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 $4,300for1,300inspectionsto$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