Mountain Dental Services is a specialized dental practice whose only service is filling cavities. Mountain has recorded the following for the past nine months: Month Number of Cavities Filled Total Cost January 300 $5,000 February 650 6,050 March 325 5,200 April 475 5,750 May 550 6,050 June 575 6,200 July 600 6,250 August 350 5,100 September 700 6,600 Required: 1. Use the high-low method to estimate total fixed cost and variable cost per cavity filled. 2. Using these estimates, calculate Mountain’s total cost for filling 450 cavities.
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1. To estimate the total fixed cost and variable cost per cavity filled using the high-low method, we first identify the months with the highest and lowest levels of activity, that is, the number of cavities filled.
The highest level of activity is in September with 700 cavities filled at a total cost of $6,600. The lowest level of activity is in January with 300 cavities filled at a total cost of $5,000.
We can now compute the variable cost per cavity by taking the difference in total costs and dividing it by the difference in the number of cavities filled:
Variable Cost per Cavity = (Total Cost at highest activity - Total Cost at lowest activity) (Number of cavities at highest activity - Number of cavities at lowest activity)
Variable Cost per Cavity = ($6,600 - $5,000) / (700 - 300)
Variable Cost per Cavity = $1,600 / 400
Variable Cost per Cavity = $4.00 per cavity
Now, to determine the fixed cost, we subtract the variable costs at either the high or low level from the total cost at the same level. We will use the high level (September) for this calculation:
Fixed Cost = Total cost at highest activity - (Variable cost per cavity * Number of cavities at highest activity)
Fixed Cost = $6,600 - ($4.00 * 700)
Fixed Cost = $6,600 - $2,800
Fixed Cost = $3,800
Therefore, the estimated total fixed cost is $3,800 and the variable cost per cavity filled is $4.00.
2. Now, to calculate Mountain's total cost for filling 450 cavities, we can use the fixed cost and variable cost per cavity that we've determined above:
Total Cost = Fixed Cost + (Variable Cost per Cavity * Number of Cavities Filled)
Total Cost for 450 Cavities = $3,800 + ($4.00 * 450)
Total Cost for 450 Cavities = $3,800 + $1,800
Total Cost for 450 Cavities = $5,600
Therefore, the estimated total cost for filling 450 cavities is $5,600.