Question

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow: 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 Summary Output Regression Statistics Multiple R 0.960 R Square 0.921 Adjusted R2 0.913 Standard Error 1,545.17 Observations 12.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7,465.99 1,566.61 4.77 0.00 3,975.37 10,956.62 Machine Hours 5.76 0.53 10.78 0.00 4.57 6.95 If the controller uses the high-low method to estimate costs, the cost equation for electricity costs is: (Round intermediate calculations to 2 decimal places.)

Answer 1

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)".