Question

Determining mixed costs—the high-low method

The manager of Trusty Car Inspection reviewed the monthly operating costs for the past year. The costs ranged from \(4,300 for 1,300 inspections to \)3,900 for 900 inspections.

Requirements

1. Use the high-low method to calculate the variable cost per inspection.

2. Calculate the total fixed costs.

3. Write the equation and calculate the operating costs for 1,000 inspections.

4. Draw a graph illustrating the total cost under this plan. Label the axes, and show the costs at 900, 1,000, and 1,300 inspections.

Short answer

1. Variable cost per inspection is $\mathbf{\$}\mathbf{1}$.
2. Fixed cost is$\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{000}$
3. Operating cost at 1,000 inspections is $\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{000}$
4. Graph shown below

Step-by-step solution

Calculation of variable cost per inspection

$\begin{array}{rcl}\mathbf{Variablecostperinspection}& \mathbf{=}& \frac{\mathbf{Changeintotalcost}}{\mathbf{Changeinvolumeofactivity}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{300}\mathbf{-}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{900}}{\mathbf{1}\mathbf{,}\mathbf{300}\mathbf{-}\mathbf{900}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{400}}{\mathbf{400}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\end{array}$

Calculation of fixed cost

$\begin{array}{rcl}\mathbf{Fixedcost}& \mathbf{=}& \mathbf{Totalmixedcost}\mathbf{-}\mathbf{Totalvariablecost}\\ & \mathbf{=}& \mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{300}\mathbf{-}\left(\$1\times 1,300\mathrm{inspections}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{300}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{300}\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Calculation of operating cost for 1,000, 900, 1,300 inspections

$\begin{array}{rcl}\mathbf{Operating} \mathbf{cost}& \mathbf{=}& \mathbf{Fixed} \mathbf{cost}\mathbf{+}\left(\mathbf{1000} \mathbf{inspections}\mathbf{\times }\mathbf{Variable} \mathbf{cost} \mathbf{per} \mathbf{inspection}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{000}\mathbf{+}\left(\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{\$}\mathbf{1}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{000}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Operating} \mathbf{cost}& \mathbf{=}& \mathbf{Fixed} \mathbf{cost}\mathbf{+}\left(\mathbf{900} \mathbf{inspections}\mathbf{\times }\mathbf{Variable} \mathbf{cost} \mathbf{per} \mathbf{inspection}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{000}\mathbf{+}\left(\mathbf{900}\mathbf{\times }\mathbf{\$}\mathbf{1}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{900}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Operating} \mathbf{cost}& \mathbf{=}& \mathbf{Fixed} \mathbf{cost}\mathbf{+}\left(\mathbf{1300} \mathbf{inspections}\mathbf{\times }\mathbf{Variable} \mathbf{cost} \mathbf{per} \mathbf{inspection}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{000}\mathbf{+}\left(\mathbf{1}\mathbf{,}\mathbf{300}\mathbf{\times }\mathbf{\$}\mathbf{1}\right)\\ & \mathbf{=}& \mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{300}\\ & & \end{array}$

Graph