Chapter 16, Problem 39P

1.

To determine

Ascertain the break-even point in sales revenue.

Explanation of Solution

Break-Even in sales revenue: The break-even in sales revenue refers to the sales volume required to cover the fixed and variable costs and left out with neither profit nor loss.

Compute the break-even in sales revenue:

$\begin{array}{c}\text{Break-even sales revenue =}\frac{\text{Total Fixed Cost}}{\text{Contribution Margin Ratio}}\\ \text{=}\frac{\text{\$157,500}}{\text{0}\text{.35}}\\ \text{=\$450,000}\end{array}$

The break-even sales revenue is $584,735.

Working notes:

Compute the contribution margin ratio:

$\begin{array}{c}\text{Contribution Margin ratio = }\frac{\text{Contribution Margin}}{\text{Sales}}\\ =\frac{\text{\$210,000}}{\text{\$600,000}}\\ =0.35\end{array}$

The contribution margin ratio is 35%.

2.

To determine

Ascertain the sales mix to break-even.

Explanation of Solution

Sales mix: Sales mix refers to relative distribution of the total sales amongst the total number of units sold by a company. It is also expressed as a percentage of units sold for each product produced with respect to the total units sold for all the products produced.

Compute the package contribution margin:

Input	Price (A)	Unit Variable cost (B)	Contribution margin $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Contribution margin $\left(\text{E = C × D}\right)$
Jay flex	$200	$130.00	$70.00	1	$70
Free weights	$75	$48.75	$26.25	4	$105
Package Total					$175

Table (1)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\text{\$157,500}}{\$175}\\ =\text{900 packages}\end{array}$

The number of break-even packages is 900.

Compute the break-even Jay-flex:

$\begin{array}{c}\text{Break-even Jay-flex }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 900}\\ =900\text{ machines}\end{array}$

The number of break-even for Jay-flex is 900 machines.

Compute the break-even free weights:

$\begin{array}{c}\text{Break-even free weights }=\text{Sales mix }\times \text{Break-even packages}\\ =4\times \text{ 900}\\ =\text{3,600 sets}\end{array}$

The number of break-even for free weights is 3,600 sets.

Working Notes:

Compute the number of units of Jay-flex:

$\begin{array}{c}\text{Number of units = }\frac{\text{Sales}\times \text{40\%}}{\text{Price per unit}}\\ =\frac{\$\text{500,000}\times \text{40\%}}{\$200}\\ =\frac{\$240,000}{\$200}\\ =1,200\text{ units}\end{array}$

The number of units of Jay-flex is 1,200.

Compute the number of units of free weights:

$\begin{array}{c}\text{Number of units = }\frac{\text{Sales}\times \text{60\%}}{\text{Price per unit}}\\ =\frac{\$\text{500,000}\times \text{60\%}}{\$75}\\ =\frac{\$360,000}{\$75}\\ =4,800\text{ units}\end{array}$

The number of units of free weights is 4,800.

Compute the price per unit for Jay-flex:

$\begin{array}{c}\text{Price per unit = }\frac{\text{Sales}}{\text{Number of units}}\\ =\frac{\$\text{390,000}\times \text{0}\text{.40}}{1,200}\\ =\frac{\$156,000}{1,200}\\ =\$130\text{ per unit}\end{array}$

The price per unit for Jay-flex is $130.

Compute the price per unit for free weights:

$\begin{array}{c}\text{Price per unit = }\frac{\text{Sales}}{\text{Number of units}}\\ =\frac{\$\text{390,000}\times \text{0}\text{.60}}{4,800}\\ =\frac{\$234,000}{4,800}\\ =\$48.75\text{ per unit}\end{array}$

The price per unit for free weights is $48.75.

3.

To determine

Compute the operating leverage and the percentage of change in profit.

Explanation of Solution

Operating leverage: Operating leverage refers to the measurement of degree of the variable costs and fixed costs used by the firm. In other words, the operating leverage refers to the amount of net income of a company for the given change is sales.

Compute the operating leverage:

$\begin{array}{c}\text{Operating leverage }=\frac{\text{Total Contribution Margin}}{\text{Profit}}\\ =\frac{\text{\$210,000}}{\text{\$52,500}}\\ =4.0\end{array}$

Compute the profit increase:

$\begin{array}{c}\text{Profit increase}=\text{Percentage increase}\times \text{Operating leverage}\\ =40\%\times 4\\ =160\%\end{array}$

The profit increase percentage is 160%.

4.

To determine

Ascertain the sales mix after the addition of a new product and analyze its feasibility.

Explanation of Solution

Compute the package contribution margin:

Input	Price (A)	Unit Variable cost (B)	Contribution margin $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Contribution margin $\left(\text{E = C × D}\right)$
Jay flex	$200	$130.00	$70.00	1	$70
Free weights	$75	$48.75	$26.25	8	$210
Jay rider	$180	$140.00	$40.00	1	$40
Package Total					$320

Table (2)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\text{\$157,500+\$5,700}}{\$320}\\ =\frac{\$163,200}{\$320}\\ =\text{510 packages}\end{array}$

The number of break-even packages is 510.

Compute the break-even Jay-flex:

$\begin{array}{c}\text{Break-even Jay-flex }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 510}\\ =510\text{ machines}\end{array}$

The number of break-even for Jay-flex is 510 machines.

Compute the break-even free weights:

$\begin{array}{c}\text{Break-even free weights }=\text{Sales mix }\times \text{Break-even packages}\\ =8\times \text{ 510}\\ =\text{4,080 sets}\end{array}$

The number of break-even for free weights is 4,080 sets.

Compute the break-even Jay-rider:

$\begin{array}{c}\text{Break-even Jay-rider }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 510}\\ =510\text{ machines}\end{array}$

The number of break-even for Jay-rider is 510 machines.

Compute the operating income:

Particulars	Amount ($)
Contribution margin from Jay-rider	$24,000
Less:
Decreased contribution margin from loss of Jay-flex sales	$42,000
Increased Fixed expenses	$5,700
Operating income	(23,700)

Table (3)

The operating loss is $23,700. The new product ‘Jay-rider’ must not be launched as it may reduce the operating income and as well the individual sale of every product.