Chapter 6, Problem 11E

Missing Data; Basic CVP Concepts L06−1, L06−9
Fill in the missing amounts in each of the eight case situations below. Each case is independent of the others. (Hint: One way to find the missing amounts would be to prepare a contribution format income statement for each case, enter the known data, and then compute the missing items.)
 a. Assume that only one product is being sold in each of the four following case situations:

 b. Assume that more than one product is being sold in each of the four following case situations:

To determine

Cost volume profit analysis: Cost volume profit analysis measures the effect on income of a company with the alteration of cost and volume of sales.

The missing amount in the table.

Answer to Problem 11E

Solution:

a) Assuming that only one product is being sold in each of the following case situations:

Case	Units Sold	Sales	Variable Expenses	Contribution Margin per Unit	Fixed Expenses	Net Operating Income(loss)
1	15,000	$180,000	$120,000	$4	$50,000	$10,000
2	4,000	$100,000	$60,000	$10	$32,000	$8,000
3	10,000	$200,000	$70,000	$13	$118,000	$12,000
4	6,000	$300,000	$210,000	$15	$100,000	($10,000)

Case 1

Contribution format income statement
	Total	Per Unit
Sales (15,000 units)	$180,000	$12.00
Variable expenses	$120,000	$8.00
Contribution Margin	$60,000	$4.00
Fixed expenses	$50,000
Net operating income	$10,000

Case 2

Contribution format income statement
	Total	Per Unit
Sales (4,000 units)	$100,000	$25.00
Variable expenses	$60,000	$15.00
Contribution Margin	$40,000	$10.00
Fixed expenses	$32,000
Net operating income	$8,000

Case 3

Contribution format income statement
	Total	Per Unit
Sales (10,000 units)	$200,000	$20.00
Variable expenses	$70,000	$7.00
Contribution Margin	$130,000	$13.00
Fixed expenses	$118,000
Net operating income	$12,000

Case 4

Contribution format income statement
	Total	Per Unit
Sales (6,000 units)	$300,000	$50.00
Variable expenses	$210,000	$35.00
Contribution Margin	$90,000	$15.00
Fixed expenses	$100,000
Net operating income	($10,000)

b) Assuming that more than one product is being sold in each of the four case situations:

Case	Sales	Variable Expenses	Average Contribution Margin Ratio	Fixed Expenses	Net Operating Income (loss)
1	$500,000	$400,000	20%	$93,000	$7,000
2	$400,000	$260,000	35%	$100,000	$40,000
3	$250,000	$100,000	60%	$130,000	$20,000
4	$600,000	$420,000	30%	$185,000	($5,000)

Case 1

Contribution format income statement
	Amounts
Sales	$500,000
Variable expenses	$400,000
Contribution Margin	$100,000
Fixed expenses	$93,000
Net operating income	$7,000

$$ $\begin{array}{l}\begin{array}{l}*AverageContributionMarginRatio=\frac{Contributionmargin}{Salesrevenue}\hfill \\ 0.2or20\% =\frac{Contributionmargin}{\$500,000}\hfill \\ ContributionMargin = \$500,000*0.20\hfill \end{array} \\ = \$100,000\end{array}$

Case 2

Contribution format income statement
	Amounts
Sales	$400,000
Variable expenses	$260,000
Contribution Margin	$140,000
Fixed expenses	$100,000
Net operating income	$40,000

Case 3

Contribution format income statement
	Amounts
Sales	$250,000
Variable expenses	$100,000
Contribution Margin	$150,000
Fixed expenses	$130,000
Net operating income	$20,000

$$

$\begin{array}{l}*AverageContributionMarginRatio=\frac{Contributionmargin}{Salesrevenue}\hfill \\ 0.6or60\% =\frac{\$150,000}{Salesrevenue}\hfill \\ SalesRevenue =\frac{\$150,000}{0.6}\hfill \\ = \$250,000\hfill \end{array}$

Case 4

Contribution format income statement
	Amounts
Sales	$600,000
Variable expenses	$420,000
Contribution Margin	$180,000
Fixed expenses	$185,000
Net operating income	($5,000)

Explanation of Solution

A contribution margin is calculated by deducting the variable expenses from the sales revenue. So, if the variable expense is missing, the contribution margin is deducted from the sales revenue and goes same in case of units. The net operating income is calculated by deducting the fixed expenses from the contribution margin. So, if the fixed expenses are missing, the operating income is deducted from the contribution margin. The contribution margin ratio is calculated by dividing the contribution margin by sales revenue. So, if the sales revenue is missing, it can be ascertained by dividing the contribution margin by the contribution margin ratio and if the contribution margin is missing, it is calculated by multiplying the contribution margin with the contribution margin ratio.

Given: a) Assume that only one product is being sold in each of the following case situations:

Case	Units Sold	Sales	Variable Expenses	Contribution Margin per Unit	Fixed Expenses	Net Operating Income(loss)
1	15,000	$180,000	$120,000	?	$50,000	?
2	?	$100,000	?	$10	$32,000	$8,000
3	10,000	?	$70,000	$13	?	$12,000
4	6,000	$300,000	?	?	$100,000	($10,000)

b) Assume that more than one product is being sold in each of the four case situations:

Case	Sales	Variable Expenses	Average Contribution Margin Ratio	Fixed Expenses	Net Operating Income (loss)
1	$500,000	?	20%	?	$7,000
2	$400,000	$260,000	?	$100,000	?
3	?	?	60%	$130,000	$20,000
4	$600,000	$420,000	?	?	($5,000)

Conclusion

The cost volume profit analysis aims determining an outcome of changes in the various variables of operations. A cost is the expenses incurred on the products which are being sold and the volume is the quantity of the products which is going to be sold. The profit is the difference between the cost incurred and sales revenue of a company. An analysis of cost volume profit helps in predicting or forecasting the various consequences of various decisions.