Question

Using the high-low method

Mark owns a machine shop. In reviewing the shop’s utility bills for the past 12 months, he found that the highest bill of \(2,600 occurred in August when the machines worked 1,200 machine hours. The lowest utility bill of \)2,300 occurred in December when the machines worked 600 machine hours.

Requirements

1. Use the high-low method to calculate the variable cost per machine hour and the total fixed utility cost.

2. Show the equation for determining the total utility cost for the machine shop.

3. If Mark anticipates using 800 machine hours in January, predict the shop’s total utility bill using the equation from Requirement 2.

Short answer

1. Variable cost per units is $ 0.50 per machine hour

Total fixed cost is $2,000

2.$\mathbf{Total}\mathbf{}\mathbf{mixed}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{=}\left(\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{units}\times \mathrm{Number}\mathrm{of}\mathrm{units}\right)\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{cost}$

3. Total mixed cost is $ 2,400

Step-by-step solution

Calculation of variable cost per machine hour and total fixed utility cost using high-low method.

$$\begin{gathered} \mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Change}\mathbf{}\mathbf{in}\mathbf{}\mathbf{total}\mathbf{}\mathbf{cost}}{\mathbf{Change}\mathbf{}\mathbf{in}\mathbf{}\mathbf{volume}\mathbf{}\mathbf{activity}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\frac{(\mathrm{Cost}\mathrm{associated}\mathrm{with}\mathrm{hi}\mathrm{gest}\mathrm{volume}-\mathrm{Cost}\mathrm{associated}\mathrm{with}\mathrm{lowest}\mathrm{volume})}{(\mathrm{Highest}\mathrm{volume}-\mathrm{Lowest}\mathrm{volume})} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{(\$2,600-\$2,300)}{(1200-600)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\frac{(\$300)}{(\$600)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{}\mathbf{per}\mathbf{}\mathbf{machine}\mathbf{}\mathbf{hour} \end{gathered}$$

$\begin{array}{rcl}\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{cost}\mathbf{}& \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{mixed}\mathbf{}\mathbf{cost}\mathbf{-}\mathbf{Total}\mathbf{}\mathbf{variable}\mathbf{}\mathbf{cost}\\ & \mathbf{=}& \mathbf{Total}\mathbf{}\mathbf{mixed}\mathbf{}\mathbf{cost}\mathbf{-}\mathbf{(}\mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{units}\mathbf{)}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{600}\mathbf{-}\mathbf{(}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{\times }\mathbf{1200}\mathbf{)}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{600}\mathbf{-}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{00}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{000}\\ & & \end{array}$

equation for determining the total utility cost for the machine shop.

$\mathbf{Total}\mathbf{}\mathbf{mixed}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{=}\left(\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\times \mathrm{Number}\mathrm{of}\mathrm{units}\right)\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{cost}$

Calculation of shop’s total utility bill using equation in step 2.

$$\begin{gathered} \mathbf{Total}\mathbf{}\mathbf{mixed}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{=}\left(\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\times \mathrm{Number}\mathrm{per}\mathrm{units}\right)\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{cost} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$0.50\times 800\mathrm{machine}\mathrm{houre}\right)\mathbf{+}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{400}\mathbf{+}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{400} \end{gathered}$$