Chapter 11, Problem 27P

a)

To determine

Compute the magnitude of operating leverage utilizing contribution margin approach for each firm.

Answer to Problem 27P

The operating leverage of Company W and Company L are 1.5 times and 2.83 times.

Explanation of Solution

Operating leverage: It is a ratio that measures the proportion of fixed cost on the total costs and the extent to which the changes in the sales volume affects the income from operations. It shows the relationship between the contribution margin and income from operations.

$\text{Magnitude of operating leverage}=\frac{\text{Contribution margin}}{\text{Net income}}$

Calculate the magnitude of operating leverage of Company W and Company L:

$\begin{array}{c}\text{Magnitude of operating leverage}=\frac{\text{Contribution margin}}{\text{Net income}}\\ =\frac{\$72,000}{\$48,000}\\ =1.5\text{times}\end{array}$

$\begin{array}{c}\text{Magnitude of operating leverage}=\frac{\text{Contribution margin}}{\text{Net income}}\\ =\frac{\$136,000}{\$48,000}\\ =2.83\text{times}\end{array}$

Hence, the operating leverage of Company W and Company L are 1.5 times and 2.83 times.

b)

To determine

Compute the change in net income in amount and change in percentage of net income.

Explanation of Solution

Given information: The sales have increased by 10% for both Company W and Company L and the selling price remains unchanged.

The formula to calculate the percentage change in net income:

$\left(\text{Percentage change in net income}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}$

Compute the change in net income in dollars:

Company Name	W	L
Variable cost per unit (a)	$ 16	$ 8
Sales revenue $\left(8,000\text{ units}\times 110\%\times \$25\right)$	$ 220,000	$ 220,000
Variable cost $\left(\text{8,000 units}\times \text{110\%}\times \text{a}\right)$	($ 140,800)	($ 70,400)
Contribution margin	$ 79,200	$ 149,600
Fixed cost	($24,000)	($88,000)
Net income	$55,200	$61,600
Percentage change	15%	28.33%

Table (1)

Calculate the percentage change in net income of Company W and Company L:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage change in net income}\\ \left(\text{Company W}\right)\end{array}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}\\ =\frac{\$55,200-\$48,000}{\$48,000}\\ =15\%\end{array}$

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage change in net income}\\ \left(\text{Company L}\right)\end{array}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}\\ =\frac{\$61,600-\$48,000}{\$48,000}\\ =28.33\%\end{array}$

Hence, the percentage change of net income of Company W and Company L is 15% and 28.33%.

c)

To determine

Compute the change in net income in amount and change in percentage of net income.

Explanation of Solution

Given information: The sales have decreased by 10% for both Company W and Company L and the selling price remains unchanged.

The formula to compute the percentage change in net income:

$\left(\text{Percentage change in net income}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}$

Compute the change in net income in dollars:

Company Name	Wood	Lake
Variable cost per unit (a)	$16.00	$8.00
Sales revenue $\left(\text{8,000 units}\times \left(10\text{0\%}-\text{10\%}\right)\times \text{\$25}\right)$	$180,000	$180,000
Variable cost $\left(\text{8,000 units}\times \left(10\text{0\%}-\text{10\%}\right)\times \text{a}\right)$	(115,200)	(57,600)
Contribution margin	64,800	122,400
Fixed cost	(24,000)	(88,000)
Net income	$40,800	$34,400
Percentage change	(15%)	(28.33%)

Table (2)

Calculate the percentage change in net income of Company W and Company L:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage change in net income}\\ \left(\text{Company W}\right)\end{array}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}\\ =\frac{\$40,800-\$48,000}{\$48,000}\\ =\left(15\%\right)\end{array}$

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage change in net income}\\ \left(\text{Company L}\right)\end{array}\right)=\frac{\text{Current year net income}-\text{Base year net income}}{\text{Base year net income}}\\ =\frac{\$34,400-\$48,000}{\$48,000}\\ =\left(28.33\%\right)\end{array}$

Hence, the percentage change of net income of Company W and Company L is (15%) and (28.33%).

d)

To determine

Write a memo regarding the analyses and advice to Person PS.

Explanation of Solution

To,

Person PS

From,

Person A

Subject: Analysis and recommendation regarding the investment

The rewards and risk of both the companies are different even though they have same amount of sales and net income. From the above analysis the operating leverage is 1.5 for Company W and 2.83 for Company L.

The analytical data indicates that income of Company L is more volatile than Company W.

Investment in Company L will be the better choice in an economy boom situation. Otherwise, Company W is considering better. An aggressive investor can choice Company L and a conservative investor can go for Company W.