

Step 4: Estimate the Total Cost for 25,000 Units

Now, estimate the total cost for producing 25,000 units using the formula:\[\text{Total Cost} = (\text{Variable Cost per Unit} \times \text{Number of Units}) + \text{Fixed Cost}\]Substitute the values:\[\text{Total Cost} = (10 \times 25,000) + 650,000\]Calculate:\[\text{Total Cost} = 250,000 + 650,000 = 900,000\]Thus, the estimated total cost for 25,000 units is $900,000.

Key Concepts

Cost Estimation

Cost estimation is a crucial aspect in the field of business and production. It involves predicting the total costs needed for producing a certain number of units. This process helps a company to plan its budget, manage resources, and set prices.

The high-low method is one common technique of cost estimation. It uses the highest and lowest activity levels to determine the variable and fixed costs. This approach is simple and quick, making it useful for understanding cost behavior.

For instance, to estimate costs accurately, production managers compare costs at two extremes of production levels. They then utilize this data to forecast costs at any desired production level.

By understanding cost estimation, businesses can make informed decisions regarding pricing, budgeting, and forecasting. This understanding directly impacts profitability and operational efficiency.

Variable Cost

Variable costs change in direct proportion to the level of production. For example, materials, labor or utility expenses are often considered variable costs. The more units a company produces, the higher the variable cost because it requires more resources. In the high-low method, the variable cost per unit is calculated by: - Taking the difference in total costs between the highest and lowest production levels. - Dividing by the difference in production units. For instance, if producing 30,000 units costs $950,000 and producing 10,000 units costs $750,000, then the variable cost per unit is $10. Variable costs are critical for businesses to understand because they impact pricing and profitability. By effectively managing these costs, companies can improve their margins and remain competitive in the market.

Fixed Cost

Fixed costs are expenses that do not change with varying levels of production. These costs include rent, salaries, and insurance. Regardless of how much a company produces, fixed costs remain constant.

In cost estimation, particularly through the high-low method, we first determine the variable cost per unit. We use it to subtract from the total cost at any chosen production level to find the fixed cost.

For example, while producing 10,000 units costs $750,000, with a determined variable cost per unit of $10, the fixed cost calculates as $650,000.

Understanding fixed costs helps businesses decide when to increase or decrease production without overspending or impacting the budget significantly. It's essential for setting a company’s long-term financial strategy and operational planning.

Production Levels

Production levels describe the amount of product a company manufactures over a specific period. These levels can significantly affect both variable and fixed costs.

When using the high-low method, identifying the highest and lowest production levels is crucial. They form the basis upon which variable costs per unit and fixed costs are calculated, allowing for a broader understanding of cost behavior across different levels of production.

For example, in the given data, the company produces between 10,000 and 30,000 units. Analyzing these extremes helps in understanding how costs shift with production scale. This insight aids businesses in optimizing production processes and maintaining cost-efficiency.

Understanding production levels ensures that companies can better align their resources with demand, anticipate financial needs, and strategically grow or scale operations.