Question

Discussion Question The Miller Company has assembled the following data pertaining to certain costs which cannot be easily identified as either fixed or variable. Miller has heard about two methods of developing cost functions called the high-low method & scattergram method and has decided to compare both methods. The table below shows monthly data collected on department costs and on the number of hours worked over a recent 12-month period. Department Costs # of Hours 37,000 3,700 23,000 1,600 37,000 4,100 47,000 4,900 33,000 3.300 39,000 4,400 32,000 3,500 33,000 4,000 17,000 1,200 18,000 1,300 22,000 1,800 20,000 1,600 a) Determine the variable cost per hour and the fixed cost using the high-low method. b) What is the equation of the total mixed cost function? c) Prepare the scatter diagram for Miller Company. d) Using the line of best-fit, determine Miller's fixed cost per month and the variable cost per hour. (use og 3000 hours.) e) Which of the two methods appear more appropriate? Explain your answer.

Answer 1

A) Variable and Fixed Cost as per the High Low Method.
First, to calculate the Variable cost,
Variable Cost = (Highest Activity Cost - Lowest Activity Cost)/(highest Activity Hours - Lowest Activity Hours)
Variable Cost = (47000 - 17000)/(4900 - 1200)
Variable Cost = $ 8.108 per hour
Now, For Fixed Cost,
Fixed Cost=Highest Activity Cost − (Variable Cost×Highest Activity Hours)​
Fixed Cost= 47000 − (8.108×4900)​
Fixed Cost= $ 7270.80
B) Equation of the Total Mixed Cost Function.
The cost function as per the high-low method is y = 7270.8 + 8.1108(x)
C) Scatter Diagram.
Month	# of Hours	Department Costs
1	1200	17000
2	1300	18000
3	1600	20000
4	1600	23000
5	1800	22000
6	3300	33000
7	3500	32000
8	3700	37000
9	4000	33000
10	4100	37000
11	4400	39000
12	4900	47000
	50000 45000 40000 35000 30000 25000 20000 15000 10000 . 5000 | 0 100 2000 300 4000 500 6000
C) Fixed Cost per month and Variable Cost per hour(using 3000 hours).
Fixed Cost as per Line of Best Fit = y-intercept = $ 9328.8
Variable Cost as per Line of Best Fit = Slope of line of best fit
To calculate slop we will take two points on line: (0,9328.80) and (3000,30000)
Variable Cost per hour = (30000-9328.80)/(3000-0)
Variable Cost per hour = $ 6.89 per hour
C) Analysis of the two methods.
As we can see that the difference in results between the two methods lies in the range of samples taken. In the first method, High Low Method, only two extreme points to determine the fixed and variable part of the costs. While in the second Scatter Graph(Diagram) Method, all the data is used for the determination of the costs. Therefore, in comparison to the High Low Method, the Scatter Graph(Diagram) Method is more appropriate because it considers all data points in analysis.