Appendix B Profitability Analysis

Appendix B Profitability Analysis

True/False Questions

1.When a company does not have a constraint, the relative profitability of its business segments should be measured by dividing their incremental profits by their total revenues.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Medium

2.Relative profitability should be measured by dividing the incremental profit from a segment by its market share.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Medium

3.The profitability index is computed by dividing the incremental profit from a segment by the amount of the constrained resource required by the segment.

Ans:True AACSB:ReflectiveThinking AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Easy

4.When long-term investment funds are the constraint and the company is choosing from among potential long-term projects, the profitability index should be computed by dividing the net present value of a project by the expected market share of the project.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Medium

5.A portrait painter has been asked to do far more portraits in the next three months than she has time to paint during that time period. To rank the possible portraits in order of their profitability, she should divide each portrait's estimated incremental profit by the amount of she intends to charge for the portrait.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Medium

6.A catering service has contracts with a number of customers to supply lunches on a daily basis. The chef has complained of the long hours she must work to prepare all of these lunches and has threatened to quit. It would be very difficult, if not impossible, to replace the chef. To reduce the pressure on the chef, some contracts may have to be cancelled. (The catering service can cancel any contract with seven days notice.) To help make this decision, the profitability of each customer should be measured by dividing the daily incremental profit from serving each customer by the amount the customer is charged for the daily meal.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Medium

7.The profitability index for a volume trade-off decision involving products should be computed by dividing the selling price of the product by the amount of the constrained resource required by one unit of the product.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Medium

8.A company that makes horsehair cowboy belts cannot meet the demand for belts due to a limited supply of artisans who know how to make the belts. To determine which models of the cowboy belts should be emphasized, the company should rank the models by dividing the unit contribution of each model by the amount of time an artisan requires to make the model.

Ans:True AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Medium

9.To encourage salespersons to sell the most profitable products, they should be paid sales commissions based on product margins–revenues less fully allocated costs.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Medium

10.When a company has a production constraint, the selling price of any new product should cover both its variable cost and the out-of-pocket cost of the constrained resource.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Hard

11.The opportunity cost of using a unit of the constrained resource in a volume trade-off decision is determined by the profitability index of the most profitable current product.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Hard

12.Absolute profitability is determined by subtracting a segment's fully allocated costs from its revenues.

Ans:False AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:4 Level:Easy

13.Measuring relative profitability makes sense only when a constraint exists that forces trade-offs among segments.

Ans:True AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:4 Level:Easy

Multiple Choice Questions

14.The profitability index in a volume trade-off decision should be computed by:

A)dividing each product's contribution margin by the amount of the constrained resource used by the product.

B)dividing each product's contribution margin by its selling price.

C)dividing each product's selling price by the amount of the constrained resource used by the product.

D)dividing each product's variable cost by its selling price.

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

15.The absolute profitability of a business segment is determined by:

A)subtracting the variable costs of the business segment from its revenue.

B)subtracting the avoidable costs of the business segment from its revenue.

C)subtracting the full costs, including allocations of common fixed costs, of the business segment from its revenue.

D)finding the larger of the segments full costs or its revenues.

Ans:B AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:4 Level:Easy

16.Needles Corporation would like to determine the relative profitability of a number of jobs. For illustration purposes, the company has provided the following data for job V42J:

Revenue...... / $186,200
Avoidable cost...... / 111,720
Incremental profit...... / $74,480
Amount of the constrained resource used by the job. / 380 hours

What is the profitability index for job V42J?

A)$294 per hour

B)0.40

C)$196 per hour

D)$490 per hour

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Easy

Solution:

Segment / Incremental Profit / Amount of Constrained Resource Required (hours) / Profitability Index
(per hour)
V42J.... / $74,480 / 380 / $196

17.Bridgewater Corporation would like to determine the relative profitability of a number of jobs. For example, the revenue from Job R48D is $78,000 and its avoidable costs amount to $70,200, resulting in an incremental profit of $7,800. Furthermore, the job requires 150 hours of the constrained resource. What is the profitability index for job R48D?

A)0.10

B)$468 per hour

C)$52 per hour

D)$520 per hour

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Easy

Solution:

Segment / Incremental Profit / Amount of Constrained Resource Required (hours) / Profitability Index
(per hour)
R48D.... / $7,800 / 150 / $52

18.Farace Corporation would like to determine the relative profitability of a number of jobs. For illustration purposes, the company has provided the following data for job P13K:

Revenue...... / $112,000
Avoidable cost...... / 78,400
Incremental profit...... / $33,600
Amount of the constrained resource used by the job...... / 280 hours
Percentage of the total company profit for the period from the job / 32%

What is the profitability index for job P13K?

A)$400 per hour

B)0.30

C)$120 per hour

D)0.32

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Easy

Solution:

Segment / Incremental Profit / Amount of Constrained Resource Required (hours) / Profitability Index
(per hour)
P13K.... / $33,600 / 280 / $120

19.Vielmas Corporation would like to determine the relative profitability of a number of jobs. For example, job Q89G has revenues of $170,500 and avoidable costs of $102,300, resulting in an incremental profit of $68,200. The job requires 310 hours of the constrained resource. The job is responsible for 11% of the company's total profit for the period. What is the profitability index for job Q89G?

A)0.11

B)$550 per hour

C)$220 per hour

D)0.40

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:1 Level:Easy

Solution:

Segment / Incremental Profit / Amount of Constrained Resource Required (hours) / Profitability Index
(per hour)
Q89G.... / $68,200 / 310 / $220

20.Papelian Corporation would like to determine the relative profitability of the company's products for purposes of making volume trade-off decisions. The company has provided the following data for product M75A:

Selling price...... / $240.00
Variable cost per unit...... / 168.00
Unit contribution margin...... / $72.00
Amount of the constrained resource used by the job. / 12 minutes
Monthly unit sales...... / 3,800 units

What is the profitability index for product M75A?

A)$273,600

B)0.30

C)$20.00 per minute

D)$6.00 per minute

Ans:D AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

M75A
Selling price...... / $240.00
Variable cost...... / 168.00
Unit contribution margin...... / $72.00
Constrained resource required per unit (minutes).. / 12
Profitability index (per minute)...... / $6.00

21.Trosper Corporation would like to determine the relative profitability of the company's products for purposes of making volume trade-off decisions. For example, the selling price of product Y82U is $264.00, its unit variable cost is $237.60, and its unit contribution margin is $26.40. One unit of the product requires 11 minutes of the constrained resource. Monthly sales are 5,200 units. What is the profitability index for product Y82U?

A)$2.40 per minute

B)0.10

C)$137,280

D)$24.00 per minute

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

Y82U
Selling price...... / $264.00
Variable cost...... / 237.60
Unit contribution margin...... / $ 26.40
Constrained resource required per unit (minutes).. / 11
Profitability index (per minute)...... / $2.40

22.Sept Corporation would like to determine the relative profitability of the company's products for purposes of making volume trade-off decisions. For illustration, the company has provided the following data for product A58E:

Selling price...... / $253.00
Variable cost per unit...... / $177.10
Amount of the constrained resource required by one unit. / 11 / grams
Monthly unit sales...... / 2,300 / units

What is the profitability index for product A58E?

A)$6.90 per gram

B)$23.00 per gram

C)0.30

D)$174,570

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

A58E
Selling price...... / $253.00
Variable cost...... / 177.10
Unit contribution margin...... / $ 75.90
Constrained resource required per unit (grams)... / 11
Profitability index (per gram)...... / $6.90

23.Mckendrick Corporation would like to determine the relative profitability of the company's products for purposes of making volume trade-off decisions. For example, the selling price of product X99M is $144.00 and its unit variable cost is $100.80. One unit of the product requires 6 ounces of the constrained resource. Monthly sales are 7,400 units. What is the profitability index for product X99M?

A)$319,680

B)0.30

C)$7.20 per ounce

D)$24.00 per ounce

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

X99M
Selling price...... / $144.00
Variable cost...... / 100.80
Unit contribution margin...... / $43.20
Constrained resource required per unit (ounces).. / 6
Profitability index (per ounce)...... / $7.20

24.Claywell Corporation has provided the following data concerning its two products:

L41M / R62D
Selling price...... / $98.00 / $480.00
Unit variable cost...... / 58.80 / 432.00
Unit contribution margin...... / $39.20 / $48.00
Amount of the constrained resource required for one unit of the product (grams) / 7 / 16
Monthly unit demand...... / 4,600 / 8,400

The profitability index for product L41M is closest to:

A)0.40

B)0.45

C)0.31

D)$5.60 per gram

Ans:D AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

L41M
Selling price...... / $98.00
Variable cost...... / 58.80
Unit contribution margin...... / $39.20
Constrained resource required per unit (grams).. / 7
Profitability index (per gram)...... / $5.60

25.Delle Corporation has provided the following data concerning its two products:

Z31X / L25X
Selling price...... / $87.00 / $64.00
Unit variable cost...... / $52.20 / $38.40
Amount of the constrained resource required for one unit of the product (ounces) / 3 / 2
Monthly unit demand...... / 6,600 / 6,700

The profitability index for product Z31X is closest to:

A)$29.00 per ounce

B)$11.60 per ounce

C)0.57

D)0.40

Ans:B AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

Z31X
Selling price...... / $87.00
Variable cost...... / 52.20
Unit contribution margin...... / $34.80
Constrained resource required per unit (ounces). / 3
Profitability index (per ounce)...... / $11.60

26.Bynum Corporation has provided the following data concerning its two products–U68 and R64:

U68 / R64
Monthly unit demand...... / 2,000 / 3,900
Selling price...... / $30.00 / $216.00
Unit variable cost...... / $24.00 / $194.40

The total amount of the constrained resource available each month is 33,200 grams. Each unit of product U68 requires 2 grams of the constrained resource and each unit of product R64 requires 8 grams. What is the maximum contribution margin the company can earn per month?

A)$90,840

B)$96,240

C)$90,772

D)$90,240

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Medium

Solution:

Computation of the profitability index:

U68 / R64
Selling price...... / $30.00 / $216.00
Variable cost...... / 24.00 / 194.40
Unit contribution margin...... / $ 6.00 / $ 21.60
Constrained resource required per unit (grams).. / 2 / 8
Profitability index (per gram)...... / $3.00 / $2.70

According to the profitability index, the most profitable product is U68.

Total constrained resource available...... / 33,200
Less constrained resource required to produce 2,000 units of U68. / 4,000
Remaining constrained resource available...... / 29,200
Less constrained resource required by 3,650 units of R64*..... / 29,200
Remaining constrained resource available...... / 0

*29,200 ÷ 8 grams per unit of R64 = 3,650 units of R64

U68 / R64 / Total
Unit contribution margin. / $6.00 / $21.60
Volume (units)...... / 2,000 / 3,650
Contribution margin.... / $12,000 / $78,840 / $90,840

27.The same constrained resource is used by four different products at Coloma Corporation. Data concerning those products appear below:

O100 / O200 / O300 / O400
Unit selling price...... / $32.50 / $27.90 / $14.80 / $41.80
Unit variable cost...... / $14.30 / $5.60 / $2.40 / $21.70
Amount of the constrained resource required / 0.47 / 0.40 / 0.29 / 0.58

The company does not have enough of the constrained resource to satisfy for demand of all four products. From the standpoint of the entire company, if it is a choice between sales of one unit of one product versus another, which product should the salespersons emphasize?

A)O100

B)O200

C)O300

D)O400

Ans:B AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Easy

Solution:

From the standpoint of the entire company, the products should be ranked on the basis of the profitability index.

O100 / O200 / O300 / O400
Unit selling price...... / $32.50 / $27.90 / $14.80 / $41.80
Unit variable cost...... / 14.30 / 5.60 / 2.40 / 21.70
Unit contribution margin...... / $18.20 / $22.30 / $12.40 / $20.10
Amount of the constrained resource required / 0.47 / 0.40 / 0.29 / 0.58
Profitability index...... / $38.72 / $55.75 / $42.76 / $34.66
Ranking...... / 3 / 1 / 2 / 4

According to the profitability index, product O200 should be emphasized.

28.Byod Corporation has four different products that use the same constrained resource. Data concerning those products appear below:

L100 / L200 / L300 / L400
Unit selling price...... / $30.90 / $28.20 / $19.00 / $36.60
Unit variable cost...... / $13.90 / $10.70 / $4.80 / $19.80
Amount of the constrained resource required / 0.40 / 0.34 / 0.20 / 0.50

A)L300

B)L400

C)L200

D)L100

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Easy

Solution:

From the standpoint of the entire company, the products should be ranked on the basis of the profitability index.

L100 / L200 / L300 / L400
Unit selling price...... / $30.90 / $28.20 / $19.00 / $36.60
Unit variable cost...... / 13.90 / 10.70 / 4.80 / 19.80
Unit contribution margin...... / $17.00 / $17.50 / $14.20 / $16.80
Amount of the constrained resource required / 0.40 / 0.34 / 0.20 / 0.50
Profitability index...... / $42.50 / $51.47 / $71.00 / $33.60
Ranking...... / 3 / 2 / 1 / 4

According to the profitability index, product L300 should be emphasized.

29.Wortham Corporation has designed a new product, E71, whose variable cost is $87.90 per unit and that requires 2.10 minutes of the constrained resource. The opportunity cost is $29.00 per minute used of the constrained resource. What is the minimum acceptable selling price for the new product?

A)$87.90

B)$148.80

C)$60.90

D)$116.90

Ans:B AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Easy

Solution:

The selling price of the new product must cover at least its variable cost and the opportunity cost of using the constrained resource:

Variable cost per unit...... / $ 87.90
Opportunity cost of using the constrained resource:
Amount of constrained resource per unit (a)...... / 2.10
Opportunity cost per unit of the constrained resource (b) / $29.00
Total opportunity cost (a) × (b)...... / 60.90
Minimum selling price...... / $148.80

30.Wesner Corporation is about to announce a new product, R58, whose variable cost is $120.20 per unit and that would require 8.40 grams of a raw material that is the constrained resource in the company. The opportunity cost to use this constrained resource is $52.00 per gram. What is the minimum acceptable selling price for the new product?

A)$557.00

B)$172.20

C)$436.80

D)$120.20

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:3 Level:Easy

Solution:

The selling price of the new product must cover at least its variable cost and the opportunity cost of using the constrained resource:

Variable cost per unit...... / $120.20
Opportunity cost of using the constrained resource:
Amount of constrained resource per unit (a)...... / 8.40
Opportunity cost per unit of the constrained resource (b) / $52.00
Total opportunity cost (a) × (b)...... / 436.80
Minimum selling price...... / $557.00

Use the following to answer questions 31-34:

The management of Gotay Corporation has provided the following data concerning its two products:

S14O / L95I
Selling price...... / $234.00 / $240.00
Unit variable cost...... / $163.80 / $144.00
Constrained resource required for one unit of the product (minutes) / 9 / 15
Monthly demand (units)...... / 700 / 490

The constrained resource is a particular machine that is available for 9,900 minutes each month.

31.How many units of product L95I should be produced each month?

A)240

B)910

C)0

D)490

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

S14O / L95I
Selling price...... / $234.00 / $240.00
Variable cost...... / 163.80 / 144.00
Unit contribution margin...... / $ 70.20 / $ 96.00
Constrained resource required per unit (minutes).. / 9 / 15
Profitability index (per minute)...... / $7.80 / $6.40

According to the profitability index, the most profitable product is S14O.

Total constrained resource available...... / 9,900
Less constrained resource required to produce 700 units of S14O. / 6,300
Remaining constrained resource available...... / 3,600
Less constrained resource required by 240* units of L95I...... / 3,600
Remaining constrained resource available...... / 0

*3,600 ÷ 15 minutes per unit of L95I = 240

32.What is the maximum contribution margin the company can earn per month?

A)$72,180

B)$96,180

C)$66,930

D)$69,757

Ans:A AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Easy

Solution:

Computation of the profitability index:

According to the profitability index, the most profitable product is S14O.

*3,600 ÷ 15 minutes per unit of L95I = 240

S14O / L95I / Total
Unit contribution margin.... / $70.20 / $96.00
Volume (units)...... / 700 / 240
Contribution margin...... / $49,140 / $23,040 / $72,180

33.Up to how much should the company be willing to pay to obtain enough of the constrained resource to satisfy demand for the two existing products?

A)$96.00 per minute

B)$7.80 per minute

C)$6.40 per minute

D)$70.20 per minute

Ans:C AACSB:Analytic AICPABB:CriticalThinking AICPAFN:Reporting LO:2 Level:Medium

Solution:

Computation of the profitability index:

34.The company is considering launching a new product that would have a variable cost of $150.00 per unit. It would require 19 minutes of the constrained resource. The absolute minimum acceptable selling price for the new product should be: