Chapter 3, Problem 19E

The controller of the South Charleston plant of Ravinia, Inc., monitored activities associated with materials handling costs. The high and low levels of resource usage occurred in September and March for three different resources associated with materials handling. The number of moves is the driver. The total costs of the three resources and the activity output, as measured by moves for the two different levels, are presented as follows:

Required:

1. 1. Determine the cost behavior formula of each resource. Use the high-low method to assess the fixed and variable components.
2. 2. Using your knowledge of cost behavior, predict the cost of each item for an activity output level of 9,000 moves.
3. 3. Construct a cost formula that can be used to predict the total cost of the three resources combined. Using this formula, predict the total materials handling cost if activity output is 9,000 moves. In general, when can cost formulas be combined to form a single cost formula?

To determine

Calculate the cost behavior formula of each resource use the high to low method to assess the fixed cost and variable components.

Explanation of Solution

High-low method: In the high-low method, the semi variable-cost approximation is calculated by using the exact data points. The high and low activity levels are selected from the data set that is available.

Calculate the cost behavior formula of each resource use the high to low method to assess the variable components.

Calculate variable cost per unit for fuel and oil forklift:

$\begin{array}{c}\begin{array}{l}\text{Variable cost per unit}\\ \text{ for forklift depreciation}\end{array})\text{ = }\frac{\text{Change in high cost and low cost}}{\text{Change in high moves and low moves}}\\ =\frac{\$1,800-\$1,800}{20,000-6,500}\\ =\$0\end{array}$

Therefore, variable cost per unit for forklift depreciation is $0 per unit.

Calculate fixed cost:

$\begin{array}{c}\text{Fixed cost =}\text{Total cost}-\text{Variable cost}\\ \text{=}\text{\$1,800}-\left(\$0\times 20,000\right)\\ =\$1,800-\$0\\ =\$1,800\end{array}$

Note: Number of moves and total cost taken from high cost and high units.

Therefore, total fixed cost is $1,800.

$\begin{array}{c}\begin{array}{l}\text{Variable cost per unit}\\ \text{ for Indirect labor}\end{array})\text{ = }\frac{\text{Change in high cost and low cost}}{\text{Change in high moves and low moves}}\\ =\frac{\$135,000-\$74,250}{20,000-6,500}\\ =\$4.50\end{array}$

Therefore, variable cost per unit for indirect labor is $4.50 per unit.

Calculate variable cost per unit for fuel and oil forklift:

$\begin{array}{c}\text{Fixed cost =}\text{Total cost}-\text{Variable cost}\\ \text{=}\text{\$135,000}-\left(\$4.50\times 20,000\right)\\ =\$135,000-\$90,000\\ =\$45,000\end{array}$

Note: Number of moves and total cost taken from high cost and high units.

Therefore, total fixed cost is $45,000.

Calculate variable cost per unit for fuel and oil forklift:

$\begin{array}{c}\begin{array}{l}\text{Variable cost per unit}\\ \text{ for fuel and oil forklift}\end{array})\text{ = }\frac{\text{Change in high cost and low cost}}{\text{Change in high moves and low moves}}\\ =\frac{\$15,200-\$4,940}{20,000-6,500}\\ =\$0.76\end{array}$

Therefore, variable cost per unit for fuel and oil forklift is $0.76 per unit.

Calculate fixed cost.

$\begin{array}{c}\text{Fixed cost =}\text{Total cost}-\text{Variable cost}\\ \text{=}\text{\$15,200}-\left(\$0.76\times 20,000\right)\\ =\$15,200-\$15,200\\ =\$0\end{array}$

Note: Number of moves and total cost taken from high cost and high units.

Therefore, total fixed cost is $0.

To determine

Predict the cost of each item for an activity output level of 9,000 moves using the knowledge of cost behavior.

Explanation of Solution

Predict the cost of each item for an activity output level of 9,000 moves using the knowledge of cost behavior.

Calculate total cost for forklift depreciation.

$\begin{array}{c}\text{Total cost =}\text{Fixed cost + variable cost}\\ \text{=}\text{\$1,800}\text{+}\left(\$0\times 9,000\text{moves}\right)\\ =\$1,800+\$0\\ =\$1,800\end{array}$

Therefore, total cost for forklift depreciation is $1,800.

Calculate total cost for indirect labor.

$\begin{array}{c}\text{Total cost =}\text{Fixed cost + variable cost}\\ \text{=}\text{\$45,000}\text{+}\left(\$4.50\times 9,000\text{moves}\right)\\ =\$45,000+\$40,500\\ =\$85,500\end{array}$

Therefore, total cost for direct labor is $85,500.

Calculate total cost for fuel and oil for forklift.

$\begin{array}{c}\text{Total cost =}\text{Fixed cost + variable cost}\\ \text{=}\text{\$0,0}\text{+}\left(\$0.76\times 9,000\text{moves}\right)\\ =\$0+\$6,840\\ =\$6,840\end{array}$

Therefore, total cost for fuel and oil for forklift is $6,840.

To determine

Construct the cost formula to predict the total cost of the three resources combined, using the formula predict the total material handling cost, if the activity output is 9,000 moves.

Explanation of Solution

Cost equation for material handling cost.

$\begin{array}{c}=\text{Forklift depreciation + Indirect labor + Fuel and oil for forklift}\\ \text{=}\text{\$1,800 +}\left(\text{\$45,000+\$4}\text{.50}\text{X}\right)+\$0.76X\\ =\$46,800+\$5.26X\end{array}$

Calculate total cost for material handling if activity output is 9,000 moves.

$\begin{array}{c}\text{Total cost =Fixed cost + Variable cost}\\ \text{=}\text{\$46,800}\text{+}\left(\$5.26\times 9,000\text{moves}\right)\\ =\$46,800+\$47,340\\ =\$94,140\end{array}$

Therefore, total cost for material handling is $94,140.