Chapter 3, Problem 1TF15

1.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and the break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The contribution margin per unit.

Answer to Problem 1TF15

The contribution margin per unit is $8.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

With the help of the given information, let us calculate the contribution margin per unit.

Calculation of contribution margin per unit:

  $\begin{array}{l}Contributionmarginperunit=\frac{Contributionmargin}{Totalnumberofunitssold}\\ =\frac{\$8000}{1000}\\ =\$8\end{array}$

Therefore, the contribution margin per unit is $8.

2.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The contribution margin ratio.

Answer to Problem 1TF15

The contribution margin ratio is 40%.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Let us now calculate the contribution margin ratio. Ratios are depicted in percentages.

Calculation of contribution margin ratio:

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Totalsales}\times 100\\ =\frac{\$8000}{\$20000}\times 100\\ =0.40\times 100\\ =40\%\end{array}$

Therefore, the contribution margin ratio is 40%.

3.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The variable expense ratio.

Answer to Problem 1TF15

The variable expense ratio is 60%.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Let us calculate the variable expense ratio.

Calculation of variable expense ratio:

  $\begin{array}{l}Variableexpenseratio=\frac{Variableexpenses}{Totalsales}\times 100\\ =\frac{\$12000}{\$20000}\times 100\\ =0.60\times 100\\ =60\%\end{array}$

Therefore, the variable expense ratio is 60%.

4.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The net operating income if sales increases to 1001 units.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

We are asked to calculate the increase in net operating income. Before proceeding, we have to calculate the contribution margin per unit.

Calculation of contribution margin per unit:

  $\begin{array}{l}Contributionmarginperunit=\frac{Contributionmargin}{Totalnumberofunitssold}\\ =\frac{\$8000}{1000}\\ =\$8\end{array}$

Therefore, the contribution margin per unit is $8.

Let us now calculate the increase in net operating income.

  $\begin{array}{l}Increaseinnetoperatingincome=Contributionmarginperunit\times increasedunitsales\\ =\$8\times 1=\$8\end{array}$

Therefore, the increase in net operating income is $8.

5.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The net operating income if sales decreases to 900 units.

Answer to Problem 1TF15

The net operating income is $1200.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Additional information:

Decrease of sales by 100 units

If total sales units = 1000 and sales has decreased to 900 units, then the decreasing sales unit will be 100. With this information, let us calculate the net operating income using the formula:

  $\begin{array}{l}Netoperatingincome=(Totalnumberofunitssold\times Sellingpriceperunit)-\\ (Totalnumberofunitssold\times variablecostperunit)-Fixedcost\\ =(900\times 20)-(90012)-6000\\ =18000-10800-6000\\ =1200\end{array}$

Therefore, the net operating income in this case is $1200.

6.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The net operating income if sales volume decreases by 100 units with an increase of $2 per unit in selling price.

Answer to Problem 1TF15

The net operating income is $3000.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Additional information:

Sales volume decreases by 100 units

Increase of $2 per unit in selling price.

Therefore, the selling price will be $20+2=\$22$ per unit; and Variable cost= $\$12$ per unit.

With the help of the given information, let us calculate the net operating income.

  $\begin{array}{l}Netoperatingincome=(Totalnumberofunitssold\times Sellingpriceperunit)-\\ (Totalnumberofunitssold\times variablecostperunit)-Fixedcost\end{array}$

  $\begin{array}{l}=(900\times 22)-(900\times 12)-6000\\ =19800-10800-6000\\ =3000\end{array}$

Therefore, the net operating income in this case is $3000.

7.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The net operating income with an increase in variable cost by $1, advertising cost by $1500 unit sales by 250 units.

Answer to Problem 1TF15

The net operating income in this case is $1250.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Additional information:

Increase in variable cost by $1

Increase in advertising cost by $1500

Increase in unit sales by 250 units.

We are told that there are additions to the to some of the cost apart from sales. Let us calculate the increase. We can make use of the values in calculating the net operating income.

Given unit sales 1000 units	Advertising cost $ 0
+ increase 250 units	+ increase $ 1500
Total unit sales 1250 units	Total advertising cost $1500

Note: The amount of advertising cost has to be considered as a fixed expense. So, the value of the advertising cost has to be added to the fixed expense.

  $Totalfixedexpenses=6000+1500=7500$

Total variable cost per unit= $\$12+1=\$13$

Now let us calculate the net operating income with the given conditions.

  $\begin{array}{l}Netoperatingincome=(Totalnumberofunitssold\times Sellingpriceperunit)-\\ (Totalnumberofunitssold\times variablecostperunit)-Fixedcost\end{array}$

Since we have calculated the required amounts, we can directly substitute the same.

  $\begin{array}{l}=(1250\times 20)-(1250\times 13)-7500\\ =25000-16250-7500\\ =1250\end{array}$

Therefore the net operating income in this case is $1250.

8.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The break-even point in unit sales.

Answer to Problem 1TF15

The break-even unit sales will be 750 units.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Since we are asked to calculate the break-even point in units, we have to consider the per-unit price of all the required variables used in the formula. With the help of the given information and earlier calculation, we are aware that the contribution margin per unit is $8.

  $Break-evenpointinunitsales=\frac{Fixedcost}{Contributionmarginperunit}$

  $\begin{array}{l}=\frac{6000}{\$8}\\ =750\end{array}$

Therefore, the break-even unit sales will be 750 units.

9.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The break-even point in dollar sales.

Answer to Problem 1TF15

The break-even sales value will be $15000.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

The formula to calculate the break-even point in unit sales is as follows:

  $\begin{array}{l}Break-evenpointindollar sales=\frac{Fixedcost}{\frac{Contributionmargin}{Totalsales}}\\ =\frac{6000}{\raisebox{1ex}{$\$8000$}\!\left/ \!\raisebox{-1ex}{$\$20000$}\right.}\\ =\frac{6000}{0.40}\\ =\$15000\end{array}$

Therefore, the break-even sales value will be $15000.

10.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The number of units to be sold to achieve a target profit of $5000.

Answer to Problem 1TF15

The expected sales units of 1375 are required to achieve a target profit of $5000.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Let us use the formula to calculate the expected sales unit:-

  $Expectedsalesunit=\frac{Fixedcost+Targetprofit}{Contributionmarginperunit}$

From the above calculations, we are aware that the contribution margin per unit is $8.

  $\begin{array}{l}=\frac{\$6000+\$5000}{\$8}\\ =\frac{\$11000}{\$8}\\ =1375\end{array}$

Therefore, the expected sales units of 1375 are required to achieve a target profit of $5000.

11.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The margin of safety in dollars along with its percentages.

Answer to Problem 1TF15

The margin of safety in percentages is 25%.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

We are informed that the total sales= $20000 with break-even sales at 15000.

The margin of safety value

  $\begin{array}{l}Marginofsafetyvalue=Totalsalesvalue-Break-evensalesvalue\\ =\$20000-\$15000\\ =\$5000\end{array}$

Therefore, the margin of safety is $5000.

To calculate the value in percentages, we need to divide it by total sales and then multiply the value by 100.

  $\begin{array}{l}Marginofsafetyinpercentages=\frac{Marginofsafetyvalue}{Totalsalesvalue}\times 100\\ =\frac{5000}{20000}\times 100\\ =25\%\end{array}$

Therefore, the margin of safety in percentages is 25%.

12.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The degree of operating leverage.

Answer to Problem 1TF15

The degree of operating leverage is 4.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

The degree of operating leverage:

Calculation of degree of operating leverage:

  $\begin{array}{l}Degreeofoperatingleverage=\frac{Costmargin}{Totalsales-variableexpense-Fixedexpense}\\ =\frac{8000}{20000-12000-6000}\\ =\frac{8000}{2000}\\ =4\end{array}$

Therefore, the degree of operating leverage is 4.

13.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

To determine: The degree of operating leverage when the percent in net operating income increases with an increase of 5% in sales.

Answer to Problem 1TF15

The increase in net operating income is 20%.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Additional information:

Increase in sales= 5%

The following formula will be helpful in calculating the increase in net operating income.

  $\begin{array}{l}Increaseinnetoperatingincome=Degreeofoperatingleverage\times Percentageincreaseinsales\\ =4\times 5=20\end{array}$ Therefore, the increase in net operating income is 20%.

14.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The degree of operating leverage when total variable expenses are $6000; total fixed expenses are $12000.

Answer to Problem 1TF15

The degree of operating leverage is 7.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Contribution margin=$8000

Net operating income=$2000

Additional information:

Total variable expenses= $6000

Total fixed expenses = $12000.

The formula suitable to the information given to us is as follows:

  $\begin{array}{l}Degreeofoperatingleverage=\frac{Sales-Variableexpense}{Totalsales-variableexpense-Fixedexpense}\\ =\frac{20000-6000}{20000-6000-12000}\\ =\frac{14000}{2000}=7\end{array}$

Therefore, the degree of operating leverage is 7.

15.

To determine

Introduction:

Margin of safety: It is supposed to be the difference amount of actual sales and break-even sales. It plays an important role by depicting the revenue value which can be reduced to equalize to the break-even point of no profit- no loss.

The estimated percent increase in net operating income of a 5% increase in sales.

Answer to Problem 1TF15

The increase in net operating income is 35%.

Explanation of Solution

Given information:

Sales volume=1000 units

Sales=$20000

Variable expenses=$12000

Contribution margin=$8000

Fixed expenses= $6000

Net operating income=$2000

Additional information:

Increase in sales=5%

The following formula will be helpful in calculating the increase in net operating income.

Increase in net operating income= Degree of operating leverage* Percentage increase in sales

Here we have considered that the degree of operating leverage is 7.

  $\begin{array}{l}Increaseinnetoperatingincome=Degreeofoperatingleverage\times Percentageincreaseinsales\\ =7\times 5=35\end{array}$ Therefore, the increase in net operating income is 35%.