Final answer:
The monthly fixed cost is the difference between the total cost at the highest level and the product of the variable cost per machine hour and high activity machine hours, which is $18,000. Total variable costs for the six months are $182,000, and total fixed costs are $108,000.
Step-by-step explanation:
To compute the variable electricity cost per machine hour, we first identify the highest and lowest activity levels and their associated costs. The highest activity level in the provided data is on July with 6,000 machine hours at $60,000, and the lowest is on December with 3,000 machine hours at $39,000. To calculate the variable cost per machine hour, we subtract the total costs and divide by the difference in machine hours:
Variable cost per machine hour = (Cost at high activity level - Cost at low activity level) / (High activity level machine hours - Low activity level machine hours)
Variable cost per machine hour = ($60,000 - $39,000) / (6,000 - 3,000) = $21,000 / 3,000 = $7 per machine hour
Next, to determine the monthly fixed electricity cost, we can use either the total cost at the highest or the lowest activity level. Using the highest level for July as an example:
Fixed cost = Total cost at high activity level - (Variable cost per machine hour × High activity level machine hours)
Fixed cost = $60,000 - ($7 × 6,000) = $60,000 - $42,000 = $18,000
For the total variable electricity costs for the six-month period, we multiply the variable cost per machine hour by the total machine hours:
Total variable costs = Variable cost per machine hour × Total machine hours for the six months
Total variable costs = $7 × 26,000 = $182,000
Finally, the fixed electricity costs for the six-month period remain constant at $18,000 a month, resulting in:
Total fixed costs = Monthly fixed cost × Number of months
Total fixed costs = $18,000 × 6 = $108,000