Chapter 6, Problem 6PB

Contribution margin, break-even sales, cost-volume-profit chart, margin of safety, and operating leverage

Belmain Co. expects to maintain the same inventories at the end of 20Y7 as at the beginning of the year. The total of all production costs for the year is therefore assumed to be equal to the cost of goods sold. With this in mind, the various department heads were asked to submit estimates of the costs for their departments during the year. A summary report of these estimates is as follows:

It is expected that 12,000 units will be sold at a price of $240 a unit. Maximum sales within the relevant range are 18,000 units.

Instructions

1. 1. Prepare an estimated income statement for 20Y7.
2. 2. What is the expected contribution margin ratio?
3. 3. Determine the break-even sales in units and dollars.
4. 4. Construct a cost-volume-profit chart indicating the break-even sales.
5. 5. What is the expected margin of safety in dollars and as a percentage of sales? (Round to one decimal place.)
6. 6. Determine the operating leverage.

To determine

Prepare an estimated income statement for 20Y7.

Explanation of Solution

Cost-Volume-Profit Analysis: It is a method followed to analyze the relationship between the sales, costs, and the related profit or loss at various levels of units sold. In other words, it shows the effect of the changes in the cost and the sales volume on the operating income of the company.

Prepare an estimated income statement for 20Y7.

Company B
Estimated Income Statement
For the year ended December 31, 20Y8
Particulars	Amount ($)	Amount ($)	Amount ($)
Sales (1)			2,880,000
Less: Cost of Goods sold:
Direct Materials (2)		600,000
Direct Labor (3)		360,000
Factory Overhead (4)		422,000
Cost of Goods Sold			(1,382,000)
Gross Profit			1,498,000
Less: Expenses:
Selling expenses:
Sales salaries and commissions (5)	388,000
Advertising	116,000
Travel	4,000
Miscellaneous selling expense (6)	14,300
Total selling expenses		522,300
Administrative expenses:
Office and Officers’ salaries	325,000
Supplies (7)	54,000
Miscellaneous administrative expenses (8)	20,700
Total administrative expenses		399,700
Total expenses			(922,000)
Income from operations			576,000

Table (1)

Working note (1):

Determine sales.

Number of units to be sold =12,000 units

Selling price per unit =$240 per unit

$\begin{array}{c}\text{Sales }=\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\times \left(\begin{array}{l}\text{Selling}\text{price}\\ \text{per}\text{unit}\end{array}\right)\\ =12,000\text{units}\times \text{\$240}\text{per}\text{unit}\\ =\$2,880,000\end{array}$

Working note (2):

Determine the cost of direct materials.

Number of units to be sold =12,000 units

Direct Materials cost per unit =$50 per unit

$\begin{array}{c}\text{Direct}\text{Materials }=\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\times \left(\begin{array}{l}\text{Direct}\text{Materials}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\\ =12,000\text{units}\times \text{\$50}\text{per}\text{unit}\\ =\$600,000\end{array}$

Working note (3):

Determine the cost of direct labor.

Number of units to be sold =12,000 units

Direct labor cost per unit =$30 per unit

$\begin{array}{c}\text{Direct}\text{Labor }=\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\times \left(\begin{array}{l}\text{Direct}\text{Labor}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\\ =12,000\text{units}\times \text{\$30}\text{per}\text{unit}\\ =\$360,000\end{array}$

Working note (4):

Determine the cost of factory overhead.

Factory overhead-Fixed =$350,000

Number of units to be sold =12,000 units

Factory overhead-Variable cost per unit =$6 per unit

$\begin{array}{c}\text{Factory}\text{overhead }=\left[\begin{array}{l}\text{Factory}\text{overhead}\\ \text{-Fixed}\text{cost}\end{array}\right]+\left[\begin{array}{c}\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Factory}\text{overhead-}\\ \text{Variable}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\end{array}\right]\\ =\$350,000+\left[12,000\text{units}\times \text{\$6}\text{per}\text{unit}\right]\\ =\$350,000+\$72,000\\ =\$422,000\end{array}$

Working note (5):

Determine the sales salaries and commissions.

Sales salaries and commissions-Fixed =$340,000

Number of units to be sold =12,000 units

Sales salaries and commissions-Variable cost per unit =$4 per unit

$\begin{array}{c}\begin{array}{l}\text{Sales}\text{salaries}\\ \text{and}\text{commissions}\end{array}]=\left[\begin{array}{l}\text{Sales}\text{salaries}\\ \text{and}\text{commissions}\\ \text{-Fixed}\text{cost}\end{array}\right]+\left[\begin{array}{c}\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Sales}\text{salaries}\\ \text{and}\text{commissions-}\\ \text{Variable}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\end{array}\right]\\ =\$340,000+\left[12,000\text{units}\times \text{\$4}\text{per}\text{unit}\right]\\ =\$340,000+\$48,000\\ =\$388,000\end{array}$

Working note (6):

Determine the miscellaneous selling expense.

Miscellaneous selling expense-Fixed =$2,300

Number of units to be sold =12,000 units

Miscellaneous selling expense-Variable cost per unit =$1 per unit

$\begin{array}{c}\begin{array}{l}\text{Miscellaneous}\\ \text{selling}\text{expense}\end{array}]=\left[\begin{array}{l}\text{Miscellaneous}\\ \text{selling}\text{expense}\\ \text{-Fixed}\text{cost}\end{array}\right]+\left[\begin{array}{c}\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Miscellaneous}\\ \text{selling}\text{expense-}\\ \text{Variable}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\end{array}\right]\\ =\$2,300+\left[12,000\text{units}\times \text{\$1}\text{per}\text{unit}\right]\\ =\$2,300+\$12,000\\ =\$14,300\end{array}$

Working note (7):

Determine the supplies.

Supplies-Fixed =$6,000

Number of units to be sold =12,000 units

Supplies-Variable cost per unit =$4 per unit

$\begin{array}{c}\text{Supplies }=\left[\begin{array}{l}\text{Supplies}\\ \text{-Fixed}\text{cost}\end{array}\right]+\left[\begin{array}{c}\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Supplies-}\\ \text{Variable}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\end{array}\right]\\ =\$6,000+\left[12,000\text{units}\times \text{\$4}\text{per}\text{unit}\right]\\ =\$6,000+\$48,000\\ =\$54,000\end{array}$

Working note (8):

Determine the miscellaneous administrative expense.

Miscellaneous administrative expense-Fixed =$8,700

Number of units to be sold =12,000 units

Miscellaneous administrative expense-Variable cost per unit =$1 per unit

$\begin{array}{c}\begin{array}{l}\text{Miscellaneous}\\ \text{administrative}\\ \text{expense}\end{array}]=\left[\begin{array}{l}\text{Miscellaneous}\\ \text{administrative}\\ \text{expense}\\ \text{-Fixed}\text{cost}\end{array}\right]+\left[\begin{array}{c}\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Miscellaneous}\\ \text{administrative}\\ \text{expense-}\\ \text{Variable}\\ \text{cost}\text{per}\text{unit}\end{array}\right)\end{array}\right]\\ =\$8,700+\left[12,000\text{units}\times \text{\$1}\text{per}\text{unit}\right]\\ =\$8,700+\$12,000\\ =\$20,700\end{array}$

To determine

Calculate the expected contribution margin ratio.

Explanation of Solution

Determine the expected contribution margin ratio.

Sales =$2,880,000 (1)

Variable cost =$1,152,000 (9)

$\begin{array}{c}\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100\\ =\frac{\text{Sales}-\text{Variable}\text{cost}}{\text{Sales}}\times 100\\ =\frac{\$2,880,000-\$1,152,000}{\$2,880,000}\times 100\\ =\frac{\$1,728,000}{\$2,880,000}\times 100\\ =60\%\end{array}$

Working note (9):

Determine the variable cost.

Number of units to be sold =12,000 units

Variable cost per unit =$96 per unit

  $\begin{array}{c}\text{Variable}\text{cost }=\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{to}\text{be}\text{sold}\end{array}\right)\times \left(\begin{array}{l}\text{Variable}\text{cost}\\ \text{per}\text{unit}\end{array}\right)\\ =12,000\text{units}\times \text{\$96}\text{per}\text{unit}\\ =\$1,152,000\end{array}$

Conclusion

Therefore, the expected contribution margin ratio is 60%.

To determine

Calculate the break-even sales in units and dollars.

Explanation of Solution

Determine the break-even sales in units.

Fixed cost =$1,152,000

Contribution margin per unit =$144 per unit (10)

$\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{Sales}\left(\text{units}\right)=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{per}\text{unit}}\\ =\frac{\$1,152,000}{\$144}\\ =8,000\text{units}\end{array}$

Working note (10):

Compute the contribution margin per unit.

Selling price per unit =$240 per unit

Variable cost per unit =$96 per unit

$\begin{array}{c}\text{Contribution}\text{Margin}\text{per}\text{unit}\text{=}\left(\begin{array}{l}\text{Selling}\text{price}\\ \text{per}\text{unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable}\text{cost}\\ \text{per}\text{unit}\end{array}\right)\\ \text{=\$240}\text{per}\text{unit}-\text{\$96}\text{per}\text{unit}\\ \text{=\$144}\text{per}\text{unit}\end{array}$

Determine the break-even sales in dollars.

Fixed cost =$1,152,000

Contribution margin ratio =60% (refer Part 2)

$\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{Sales}\left(\text{Dollars}\right)=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{ratio}}\\ =\frac{\$1,152,000}{60\%}\\ =\$1,152,000\times \frac{100}{60}\\ =\$1,920,000\end{array}$

Conclusion

Therefore, the break-even sales in units is 8,000 units and dollars is $1,920,000.

To determine

Construct a cost-volume-profit chart indicating the break-even sales.

Explanation of Solution

Construct a cost-volume-profit chart indicating the break-even sales.

Figure (1)

The volume in units of sales is shown on the horizontal axis. The maximum relevant range is 18,000 units. The sales and the total costs (fixed cost and variable cost) in dollars is shown on the vertical axis. The maximum relevant range of sales and total costs is $4,500,000.

The total sales line is drawn right upward by connecting the first point at $0 to the second point at $4,320,000$\left[\text{18,000}\text{units×\$240}\text{per}\text{unit}\right]$ for 18,000 units (maximum relevant range on the horizontal axis).

The total cost line is drawn right upward by connecting the first point at $1,152,000 (fixed cost) on the vertical axis to the second point at $\$2,880,000\left[\$1,152,000+\text{\$1,728,000}\right]$ to the end of the relevant range. The variable cost is $\$1,728,000\left(18,000\text{units×\$96}\text{per}\text{unit}\right)$.

The break-even point is the intersection point where the total sales line and total cost line meet. The vertical dotted line drawn downward from the intersection point reaches at 8,000 units. It indicates the break-even sales (units). The horizontal line drawn to the left towards the vertical axis reaches at $1,920,000. It indicates the break-even sales (dollars). Refer Part 3 for the break-even values.

The operating profit area is the area where the total sales line exceeds the total cost line. However, the operating loss area is the area where the total cost exceeds the total sales line.

To determine

Calculate the expected margin of safety in dollars and as a percentage of sales.

Explanation of Solution

Determine the expected margin of safety in dollars.

Sales =$2,880,000 (1)

Sales at break-even point =$1,920,000 (refer Part 3)

$\begin{array}{c}\text{ Margin}\text{of}\text{Safety}\left(\text{Dollars}\right)=\text{Sales}-\text{Sales}\text{at}\text{Break-Even}\text{Point}\\ =\$2,880,000-\$1,920,000\\ =\$960,000\end{array}$

Determine the expected margin of safety as a percentage of sales.

Sales =$2,880,000 (1)

Margin of Safety in dollars =$960,000

$\begin{array}{c}\text{ Margin}\text{of}\text{Safety}\left(\%\right)=\frac{\text{Margin}\text{of}\text{Safety}\text{in}\text{dollars}}{\text{Sales}}\times 100\\ =\frac{\$960,000}{\$2,880,000}\times 100\\ =33.3\%\end{array}$

Conclusion

Therefore, the expected margin of safety in dollars is $960,000 and as a percentage of sales is 33.3%.

To determine

Calculate the operating leverage.

Explanation of Solution

Determine the operating leverage.

Contribution margin =$1,728,000 (11)

Income from operations =$576,000 (refer Table 1)

$\begin{array}{c}\text{ Operating}\text{leverage}=\frac{\text{Contribution}\text{Margin}}{\text{Income}\text{from}\text{operations}}\\ =\frac{\$1,728,000}{\$576,000}\\ =3\end{array}$

Working note (11):

Determine the contribution margin

Sales =$2,880,000 (1)

Variable cost =$1,152,000 (9)

$\begin{array}{c}\text{Contribution}\text{Margin}=\text{Sales}-\text{Variable}\text{cost}\\ =\$2,880,000-\$1,152,000\\ =\$1,728,000\end{array}$

Conclusion

Therefore, the operating leverage is 3.