3.3 Analysis of costs into fixed and variable elements:
　　High-low method
　　Step 1 – select the highest and lowest activity levels, and their associated costs
　　Step 2 – find the variable cost per unit
　　Step 3 – find the fixed cost by substitution, using either the high or low activity level.
　　Example 1:
　　Using high-low method to calculate the fixed and variable elements of the following costs:
　　Month Units produced Costs （$）
　　July 340 2,260
　　August 300 2,160
　　September 380 2,320
　　October 420 2,400
　　November 400 2,300
　　December 360 2,266
　　Solution:
　　Step 1- Select the highest and lowest activity levels, and their associated costs
　　Month Units produced Cost （$）
　　Highest activity level: October 420 2,400
　　Lowest activity level: August 300 2,160
　　Step 2 – find the variable cost per unit
　　Total cost at high activity level – total cost at low activity level
　　Variable cost per unit = total units at high activity level – total units at low activity level
　　= 2400 – 2160 = $2/unit
　　420 – 300
　　Step 3 – find the fixed cost by substitution, using either the high or low activity level.
　　Fixed cost = （total cost at high activity level） – （total cost at high activity level x variable cost per unit）
　　= $2,400 - $2 /unit x 420 units = $1,560
　　High- low method with stepped fixed cost
　　Sometimes fixed costs are only fixed within certain levels of activity and increase in steps as activity increases:
　　· The high low method can still be used to estimate fixed and variable costs
　　· Adjustments need to be made for the fixed costs based on the activity level under consideration.
　　Example 2:
　　An organization has the following total costs at three activity levels:
　　Activity levels （units） 12,750 15,100
　　Total cost $73,950 $83,585
　　Variable cost per unit is constant within this activity range and there is a step up of $4,700 in the total fixed costs when the activity level exceeds 14,000 units.
　　Required: what is the total cost at an activity level of 14,500 units?
　　Solution:
　　Unit produced Cost （$）
　　Highest activity level： 15100 73950
　　Lowest activity level: 12750 83585- 4700
　　Variable cost = （83585-4700 – 73950）/ （15100- 12750） = $2.1/unit
　　Fixed cost exceeds 14500 units = 83585 - $2.1 x 15100 = $51,875
　　Total cost for 14500 units = $51,875 + $2.1 x 14500 units = $82,325
　　High –low method with changes in the variable cost per unit
　　Sometimes there may be changes in the variable cost per unit, and the high low method can still be used to determine the fixed and variable elements of semi-variable costs. The variable cost per unit may change because:
　　· Prices may be forecast to increase in future periods
　　· Bulk discounts may be available for purchasing resources in large quantities.　Example 3:
　　The following information relates to the manufacture of product LL in 2009.
　　Output （units） Total cost （$）
　　200 7,000
　　300 8,000
　　400 8,600
　　For output volumes above 350 units, the variable cost per unit falls by 10%. （Note: this fall applies to all units – not just the excess above 350.）
　　Required: estimate the cost of producing 450 units of Product LL in 2010.
　　Solution:
　　If output volumes below 350 units: variable cost = （8000 – 7000）/ （300-200）
　　= $10/unit
　　If output volume above 350 units: variable cost = $10 x 90% = $9
　　Fixed cost = $8,600 – 400 x $9 = $5,000
　　Total cost for 450 units = $5,000 + 450 units x $9 = $9,050
　　Example 4:
　　1. Which of the following best describe a controllable cost?
　　A. A cost which arises from a decision already taken, which cannot, in the short run, be changed.
　　B. A cost for which the behavior pattern can be easily analyzed to facilitate valid budgetary control comparisons.
　　C. A cost which can be influenced by its budget holder.
　　D. A specific cost of an activity or business which would be avoided it the activity or business did not exist.
　　Solution: C
　　Controllable costs are items of expenditure which can be directly influenced by a given manager within a given time span.
　　Example 5:
　　A manufacturing firm is very busy and overtime is being worked.
　　How would the amount of overtime premium contained in direct wages normally be classified?
　　A. Part of prime cost
　　B. Factory overheads
　　C. Direct labor costs
　　D. Administrative overheads
　　Solution: B
　　Overtime premium is always classified as factory overhead unless it is:
　　Worked at the specific request of a customer to get his order completed
　　Worked regularly by a production department in the normal course of operations, in which case it is usually incorporated into the direct labor hourly rate.
　　Example 6:
　　A company employs four supervisors to oversee the factory production of all its products. How would the salaries paid to these supervisors be classified?
　　A. As a direct labour cost
　　B. As a direct production expense
　　C. As a production overhead
　　D. As an administration overhead
　　Solution:
　　The supervisors are engaged in the production activity, therefore option D can be eliminated. They supervise the production of all products, therefore their salaries are indirect costs because they cannot be specifically identified with a cost unit. This eliminates options A and B. The salaries are indirect production overhead costs, therefore option C is correct.
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