Chapter 20: Q23E (page 1125)

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

Expert verified

Variable cost per inspection is $$ 1$ .
Fixed cost is $$ 3, 000$
Operating cost at 1,000 inspections is $$ 4, 000$
Graph shown below

Step by step solution

Calculation of variable cost per inspection

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

Calculation of fixed cost

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

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

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

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

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