Chapter 10, Problem 9P

Grand Canyon Manufacturing Inc. produces and sells a product with a price of $100 per unit. The following cost data have been prepared for its estimated upper and lower limits of activity:

Overhead:

Selling and administrative expenses:

Required:

1. 1. Classify each cost element as either variable, fixed, or semi-variable. (Hint: Recall that variable expenses must go up in direct proportion to changes in the volume of activity.)
2. 2. Calculate the break-even point in units and dollars. (Hint: First use the high-low method illustrated in Chapter 4 to separate costs into their fixed and variable components.)
3. 3. Prepare a break-even chart.
4. 4. Prepare a contribution income statement, similar in format to the statement appearing on page 540, assuming sales of 5,000 units.
5. 5. Recompute the break-even point in units, assuming that variable costs increase by 20% and fixed costs are reduced by $50,000.

To determine

Classify the each cost element as either variable, fixed or semi-variable.

Explanation of Solution

Classify the each cost element as either variable, fixed or semi-variable as follows:

• Variable costs vary with the number of units produced or for the services provided. For example, the labor costs increase if the number of labor hours is increased, and the labor costs decrease if the number of labor hours is decreased. Direct material, direct labor and indirect material are considered as the variable costs.
• Fixed Cost is a cost which is constant in the short run, it is not related to any change in the production of goods or service, it will be fixed disregarding of increase or decrease in output. Fixed cost is generally incurred on fixed assets in long run. Depreciation, office salary and advertising are considered as the fixed cost.
• Semi variable costs are the cost that changes based on the changes in the production, but it is not proportionately. Indirect labor, sales salaries and other expense are considered as semi-variable cost.

To determine

Calcualte the break even point in units and dollars.

Explanation of Solution

Calcualte the break even point in units and dollars as follows:

$\begin{array}{c}\begin{array}{l}\text{Break even sales }\\ \text{volume in units}\end{array}\}\text{ = }\frac{\text{Total fixed costs}}{\left(\begin{array}{l}\text{Selling price per unit}-\\ \text{Variable cost per unit}\end{array}\right)}\\ =\frac{\$140,000(3)}{\$100-\$56.25(1)}\\ =\frac{\$140,000}{\$43.75}\\ =3,200\text{ units}\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Break even sales }\\ \text{volume}\end{array}\}\text{ = }\frac{\text{Total fixed cost}}{1-\left(\frac{\text{Variable cost per unit}}{\text{Sales price unit}}\right)}\\ =\frac{\$140,000(3)}{1-\left(\frac{\$56.25(1)}{\$100}\right)}\\ =\$320,000\end{array}$

Working note (1):

Calcualte the vairable cost per unit:

$\begin{array}{c}\begin{array}{l}\text{Variable cost }\\ \text{per unit}\end{array}\}\text{ = }\left(\frac{\text{Change in total costs}}{\text{Change in production}}\right)\\ =\frac{\$477,500-\$365,000}{6,000\text{ units}-4,000\text{ units}}\\ =\$56.25\end{array}$

Working note (2):

Calculate the variable cost for 4,000 units.

$\begin{array}{c}\text{Variable cost = Number of units}\times \text{Variable cost per unit}\\ \text{=4,000 units}\times \text{\$56}\text{.25}\\ \text{=\$225,000}\end{array}$

Working note (3):

Calcualte the fixed cost:

$\begin{array}{c}\text{Fixed cost = }\left(\text{Total costs}-\text{Variable costs for 4,000 units}\right)\\ =\$365,000-\$225,000(2)\\ =\$140,000\end{array}$

To determine

Prepare a break-even chart.

Explanation of Solution

Prepare a break-even chart as follows:

To determine

Prepare a contribution income statement of company G.

Explanation of Solution

Prepare a contribution income statement of company G as follows:

Company G
Income statement
For the year ended ---
Particulars	Amount ($)
Sales $\left(5,000\text{ units}\times \text{\$100}\right)$	$ 500,000
Less: Variable cost $\left(5,000\text{ units}\times \text{\$100}\right)$	$281,250
Contribution margin	$218,250
Less: Fixed costs (3)	$140,000
Net operating income	$ 78,750

Table (1)

To determine

Calculate the break-even point in units, assume that the variable costs is increased by 20% and fixed cost is decreased by $50,000.

Explanation of Solution

Calculate the break-even point in units, assume that the variable costs is increased by 20% and fixed cost is decreased by $50,000 as follows:

$\begin{array}{c}\begin{array}{l}\text{Break even sales }\\ \text{volume in units}\end{array}\}\text{ = }\frac{\text{Total fixed costs}}{\left(\begin{array}{l}\text{Selling price per unit}-\\ \text{Variable cost per unit}\end{array}\right)}\\ =\frac{\$90,000(4)}{\$100-\$67.50(5)}\\ =\frac{\$140,000}{\$32.50}\\ =2,769\text{ units}\end{array}$

Working note (4):

Calcualte the decrase in fixed cost:

$\begin{array}{c}\text{Decrease in fixed cost = }\left(\text{Actual fixed cost (3)}-\text{Decrased fixed cost}\right)\\ =\$140,000-\$50,000\\ =\$90,000\end{array}$

Working note (5):

Calcualte the increase in variable cost:

$\begin{array}{c}\text{Increase in variable costs = }\left(\begin{array}{l}\text{Variable cost per unit (1)+}\\ \left(\text{Variable cost per unit}\times \text{20\%}\right)\end{array}\right)\\ =\$56.25+\left(\$56.25\times 20\%\right)\\ =\$56.25+\$11.25\\ =\$67.50\end{array}$