Profitability Analysis - WordPress.com · Web view1. When a company does not have a constraint, the relative profitability of its business segments should be measured by dividing

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 AICPA BB: Critical Thinking AICPA FN: Reporting LO: 1 Level: Medium

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


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: Reflective Thinking AICPA BB: Critical Thinking AICPA FN: 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.


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.


Garrison/Noreen/Brewer, Managerial Accounting, Twelfth Edition B-3


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.


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.


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 AICPA BB: Critical Thinking AICPA FN: 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.


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 AICPA BB: Critical Thinking AICPA FN: Reporting LO: 3 Level: Hard

B-4 Garrison/Noreen/Brewer, Managerial Accounting, Twelfth Edition


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 AICPA BB: Critical Thinking AICPA FN: 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 AICPA BB: Critical Thinking AICPA FN: 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 AICPA BB: Critical Thinking AICPA FN: 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 AICPA BB: Critical Thinking AICPA FN: 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 AICPA BB: Critical Thinking AICPA FN: 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........................................................................ $186,200Avoidable 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 hourB) 0.40C) $196 per hourD) $490 per hour

Ans: C AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 1 Level: Easy

Solution:

SegmentIncremental

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) 0.10B) $468 per hourC) $52 per hourD) $520 per hour




Solution:

SegmentIncremental

Profit



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.............................. $112,000Avoidable cost................... 78,400 Incremental profit............... $ 33,600

Amount of the constrained resource used by the job........................ 280 hoursPercentage of the total company profit for the period from the job.. 32%

What is the profitability index for job P13K?A) $400 per hourB) 0.30C) $120 per hourD) 0.32


Solution:

SegmentIncremental

Profit



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) 0.11B) $550 per hourC) $220 per hourD) 0.40


Solution:

SegmentIncremental

Profit



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................................... $240.00Variable cost per unit..................... 168.00 Unit contribution margin................ $ 72.00

Amount of the constrained resource used by the job... 12 minutesMonthly unit sales........................................................ 3,800 units

What is the profitability index for product M75A?A) $273,600B) 0.30C) $20.00 per minuteD) $6.00 per minute

Ans: D AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 2 Level: Easy



Solution:

Computation of the profitability index:M75A

Selling price.............................................................. $240.00Variable cost............................................................. 168.00 Unit contribution margin........................................... $ 72.00 Constrained resource required per unit (minutes)..... 12Profitability 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 minuteB) 0.10C) $137,280D) $24.00 per minute


Solution:

Computation of the profitability index:Y82U

Selling price.............................................................. $264.00Variable cost............................................................. 237.60 Unit contribution margin........................................... $ 26.40 Constrained resource required per unit (minutes)..... 11Profitability 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.......................................................................... $253.00Variable cost per unit............................................................ $177.10Amount of the constrained resource required by one unit.... 11 gramsMonthly unit sales................................................................. 2,300 units

What is the profitability index for product A58E?A) $6.90 per gramB) $23.00 per gramC) 0.30D) $174,570


Solution:

Computation of the profitability index:A58E

Selling price.............................................................. $253.00Variable cost............................................................. 177.10 Unit contribution margin........................................... $ 75.90 Constrained resource required per unit (grams)........ 11Profitability 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) $319,680B) 0.30C) $7.20 per ounceD) $24.00 per ounce




Solution:

Computation of the profitability index:X99M

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

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

L41M R62DSelling price.................................................................... $98.00 $480.00Unit 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) 0.40B) 0.45C) 0.31D) $5.60 per gram


Solution:

Computation of the profitability index:L41M

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



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

Z31X L25XSelling price.................................................................... $87.00 $64.00Unit variable cost............................................................ $52.20 $38.40Amount of the constrained resource required for one

unit of the product (ounces)......................................... 3 2Monthly unit demand...................................................... 6,600 6,700

The profitability index for product Z31X is closest to:A) $29.00 per ounceB) $11.60 per ounceC) 0.57D) 0.40


Solution:

Computation of the profitability index:Z31X

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



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

U68 R64Monthly unit demand.................. 2,000 3,900Selling price................................ $30.00 $216.00Unit 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) $90,840B) $96,240C) $90,772D) $90,240

Ans: A AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 2 Level: Medium



Solution:

Computation of the profitability index:U68 R64

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

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

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

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

U68 R64 TotalUnit contribution margin.... $6.00 $21.60Volume (units)................... 2,000 3,650Contribution 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 O400Unit selling price............................ $32.50 $27.90 $14.80 $41.80Unit variable cost........................... $14.30 $5.60 $2.40 $21.70Amount 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) O100B) O200C) O300D) O400


Solution:

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

O100 O200 O300 O400Unit selling price........................................ $32.50 $27.90 $14.80 $41.80Unit variable cost....................................... 14.30 5.60 2.40 21.70Unit contribution margin............................ $18.20 $22.30 $12.40 $20.10Amount of the constrained resource

required................................................... 0.47 0.40 0.29 0.58Profitability index...................................... $38.72 $55.75 $42.76 $34.66Ranking...................................................... 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 L400Unit selling price............................ $30.90 $28.20 $19.00 $36.60Unit variable cost........................... $13.90 $10.70 $4.80 $19.80Amount of the constrained

resource required........................ 0.40 0.34 0.20 0.50

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) L300B) L400C) L200D) L100


Solution:


L100 L200 L300 L400Unit selling price........................................ $30.90 $28.20 $19.00 $36.60Unit variable cost....................................... 13.90 10.70 4.80 19.80Unit contribution margin............................ $17.00 $17.50 $14.20 $16.80Amount of the constrained resource


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) $87.90B) $148.80C) $60.90D) $116.90


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............................................................ $ 87.90Opportunity cost of using the constrained resource:

Amount of constrained resource per unit (a)..................... 2.10Opportunity cost per unit of the constrained resource (b). $29.00Total 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) $557.00B) $172.20C) $436.80D) $120.20




Solution:


Variable cost per unit............................................................ $120.20Opportunity cost of using the constrained resource:



Use the following to answer questions 31-34:

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

S14O L95ISelling price............................................... $234.00 $240.00Unit variable cost....................................... $163.80 $144.00Constrained resource required for one unit

of the product (minutes)......................... 9 15Monthly 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) 240B) 910C) 0D) 490


Solution:

Computation of the profitability index:S14O L95I

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

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

Total constrained resource available................................................. 9,900Less constrained resource required to produce 700 units of S14O... 6,300Remaining constrained resource available........................................ 3,600Less constrained resource required by 240* units of L95I............... 3,600Remaining 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) $72,180B) $96,180C) $66,930D) $69,757


Solution:



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

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

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

S14O L95I TotalUnit contribution margin.......... $ 70.20 $96.00Volume (units)......................... 700 240Contribution 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 minuteB) $7.80 per minuteC) $6.40 per minuteD) $70.20 per minute

Ans: C AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 2 Level: Medium

Solution:



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:A) $271.60B) $150.00C) $298.20D) $156.40




Solution:


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

New product:Variable cost per unit............................................. $150.00Opportunity cost per unit (19 minutes × $6.40)..... 121.60Minimum acceptable selling price......................... $271.60


Farthing Corporation's two products have the following characteristics:

H84T C22TSelling price....................... $288.00 $38.00Unit variable cost............... $259.20 $34.20Monthly demand (units)..... 410 3,330

The constrained resource is a particular machine that is available for 9,700 minutes each month. Each unit of product H84T requires 16 minutes on this machine and each unit of product C22T requires 2 minutes on this machine.



35. How many units of product H84T should be produced each month?A) 190B) 0C) 826D) 410


Solution:

Computation of the profitability index:H84T C22T

Selling price.............................................................. $288.00 $38.00Variable cost............................................................. 259.20 34.20 Unit contribution margin........................................... $ 28.80 $ 3.80 Constrained resource required per unit (minutes)..... 16 2Profitability index (per minute)................................ $1.80 $1.90

According to the profitability index, the most profitable product is C22T.

Total constrained resource available................................................. 9,700Less constrained resource required to produce 3,330 units of C22T 6,660Remaining constrained resource available........................................ 3,040Less constrained resource required by 190 units of H84T............... 3,040Remaining constrained resource available........................................ 0

*3,040 ÷ 16 minutes per unit = 190





Solution:



According to the profitability index, the most profitable product is C22T.

Total constrained resource available................................................. 9,700Less constrained resource required to produce 3,330 units of C22T 6,660Remaining constrained resource available........................................ 3,040Less constrained resource required by 190 units of H84T............... 3,040Remaining constrained resource available........................................ 0

*3,040 ÷ 16 minutes per unit = 190




Ans: D AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 3 Level: Medium

Solution:



38. The company is considering launching a new product that would have a variable cost of $69.00 per unit and no avoidable fixed costs. It would require 18 minutes of the constrained resource. The absolute minimum acceptable selling price for the new product should be:A) $103.20B) $69.00C) $101.40D) $70.80




Solution:



New product:Variable cost per unit................................................ $ 69.00Opportunity cost per unit (18 minutes × $1.80)........ 32.40Minimum acceptable selling price............................ $101.40


Mackynen Products Inc. makes two products–P99V and U15X. Product P99V's selling price is $20.00 and its unit variable cost is $12.00. Product U15X's selling price is $50.00 and its unit variable cost is $30.00. The monthly demand is 3,730 units for product P99V and 720 units for U15X. The constrained resource is a particular machine that is available for 10,300 minutes each month. Each unit of product P99V requires 2 minutes on this machine and each unit of product U15X requires 10 minutes on this machine.



39. How many units of product U15X should be produced each month?A) 284B) 720C) 0D) 1,466


Solution:

Computation of the profitability index:P99V U15X

Selling price.............................................................. $20.00 $50.00Variable cost............................................................. 12.00 30.00 Unit contribution margin........................................... $ 8.00 $20.00Constrained resource required per unit (minutes)..... 2 10Profitability index (per minute)................................ $4.00 $2.00

According to the profitability index, the most profitable product is P99V.

Total constrained resource available................................................. 10,300Less constrained resource required to produce 3,730 units of P99V 7,460Remaining constrained resource available........................................ 2,840Less constrained resource required by 284 units of U15X*............. 2,840Remaining constrained resource available........................................ 0

*2,840 ÷ 10 minutes per unit = 284 units





Solution:



According to the profitability index, the most profitable product is P99V.

Total constrained resource available................................................. 10,300Less constrained resource required to produce 3,730 units of P99V 7,460Remaining constrained resource available........................................ 2,840Less constrained resource required by 284 units of U15X*............. 2,840Remaining constrained resource available........................................ 0

*2,840 ÷ 10 minutes per unit = 284 units

P99V U15X TotalUnit contribution margin.......... $8.00 $20.00Volume (units)......................... 3,730 284Contribution margin................. $29,840 $5,680 $35,520




Ans: B AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 3 Level: Medium

Solution:







Solution:



New product:Variable cost per unit................................................ $157.00Opportunity cost per unit (19 minutes × $2.00)........ 38.00Minimum acceptable selling price............................ $195.00


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

M93U R20WSelling price........................................ $272.00 $124.00Unit variable cost................................ $190.40 $74.40Constrained resource required for one

unit of the product (minutes).......... 8 4Monthly demand (units)..................... 960 2,030




43. How many units of product M93U should be produced each month?A) 1,975B) 285C) 0D) 960


Solution:

Computation of the profitability index:M93U R20W


According to the profitability index, the most profitable product is R20W.

Total constrained resource available................................................. 10,400Less constrained resource required to produce 2,030 units of R20W 8,120Remaining constrained resource available........................................ 2,280Less constrained resource required by 285 units of M93U*............ 2,280Remaining constrained resource available........................................ 0

*2,280 minutes ÷ 8 minutes per unit = 285 units





Solution:

Computation of the profitability index:M93U R20W



Fairless Corporation's two products have the following characteristics:

N64J V96ISelling price......................... $78.00 $304.00Unit variable cost................. $46.80 $243.20Monthly demand (units)...... 2,440 360

The constrained resource is a particular machine that is available for 9,600 minutes each month. Each unit of product N64J requires 3 minutes on this machine and each unit of product V96I requires 19 minutes on this machine.



45. How many units of product V96I should be produced each month?A) 745B) 0C) 120D) 360


Solution:

Computation of the profitability index:N64J V96I

Selling price.............................................................. $78.00 $304.00Variable cost............................................................. 46.80 243.20Unit contribution margin........................................... $31.20 $ 60.80Constrained resource required per unit (minutes)..... 3 19Profitability index (per minute)................................ $10.40 $3.20

According to the profitability index, the most profitable product is N64J.

Total constrained resource available................................................. 9,600Less constrained resource required to produce 2,440 units of N64J 7,320Remaining constrained resource available........................................ 2,280Less constrained resource required by 120 units of V96I*............... 2,280Remaining constrained resource available........................................ 0

*2,280 minutes ÷ 19 minutes per unit = 120





Solution:

Computation of the profitability index:N64J V96I

Selling price.............................................................. $78.00 $304.00Variable cost............................................................. 46.80 243.20Unit contribution margin........................................... $31.20 $ 60.80Constrained resource required per unit (minutes)..... 3 19Profitability index (per minute)................................ $10.40 $3.20


Penders Products Inc. makes two products–T40U and A47M. Product T40U's selling price is $180.00 and its unit variable cost is $162.00. Product A47M's selling price is $24.00 and its unit variable cost is $19.20. The monthly demand is 520 units for product T40U and 2,040 units for A47M. The constrained resource is a particular machine that is available for 10,200 minutes each month. Each unit of product T40U requires 15 minutes on this machine and each unit of product A47M requires 3 minutes on this machine.



47. How many units of product T40U should be produced each month?A) 0B) 520C) 928D) 272


Solution:

Computation of the profitability index:T40U A47M


According to the profitability index, the most profitable product is A47M.

Total constrained resource available................................................. 10,200Less constrained resource required to produce 2,040 units of A47M 6,120Remaining constrained resource available........................................ 4,080Less constrained resource required by 272 units of T40U*............. 4,080Remaining constrained resource available........................................ 0






Solution:

Computation of the profitability index:T40U A47M



The management of Savarese Corporation has provided the following data concerning its two products–I85 and S47:

I85 S47Monthly demand (units)................. 3,040 680Selling price................................... $24.00 $118.80Unit variable cost........................... $16.80 $92.40

The constrained resource is a particular machine that is available for 9,600 minutes each month. Each unit of product I85 requires 2 minutes on this machine. Each unit of product S47 requires 11 minutes on this machine.





Solution:

Computation of the profitability index:I85 S47


Total constrained resource available................................................. 9,600Less constrained resource required to produce 3,040 units of I85. . . 6,080Remaining constrained resource available........................................ 3,520Less constrained resource required by 320 units of S47*................. 3,520Remaining constrained resource available........................................ 0


I85 S47 TotalUnit contribution margin.......... $7.20 $26.40Volume (units)......................... 3,040 320Contribution margin................. $21,888 $8,448 $30,336





Solution:

Computation of the profitability index:I85 S47




Hofheimer Corporation's two products have the following characteristics:

S00Y Y85SSelling price................................... $57.00 $60.00Unit variable cost........................... $51.30 $54.00Monthly demand (units)................. 2,150 640

The constrained resource is a particular machine that is available for 10,100 minutes each month. Each unit of product S00Y requires 3 minutes on this machine and each unit of product Y85S requires 10 minutes on this machine.





Solution:

Computation of the profitability index:S00Y Y85S

Selling price.............................................................. $57.00 $60.00Variable cost............................................................. 51.30 54.00 Unit contribution margin........................................... $ 5.70 $ 6.00Constrained resource required per unit (minutes)..... 3 10Profitability index (per minute)................................ $1.90 $0.60

According to the profitability index, the most profitable product is S00Y.

Total constrained resource available................................................. 10,100Less constrained resource required to produce 2,150 units of S00Y 6,450Remaining constrained resource available........................................ 3,650Less constrained resource required by 365 units of Y85S*.............. 3,650Remaining constrained resource available........................................ 0


S00Y Y85S TotalUnit contribution margin.......... $5.70 $6.00Volume (units)......................... 2,150 365Contribution margin................. $12,255 $2,190 $14,445





Solution:

Computation of the profitability index:S00Y Y85S

Selling price.............................................................. $57.00 $60.00Variable cost............................................................. 51.30 54.00 Unit contribution margin........................................... $ 5.70 $ 6.00Constrained resource required per unit (minutes)..... 3 10Profitability index (per minute)................................ $1.90 $0.60



Rao Products Inc. makes two products–N17O and A57Y. Product N17O's selling price is $120.00 and its unit variable cost is $108.00. Product A57Y's selling price is $30.00 and its unit variable cost is $18.00. The monthly demand is 470 units for product N17O and 1,470 units for A57Y. The constrained resource is a particular machine that is available for 10,200 minutes each month. Each unit of product N17O requires 15 minutes on this machine and each unit of product A57Y requires 5 minutes on this machine.





Solution:

Computation of the profitability index:N17O A57Y

Selling price.............................................................. $120.00 $30.00Variable cost............................................................. 108.00 18.00 Unit contribution margin........................................... $ 12.00 $12.00Constrained resource required per unit (minutes)..... 15 5Profitability index (per minutes)............................... $0.80 $2.40

According to the profitability index, the most profitable product is A57Y.

Total constrained resource available................................................. 10,200Less constrained resource required to produce 1,470 units of A57Y 7,350Remaining constrained resource available........................................ 2,850Less constrained resource required by 190 units of N17O*............. 2,850Remaining constrained resource available........................................ 0


N17O A57Y TotalUnit contribution margin.......... $12.00 $12.00Volume (units)......................... 190 1,470Contribution margin................. $2,280 $17,640 $19,920





Solution:

Computation of the profitability index:N17O A57Y

Selling price.............................................................. $120.00 $30.00Variable cost............................................................. 108.00 18.00 Unit contribution margin........................................... $ 12.00 $12.00Constrained resource required per unit (minutes)..... 15 5Profitability index (per minutes)............................... $0.80 $2.40

New product:Variable cost per unit................................................ $142Opportunity cost per unit (10 minutes × $0.80)........ 8Minimum acceptable selling price............................ $150


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

G90K E17GSelling price................................................................. $160.00 $75.00Unit variable cost......................................................... $128.00 $45.00Constrained resource required for one unit of the

product (minutes)..................................................... 10 3Monthly demand (units)............................................... 650 2,210




55. How many units of product G90K should be produced each month?A) 650B) 0C) 377D) 1,313


Solution:

Computation of the profitability index:G90K E17G


According to the profitability index, the most profitable product is E17G.

Total constrained resource available................................................. 10,400Less constrained resource required to produce 2,210 units of E17G 6,630Remaining constrained resource available........................................ 3,770Less constrained resource required by 377 units of G90K*............. 3,770Remaining constrained resource available........................................ 0






Solution:

Computation of the profitability index:G90K E17G


According to the profitability index, the most profitable product is E17G.

Total constrained resource available................................................. 10,400Less constrained resource required to produce 2,210 units of E17G 6,630Remaining constrained resource available........................................ 3,770Less constrained resource required by 377 units of G90K*............. 3,770Remaining constrained resource available........................................ 0


G90K E17G TotalUnit contribution margin.......... $32.00 $30.00Volume (units)......................... 377 2,210Contribution margin................. $12,064 $66,300 $78,364


Finlayson Corporation's two products have the following characteristics:

B06G P87GSelling price....................... $260.00 $38.00Unit variable cost............... $234.00 $26.60Monthly demand (units)..... 610 2,990

The constrained resource is a particular machine that is available for 9,600 minutes each month. Each unit of product B06G requires 10 minutes on this machine and each unit of product P87G requires 2 minutes on this machine.



57. How many units of product B06G should be produced each month?A) 610B) 0C) 1,208D) 362


Solution:

Computation of the profitability index:B06G P87G

Selling price.............................................................. $260.00 $38.00Variable cost............................................................. 234.00 26.60Unit contribution margin........................................... $ 26.00 $11.40Constrained resource required per unit (minutes)..... 10 2Profitability index (per minute)................................ $2.60 $5.70

According to the profitability index, the most profitable product is P87G.

Total constrained resource available................................................. 9,600Less constrained resource required to produce 2,990 units of P87G 5,980Remaining constrained resource available........................................ 3,620Less constrained resource required by 362 units of B06G*............. 3,620Remaining constrained resource available........................................ 0






Solution:

Computation of the profitability index:B06G P87G

Selling price.............................................................. $260.00 $38.00Variable cost............................................................. 234.00 26.60Unit contribution margin........................................... $ 26.00 $11.40Constrained resource required per unit (minutes)..... 10 2Profitability index (per minute)................................ $2.60 $5.70

According to the profitability index, the most profitable product is P87G.

Total constrained resource available................................................. 9,600Less constrained resource required to produce 2,990 units of P87G 5,980Remaining constrained resource available........................................ 3,620Less constrained resource required by 362 units of B06G*............. 3,620Remaining constrained resource available........................................ 0


B06G P87G TotalUnit contribution margin.......... $26.00 $11.40Volume (units)......................... 362 2,990Contribution margin................. $9,412 $34,086 $43,498


Coughlin Products Inc. makes two products–O58J and K04S. Product O58J's selling price is $140.00 and its unit variable cost is $112.00. Product K04S's selling price is $78.00 and its unit variable cost is $62.40. The monthly demand is 730 units for product O58J and 2,390 units for K04S. The constrained resource is a particular machine that is available for 10,300 minutes each month. Each unit of product O58J requires 10 minutes on this machine and each unit of product K04S requires 3 minutes on this machine.



59. How many units of product O58J should be produced each month?A) 1,447B) 313C) 0D) 730


Solution:

Computation of the profitability index:O58J K04S


According to the profitability index, the most profitable product is K04S.

Total constrained resource available................................................. 10,300Less constrained resource required to produce 2,390 units of K04S 7,170Remaining constrained resource available........................................ 3,130Less constrained resource required by 313 units of O58J*.............. 3,130Remaining constrained resource available........................................ 0






Solution:

Computation of the profitability index:O58J K04S


According to the profitability index, the most profitable product is K04S.

Total constrained resource available................................................. 10,300Less constrained resource required to produce 2,390 units of K04S 7,170Remaining constrained resource available........................................ 3,130Less constrained resource required by 313 units of O58J*.............. 3,130Remaining constrained resource available........................................ 0


O58J K04S TotalUnit contribution margin.......... $28.00 $15.60Volume (units)......................... 313 2,390Contribution margin................. $8,764 $37,284 $46,048


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

R100 R200 R300 R400Unit selling price............................... $32.30 $27.30 $16.60 $32.20Unit variable cost.............................. 14.50 7.90 4.50 16.10 Unit contribution margin................... $17.80 $19.40 $12.10 $16.10Amount of the constrained resource

required.......................................... 0.47 0.39 0.23 0.58Profitability index............................. $37.87 $49.74 $52.61 $27.76

The company does not have enough of the constrained resource to satisfy for demand of all four products.



61. If salespersons are paid commissions that are a set percentage of sales, which product would they prefer to sell? In other words, if it is a choice between selling one unit of one product and one unit of another, which product would they prefer to sell?A) R200B) R100C) R400D) R300


Solution:If the salespersons are paid commissions that are a set percentage of sales, then they will favor the products with the highest selling prices. Since product R100 has the highest selling price, it will be the product salespersons prefer to sell.

62. 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) R100B) R200C) R300D) R400


Solution:


R100 R200 R300 R400Unit selling price..................................... $32.30 $27.30 $16.60 $32.20Unit variable cost.................................... 14.50 7.90 4.50 16.10 Unit contribution margin......................... $17.80 $19.40 $12.10 $16.10Amount of the constrained resource

required................................................ 0.47 0.39 0.23 0.58Profitability index................................... $37.87 $49.74 $52.61 $27.76Ranking................................................... 3 2 1 4

According to the profitability index, product R300 should be emphasized.




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

U100 U200 U300 U400Unit selling price............................. $31.70 $21.00 $14.80 $36.00Unit variable cost............................. $10.10 $6.90 $2.10 $18.70Amount of the constrained resource

required........................................ 0.49 0.35 0.26 0.59


63. If salespersons are paid commissions that are a set percentage of sales, which product would they prefer to sell? In other words, if it is a choice between selling one unit of one product and one unit of another, which product would they prefer to sell?A) U400B) U100C) U200D) U300


Solution:If the salespersons are paid commissions that are a set percentage of sales, then they will favor the products with the highest selling prices. Since product U400 has the highest selling price, it will be the product salespersons prefer to sell.

64. 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) U100B) U200C) U400D) U300




Solution:


U100 U200 U300 U400Unit selling price..................................... $31.70 $21.00 $14.80 $36.00Unit variable cost.................................... 10.10 6.90 2.10 18.70Unit contribution margin......................... $21.60 $14.10 $12.70 $17.30Amount of the constrained resource


According to the profitability index, product U300 should be emphasized.

Essay Questions

65. Bozich Corporation is considering six jobs for the upcoming period. Those jobs are listed below, along with relevant data.

Incremental Profit



Job 1........... $13,896 36Job 2........... $7,316 31Job 3........... $11,590 38Job 4........... $14,148 36Job 5........... $4,080 12Job 6........... $9,216 24

The total amount of the constrained resource that is available during the upcoming period is 108 hours.

Required:

a. Determine which jobs should be accepted for the upcoming period.b. Determine the total incremental profit for the upcoming period if your plan from

part (a) above is adopted.



Ans:

a. Rank the segments on the basis of the profitability index:

SegmentIncremental

Profit



Profitability Index

(per hour)Job 1........... $13,896 36 $386Job 2........... $7,316 31 $236Job 3........... $11,590 38 $305Job 4........... $14,148 36 $393Job 5........... $4,080 12 $340Job 6........... $9,216 24 $384

Segment

Profitability Index

(per hour)



Cumulative Amount of Constrained


Job 4........... $393 36 36Job 1........... $386 36 72Job 6........... $384 24 96Job 5........... $340 12 108Job 3........... $305 38 146Job 2........... $236 31 177

Job 4, Job 1, Job 6, and Job 5 should be accepted.

b.Incremental Profit

Job 4........... $14,148Job 1........... 13,896Job 6........... 9,216Job 5........... 4,080 Total........... $41,340

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 1 Level: Easy



66. Polosky LLC is a consulting firm that is considering six projects for the upcoming period. The six projects under consideration are listed below, along with relevant data.

Incremental Profit



Project 1..... $6,555 23Project 2..... $5,904 16Project 3..... $5,980 23Project 4..... $7,018 22Project 5..... $4,872 14Project 6..... $5,820 15

The managing partner's time is the constraint in the firm. Only 67 hours of this constrained resource are available during the upcoming period.

Required:

a. Determine which projects should be accepted for the upcoming period.b. Determine the total incremental profit for the upcoming period if your plan from

part (a) above is adopted.



Ans:

a. Rank the projects on the basis of the profitability index:

SegmentIncremental

Profit



Profitability Index

(per hour)Project 1..... $6,555 23 $285Project 2..... $5,904 16 $369Project 3..... $5,980 23 $260Project 4..... $7,018 22 $319Project 5..... $4,872 14 $348Project 6..... $5,820 15 $388

Segment

Profitability Index

(per hour)



Cumulative Amount of Constrained


Project 6..... $388 15 15Project 2..... $369 16 31Project 5..... $348 14 45Project 4..... $319 22 67Project 1..... $285 23 90Project 3..... $260 23 113

Project 6, Project 2, Project 5, and Project 4 should be accepted.

b.Incremental Profit

Project 6..... $ 5,820Project 2..... 5,904Project 5..... 4,872Project 4..... 7,018 Total........... $23,614




67. Salus Corporation is considering the following six long-term projects:

Net Present Value Investment RequiredProject 1..... $19,436 $11,300Project 2..... $19,000 $12,500Project 3..... $33,174 $19,400Project 4..... $20,825 $17,500Project 5..... $26,398 $19,700Project 6..... $20,294 $14,600

Only $57,800 is available for investment in these projects.

Required:

a. Determine which projects should be accepted.b. Determine the total net present value of all of the accepted projects if your plan

from part (a) above is adopted.

Ans:

a. Rank the projects on the basis of the profitability index:

Segment Net Present Value Investment Required Profitability IndexProject 1..... $19,436 $11,300 1.72Project 2..... $19,000 $12,500 1.52Project 3..... $33,174 $19,400 1.71Project 4..... $20,825 $17,500 1.19Project 5..... $26,398 $19,700 1.34Project 6..... $20,294 $14,600 1.39

SegmentProfitability

IndexInvestment Required

Cumulative Investment Required

Project 1..... 1.72 $11,300 $11,300Project 3..... 1.71 $19,400 $30,700Project 2..... 1.52 $12,500 $43,200Project 6..... 1.39 $14,600 $57,800Project 5..... 1.34 $19,700 $77,500Project 4..... 1.19 $17,500 $95,000

Project 1, Project 3, Project 2, and Project 6 should be accepted.

b.



Net Present ValueProject 1..... $19,436Project 3..... 33,174Project 2..... 19,000Project 6..... 20,294 Total........... $91,904




68. Saraiva Corporation has two products that use the same constrained resource–a critical raw material.

R28 Z55Selling price.............................................................. $182.00 $144.00Variable cost............................................................. $127.40 $86.40Constrained resource required per unit (grams)........ 7 16Demand (units).......................................................... 1,080 440

The total amount of the constrained resource available is 9,800 grams.

Required:

a. Which product is most profitable, given the company's constraint?b. How much of each product should be produced?c. What is the total contribution margin if your plan in part (b) above is followed?d. The company is considering launching a new product whose variable cost is $223

and that requires 24 grams of the constrained resource. What is the minimum selling price for the new product?

Ans:

a. Computation of the profitability index:R28 Z55

Selling price........................................................... $182.00 $144.00Variable cost.......................................................... 127.40 86.40 Unit contribution margin........................................ $ 54.60 $ 57.60 Constrained resource required per unit (grams)..... 7 16Profitability index.................................................. $7.80 $3.60

According to the profitability index, the most profitable product is R28.

b.Total constrained resource available.................................................. 9,800Less constrained resource required to produce 1,080 units of R28.... 7,560Remaining constrained resource available......................................... 2,240Less constrained resource required by 140 units of Z55.................... 2,240Remaining constrained resource available......................................... 0

c.R28 Z55 Total

Unit contribution margin................ $54.60 $57.60Volume........................................... 1,080 140



Contribution margin....................... $58,968 $8,064 $67,032

d. Selling price of new product > $223.00 + ($3.60 per gram × 24 grams) = $223.00 + $86.40 = $309.40

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 2,3 Level: Medium



69. The constraint at Parchman Inc. is a key raw material. A total of 9,600 ounces of this constrained resource are available. Data concerning the company's two products, Y58 and J06, appear below:

Y58 J06Demand (units)....... 1,850 3,700Selling price........... $112.00 $44.00Variable cost.......... $78.40 $26.40

Each unit of product Y58 requires 4 ounces of the constrained raw material; each unit of product J06 requires 2 ounces.

Required:

a. In the present circumstances, which product is most profitable?b. How much of each product should be produced?c. The company is considering launching a new product whose variable cost is $269

and that requires 26 ounces of the constrained resource. What is the minimum acceptable selling price for the new product?



Ans:

a. Computation of the profitability index:Y58 J06

Selling price.............................................................. $112.00 $44.00Variable cost............................................................. 78.40 26.40 Unit contribution margin........................................... $ 33.60 $17.60Constrained resource required per unit (ounces)...... 4 2Profitability index..................................................... $8.40 $8.80

According to the profitability index, the most profitable product is J06.

b.Total constrained resource available................................................ 9,600Less constrained resource required to produce 3,700 units of J06... 7,400Remaining constrained resource available....................................... 2,200Less constrained resource required by 550 units of Y58.................. 2,200Remaining constrained resource available....................................... 0

Produce 3,700 units of J06 and 550 units of Y58.

c. Selling price of new product > $269.00 + ($8.40 per ounce × 26 ounces) = $269.00 + $218.40 = $487.40

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Reporting LO: 2,3 Level: Medium



70. Wentland Corporation has two products, G10 and K99, that use the same constrained resource–a critical raw material. Data concerning those products follow:

G10 K99Selling price........................................................... $56.00 $110.00Variable cost.......................................................... $39.20 $88.00Constrained resource required per unit (grams)..... 7 10Demand (units)....................................................... 980 710

The total amount of the constrained resource available is 10,000 grams.

Required:

a. Which product is most profitable, given the company's constraint?b. How much of each product should be produced?c. What is the total contribution margin if your plan in part (b) above is followed?

Ans:

a. Computation of the profitability index:G10 K99

Selling price........................................................... $56.00 $110.00Variable cost.......................................................... 39.20 88.00 Unit contribution margin........................................ $16.80 $ 22.00 Constrained resource required per unit (grams)..... 7 10Profitability index (per gram)................................ $2.40 $2.20

According to the profitability index, the most profitable product is G10.

b.Total constrained resource available................................................. 10,000Less constrained resource required to produce 980 units of G10..... 6,860 Remaining constrained resource available........................................ 3,140Less constrained resource required by 314 units of K99.................. 3,140 Remaining constrained resource available........................................ 0

c.G10 K99 Total

Unit contribution margin.... $16.80 $22.00Volume (units)................... 980 314Contribution margin........... $16,464 $6,908 $23,372




71. The constrained resource at Else Corporation is a key raw material. A total of 9,500 ounces of the constrained resource are available. Data concerning the company's two products, U46 and P83, follow:

U46 P83Demand (units)....... 1,140 630Selling price........... $170.00 $70.00Variable cost.......... $153.00 $42.00

Product U46 requires 5 ounces of the constrained resource; product P83 requires 10 ounces.

Required:a. Which product is most profitable, given the company's constraint?b. How much of each product should be produced?c. What is the total contribution margin if your plan in part (b) above is followed?

Ans:

a. Computation of the profitability index:U46 P83

Selling price.............................................................. $170.00 $70.00Variable cost............................................................. 153.00 42.00 Unit contribution margin........................................... $ 17.00 $28.00Constrained resource required per unit (ounces)...... 5 10Profitability index (per ounce).................................. $3.40 $2.80

According to the profitability index, the most profitable product is U46.

b.Total constrained resource available................................................. 9,500Less constrained resource required to produce 1,140 units of U46. . 5,700Remaining constrained resource available........................................ 3,800Less constrained resource required by 380 units of P83................... 3,800Remaining constrained resource available........................................ 0

c.U46 P83 Total

Unit contribution margin.......... $17.00 $28.00Volume (units)......................... 1,140 380Contribution margin................. $19,380 $10,640 $30,020




72. Delapena Corporation has four products that use the same constrained resource. Data concerning those products appear below:

M100 M200 M300 M400Unit selling price..................................... $35.70 $23.30 $18.00 $45.10Unit variable cost.................................... $17.10 $6.10 $4.00 $24.40Amount of the constrained resource

required............................................... 0.41 0.35 0.22 0.55


Required:

a. If salespersons are paid commissions that are a set percentage of sales, which product would they prefer to sell? In other words, if it is a choice between selling one unit of one product and one unit of another, which product would they prefer to sell?

b. 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?

Ans:

a. If the salespersons are paid commissions that are a set percentage of sales, then they will favor the products with the highest selling prices. Since product M400 has the highest selling price, it will be the product salespersons prefer to sell.

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

M100 M200 M300 M400Unit selling price........................................ $35.70 $23.30 $18.00 $45.10Unit variable cost....................................... 17.10 6.10 4.00 24.40 Unit contribution margin............................ $18.60 $17.20 $14.00 $20.70Amount of the constrained resource


According to the profitability index, product M300 should be emphasized.




73. The management of Garding Corporation is reviewing its policies concerning compensation of salespersons. The company has four products that use the same constrained resource. Data concerning those products appear below:

M100 M200 M300 M400Unit selling price..................................... $31.20 $28.00 $13.70 $47.00Unit variable cost.................................... $15.00 $7.00 $4.00 $32.90Amount of the constrained resource

required................................................ 0.43 0.34 0.21 0.53


Required:

a. If salespersons are paid commissions that are a set percentage of sales, which product would they prefer to sell? In other words, if it is a choice between selling one unit of one product and one unit of another, which product would they prefer to sell?

b. 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?



Ans:

a. If the salespersons are paid commissions that are a set percentage of sales, then they will favor the products with the highest selling prices. Since product M400 has the highest selling price, it will be the product salespersons prefer to sell.

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

M100 M200 M300 M400Unit selling price..................................... $31.20 $28.00 $13.70 $47.00Unit variable cost.................................... 15.00 7.00 4.00 32.90 Unit contribution margin......................... $16.20 $21.00 $9.70 $14.10Amount of the constrained resource


According to the profitability index, product M200 should be emphasized.




74. Gala Corporation has designed a new product, E70, whose variable cost is $127.90 per unit and that requires 5.40 minutes of the constrained resource. The opportunity cost is $50.00 per minute used of the constrained resource.

Required:

What advice would you give to the company concerning the price that should be charged for the new product E70?

Ans:








75. Zambrano Corporation is about to launch a new product, U34, whose variable cost is $137.80 per unit and that would require 6.10 centiliters of a key raw material that is the company's constrained resource. The opportunity cost of this raw material is $67.00 per centiliter used.

Required:

What advice would you give to the company concerning the price that should be charged for the new product U34?

Ans:









Documents

Profitability Analysis - WordPress.com · Web view1. When a company does not have a constraint, the relative profitability of its business segments should be measured by dividing