Chapter 6, Problem 11E

Calculating Target Profit, Margin of Safety, Degree of Operation Leverage
Refer to the information regarding Dana’s Ribbon World in E6-10.
1. Suppose Dana’s would like to generate a profit of $800. Determine how many rosettes must sell to achieve this target profit.
2. If Dana’s sells 1,100 rosettes, compute its margin of safety in units, in sales dollar, and as a percentage of sales.
3. Calculate Dana’s degree of operating leverage if sells 1,100 rosettes.
4. Using the degree of operating leverage, calculate the change in Dana’s profit if unit sales drop to 935 units. Confirm this by preparing a new contribution margin income statement.

To determine

(a)

Concept introduction:

Contribution Margin:

The margin of profit which is computed after considering the variable cost only and not the fixed costis known as contribution. In other words, it means the contribution made by selling the product after covering its variable cost to the company.

Target Profit:

The target profit is that profit which a company decides to achieve and this analysis helps in determinig the level of sales by which this target can be achieved.

The number of rosettes to be sold to achieve target profit of $\$800$.

Answer to Problem 11E

The target sale point in units is $\text{1,207 units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$3.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$1.60\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$1.40$

The number units to be sold for achieving the target profit are calculated as:

$\begin{array}{c}\text{Target Sales}=\frac{\text{Fixed Cost}+\text{Target Profit}}{\text{Contribution Margin}}\\ =\frac{\$889+\$800}{\$1.40}\\ =1,207\text{ units}\end{array}$

To determine

(b)

Concept introduction:

Breakeven Point:

The level of sales where the company is neither on profit nor loss is termed as breakeven point. In other words, that level of sales at which the fixed cost of the business is recovered.

Margin of Safety:

The margin of safety is the margin enjoyed by the company which is achieved over and above the breakeven sales. It is a difference of actual sales and breakeven sales.

To compute:

The margin safety in units and percentage of sales if the sales price is $\$3$ per rosette and actual units sold is $1,100$.

Answer to Problem 11E

The margin safety in units and percentage of sales is $42.27\%$.

Explanation of Solution

The actual sales amount to $\$3,300\left(1100\text{ rosette}\times \text{\$3}\right)$

The breakeven sales amount to $\$1,905\left(\text{635 canoes}\times \text{\$3}\right)$

The margin of safety in terms of units is calculated as:

$\begin{array}{c}\text{Margin of Safety}=\frac{\text{Actual Sales}-\text{Breakeven Sales}}{\text{Actual Sales}}\\ =\frac{1,100-635}{1,100}\\ =42.27\%\end{array}$

The margin of safety in terms of percentage of sales is calculated as:

$\begin{array}{c}\text{Margin of Safety}=\frac{\text{Actual Sales}-\text{Breakeven Sales}}{\text{Actual Sales}}\\ =\frac{\$3,300-\$2,905}{\$3,300}\\ =42.27\%\end{array}$

To determine

(c)

Concept introduction:

Degree of operating leverage:

The degree of oprating leverage refers to the level of fixed cost incurred for operating the business, and the higher leverage means there is a high fixed cost. It is computed by dividing the contribution margin with net operating income.

The degree of operating leverage at the levelof sale of $1,100$ rosettes.

Answer to Problem 11E

The degree of operating leverage is $\text{2}\text{.365 times}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$3.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$1.60\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$1.40$

Thetotal contribution margin and net operating income are calculated as:

$\begin{array}{c}\text{Total Contribution Margin}=\text{Actual sales units}\times \text{Contribution margin}\\ =1,100\text{ units}\times \$1.40\text{ per unit}\\ =\$1,540\end{array}$

$\begin{array}{c}\text{Net Operating Income}=\text{Total Contribution margin}-\text{Fixed cost}\\ =\$1,540-\$889\\ =\$651\end{array}$

The degree of operating leverage is calculated as:

$\begin{array}{c}\text{Degree of Operating Leverage}=\frac{\text{Contribution Margin}}{\text{Net Operating Income}}\\ =\frac{\$1,540}{\$651}\\ =2.365\text{ times}\end{array}$

To determine

(d)

Concept introduction:

Degree of operating leverage:

The degree of oprating leverage refers to the level of fixed cost incurred for operating the business, and the higher leverage means there ia a high fixed cost. It is computed by dividing the contribution margin with net operating income.

The change in profit on the basis of degree of operating leverage if the sales price is reduced to $935$ units.

Answer to Problem 11E

The change in profit on the basis of degree of operating leverage, if the sales price is reduced to $935$ units, comes to reduction in profit by $35.48\%$.

Explanation of Solution

The percentage of sales decrease is:

$\begin{array}{c}\text{Sale Decrease}=\frac{1,100-935}{1,100}\\ =15\%\end{array}$

Operating Leverage is $2.365\text{ times}$.

Change in Profit is calculated as:

$\begin{array}{c}\text{Change}\left(\%\right)=\text{Decrease in Sales}\left(\%\right)\times \text{Degree of operating leverage}\\ \text{=15\%}\times \text{2}\text{.365}\\ \text{=35}\text{.48\%}\end{array}$

This means when the sale will decrease, it will lead to reduction in the profit by $35.48\%$.

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$3.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$1.60\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$1.40$
No. of units		$935$
Contribution margin		$\$1,309$
Less: Fixed cost		$\$889$
Net Income		$\$420$