Problem 8 - Accounting

Question

Great Plains Railroad decided to use the high-low method and operating data from the past six months to estimate the fixed and variable components of transportation costs. The activity base used by Great Plains Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved. \begin{tabular}{lrc} & Transportation Costs & Gross-Ton Miles \\ \hline January & \(\$ 1,050,000\) & 285,000 \\ February & \(1,150,000\) & 325,000 \\ March & \(1,350,000\) & 400,000 \\ April & \(1,000,000\) & 250,000 \\ May & \(1,225,000\) & 375,000 \\ June & \(1,600,000\) & 450,000 \end{tabular} Determine the variable cost per gross-ton mile and the fixed cost.

Step-by-Step Solution

Answer

Variable cost is $3 per gross-ton mile; fixed cost is $250,000.

Step 1: Identify High and Low Activity Levels

Examine the given dataset and identify the periods with the highest and lowest levels of activity in terms of gross-ton miles. Here, June has the highest value with 450,000 gross-ton miles, and April has the lowest with 250,000 gross-ton miles.

Step 2: Note Corresponding Costs

For the highest activity level (June), the cost is $1,600,000, and for the lowest activity level (April), the cost is $1,000,000. These figures will be used to calculate the variable cost per gross-ton mile.

Step 3: Calculate Variable Cost per Gross-Ton Mile

Use the high-low method formula for variable cost: \[ \text{Variable Cost per Gross-Ton Mile} = \frac{\text{Cost at High Level} - \text{Cost at Low Level}}{\text{High Activity Level} - \text{Low Activity Level}} \]Substitute the identified values:\[ \text{Variable Cost per Gross-Ton Mile} = \frac{1,600,000 - 1,000,000}{450,000 - 250,000} = \frac{600,000}{200,000} = 3 \text{ dollars per gross-ton mile} \]

Step 4: Calculate Fixed Cost

Using the variable cost from Step 3, we can calculate the fixed cost. Rearrange the cost equation for one of the points, say April:\[ \text{Total Cost} = (\text{Variable Cost per GTM} \times \text{GTM}) + \text{Fixed Cost} \]Substituting April's values:\[ 1,000,000 = (3 \times 250,000) + \text{Fixed Cost} \]\[ 1,000,000 = 750,000 + \text{Fixed Cost} \]\[ \text{Fixed Cost} = 1,000,000 - 750,000 = 250,000 \text{ dollars} \]

Key Concepts

Variable Costs

The concept of variable costs is fundamental to understanding transportation expenses, especially in activities like those undertaken by Great Plains Railroad. Variable costs change in direct proportion to the activity level. In this exercise, the activity level is measured in terms of gross-ton miles (GTM).
Variable costs are calculated using the high-low method. Here’s a quick reminder of what the high-low method does: it identifies the periods with the highest and lowest activity levels to calculate the variable cost per unit. This is done by:

• Taking the difference in total costs between the high and low activity levels
• Dividing that difference by the change in activity level (GTM in this case)

So, using the exercise data from the months of June and April, we calculated:
The formula is: \[ \text{Variable Cost per GTM} = \frac{\text{Cost at High Level} - \text{Cost at Low Level}}{\text{High Activity Level} - \text{Low Activity Level}} \]
Plugging in the numbers:\[ \frac{1,600,000 - 1,000,000}{450,000 - 250,000} = 3 \text{ dollars per gross-ton mile} \]This means for every GTM, the cost increases by $3, reflecting how variable costs directly fluctuate with activity levels.

Fixed Costs

Like variable costs, fixed costs are an essential part of estimating a company's transportation expenses, but they behave differently. Fixed costs remain constant regardless of the level of activity. This means that even if Great Plains Railroad doesn't move any goods, there will still be costs incurred.
To find fixed costs, we use the variable cost estimated earlier. We choose a month, such as April in this example (where transportation costs were \(1,000,000 with 250,000 GTM), and plug those into the equation:

• Total Cost = (Variable Cost per GTM \( \times \) GTM) + Fixed Cost

Using April's numbers, the equation becomes:\[ 1,000,000 = (3 \times 250,000) + \text{Fixed Cost} \]This simplifies to:\[ 1,000,000 = 750,000 + \text{Fixed Cost} \]Solving for Fixed Cost:\[ 250,000 \text{ dollars} \]Thus, the fixed costs for the Great Plains Railroad operations amount to \)250,000.
This fixed cost could include expenses like managerial salaries or property taxes, which do not change with the level of railroad activity.

Gross-Ton Miles

Gross-ton miles (GTM) is a measure used by railroads to quantify their operational activity. It combines the weight of goods transported and the distance they travel. Simply put, it's calculated by multiplying the total tons of freight by the miles moved.
Railroad companies utilize GTM as a base to better understand their transportation costs and efficiency. It's like the heartbeat of the railroad's operations, indicating how much work is being done. The higher the GTM, the busier and likely more costly the operation.
In our exercise, GTM is crucial because it's used in the high-low method to determine both variable and fixed costs. Higher GTM typically leads to increased variable costs, as seen with the Great Plains Railroad. Understanding the GTM allows railroads to manage and optimize these costs effectively.

• Helps in planning and forecasting expenses
• Provides a clear metric for operational efficiency
• Aids in decision-making concerning resource allocation

The relationship between transportation costs and GTM helps companies like Great Plains Railroad set competitive rates while maintaining profitability.