Financial & Managerial Accounting
Financial & Managerial Accounting
17th Edition
ISBN: 9780078025778
Author: Jan Williams, Susan Haka, Mark S Bettner, Joseph V Carcello
Publisher: McGraw-Hill Education
Question
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Chapter 20, Problem 5E

a.

To determine

Compute the missing amount using contribution margin per unit.

a.

Expert Solution
Check Mark

Explanation of Solution

Contribution Margin:

The process or theory which is used to judge the benefit given by each unit of the goods produced is called as contribution margin.

The contribution margin is the difference between the selling price and the cost of the product.

Formula to compute the unit contribution margin:

Unit Contribution Margin=Unit Sales PricePer Unit Variable Cost

SalesVariable CostsContribution Margin Ratio per UnitFixed CostsOperating IncomeUnits Sold
(1)$200,000$120,000$20$55,000$25,0004,000
(2)180,000105,0001545,00030,0005,000
(3)600,000360,00030150,00090,0008,000

Table (1)

Working notes:

Calculate the amount of sales:

Step 1: Calculate the unit variable cost:

Unit variable cost = (Total variable costUnits sold)($120,0004,000)=$30

Step 2: Calculate the unit sales price:

Unit Contribution Margin=Unit Sales PricePer Unit Variable Cost$20=Sales Price$30Unit Sales Price=$20+$30Unit Sales Price=$50

Step 3: Calculate the amount of sales using contribution margin per unit:

Amount of sales =Units Sold×Unit Sales Price=4,000×$50=$200,000

Calculate the amount of variable costs using contribution margin per unit:

Contribution margin per unit = (SalesVaraible costUnits sold)$15=($180,000Varaible cost5,000)Varaible cost=$180,000$15×5,000Varaible cost=$180,000$75,000=$105,000

Calculate the amount of variable costs using contribution margin per unit:

Contribution margin per unit = (SalesVaraible costUnits sold)$30=($600,000Varaible cost8,000)Varaible cost=$600,000$15×8,000Varaible cost=$600,000$240,000=$360,000

Calculate contribution margin ratio per unit:

Step 1: Calculate unit variable cost.

Unit variable cost = (Total variable costUnits sold)($105,0005,000)=$21

Step 2: Calculate the unit sales price.

Unit sales cost = (Total sales costUnits sold)($180,0005,000)=$36

Step 3: Calculate contribution margin ratio per unit:

Unit Contribution Margin=Unit Sales PricePer Unit Variable Cost=$36$21=$15

Calculate the amount of fixed costs:

Step 1: Calculate contribution margin.

Contribution Margin=SalesVariable cost=$200,000$120,000=$80,000

Step 2: Calculate the amount of fixed costs.

Operating income=Contribution marginFixed cost$25,000=$80,000Fixed costFixed cost=$80,000$25,000=$55,000

Calculate the amount of units sold using contribution margin per unit:

Contribution margin per unit = (SalesVaraible costUnits sold)$30=($600,000$360,000Units sold)Units sold=[(600,000$360,000)$30]Units sold=$240,000$30=$8,000

b.

To determine

Compute the missing amount using contribution margin ratio.

b.

Expert Solution
Check Mark

Explanation of Solution

Contribution Margin Ratio: The contribution margin ratio shows the amount of difference in the actual sales value and the variable expenses in percentage. This margin indicates that percentage which is available for sale above the fixed costs and the profit.

Contribution margin ratio = [(SalesVariable cost)Contribution marginSales]×100

SalesVariable CostsMargin Ratio (%)Fixed CostsOperating Income
(1)$900,000$720,00020%$85,000$95,000
(2)600,000360,00040%165,00075,000
(3)500,000350,00030%90,00060,000

Table (1)

Working notes:

Calculate the contribution margin ratio:

Contribution margin ratio = [(SalesVariable cost)Sales]×100=[($900,000$720,000)$900,000]×100=20%

Calculate the amount of fixed costs:

Step 1: Calculate contribution margin.

Contribution Margin=SalesVariable cost=$900,000$720,000=$180,000

Step 2: Calculate the amount of fixed costs.

Operating income=Contribution marginFixed cost$95,000=$180,000Fixed costFixed cost=$180,000$95,000=$85,000

Calculate the amount of variable cost using contribution margin ratio:

Contribution margin ratio = [(SalesVariable cost)Sales]×10040%=[($600,000Variable cost)$600,000]×100Variable cost=[$600,000($600,000×40%)]Variable cost=($600,000$240,000)=$360,000

Calculate the amount of fixed costs:

Step 1: Calculate contribution margin.

Contribution Margin=SalesVariable cost=$600,000$360,000=$240,000

Step 2: Calculate the amount of fixed costs.

Operating income=Contribution marginFixed cost$75,000=$240,000Fixed costFixed cost=$240,000$75,000=$165,000

Calculate the amount of sales using contribution margin ratio:

Step 1: Calculate the amount of fixed costs.

Operating income=Contribution marginFixed cost$60,000=Contribution margin$90,000Contribution margin=$60,000$90,000=$150,000

Step 2: Calculate the amount of sales using contribution margin ratio:

Contribution margin ratio = [Contribution marginSales]×10030%=[$150,000Sales]×100Sales=$150,000.3Sales=$500,000

Calculate the amount of variable cost using contribution margin ratio:

Contribution margin ratio = [(SalesVariable cost)Sales]×10030%=[($500,000Variable cost)$500,000]×100Variable cost=[$500,000($500,000×30%)]Variable cost=($500,000$150,000)=$350,000

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Chapter 20 Solutions

Financial & Managerial Accounting

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