Chapter 9, Problem 42P

1.

To determine

Prepare contribution income statement.

Explanation of Solution

Compute the contribution income statement:

Contribution Income Statement
Particulars	Gasoline	Food	Other	Total
Sales revenue	$100,000	$60,000	$40,000	$200,000
Less: Coupons redeemed	$15,000			$15,000
Cost of sales	$75,000	$36,000	$20,000	$131,000
Contribution margin	$10,000	$24,000	$20,000	$54,000
Less: Fixed costs				$60,500
Pre-tax profit (loss)				-$6,500

Working notes:

Determine the amount of fixed cost:

Particulars	Amount
Labor ($10,000 + $2,500)	$12,500
Rent, power, supplies, etc.	$40,000
Depreciation	$7,500
Coupon printing cost	$500
Total monthly fixed costs	$60,500

Determine the redeemed coupons:

$\begin{array}{c}\text{Redeemed coupons}\}\text{ = Total coupon}\times \text{Distributed percentage}\\ \text{= }\frac{\$200,000\times 75\%}{10}\\ \text{=}\frac{\$150,000}{\$10}\\ =15,000\end{array}$

Determine the cost of sales:

$\begin{array}{c}\text{Cost of sales}\}\text{ = }\left(\frac{\text{Sales revenue}}{\text{Per gallon}}\right)\times \text{Cost per gallon}\\ \text{= }\left(\frac{\$100,000}{\$2,50}\right)\text{×\$1}\text{.875}\\ \text{=\$40,000×\$1}\text{.875}\\ =\$75,000\end{array}$

2.

To determine

Determine the break-even sales in dollars based on weighted average contribution margin ratio.

Explanation of Solution

Compute the break-even sales in dollars:

$\begin{array}{c}\text{Break even sales in dollars}\}\text{ = }\left(\frac{\text{Total fixed costs }}{\begin{array}{l}\text{Weighted-average }\\ \text{contribution margin ratio}\end{array}}\right)\\ \text{= }\frac{\$60,500}{27\%}\\ =\$224,074\end{array}$

Working notes:

Determine the weighted average contribution margin ratio:

$\begin{array}{c}\begin{array}{l}\text{Weighted contribution }\\ \text{margin ratio}\end{array}\}\text{ = }\left(\frac{\text{Total contribution margin }}{\text{ Total sales dollars}}\right)\times 100\%\\ \text{= }\frac{\$54,000}{\$200,000}\\ \text{= 27\%}\end{array}$

3.

To determine

Determine the composition of total break even sales in dollars for three products:

Explanation of Solution

Compute the composition of total break even sales in dollars for three products:

Particulars	Amount
Gasoline (0.50 × $224,074)	$112,037
Food/beverage (0.30 × $224,074)	$67,222
Other (0.20 × $224,074)	$44,815
Total	$224,074

Working notes:

Determine the sales mix percentage for “G”:

$\begin{array}{c}\text{Sales mix percentage}\}\text{ = }\frac{\text{Gasoline sales}}{\text{Total coupon}}\\ \text{= }\frac{\$100,000}{\$200,000}\\ \text{= }0.50\end{array}$

Determine the sales mix percentage for “F”:

$\begin{array}{c}\begin{array}{l}\text{Sales mix }\\ \text{percentage food}\end{array}\}\text{ = }\frac{\text{ Sales of food}}{\text{Total coupon}}\\ \text{= }\frac{\$60,000}{\$200,000}\\ \text{= }0.30\end{array}$

Determine the sales mix percentage for “O”:

$\begin{array}{c}\begin{array}{l}\text{Sales mix }\\ \text{percentage "other"}\end{array}\}\text{ = }\frac{\text{ Sales "Other"}}{\text{Total coupon}}\\ \text{= }\frac{\$40,000}{\$200,000}\\ \text{= }0.20\end{array}$

4.

To determine

Determine the profit or loss before tax:

Explanation of Solution

Compute the profit or loss before tax:

Particulars	Amount
Sales revenue   ($200,000 × 1.2)	$240,000
Less: Variable costs	$156,000
Contribution margin                                   ($240,000 × 35%)	$84,000
Less: Fixed costs	$60,500
Profit before tax	$23,500

5.

To determine

Indicate the factors that make sensitivity analysis prevailing in decision-making.

Explanation of Solution

The sensitivity analysis is utilized to deal with uncertainty in an efficient manner. The three factors are as follows:

1. 1. The availability of computers and spreadsheets made easy to determine the changing one or more factors.
2. 2. The business environment is considered to be more dynamic and competitive in nature. An increase in productivity, competition, consumer taste and preference, shirted life cycle and technology make sensitivity analysis widely used factor.
3. 3. The analysis identifies the key variables and assumption that affect the financial results, thus the variables can be modified to obtain information.

6.

To determine

Indicate the factors that make sensitivity analysis prevailing in decision-making.

Explanation of Solution

The conventional measures associated with CVP analysis are as follows:

• Degree of operating leverage.
• The margin of safety and margin of safety ratio.

The sensitivity analysis is as follows:

• “if” analysis
• Preparation of decision tables and expected values.