Question

The Fuller Company has assembled the following data pertaining to certain costs which cannot be easily identified as either fixed or variable. Fuller 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 costs and on the number of hours worked over a recent 12-month period.

                                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, clearly showing any outliers.

d) Using the line of best-fit, determine Fuller’s fixed cost per month and the variable cost per hour. (Use 0 & 3000 hours.)

e) In view of Fuller’s cost behaviour pattern, which of the two methods appear more appropriate? Explain your answer.

Answer 1

1. The variable cost per hour and fixed cost using high-low method

Variable Cost per hour = Cost at highest level - Cost at lowest level

hours at highest level - hours at lowest level

Variable cost per hour = (47000-17000)/(4900-1200)

= $8.1081 per hour

Fixed cost = Total cost - variable cost

= 47000 - (8.1081 x 4900) = 17000-(8.1081x1200)

= $7270

2. Equation of mixed cost function

Y = $7270 + $8.1081x

where,

Y = Total cost

x = Total hours

3. Scatter Diagram

4. Using the line of best fit, Fuller's fixed cost per month and Variable cost per hour

Fixed cost = y - intercept = $9000

Variable cost per hour = Slope of regression line

To calculate slope, we will take two points on line: (0, $9000) and (3000, 30000)

Variable cost per hour = ($30000-$9000) / (3000 -0) = $7 per hour

5. In view of Fuller's cost behavior pattern, Scatter Graph is appearing to be more appropriate.

Scatter graph method uses all the data related to cost, not just the cost at the highest and lowest level.

Fuller's cost is changing every month so it better to use Scatter graph method.