A department of Alpha Co. incurred the following costs for the month of September. Variable costs, and the variable portion of mixed costs, are a function of the number of units of activity:

Activity level in units

3,500

Variable costs

$

7,000

Fixed costs

30,000

Mixed costs

21,100

Total costs

$

58,100

During October the activity level was 7,800 units, and the total costs incurred were $68,500.

Required:

a. Calculate the variable costs, fixed costs, and mixed costs incurred during October.

b. Use the high-low method to calculate the cost formula for mixed cost. (Do not round intermediate calculations and round your answers to 2 decimal places.)

a. Costs incurred during October:

Variable = $15600

Fixed = $30000

Mixed = $22900

b. Mixed cost = 0.42x + 19634.88

Explanation:

a.

Based on the September data, the variable costs per unit were:

Variable costs per unit = 7000 / 3500 = $2 per unit

The variable costs are the costs that vary with the changes in output level. The fixed costs on the other hand, remain fixed in the short run.

Thus the fixed costs will remain $30000 for October also. The Variable costs for October will be = 2 * 7800 = $15600 The mixed costs for October will be = Total costs - Fixed costs - Variable costs Mixed costs-October = 68500 - 30000 - 15600 = $22900

b.

The high-low method is used to calculate the variable component in a mixed cost.

The variable cost per unit under High-low method is:

Variable cost per unit = (Highest activity cost - lowest activity cost) / (Highest activity level - lowest activity level)

Variable cost per unit = (22900 - 21100) / (7800 - 3500)

Variable cost per unit = $0.4186046512 rounded off to $0.42 per unit

Thus, the fixed cost component under mixed cost

Fixed cost component = 22900 - 0.4186046512 * (7800) = $19634.88

The cost formula for mixed cost is:

Mixed cost = 0.42x + 19634.88

Where x is the number of units.