High-Low Method for a Service Company Continental 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 Continental Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved. Transportation Costs Gross-Ton Miles.

To apply the high-low method for estimating the fixed and variable components of transportation costs based on the provided data, you will need the following steps: 1. **Identify the Highest and Lowest Activity Levels**: Look at the gross-ton miles for the past six months and identify the highest and lowest values. 2. **Determine the Corresponding Transportation Costs**: Find the transportation costs that correspond to the highest and lowest gross-ton miles. 3. **Calculate the Variable Cost per Unit**: Use the formula: \[ \text{Variable Cost per Unit} = \frac{\text{Cost at Highest Activity} - \text{Cost at Lowest Activity}}{\text{Gross-Ton Miles at Highest Activity} - \text{Gross-Ton Miles at Lowest Activity}} \] 4. **Calculate Total Fixed Costs**: Once you have the variable cost per unit, you can use either the highest or lowest activity level to calculate the total fixed costs using the formula: \[ \text{Total Fixed Costs} = \text{Total Cost} - (\text{Variable Cost per Unit} \times \text{Gross-Ton Miles}) \] 5. **Formulate the Cost Equation**: Finally, you can express the total transportation costs as a function of gross-ton miles: \[ \text{Total Transportation Costs} = \text{Total Fixed Costs} + (\text{Variable Cost per Unit} \times \text{Gross-Ton Miles}) \] ### Example Calculation Let's assume you have the following data for the past six months: | Month | Gross-Ton Miles | Transportation Costs | |-------|------------------|----------------------| | 1 | 10,000 | $50,000 | | 2 | 15,000 | $70,000 | | 3 | 20,000 | $90,000 | | 4 | 25,000 | $110,000 | | 5 | 30,000 | $130,000 | | 6 | 5,000 | $30,000 | 1. **Identify Highest and Lowest Activity Levels**: - Highest: 30,000 gross-ton miles with $130,000 costs. - Lowest: 5,000 gross-ton miles with $30,000 costs. 2. **Calculate Variable Cost per Unit**: \[ \text{Variable Cost per Unit} = \frac{130,000 - 30,000}{30,000 - 5,000} = \frac{100,000}{25,000} = 4 \] So, the variable cost per gross-ton mile is $4. 3. **Calculate Total Fixed Costs**: Using the highest activity level: \[ \text{Total Fixed Costs} = 130,000 - (4 \times 30,000) = 130,000 - 120,000 = 10,000 \] 4. **Formulate the Cost Equation**: \[ \text{Total Transportation Costs} = 10,000 + (4 \times \text{Gross-Ton Miles}) \] ### Conclusion Using the high-low method, you have estimated that the fixed costs are $10,000 and the variable cost is $4 per gross-ton mile. The total transportation cost can be expressed as: \[ \text{Total Transportation Costs} = 10,000 + 4 \times \text{Gross-Ton Miles} \] You can now use this equation to estimate transportation costs for any level of gross-ton miles within the relevant range.