Question

high-low method

the manufacturing costs of schroeder industries for the first three months of the year follow:

\

$$\begin{tabular}{lrr} & total costs & units produced \\\\ \\hline january & \\$3,750,000 & 40,000\\text{ units} \\\\ february & 3,875,000 & 45,000 \\\\ march & 4,250,000 & 60,000 \\end{tabular}$$

using the high-low method, determine (a) the variable cost per unit and (b) the total fixed cost.

a. variable cost per unit \\$
b. total fixed cost \\$

Explanation:

Identify high and low activity levels

Analyze the units produced to find the highest and lowest activity levels.

• Highest activity (High): March with \(60,000\) units and total cost of \(\$4,250,000\).
• Lowest activity (Low): January with \(40,000\) units and total cost of \(\$3,750,000\).

Calculate variable cost per unit

Use the high-low formula to find the variable cost per unit.

• Formula:

$$ \text{Variable Cost per Unit} = \frac{\text{High Cost} - \text{Low Cost}}{\text{High Activity} - \text{Low Activity}} $$

• Calculation:

$$ \text{Variable Cost per Unit} = \frac{\$4,250,000 - \$3,750,000}{60,000 - 40,000} = \frac{\$500,000}{20,000} = \$25 $$

Calculate total fixed cost

Use the total cost formula at either the high or low activity level.

• Formula:

$$ \text{Total Fixed Cost} = \text{Total Cost} - (\text{Variable Cost per Unit} \times \text{Activity Level}) $$

• Using the high level (March):

$$ \text{Total Fixed Cost} = \$4,250,000 - (\$25 \times 60,000) = \$4,250,000 - \$1,500,000 = \$2,750,000 $$

• Verification using the low level (January):

$$ \text{Total Fixed Cost} = \$3,750,000 - (\$25 \times 40,000) = \$3,750,000 - \$1,000,000 = \$2,750,000 $$

Answer:

Question a

a. Variable cost per unit: <blank>\$25</blank>

Question b

b. Total fixed cost: <blank>\$2,750,000</blank>