Chapter 3, Problem 1AE

1.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as the degree of operating leverage.

To evaluate: The degree of operating leverage if the fixed expenses is $270000.

Answer to Problem 1AE

We have derived the degree of operating leverage as 10 and the margin of safety percentage is 10%. When compared to our previous calculation the margin of safety was 20%. We can experience the rise in break-even point with a decrease in the margin of safety.

Explanation of Solution

To calculate the degree of operating leverage when fixed expenses is $270000, firstly we have to calculate the degree of operating leverage when the fixed expense is $240000. We are given this task to educate ourselves and know the importance of Excel application. By doing this, we arrive at some formulas, which will simplify the job of calculation. The only effort from our side is to change the respective figures in the respective cells. However, let us just brief ourselves about the list of formulas useful in the following calculation.

$\begin{array}{l}Contributionmarginperunit\hfill \end{array}=Sellingpriceperunit-Variablecostperunit$

$CMratio=\frac{Contributionmargin}{Sellingpriceperunit}$

$Variableexpenseratio=\frac{Variablepriceperunit}{Sellingpriceperunit}$

$Break-eveninunitsales=\frac{Fixedexpense}{Contributionmargin}$

$Break-evenindollarsales=\frac{Fixedexpense}{CMratio}$

$\begin{array}{l}Marginofsafetyindollars=\\ (UnitSales*Sellingpriceperunit)-Break-evenindollarsales\end{array}$

$\begin{array}{l}Marginofsafetyinpercentage=\\ \frac{Marginofsafetyindollars}{Numberofunitssold\times sellingpriceperunit)}\end{array}$

$Sales=Numberofunitssold\times Sellingpriceperunit$

$Variableexpenses=Numberofunitssold\times variablecostpriceperunit$

$\begin{array}{l}Contributionmargin\hfill \end{array}=Sales-Variablecost$

$Netoperatingincome-Contributionmargin-fixedexpenses$

$Degreeofoperatingleverage=\frac{Netoperatingincome}{Fixedexpenses}$

Let us now calculate the degree of operating leverage when the fixed expenses are $240000.

Given information:

Unit Sale 2000 units

Selling price 60 per unit

Variable expenses 45 per unit

Fixed expenses 240000

The degree of operating leverage using Excel application:

	$Amount using Excel formulas
Selling price per unit	60
Variable expenses per unit	45
Contribution margin per unit	15
CM ratio	0.25 or 25%
Variable expense ratio	0.75 or 75%
Break-even analysis:
Break-even in unit sales	16000
Break-even in dollar sales	960000
Margin of safety:
Margin of safety in dollars	240000
Margin of safety in percentage	0.2 or 20%
Degree of operating leverage:
Sales	1200000
Variable expenses	900000
Contribution margin	300000
Fixed expenses	240000
Net operating income	60000
Degree of operating leverage	5

Having all the other information the same, to change the value in the cell against Fixed expenses as $270000. Excel application is so worthy that it does the job easily once we specify the required formulas.

Similarly, by using the above- mentioned formulas, to calculate the degree of operating leverage when the fixed expenses are $270000.

	$Amount using Excel formulas
Selling price per unit	60
Variable expenses per unit	45
Contribution margin per unit	15
CM ratio	0.25 or 25%
Variable expense ratio	0.75 or 75%
Break-even analysis:
Break-even in unit sales	18000
Break-even in dollar sales	1080000
Margin of safety:
Margin of safety in dollars	120000
Margin of safety in percentage	0.1 or 10%
Degree of operating leverage:
Sales	1200000
Variable expenses	900000
Contribution margin	300000
Fixed expenses	270000
Net operating income	30000
Degree of operating leverage	10

Finally, to derive the degree of operating leverage which is 10 and the margin of safety percentage is 10%. To compare the previous calculation the margin of safety was 20%. Experience the rise in break-even point with a decrease in the margin of safety.

2.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as degree of operating leverage.

Requirement 2

The degree of operating leverage and margin of safety in percentage using Excel.

Answer to Problem 1AE

The degree of operating leverage is 8 and the margin of safety is 13%.

Explanation of Solution

Given information:

Unit Sale 2000 units

Selling price 60 per unit

Variable expenses 45 per unit

Fixed expenses 240000

Let us now calculate the degree of operating income using Excel application. Since we are advised to use the Excel application, only the values are depicted in the calculation shown below.

	$ Amount using Excel formula
Selling price per unit	120
Variable expenses per unit	72
Contribution margin per unit	48
CM ratio	0.4 or 40%
Variable expense ratio	0.6 or 60%
Break-even analysis:
Break-even in unit sales	8750
Break-even in dollar sales	1050000
Margin of safety:
Margin of safety in dollars	150000
Margin of safety in percentage	0.125 or 13% approx..
Degree of operating leverage:
Sales	1200000
Variable expenses	720000
Contribution margin	480000
Fixed expenses	420000
Net operating income	60000
Degree of operating leverage	8

Hence, we can conclude that the degree of operating leverage is 8 and the margin of safety is 13%.

3.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as the degree of operating leverage.

Requirement 3

The percentage change in net operating income if sales is increased by 15%.

Answer to Problem 1AE

The percentage change in net operating income when there is an increase in sales by 15% is 120%.

Explanation of Solution

Given information:

Unit Sale 2000 units

Selling price 60 per unit

Variable expenses 45 per unit

Fixed expenses 240000

We are asked to calculate the net operating income if there is a percentage increase of 15% in unit sales.

Now, we have to calculate the percentage of change in net operating income.

Percentage change in net operating income can be known by multiplying the degree of operating leverage with the given percentage change in sales.

  $\begin{array}{l}Percentagechangeinnetoperatingincome=Degreeofoperating\\ leverage\times Percentagechangeinsales\\ =8\times 15\%\\ =120\%\end{array}$

Therefore, the percentage change in net operating income when there is an increase in sales by 15% is 120%.

4.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as the degree of operating leverage.

Requirement 4

The net operating income of the company with the increased sales figures.

Answer to Problem 1AE

The degree of operating leverage is 4.18.

Explanation of Solution

Calculation of sales after increase of percentage:

Sales= 10000 units

  $15\%increase=10000\times \frac{15}{100}\Rightarrow 1500$

So, the sales of $10000+1500=11500$ units have to be considered for further calculations.

From the above calculation in (2), we are aware that the net operating income is $60000. So, using this information we will calculate the increase of 120%. The end result will be $132000. The same thing is depicted in the calculation given below:

	$ Amount using Excel formula
Selling price per unit	120
Variable expenses per unit	72
Contribution margin per unit	48
CM ratio	0.4 or 40%
Variable expense ratio	0.6 or 60%
Break-even analysis:
Break-even in unit sales	8750
Break-even in dollar sales	1050000
Margin of safety:
Margin of safety in dollars	330000
Margin of safety in percentage	0.24 or 24%
Degree of operating leverage:
Sales	1380000
Variable expenses	828000
Contribution margin	552000
Fixed expenses	420000
Net operating income	132000
Degree of operating leverage	4.18

Therefore, the degree of operating leverage is 4.18.

5.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as the degree of operating leverage.

Requirement 5a

The break-even of unit sales, margin of safety in dollars and degree of operating leverage.

Answer to Problem 1AE

The break-even unit sales are 480 units; margin of safety in dollars is $1200000; and degree of operating leverage is 5.

Explanation of Solution

Given information:

Unit Sale 2000 units

Selling price 60 per unit

Variable expenses 45 per unit

Fixed expenses 240000

We are asked to calculate the break-even unit sales, the margin of safety in dollars and degree of operating leverage. To do this, we have to repeat the whole process of calculation of the degree of operating leverages with the new given data.

Data	Amount in $
Unit sales	600	units
Selling price per unit	10000	Per unit
Variable expenses per unit	7500	per unit
Fixed expenses	1200000

Calculation of degree of operating leverage:

	$ Amount using Excel formula
Selling price per unit	10000
Variable expenses per unit	7500
Contribution margin per unit	2500
CM ratio	0.25 or 25%
Variable expense ratio	0.75 or 75%
Break-even analysis:
Break-even in unit sales	480
Break-even in dollar sales	4800000
Margin of safety:
Margin of safety in dollars	1200000
Margin of safety in percentage	0.20 or 20%
Degree of operating leverage:
Sales	6000000
Variable expenses	4500000
Contribution margin	1500000
Fixed expenses	1200000
Net operating income	300000
Degree of operating leverage	5.00

Therefore, the break-even unit sales are 480 units; margin of safety in dollars is $1200000; and degree of operating leverage is 5.

5a.

To determine

Introduction:

Degree of operating leverage: When we observe any business transactions, we observe that the operating income of the company is fluctuating according to the changes in the sales. The measurement of this sort of fluctuation can be termed as the degree of operating leverage.

Requirement 5b

The degree of operating income leverage when the aim is to sell 600 units per year.

Answer to Problem 1AE

The excel application gives an error message “#DIV/0!” as the divisor is 0. Therefore, it is advised to proceed with the plan discussed in 5(a).

Explanation of Solution

The given information is as follows:

Data	Amount in $
Unit sales	600	units
Selling price per unit	9000	Per unit
Variable expenses per unit	7500	per unit
Fixed expenses	900000

Calculation of degree of operating leverage:

	Amount using Excel formula
Selling price per unit	9000
Variable expenses per unit	7500
Contribution margin per unit	1500
CM ratio	0.16 or 17%
Variable expense ratio	0.83 or 83%
Break-even analysis:
Break-even in unit sales	600
Break-even in dollar sales	5400000
Margin of safety:
Margin of safety in dollars	0
Margin of safety in percentage	0.00
Degree of operating leverage:
Sales	5400000
Variable expenses	4500000
Contribution margin	900000
Fixed expenses	900000
Net operating income	0
Degree of operating leverage	#DIV/0!

From the above calculation, it is clear that the execution of this plan is not working properly as it is resulting in any net operating income. Since net operating income is 0, the excel sheet is showing the error message “#DIV/0!” as the divisor is 0. Therefore, it is advised to proceed with the plan discussed in 5(a).