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Answer:
If the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".
Step-by-step explanation:
Note: The data needed to estimate costs using the high-low method is merged together. It is therefore sorted before answering the question as follows:
Month Machine Hours Electricity Costs
January 2,000 $18,950
February 2,400 $22,100
March 1,400 $14,050
April 2,600 $24,100
May 3,300 $28,800
June 2,800 $23,100
July 3,600 $25,300
August 3,000 $23,300
September 1,500 $16,600
October 3,200 $27,100
November 4,200 $32,100
December 3,700 $28,300
The explanation of the answer is now provided as follows:
Step 1: Calculation of variable cost per hour
From the data above, the highest Machine Hours and Electricity Costs occur in November, while the lowest occur in March. Therefore, we have:
Variable cost per hour = (Highest Electricity Costs - Lowest Electricity Costs) / (Highest Machine Hours - Lowest Machine Hours = ($32,100 - $14,050) / (4,200 – 1,400) = $18,050 / $2,800 = 6.44642857142857
Rounding to 2 decimal places as required, we have:
Variable cost per hour = $6.45
Therefore, the variable-cost components using the high-low method is $6.45.
Step 2: Calculation of total fixed cost
The formula for calculating the total cost is given as follows:
Total cost = Total Fixed Cost + Total Variable Cost ................. (1)
Where;
Total Variable Cost = Variable cost per hour * Machine hours at a particular Electricity Costs
Using highest levels of activity and substitute into equation (1), we have:
$32,100 = Total Fixed Cost + ($6.45 * 4,200)
Total Fixed Cost = $32,100 - ($6.45 * 4,200) = $32,100 - $27,090 = $5,010
Therefore, the fixed-cost components using the high-low method is $5,010.
Step 3: Derivation of the cost equation for electricity costs
The cost equation for electricity costs can be obtained based on the total cost function given in equation (1) above, where:
Total Fixed Cost = $5,010
Total Variable Cost = Variable cost per hour * Machine hours = $6.45 * Machine hours
Substituting the values into equation (1), we have:
Total cost = $5,010 + ($6.45 * Machine hours)
Therefore, if the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".
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