Question

Yarrawonga Company’s management accountant has collected the following information:

Units of Output 30 000 Units 42 000 Units

Direct materials $180 000 $252 000

Workers' wages 1 080 000 1 512 000

Supervisors' salaries 312 000 312 000

Equipment depreciation 151 200 151 200

Maintenance 81 600 110 400

Utilities 384 000 528 000

Total $2 188 800 $2 865 600

Required:

Using the high-low method and the information provided above:

a. Identify the linear cost function equation (5 marks)

b. Estimate the total cost at 36 000 units of output (1 mark)

c. Explain the managers about the potential use of nonlinear curves in cost functions and

cost analysis. Give two examples

Answer 1

1). Lower activity level = 30,000 units
Cost at lower level = $2,188,800
Higher activity level = 42,000 units
Cost at higher level = $2,865,600

Variable cost per unit = (Cost at higher level - Cost at lower level) / (Higher level - Lower level)
= ($2,865,600 - $2,188,800) / (42000 - 30000)
= $676,800 / 12000
= $56.4 per unit

Fixed cost = Total cost at lower level - Variable cost at lower level
= $2,188,800 - (30,000 * $56.4)
= $496,800

linear cost function = Y = a + bX
Y = $496,800 + $56.4X

2). Total cost of 36,000 units
Y = $496,800 + $56.4 * 36,000
Y = $2,527,200 i.e. Total cost

3). Cost functions are not always linear. A nonlinear cost function is a cost function for which the graph of total costs is not a straight line within the relevant range of operations. One example is a series of straight-line segments that change their slopes at critical intersection points within the range of operation. Another example would be a step function. A step function is a function where the cost remains the same over various ranges of the level of activity, but the cost increases by discrete amounts (or steps) as the level of activity advances from one range to another. In addition to the examples mentioned above, there are situations where the cost or use of resources can be represented by a curve instead of a single straight line or a group of segmented straight lines. One example of a curve is a learning curve. A learning curve is a function that measures how labor-hours per unit decline as units of production increase because workers are learning and becoming better at their jobs.