Chapter 7, Problem 45E

1.

To determine

Calculate the sales mix of portable grills, stationary grills and smokers.

Answer to Problem 45E

The sales mix of portable grills, stationary grills and smokers is 4:10:1.

Explanation of Solution

Sales Mix:

Sales mix refers to the proportion of different products that is sold. It is expressed in the ratio of sales of the products. The ratio of sales mix is reduced to the lowest whole units.

Use the following formula to calculate sales mix for portable grills:

$Salesmix=\frac{Numberofportablegrills}{Totalnumberofitems}$

Substitute 20,000 for number of portable grills and 75,000¹ for total number of items in the above formula.

$\begin{array}{c}Salesmix=\frac{20,000}{75,000}\\ =\frac{4}{15}\end{array}$

Therefore, sales mix for Portable grills is $\frac{4}{15}$.

Use the following formula to calculate sales mix for stationary grills:

$Salesmix=\frac{Numberofstationarygrills}{Totalnumberofitems}$

Substitute 50,000 for number of Portable grills and 75,000¹ for total number of items in the above formula.

$\begin{array}{c}Salesmix=\frac{50,000}{75,000}\\ =\frac{10}{15}\end{array}$

Therefore, sales mix for stationary grills is $\frac{10}{15}$.

Use the following formula to calculate sales mix for smokers:

$Salesmix=\frac{Numberofsmokers}{Totalnumberofitems}$

Substitute 5,000 for number of smokers and 75,000¹ for total number of items in the above formula.

$\begin{array}{c}Salesmix=\frac{5,000}{75,000}\\ =\frac{1}{15}\end{array}$

Therefore, sales mix for smokers is $\frac{1}{15}$.

The portable grills and stationary grills sold were four times and ten times respectively of the number of smokers sold. Therefore, the sales mix is 4:10:1.

Working Note:

1. Calculation of total number of items:

$\begin{array}{c}Totalnumberofitems=\left(\begin{array}{l}Numberofportablegrillssold\\ +Numberofstationarygrillssold\\ +Numberofsmokerssold\end{array}\right)\\ =20,000+50,000+5,000\\ =75,000\mathrm{units}\end{array}$

2.

To determine

Calculate the break-even quantity of each product.

Answer to Problem 45E

Break-even quantity for Portable grills, stationary grills and smokers are 8,600 units and 21,500  and 2,150 units units respectively.

Explanation of Solution

Break-Even Point:

The point or situation where the amount of total cost is equivalent to total revenue is known as the break-even point. It is the point where there is no loss or no profit.

The package of portable grills, stationary grills and smokers is given below:

Product	Price ($) A	Unit Variable Cost ($) B	Unit Contribution Margin ($) C $\left(A-B\right)$	Sales Mix D	Package Unit Contribution Margin ($) $\left(C\times D\right)$
Portable grills	90	45	45	4	180
Stationary grills	200	130	70	10	700
Smokers	250	140	110	1	110
Total					990

Table (1)

Use the following formula to calculate break-even quantity:

$\text{Break-}\mathrm{even}quantity=\frac{\text{Total fixed cost}}{\mathrm{Contribution}margin}$

Substitute $2,128,500 for total fixed cost and $990 for contribution margin in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$2,128,500}{\$990}\\ =2,150units\end{array}$

Therefore, break-even quantity is 2,150 units.

Use the following formula to calculate break-even quantity for Portable grills:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 2,150 for number of units and 4 for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=2,150\times 4\\ =8,600\text{units}\end{array}$

Therefore, the break-even quantity for Portable grills is 8,600 units.

Use the following formula to compute break-even point for stationary grills:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 2,150 for number of units and 10 for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=2,150\times 10\\ =21,500\text{units}\end{array}$

Therefore, the break-even quantity of stationary grills is 21,500 units.

Use the following formula to compute break-even point for smokers:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 2,150 for number of units and 1 for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=2,150\times 1\\ =2,150\text{units}\end{array}$

Therefore, the break-even quantity of smokers is 2,150 units.

3.

To determine

Construct an income statement for Company TQ. Also calculate overall contribution margin ratio and overall break-even sales revenue.

Explanation of Solution

Income Statement:

The statement that shows revenue and expenses incurred over a period of time (usually one year) is called an income statement. It is used for external financial reporting as it helps the outsiders and investors in evaluating the firm’s financial health.

Contribution Margin Ratio:

The sales percentage remaining after covering the amount of total variable cost is known as the contribution margin ratio. It is the available sales dollar percentage which will be used to cover the total fixed cost.

Break-Even Sales Revenue:

Break-even sales revenue can be evaluated by dividing the total amount of fixed cost by the contribution margin ratio.

The following table represents the income statement of Company TQ:

Company TQ
Income Statement
	Amount ($)
Sales revenue	13,050,0002
Less: Variable cost	8,100,0003
Contribution margin	4,950,000
Less: Fixed cost	2,128,500
Operating income	2,821,500

Table (1)

Therefore, the operating income of Company CRP will be $2,821,500.

Use the following formula to calculate overall contribution margin ratio:

$\text{Contribution margin ratio}=\frac{\text{Contribution margin}}{\text{Sales}}$

Substitute $4,950,000 for contribution margin and $13,505,000 for sales in the above formula.

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\$4,950,000}{\$13,505,000}\\ =0.3793\end{array}$

Therefore, the contribution margin ratio is 0.3793.

Use the following formula to calculate break-even sales revenue:

$\text{Break-even sales revenue}=\frac{\text{Total fixed cost}}{\text{Contribution margin ratio}}$

Substitute $2,128,500 for the total fixed cost and 0.3793 for contribution margin ratio in the following formula.

$\begin{array}{c}\text{Break-even sales revenue}=\frac{\$2,128,500}{0.3793}\\ =\$5,611,653\end{array}$

Therefore, the break-even sales revenue is $5,611,653.

Working Note:

2. Calculation of sales:

$\begin{array}{c}Sales=\left(\begin{array}{l}\left(Priceofportablegrills\times Unitssold\right)\\ +\left(Priceofstationarygrills\times Unitssold\right)\\ +\left(Priceofsmokers\times Unitssold\right)\end{array}\right)\\ =\left(\$90\times 20,000\right)+\left(\$200\times 50,000\right)+\left(\$250\times 5,000\right)\\ =\$1,800,000+\$10,000,000+\$1,250,000\\ =\$13,505,000\end{array}$

3. Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=\left(\begin{array}{l}\left(Variable\cos tofportablegrills\times Unitssold\right)\\ +\left(Variable\cos tofstationarygrills\times Unitssold\right)\\ +\left(Variable\cos tofsmokers\times Unitssold\right)\end{array}\right)\\ =\left(\$45\times 20,000\right)+\left(\$130\times 50,000\right)+\left(\$140\times 5,000\right)\\ =\$900,000+\$6,500,000+\$700,000\\ =\$8,100,000\end{array}$

4.

To determine

Calculate margin of safety.

Answer to Problem 45E

The margin of safety is $7,438,347.

Explanation of Solution

Margin of Safety:

The number of units sold or the income earned in excess of the break-even sales is known as margin of safety. It is calculated by deducting the break-even sales from the sales revenue.

Use the following formula to calculate the margin of safety:

$\text{Margin of safety}=\text{Sales}-\text{Break-even }sales\text{}revenue$

Substitute $13,505,000 for sales and $5,611,653 for break-even sales revenue in the above formula.

$\begin{array}{c}\text{Margin of safety}=\$13,505,000-\$5,611,653\\ =\$7,438,347\end{array}$

Therefore, the margin of safety in sales dollars is $7,438,347.