Average maintenance costs are $1.50 per machine-hour at an activity level of 8,000 machine-hours and $1.20 per machine-hour at an activity level of 13,000 machine-hours. Assuming that this activity is within the relevant range, total expected maintenance cost for a budgeted activity level of 10,000 machine-hours would be closest to?
A)$15,000.
B)$16,128.
C)$13,440.
D)$11,433.

Question

Quizplus · Accepted Answer

The total expected maintenance cost can be calculated using the high-low method to determine the variable and fixed components of the cost. The variable cost per machine-hour is calculated as the change in total cost divided by the change in machine-hours. The fixed cost is then calculated by subtracting the total variable cost at either activity level from the total cost at that level. Finally, the total cost at the budgeted activity level is calculated by adding the fixed cost to the variable cost at the budgeted level.1. Calculate variable cost per machine-hour:$$ \text{Variable Cost per Machine-Hour} = \frac{($1.50 - $1.20)}{(8,000 - 13,000 \text{ machine-hours})} = \frac{$0.30}{-5,000} = -$0.06 $$(Note: The negative sign indicates a decrease in cost per machine-hour as activity increases, which is not typical for variable costs. However, for the purpose of this calculation, we'll use the absolute value to find the variable cost component.)2. Calculate total variable cost at each activity level and determine fixed cost:$$ \text{Total Variable Cost at 8,000 machine-hours} = 8,000 \times $1.50 = $12,000 $$$$ \text{Total Variable Cost at 13,000 machine-hours} = 13,000 \times $1.20 = $15,600 $$(These calculations are incorrect based on the initial approach; they should calculate the total cost at each level, not the variable cost. The correct approach is outlined below.)Correct Approach:1. Calculate the variable cost per machine-hour:$$ \text{Change in Cost} = (13,000 \times $1.20) - (8,000 \times $1.50) $$$$ \text{Change in Machine-Hours} = 13,000 - 8,000 $$$$ \text{Variable Cost per Machine-Hour} = \frac{\text{Change in Cost}}{\text{Change in Machine-Hours}} $$2. Calculate the fixed cost:$$ \text{Fixed Cost} = \text{Total Cost} - (\text{Variable Cost per Machine-Hour} \times \text{Machine-Hours}) $$3. Calculate the total expected maintenance cost at 10,000 machine-hours:$$ \text{Total Expected Maintenance Cost} = (\text{Variable Cost per Machine-Hour} \times 10,000) + \text{Fixed Cost} $$Given the error in the initial step, let's correct the calculation:1. Variable cost per machine-hour:$$ \text{Variable Cost per Machine-Hour} = \frac{($15,600 - $12,000)}{(13,000 - 8,000)} = \frac{$3,600}{5,000} = $0.72 $$2. Calculate fixed cost (using one of the points, e.g., 13,000 machine-hours):$$ \text{Total Cost at 13,000 machine-hours} = 13,000 \times $1.20 = $15,600 $$$$ \text{Fixed Cost} = \text{Total Cost} - (\text{Variable Cost per Machine-Hour} \times \text{Machine-Hours}) $$$$ \text{Fixed Cost} = $15,600 - ($0.72 \times 13,000) $$$$ \text{Fixed Cost} = $15,600 - $9,360 = $6,240 $$3. Calculate total expected maintenance cost at 10,000 machine-hours:$$ \text{Total Expected Maintenance Cost} = ($0.72 \times 10,000) + $6,240 = $7,200 + $6,240 = $13,440 $$Therefore, the closest total expected maintenance cost for a budgeted activity level of 10,000 machine-hours is $13,440.

Average Maintenance Costs Are $1