Chapter 7, Problem 58P

Polaris Inc. manufactures two types of metal stampings for the automobile industry: door handles and trim kits. Fixed cost equals $146,000. Each door handle sells for $12 and has variable cost of $9; each trim kit sells for $8 and has variable cost of $5.

Required:

1. 1. What are the contribution margin per unit and the contribution margin ratio for door handles and for trim kits?
2. 2. If Polaris sells 20,000 door handles and 40,000 trim kits, what is the operating income?
3. 3. How many door handles and how many trim kits must be sold for Polaris to break even?
4. 4. CONCEPTUAL CONNECTION Assume that Polaris has the opportunity to rearrange its plant to produce only trim kits. If this is done, fixed costs will decrease by $35,000, and 70,000 trim kits can be produced and sold. Is this a good idea? Explain.

To determine

Calculate contribution margin per unit and contribution margin ratio.

Answer to Problem 58P

Contribution margin for door handle and trim kit is $3 and $3 respectively and contribution margin ratio is 0.25 and 0.375 respectively.

Explanation of Solution

Contribution margin:

Contribution margin can be defined as the amount obtained after deducting the variable expense from sales revenue. It means the amount of sales left after covering the variable expenses.

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.

Use the following formula to calculate contribution margin per unit:

Items	Selling Price ($) A	Variable Cost ($) B	Contribution Margin ($) C $\left(A-B\right)$	Contribution Margin Ratio $\left(C/A\right)$
Door handle	12	9	3	0.25
Trim kit	8	5	3	0.375

Table (1)

Therefore, contribution margin for door handle and trim kit is $3 and $3 respectively whereas contribution margin ratio is 0.250 and 0.375 respectively.

To determine

Calculate the operating income if company PI sells 20,000 door handles and 40,000 trim kits.

Answer to Problem 58P

The operating income is $34,000.

Explanation of Solution

Operating Income:

The amount of earnings before charging any interest and tax is known as operating income. It is calculated by deducting the amount of expense by the sales revenue.

Calculate operating income:

Accounts Title	Amount ($)
Contribution margin	180,0001
Less: Fixed cost	146,000
Operating income	34,000

Table (2)

Therefore the operating income is $34,000.

Working Note:

1. Calculation of contribution margin:

$\begin{array}{c}Contributionmargin=Contributionmarginofdoorhandles+Contributionmarginoftrimkits\\ =\left(\$3\times 20,000\right)\times \left(\$3\times 40,000\right)\\ =\$60,000+\$120,000\\ =\$180,000\end{array}$

To determine

Find out the break-even quantity for door handles and trim kits.

Answer to Problem 58P

Break-even quantity for door handles and trim kits are 16,222 and 32,444 units respectively.

Explanation of Solution

The package of door handles and trim kits 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 ($) $\left(C\times D\right)$
Door handles	12	9	3	1	3
Trim kits	8	5	3	2	6
Total					9

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 $146,000 for total fixed cost and $9 for contribution margin in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$146,000}{\$9}\\ =16,222units\end{array}$

Therefore, break-even quantity is 16,222 units.

Use the following formula to calculate break-even quantity for door handles:

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

Substitute 16,222 units for number of units and 1¹ for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=16,222\times 1\\ =16,222\text{units}\end{array}$

Therefore, the break-even quantity for door handles is 16,222 units.

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

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

Substitute 16,222 units for number of units and 2¹ for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=16,222\times 2\\ =32,444\text{units}\end{array}$

Therefore, the break-even quantity for trim kits is 32,444 units.

Working Note:

1. Calculation of sales mix:

Ratio for door handles:

$\begin{array}{c}Ratio=\frac{Numberofvases}{Totalnumberofitems}\\ =\frac{20,000}{60,000}\\ =\frac{1}{3}\end{array}$

Ratio for trim kits:

$\begin{array}{c}Ratio=\frac{Numberofvases}{Totalnumberofitems}\\ =\frac{40,000}{60,000}\\ =\frac{2}{3}\end{array}$

The sales mix ratio for door handles and trim kits is 1:2.

To determine

State whether the opportunity to rearrange the plant to produce only trim kits is a good idea.

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.

The following table represents the income statement:

Company PI
Income Statement
	Amount ($)
Sales revenue	560,0002
Less: Variable cost	350,0003
Contribution margin	210,000
Less: Fixed cost	111,000
Operating income	99,000

Table (1)

Therefore, the operating income of Company PI will be$99,000.

The operating income is $99,000 when only trim kits are produced as compared $34,000 when door handles and trim kits are produced. Therefore, it is a good idea to produce only trim kits.

Working Note:

2. Calculation of sales:

$\begin{array}{c}Sales=\left(Priceof\text{trim}\text{kit}\times Unitsproduced\right)\\ =\left(\$8\times 70,000\right)\\ =\$560,000\end{array}$

3. Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=Variable\cos tof\text{trim}\text{kit}\times Unitsproduced\\ =\left(\$5\times 70,000\right)\\ =\$350,000\end{array}$