Consulting Math Drills Full Cases v6.2 PDF [PDF]

Zitiervorschau

WWW.MCONSULTINGPREP.COM

Consulting Math Drills Full Cases

For more free and detailed materials on Management Consulting Preparation, visit www.MConsultingPrep.com © 2013 MConsultingPrep, Inc.

Full Cases

Consulting Math Drills – Full Cases

Practice Package Overview and Instructions This practice package has been developed to provide samples of the actual Math calculations candidates have to perform throughout the Management Consulting Recruiting process including entrance tests (E.g: McKinsey Problem Solving Test, BCG Potential Test) and case interviews. This package assesses your ability to accurately and quickly calculate math business problems. This practice package contains 50 Math Full Cases divided into 14 hurdles. All questions in this package are Full Math Cases. Each case usually has 3-4 questions and requires complicated calculations to solve. Remember that of the two criteria (1) accuracy and (2) quickness, accuracy is more important in case interviews. Interviewers would rather allow more time for candidates to perform calculations correctly than to get quick but wrong answers. In entrance tests (McKinsey PST or BCG Potential Test), a balanced approach should be targeted. Since time allowed for those tests is very tight, slowing down to get perfectly accurate answers may not be beneficial. While completing this practice package, do no use any electronic devices (e.g., calculator, computer) when performing calculations to answer the questions. Depending on your purpose of using this package (for Case Interview Prep or for Entrance Test Prep), the appropriate methods of using this package are different. Case Interview Prep: Divide your practice into small hurdles, 3 or 4 cases each. Target 100% accuracy. Any score less than 100% is considered as failed. When you can consistently pass hurdles, try to reduce the time. You may practice calculating out loud as if you are presenting your calculations to interviewers. Entrance Test Prep (McKinsey PST or BCG Potential Test): Divide your practice into small hurdles, 3 or 4 cases each. Only allow yourself 3-4 minutes per case (start with 4 then gradually moving down to 3). Then try to increase the number of correct answers within the pre-targeted time allowed. Please let us know if you have any doubt about any question or answer key is. Good luck with your studies!

PLEASE GO ON TO THE NEXT PAGE 1

Full Cases

Hurdle 1

Case 1: Thailand Beer factory Below are data on total revenue and cost of a beer factory in Thailand gathered from the past 3 years: Revenue Cost

2008 $40 $350

2009 $60 $360

2010 $80 $370

Assume the Fixed Cost and Price stay the same while the Variable Cost varies by units sold. 1.1: How much is Fixed Cost? 1.2: If Revenue in 2011 was $200, how much would Profit have been? 1.3: In 2010, the factory produced at 16% of its full capacity. What capacity level (in %) should it have produced to break even? 1.4: Assume the Factory can raise its price by 20%. How many percent of the current number of units sold would the new number of units sold be for the factory to break even? 1.5: To increase its full capacity, the factory intends to open 1 night shift, making it 3 shifts in total per day compared to 2 shifts per day currently. Assume all ratios, rates and prices stay the same, what capacity level (in %) should the factory produce now to break even? 1.6: The factory opens a night shift. However, it has to pay overtime workers 1.5 times the normal rate. Assume that Labor Cost is 50% of Variable Cost, what capacity level (in %) does the factory need to produce to break even?

PLEASE GO ON TO THE NEXT PAGE 2

Full Cases Case 2: Electronics Retailer

NK Electronics is an office and household appliances retailer, and has provided the following information on their business: Water Purifier Cookers Air-conditioners Vacuums

Average Monthly Sales $22,370 $66,865 $84,420 $53,190

Average Mark-up % 150% 175% 240% 190%

2.1: Calculate the annual Cost of each appliance section. 2.2: The Air-Conditioner section requires an annual Fixed Cost of $200,000, while the Vacuum section requires only $160,000 per year. Given that NK Electronics sells an average of 25 purifiers, 32 cookers, 8 air-conditioners, and 12 vacuums per month. Calculate the average Variable Cost per item of each of these sections. 2.3: The managers want to improve the Profitability of the Cooker and Water Purifier sections, and thus decide to add an extra 10% to the average Mark-up % of each section. Given that the annual Fixed Cost for each section is $180,000 and $120,000, respectively, calculate the new monthly average Profit and % change in the Profit of each section.

PLEASE GO ON TO THE NEXT PAGE 3

Full Cases Case 3: Dishwasher Producer

Below are data of a Dishwasher producer’s business: Size of Dishwasher Small Medium Large

Share in total Revenue 25% 38% 37%

Mark-up percentage 150% 170% 185%

3.1: 1,650 units of small dishwashers were sold last year, bringing in a Revenue of $1,483,350. Given that 1,800 units of medium dishwashers were sold that year, calculate the Cost of Goods Sold per 1 medium dishwasher. 3.2: The Cost of Goods Sold per 1 large dishwasher is $550. Calculate the share in quantity sold of each type of dishwasher. 3.3: Cost of Goods Sold per 1 small dishwasher will be increased by 10%, while the Total Quantity sold is going to drop by 18%. If the Revenue of this division is to be maintained, its Selling Price will have to change by how many percent? Assume that all other factors stay constant, calculate the new mark-up % of the small dishwasher division.

PLEASE GO ON TO THE NEXT PAGE 4

Full Cases Case 4: Tea Retailing Stand

Below are data on the business of a Tea Retailing Stand in town: Type of tea Milky Tea Honey Tea Lemon Tea

Revenue $16,500 $17,220 $16,850

Share in Total Expenses 23% 24.5% 21.6%

4.1: Profitability of Milky Tea is 21% of its revenue. Calculate Profitability (% of revenue) of the other 2 items. 4.2: Expenses per Unit are $9 / unit for Milky Tea, $10 / unit for Honey Tea and $11.5 / unit for Lemon Tea. What is the Selling Price of each item? 4.3: Selling Price per Unit of Honey Tea will be increased by $1.50, while its share in Expenses will go up to 26%. Assume that all other factors stay constant, how many more units of Honey Tea will have to be sold to maintain its Profitability?

PLEASE GO ON TO THE NEXT PAGE 5

Full Cases

Hurdle 2

Case 5: Dental Clinic

St. Paul Dental Clinic is well-known for its good services and a friendly environment. Below is the data on some of their services: Services Tooth Extractions Root Canals Fillings Cleanings

Fee charged to Clients $5 $28.50 $25.90 $18

Variable Cost on the Clinic $2.75 $19 $14 $8

5.1: St. Paul Dental Clinic breaks even at 6,500 patients for each service. Calculate the total monthly Fixed Cost of the clinic. 5.2: Root Canals division contributes a share of 40% in the clinic’s total Gross Profit (in dollar value). Given that there were 8,000 patients who came to the clinic for Root Canals last month, calculate the Gross Profit of St. Paul Dental Clinic? 5.3: For every dollar of the fee gained from Fillings, the clinic generates $0.22 Net Profit. If the total Cost of Fillings service for the clinic last month was $94,850, what was the Net Profit of the Fillings service?

PLEASE GO ON TO THE NEXT PAGE 6

Full Cases Case 6: University Students Recruitment Below are data on student recruiting requirements of a University: Type of student Domestic International

Number of Students Recruited 4,000 1,000

Capture rate 50% 10%

Number of Qualified Students 20,000 2,000,000

Given that: -

Number of Qualified Students is the number of students that meet the minimum requirements to submit their application to the university. Application Rate is the percentage of qualified students that apply to the university. Acceptance Rate is the percentage of applications that are accepted to the university. Capture Rate is the percentage of accepted students that actually attend the university.

6.1: Assuming that the Acceptance Rate is 100%, what would the Application Rate of the Domestic group have to be to ensure that the University recruits enough Domestic students? 6.2: Assuming that the Acceptance Rate is 100%, what would the Application Rate of the International group have to be to ensure that the University recruits enough International students? 6.3: Assuming that the Acceptance Rate is below or equal 50%, what would the Application Rate of the Domestic group have to be to ensure that the University recruits enough Domestic students? 6.4: Assuming that the Acceptance Rate is below or equal 50%, what would the Application Rate of the International group have to be to ensure that the University recruits enough International students? 6.5: Assuming that the University cannot go beyond a 60% Application Rate for the Domestic group. What would the Application Rate of the International group have to be to ensure that the University maintains its Acceptance Rate below or equal 50% for both groups and still recruits enough students from each group?

PLEASE GO ON TO THE NEXT PAGE 7

Full Cases Case 7: Movie Cinema Below are all the figures on a per-day basis of a movie cinema: Tickets Available Demand on weekdays Demand on Weekends Ticket Price on weekdays Ticket Price on weekends

3D VIP seats 100 30 100 $10 $12

3D Normal seats 500 350 600 $8 $10

I-Max seats 200 70 220 $6 $7

2D seats 1000 600 1400 $5 $6

(Notice: Weekdays: Monday -Thursday; Weekends: Friday – Sunday) The Cinema is considering changing its ticket prices. It is predicted that a 10% change in price would result in a 20% change in demand.

7.1: The Cinema is going to reduce weekday ticket prices by 10% (applied to all 4 types of seat). How many US dollars will the new total Revenue generated on weekdays be higher/lower than before the price change? 7.2: The Cinema is going to raise weekend ticket prices by 10% (applied to all 4 types of seat). How many US dollars will the new total Revenue generated on weekends be higher/lower than before the price change?

PLEASE GO ON TO THE NEXT PAGE 8

Full Cases Case 8: Milk Farm

Queen Anne is a big farm of milk cows and a major supplier of fresh milk.

Organic milk Whole milk Jersey milk

Market share by Volume 36% 33% 38.2%

Market share by Value 35% 34.8% 36.4%

Price / liter $6.50 $5.90 $7.75

8.1: Last quarter, the total Value of the three milk markets was $1.20 million, $1.08 million and $1.24 million, respectively. Calculate the total Volume of each milk market during the previous quarter. 8.2: The farm owners expect an increase of 14% in Volume across all three divisions in the upcoming quarter as demand is increasing rapidly. However, they decide not to raise prices to attract more buyers. As a result, the farm’s market share by Value will be unchanged. Calculate the total Value of each milk market in this case. 8.3: In another scenario, the farm owners decide to raise the price of each type of milk by 12%. As a result, market share by Value remains unchanged, but with the total Value of each market increasing by 26.5% compared to the previous quarter. Calculate the % change in volume of each division.

PLEASE GO ON TO THE NEXT PAGE 9

Full Cases

Hurdle 3

Case 9: Bungy Jump

Paradise Park has just opened a new game “Bungy Jump” and below are data on revenue generated from this game area in the first year: st

1 Quarter 2nd Quarter 3rd Quarter 4th Quarter

Revenue from Adult players $30,000 $28,500 $29,300 $26,000

Revenue from Children players $22,000 $23,400 $22,800 $24,900

9.1: Given that in any particular month, the ratio between the number of Adult and Children players is 4 : 7. Calculate the ticket fees for Adults and Children, assuming that there is a total of 850 people that go Bungy Jump every month. 9.2: For every dollar of Revenue from Adults, $0.37 is spent on Electricity and no cost on Maintenance. For every dollar of Revenue from Children, $0.29 is spent on Maintenance and no cost on Electricity. Given that the monthly ratio Expense / Revenue of this business is 0.86 : 1, calculate the share of Electricity and Maintenance in the Monthly Expense. 9.3: Will it be able to achieve an annual Profitability of 17% at the current level of monthly Revenue & Expense?

PLEASE GO ON TO THE NEXT PAGE 10

Full Cases Case 10: How to make use of free cash?

Lot of Cash, Inc. currently has $100 million in their free cash account. They are investigating investment options in order to make the most out of that free cash. Below is the Return (in %) on 4 investment options: Bank Savings Bond Stock Real Estate

Best Scenario 4% 10% 25% 20%

Worst Scenario 2.5% 0% -10% -5%

Maximum Fund Usage 100% 60% 80% 50%

Assume that: -

Our best guess for the Return on Investment is the average of Best and Worst scenarios. Risk is measured by the difference (in dollar value) between the Best and Worst scenarios.

10.1: Rank all four options in terms of Return on Investment (in dollar value) from highest to lowest. 10.2: Rank all four options in terms of Risk (in dollar value) from highest to lowest. 10.3: Lot of Cash, Inc. would like to ensure that even in the worst scenario they cannot lose more money with Stock than they would with Real Estate. One possible way to do this is to change the Fund Usage percentage for Stock. What would the new Maximum Fund Usage percentage for Stock be?

PLEASE GO ON TO THE NEXT PAGE 11

Full Cases Case 11: The Laundromat Smooth Laundry is a newly-opened Laundromat located near a luxury apartment building, targeting “big earners” as its potential clients. It has dry cleaners and normal washing machines offered at different prices, the data of which presented below: Weight of clothes < 3 kg 3-6 Kg >6 kg

Dry Cleaner $35 $55 $70

Washing Machine $20 $32 $45

2011 is a leap year, and Jan 1st is a Saturday.

11.1: Fred is a regular customer of Smooth Laundry. He uses its services twice a week. He uses a washing machine for 3 kg of casual clothes on Sundays and a dry cleaner for 1 kg of work clothes on Fridays. At the end of the year he gets a 10% refund for each service that he has used. How much did Fred pay for laundry during 2011 and how much did he get back from the refund? 11.2: If Smooth Laundry offers Fred a Loyal Customer card, he will get a 5% discount on every service. However, at the end of the year Fred will only get 5% of the total amount as refund. Should Fred take this offer? Show your calculations. 11.3: How many percent can Fred save if he only goes to the Laundromat once on Sunday and once on Friday per month? Round up your answer to 2 decimal places.

PLEASE GO ON TO THE NEXT PAGE 12

Full Cases Case 12: Travel Agent

TFG Travel is a newly established tourism agent that offers both domestic and international tours. Below is a brief review of TFG’s performance during the Second Quarter of 2011:

Domestic tours International tours

Average Price per Adult $370 $855

Average Price per Child $345 $820

Quarterly Profit $418,500 $762,900

12.1: Given that the ratio between the number of Adult tourists and Child tourists is 7 : 3 and TFG has a Profitability of 13.4% of revenue for both groups in this quarter. Calculate the quantities of Adult and Child tourists on Domestic tours. 12.2: Due to expenses being greater (transportation, accommodation, etc.) over time because of inflation, TFG is forced to increase its price for International tours by 14%. Despite the price rise, TFG maintains the same profit level as last quarter. If TFG wants to have a Profitability of 11% and the ratio between the number of Adult tourists and Child tourists be 6 : 4, how much would the total amount of expenses on each kind of tourist in International tours?

PLEASE GO ON TO THE NEXT PAGE 13

Full Cases

Hurdle 4

Case 13: Cake Bakery

Below is the data on the business of a well-known bakery in the city: Type of cake Birthday cake Wedding cake Small cake

Average price / piece $25 $40 $12

Share in total Profit 28% 25% 32%

13.1: Last year, Profitability of the Birthday Cake division was 18%, and 3,200 birthday cakes were sold. Given that the ratio between the number of Birthday cakes and Wedding cakes sold was 5 : 2, calculate Profitability of Wedding Cakes. 13.2: Calculate the share in Revenue of each division. Given that the ratio between the number of Wedding Cakes and Small Cakes sold is 3 : 7. 13.3: The Small cake division will have its average price / piece increased in hopes of improving its Revenue. However, the quantity sold will drop by 8% as a result of this price change. If total Profit goes up 1.2 times, and all other conditions of the Small Cake division are to stay unchanged, by how many percent will its average price have to change?

PLEASE GO ON TO THE NEXT PAGE 14

Full Cases Case 14: Contract Factory

Contract Factory (CF) is a kind of factory that mainly manufactures contracts for other companies. Contract Factories do not usually have their own unique products. Instead, they make products specified by their clients in contracts. Sometimes, Contract Factory also provides Value Added Services (VAS) for premiums. Below is the data on 2 Contract Factories and the industry as a whole in a specific year: Total Revenue Revenue from Manufacturing Revenue from Value Added Services (VAS) Revenue from Other Sources Number of VAS per Manufacturing Contract

CF A $1 billion 80% 10%

CF B $1.5 billion 60% 30%

Industry $12 billion 70% 20%

10% 0.5

10% 1.5

10% 0.25

14.1: Suppose that CF A sells one Manufacturing contract for $200 million. On average, how much does CF A charge for one unit of VAS? 14.2: Suppose that CF B sells one Manufacturing contract for $300 million. On average, how much does CF B charge for one unit of VAS? 14.3: Suppose that CF A can triple its Revenue from Other Sources. What will the new market share of Other Sources be in terms of total Revenue?

PLEASE GO ON TO THE NEXT PAGE 15

Full Cases Case 15: Australian Burger King Chain

Below is the data on wages and working hours of 4 types of employees at a typical Australian Burger King Restaurant: Type of employee Cashier Cook Assistant Manager Shift Manager

Hourly Wages $8 $7.70 $10.10 $9.40

Work hours per Week 30 49 60 56

15.1: There are 300 Burger King Restaurants in Australia, with an average of 8 cashiers, 12 cooks, 6 assistant managers and 4 shift managers per restaurant. Calculate the annual Wages Expense of the whole Australian Burger King Chain. 15.2: Wages Expense accounts for 35% of an Australian Burger King Restaurant’s Sales. The Australian Burger King Chain is planning to increase the wages for some types of employees to improve work efficiency. Specifically, cooks will be paid $8.20 per hour and assistant managers will get $10.60 per hour. Calculate the % change in Sales that is expected to correspond with this wage rise. 15.3: The Australian Burger King Chain wants to open 20 more restaurants in the country, but does not want to increase the threshold for the Wages Expense. What is the number of cooks it will have to cut down on?

PLEASE GO ON TO THE NEXT PAGE 16

Full Cases Case 16: Vehicle Dealer

Below is the data on a Vehicle dealer’s business: New Vehicle Used Vehicle

Quantity Sold 15,050 38,400

Net Profit $60,250,000 $39,600,000

Profitability 16.5% 11.2%

16.1: Calculate the Revenue and the average Selling Price per vehicle of each division. 16.2: The dealer wants to increase Net Profit of Used Vehicles by 18% with a Quantity Sold of 39,720. Calculate the % change in Selling Price needed to achieve this. 16.3: Profitability of New Vehicles dropped by 2%. However, Quantity Sold increased by 8.5% as the Selling Price decreased 1.5 times. Calculate the % change in Expenses for this division.

PLEASE GO ON TO THE NEXT PAGE 17

Full Cases

Hurdle 5 Case 17: Software shop

Below are some brief data on the business of a Software shop in the first quarter of a year: Revenue Expense

Month 1 $15,000 $8,200

Month 2 $16,500 $10,400

Month 3 $14,800 $9,300

17.1: Rank the Profitability (in %) of each month from highest to lowest. 17.2: The shop expects an average quarterly Profitability of 45% in the next quarter, as Expense will drop 1.15 times. Calculate the % change in quarterly Revenue to correspond with these conditions. 17.3: On average, for every dollar of Revenue generated, $0.28 is spent on the Rental fee. At the current Profitability level, how much will the shop have to pay for Rental fee at the end of the year? What is the share of the Rental fee in the the shop’s annual Expenses?

PLEASE GO ON TO THE NEXT PAGE 18

Full Cases Case 18: Airplane seating options

Jet Air is a newly established airline with only one Boeing 737 in its fleet. Currently the B-737 contains 200 economy seats. The airline is considering implementing business and first class seats into the plane. Below is some data on seating options available in the B-737: Seating option Economy Business First class

Space required per seat (unit) 1 1.5 2

Average Fare per seat $100 $200 $500

18.1: Assume that economy seats are always fully occupied. If the airline only wants to place 150 economy seats and have business seats fill the rest of the plane, what is the minimum business seats occupation percentage needed to ensure that the airline has at least as much revenue as before? 18.2: We know that the demand per flight for each seat type is always 200, 10, 4 respectively (economy, business, first). What is the best seating allocation for the airline? Assume that the goal is to maximize its revenue. 18.3: Assuming that the client has already built the plane with 10 first class seats, 20 business class seats. With the demand stated in the previous question (200, 10, 4), what is the maximum amount of revenue the airline can generate from one flight? Assume that the airline will use all possible strategies to generate the most revenue from that one flight.

PLEASE GO ON TO THE NEXT PAGE 19

Full Cases Case 19: Plumbers

Alvin is the owner of a plumbing service provider in Oslo. Below is the number of cases that Alvin’s business undertook in the first quarter of 2010: Domestic Commercial Downtown Suburb

Installation service 14 15 N/A 9

Maintenance service 160 240 302 N/A

Repair service 325 N/A 160 220

19.1: Calculate the percentage of Downtown Installation, Suburb Maintenance and Commercial Repair cases in total cases. 19.2: After a marketing promotion, Alvin hopes the new number of Domestic Repair cases will increase by a number equal to 25% that of the total Repair cases. Calculate the % change in the number of monthly Domestic cases done by Alvin’s business after this marketing promotion. 19.3: If the number of Suburb Maintenance cases decreases by a number equal to 30% that of Commercial Repair cases, what will the new share of Maintenance and Suburb cases in the total number of cases be?

PLEASE GO ON TO THE NEXT PAGE 20

Full Cases Case 20: Ship building company

Blue Ocean shipyard is a ship building company and it is currently working on two big ships, the data of which is as follows: Number of Shipwright Ship A Ship B

Maximum Capacity (ton) 600 450

310 245

Cost $3,250,000 $2,530,000

20.1: 35% of ship A’s cost is for wages of shipwrights, while 30% of ship B’s cost is for wages of shipwrights. Assuming that the wages of shipwrights are equal for both ships, on which ship do shipwrights get paid more and by how many percent? 20.2: For every dollar of wages paid to shipwrights, the shipyard managers expect to get $5.20 and $4.75, respectively, for ship A and ship B, in return. Calculate Gross Profit Margin for each ship. 20.3: The client agrees to pay $7,800 per ton of capacity, and this applies to both ships. Which ship is more profitable and more efficient in the usage of its workforce?

PLEASE GO ON TO THE NEXT PAGE 21

Full Cases

Hurdle 6

Case 21: Stuffed Toys Retailer

Below are data on the business of a stuffed toys retailer in the city: Type of stuffed toys Teddy Bear Donald Duck Lion King

Selling Price / Unit $25.50 $19.90 $22

Variable Cost / Unit $12 $8.50 $10.20

21.1: At Unit Sales level of 50,000 for each brand, the Profit is $20,000, $18,000 and $21,500, respectively. Calculate the Fixed Cost of each brand. 21.2: Given that the Variable Cost per Unit of the Teddy Bear brand is increased 1.35 times and its Fixed Cost is 15% lower than the current level, calculate the % change in Sales for the Teddy Bear brand at the break-even point. 21.3: If the Lion King brand is to have a Profitability rate of 24% when 75,000 units have been sold, by how many percent would the Selling Price per Unit have to be changed?

PLEASE GO ON TO THE NEXT PAGE 22

Full Cases Case 22: Cost Management of a Gas Station

A newly opened gas station is having trouble with managing the Cost of Operation. Below is the data on its cost structure in the first three months of 2011: Month January February March

Gasoline cost $159,000 $131,100 $176,700

Electricity cost $8,550 $8,420 $8,680

Wages $23,560 $21,280 $23,560

22.1: Calculate the average monthly Cost of Operation for this gas station and the average annual Cost to keep this gas station running. 22.2: The gas station wishes to obtain a Gross Profit Margin of 0.44 in April compared to 0.30 in March. Calculate the % of increase in Sales that the gas station should aim for in order to achieve the desired Gross Profit Margin. 22.3: Given that the Fixed Cost for the gas station is $60,000 per month, and the gas station has kept the price at $3.80 / gallon throughout the 1st quarter of 2011. On average, how many gallons does the gas station have to sell per month to break even?

PLEASE GO ON TO THE NEXT PAGE 23

Full Cases Case 23: Cable TV and Internet Services

SCTV is a provider of cable TV as well as household Internet services. It is having trouble with competitiveness and its market share is threatened. Here are some annual figures related to the situation: (Y.o.Y = Year over Year) Providers SCTV HTVC VTC VCTV

Income from Income from Cable TV service Household Internet service $230,400,000 $110,942,400 $144,360,000 $57,744,000 $130,152,000 $62,832,000 $79,788,000 $25,779,600

Miscellaneous Income $38,010,000 $21,470,000 $20,615,000 $14,280,000

Y.o.Y % change 2.3% 13.6% 6.5% 9.2%

23.1: Calculate the market share of SCTV in the Cable TV market and Household Internet market. 23.2: Given that SCTV charges $6 / month for Cable TV and $2.90 / month for Household Internet while HTVC charges only $5 / month for Cable TV and $2.50 / month for Household Internet. Calculate the number of Cable TV subscribers and Household Internet subscribers of SCTV and HTVC from last year to this year. 23.3: SCTV is considering lowering the monthly fees of Cable TV and Household Internet in order to achieve a Y.o.Y % change of 7%. If the growth rate of subscribers of each service increases by 16% as a result of this price change, calculate the new fees that SCTV plans to charge for both services.

PLEASE GO ON TO THE NEXT PAGE 24

Full Cases Case 24: Bus Service Provider

Below is the data on business of a Bus Service Provider in town: Type of clients Child Adult Senior

Monthly Fare $90 $135 $70

Average monthly Quantity of clients 14,000 26,700 8,300

24.1: Calculate the % share in Revenue of each Fare category. 24.2: For every dollar of Revenue the company makes, $0.32 will be contributed to Gas Expense, which adds up to a 45% share in Total Expenses. Calculate Net Profit (in dollar value) and Profitability (in %) of the company last month. 24.3: Given that the average monthly quantity of children using the services of this company has increased by 15%, monthly fare for a senior client has dropped by $5 and Expense has decreased 1.2 times, calculate the % change in Net Profit and the new Profitability (in %) of the company.

PLEASE GO ON TO THE NEXT PAGE 25

Full Cases

Hurdle 7

Case 25: Casio Calculator Retailer

Below is the data on the business of a local Casio Calculator Retailer in 2010: Type of Calculator FX 970G FX 950ii FX 900ES

Units Sold 150,700 164,200 153,800

Share in total Revenue 30.3% 37.7% 32%

25.1: An FX 900ES has a price of $89. Calculate the Selling Price of the other 2 types of calculators. 25.2: The Cost of Goods Sold for each FX 970G calculator is $32 and the Net Profit made by each FX 970G is $18. Calculate the Gross Profit Margin and Profit / Revenue ratio of the FX970G brand. 25.3: The total Cost of Goods Sold of the FX 900ES brand is $4,351,300 and its Net Profitability is 28%. Calculate the amount of Expenses spent on each FX 900ES calculator for every dollar of Sales.

PLEASE GO ON TO THE NEXT PAGE 26

Full Cases Case 26: Cosmetics Retailer

Thorakao is a well-known retailer of various cosmetic brands. Here are the statistics on Thorakao’s Unit Sales over the last 12 months: Jan – April May – Aug Nov – Dec

Avon 4,850 4,300 4,680

Shiseido 4,820 4,950 4,760

L’Oreal 3,770 4,150 4,540

26.1: Calculate the Sales growth of each cosmetic brand from one period to the next and the overall Sales growth of Thorakao. 26.2: The annual Sales, by value, of Thorakao is $1,080,000. Avon’s share in value of Sales is 28%, Shiseido’s share is 35.5% and the rest is L’Oreal’s. Calculate the average Selling Price per unit of each cosmetic brand. 26.3: Predictions for Sales in the next Jan - Apr period are as follow: 12% decrease in quantity for Avon due to an increase of $5 in the average selling price, 8% increase in Shiseido’s value of Sales. Assuming that the average selling price for L’Oreal products will not change and all % change is compared to last year’s Jan – Apr period, what is the % change in the required quantity of L’OReal’s products sold for Thorakao to achieve its goal? It should be noted that Thorakao expects that Sales for the upcoming Jan-Apr period will be equal to 40% of the total sales of the previous year.

PLEASE GO ON TO THE NEXT PAGE 27

Full Cases Case 27: Hoa Vien Restaurant

Hoa Vien Restaurant serves two kinds of fresh beer: Yellow and Black offered in three glass sizes: Small, Medium and Large. Costs and Prices are as follow: Cost per Litre (L) Cost of glass Small (0.5L) Medium (0.8L) Large (1.5L)

Yellow beer $1 $0.5 $3 $4.75 $6

Black beer $0.75 $0.5 $2 $4.5 $5.5

On average, Hoa Vien Restaurant serves 297L of Yellow beer and 220L of Black beer per night.

27.1: Calculate the mark-up percentages for the Yellow and Black beers in Medium and Large glasses. Round up your answer to 2 decimal places. 27.2: The number of Medium glasses sold is half the number of Small and Large glasses combined. Revenue of Large glasses is equal to the Revenue of Small and Medium glasses combined. Calculate the number of Yellow and Black glasses served and the profit (in US dollars) Hoa Vien Restaurant can make per night. 27.3: Hoa Vien Restaurant states in the Menu that each glass can be sold for $8 as a souvenir and it automatically charges $8 for each glass broken by customers. On a typical day, 1 out of 29 small glasses is broken, the same ratio goes for medium glasses, and that of large glasses is 1 out of 61. What is the largest percentage that Hoa Vien’s Profit can increase when compared to a night when no glasses are broken? (Round up your answer to 2 decimal places).

PLEASE GO ON TO THE NEXT PAGE 28

Full Cases Case 28: Light bulbs producer

Below are data on the business of a light bulb producer: Type of light bulbs Type 1 Type 2 Type 3

Selling price / unit $25 $20 $18

Fixed Cost $150,000 $120,000 $115,000

28.1: Type 1 division breaks even at the Sales level of $720,000. Calculate the Variable Cost per unit of the Type 1 Light bulb. 28.2: Type 2 division makes a loss of $5,000 at Unit Sales of 10,000 units. Calculate the Variable Cost per unit of the Type 2 Light bulb. 28.3: Under the current conditions, Type 3 division makes a profit of $50,000 for 18,000 bulbs sold. If Variable Cost per unit is to be increased by 5%, calculate the % change in the Unit Sales level at the break-even point.

PLEASE GO ON TO THE NEXT PAGE 29

Full Cases

Hurdle 8

Case 29: Basketball shoes

A sports outfit retailing shop imports basketball shoes from two sources: domestically made and foreign made. Information on prices and costs of basketball shoes in 2010 is as follows: Quantity sold (in pairs) Selling price Import cost (% of price) Tariff on imported value Warehousing cost

Domestically made shoes 196 $25 60% N/A 20%

Overseas made shoes 213 $32 50% 15% 15%

29.1: How many pairs of each type of shoes will need to be sold so that the shop can break even? Assume that Import cost, Tariff and Warehousing are all Variable Costs, Fixed Cost for the domestically made shoes division is $850 and for the foreign made shoes division is $900. 29.2: Which division of shoes is more profitable? By how much, in dollar value? 29.3: After a long protest by importers, the Government decided to reduce the tariff on imported value down to 9%. What is the new Revenue of the foreign-made shoes division at the breakeven point?

PLEASE GO ON TO THE NEXT PAGE 30

Full Cases Case 30: Cereal Manufacturer

Chopper Cereal is having a tough time with its Profitability. All figures related to the problem are as follows: Product package (580g) Honey Bee Cereal Choco Chimp Cereal Fruit Frenzy Cereal

Selling price per package $9.75 $9.40 $9.25

Cost of Production per Package $3.50 $3.20 $3

Revenue of the 1st quarter $477,750 $490,680 $501,350

Given that the quarterly Fixed Cost for the Production of each Cereal brand is $270,000.

30.1: Find the break-even Unit of Sales for each of Chopper Cereal’s brands and calculate the Profit / Loss and Profitability (in %) of each brand in the first quarter. 30.2: Chopper Cereal intends to launch an advertising campaign which will hopefully increase the second quarter’s Revenue of each brand by 12%. However, this campaign will also raise the quarterly Fixed Cost by an extra $130,000. Calculate the effect(s) of this decision on the second quarter’s Profit, and decide whether or not it would be a good decision. 30.3: Assume that Chopper Cereal did not go for the advertising campaign, but went for a decrease in Selling Price. Each cereal brand experienced a 15% drop in selling price. The directors hoped that it would increase the second quarter’s Revenue of each brand by 22%. Calculate the new Profitability (in %) resulted from this decision.

PLEASE GO ON TO THE NEXT PAGE 31

Full Cases Case 31: Fertilizer Manufacturer

Below are data on sales of 2 types of fertilizer sold by a Fertilizer Manufacturer: Quantity sold (in package) Revenue Profit

Type A 227,000 $13,597,300 $2,584,000

Type B 268,000 $12,033,200 $1,925,312

31.1: Calculate the Selling Price and the proportion of sales that goes to profit of both types of fertilizers. 31.2: The mark-up percentages for Type A and Type B are 145% and 130%, respectively. Calculate the Expense that the manufacturer spent on each type of fertilizer. 31.3: As Cost of Production tends to increase by 16%, the manufacturer is considering raising the mark-up percentage each fertilizer by 10%. Given that the manufacturer wants a 32% increase in Revenue of each type, calculate the % change in Quantity sold of each type that corresponds to all the conditions mentioned above.

PLEASE GO ON TO THE NEXT PAGE 32

Full Cases Case 32: Carpet Factory

Below are data on 3 carpet models of a Carpet Factory: Model Persian Arabian Indian

Selling Price per Unit $189.50 $154.50 $168.25

Share by Units sold 28.5% 29.2% 30.3%

Share by Profit 30.5% 29% 31.5%

32.1: Given that the factory supplies 12,760 carpets to the market, calculate its Total Revenue from all three models. 32.2: The Fixed Cost of Production for each carpet model can be covered by 55% of its current Revenue. Given that the factory breaks even at 2,500 carpets of each model, calculate the Variable Cost of producing one carpet of each model. 32.3: Given the current conditions, the factory is able to make a Total Profit of $893,200. The factory managers want to improve Profit from each model of carpet by 12% by dropping Fixed Cost by 4% and raising the Selling Price. Calculate the % change in Selling Price of each carpet model to achieve the desired Profit.

PLEASE GO ON TO THE NEXT PAGE 33

Full Cases

Hurdle 9

Case 33: Cooking Oil Retailer

Below are data on the business of a Cooking Oil producer in town: Olive Oil Cod-liver Oil Peanut Oil

Price / Unit $24.50 $19.90 $15

Share in Quantity 28.2% 35% 36.8%

Variable Cost / Unit $10 $7.75 $5.30

33.1: 200,000 units of Cod-liver Oil were produced and supplied, making a profit of $1,150,000. Calculate Profit / Loss of the other two oils. Assume that all three divisions share the same fixed cost. 33.2: Olive oil’s Variable Cost / Unit will increase by $1.40, but its share in quantity will also rise to 29%. However, the actual Total Unit Production will not change from the previous period. Calculate the % change in Profit of Olive oil division and its new Profitability. 33.3: Peanut oil division wants to improve its Profitability by an extra 1.2%. With the share in quantity dropping to 34.5%, calculate the % change in price in order to achieve the desired Profitability. Assume that Total Unit Production remains constant.

PLEASE GO ON TO THE NEXT PAGE 34

Full Cases Case 34: Eggs retailer

Below are data on the business of an egg retailer in town: Chicken eggs Duck eggs Quail eggs

Sales $118,800 $47,025 $80,080

Share in Profit 38.5% 27.5% 34.0%

Note: eggs are sold in dozens.

34.1: Chicken eggs division has an Expense / Sales ratio of 0.78 : 1. Calculate the Expense / Sales ratio of the other 2 divisions of eggs. 34.2: 9,100 dozens of quail eggs were sold. Calculate the Profit gained per egg (in dollar value). 34.3: Expense on duck eggs is reduced 1.15 times, along with a 10% increase in Selling Price. Calculate the % change in Profit and the new share of Profit. Given that a quantity of 8,250 dozen duck eggs were sold and the total profit remains constant.

PLEASE GO ON TO THE NEXT PAGE 35

Full Cases Case 35: Kayak Rentals

Below are data on the Rental fee and Total fixed cost of 2 kinds of kayaks rented by a family business: Single Kayak Double Kayak

Rental fee / hour $15 $25

Total Fixed Cost $15,500 $18,000

35.1: There are 20 single kayaks available for rent. In order to break even, the family has to earn $75,000 from the rental fee. Calculate the variable cost per Single Kayak. 35.2: Double Kayaks make a profit of $10,000 in 500 hours. Given that the variable cost per Double Kayak is $8, how many Double Kayaks are there? 35.3: Calculate the profitability (in percentage) of each type of kayak in 100 days of full capacity.

PLEASE GO ON TO THE NEXT PAGE 36

Full Cases

Hurdle 10

Case 36: Rice Growing Plant

A farmer has 3 plants on which he grows rice to earn his living. Below are data on the area and capacity of each plant: Plant A Plant B Plant C

Area (ha) 0.8 0.65 0.72

Capacity (kg) 325 240 295

36.1: Which plant has the best productivity per ha? 36.2: Plant A has a profitability of $1830 kg / ha and rice produced here has a profitability of 18.5%; Plant B has a profitability of $1,640 kg / ha and rice produced here has a profitability of 20%. Calculate the difference (in %) in the selling price per kg of rice produced in Plant A and Plant B. 36.3: Plant C requires a variable cost of $14 per kg of rice and a fixed cost of $700. If the farmer wants a Gross Profit Margin of 0.38 at the current level of production, what should the selling price per kg of rice in Plant C be?

PLEASE GO ON TO THE NEXT PAGE 37

Full Cases Case 37: TFG Travel

TFG Travel is a new tourism agent that offers both domestic and international tours. The following is a brief review of TFG’s price level and profit during the second quarter of 2011:

Domestic tours International tours

Avrg. Price per Adult $370 $855

Avrg. Price per Child $345 $820

Quarterly Profit $418,500 $762,900

37.1: Given that the ratio between adult tourists and child tourists is 7 : 3 and TFG has a Profitability of 13.4% in the second quarter. Calculate the total quantity of both adult and child tourists of all Domestic tours. 37.2: Due to increases in expenses (transportation, accommodation, etc.) over time because of inflation, TFG has to increase the price levels for both adult and child tourists in all International tours by 14%. Despite the price rise, TFG aims to maintain the same profit level in the third quarter as that of the second quarter. If TFG wants to have Profitability of 11% and the ratio between adult and child tourist is to be 6 : 4, how much would total expenses on each type of tourist be?

PLEASE GO ON TO THE NEXT PAGE 38

Full Cases Case 38: Imported Fruit Shop

Below is data on the selling price and mark-up percentage of types of imported grapes available in an imported fruit shop: Grape Type A Grape Type B

Selling price per kg $17 $20.5

Mark-up percentage 150% 250%

38.1: What is the cost of importing 1 kg of type A grapes? 38.2: If the cost per kg of type A grapes found out in 38.1 doubled that of grape type B, what would be the mark-up percentage of both types of grape combined? 38.3: The shop offers a discount of 10% on a total bill of more than 10 kg of each type of grape. A customer bought 18 kg of Grapes type A and 12 kg of Grapes type B. What was the profit the shop earned from this customer?

PLEASE GO ON TO THE NEXT PAGE 39

Full Cases

Hurdle 11 Case 39: Andy’s Laptop Distributor

Andy’s Laptop Distributor is a one month old laptop distributing store in a local town. Below is its weekly business data since opening:

Week 1 Week 2 Week 3 Week 4

Laptop A # Sold Revenue 34 $27,880 22 $18,040 19 $15,580 31 $25,420

Laptop B # Sold Revenue 11 $18,370 29 $48,430 11 N/A 31 $65,100

Laptop C # Sold Revenue 6 $19,500 21 $68,250 30 $97,500 N/A $103,675

39.1: Seeing that laptop C was selling very well over the first 3 weeks, the business team of the store decided to increase its price by 10%. What is the number of C laptops sold in the fourth week? 39.2: In the first 2 weeks, the mark-up percentage of laptop A was 45% and increased to 70% in the last 2 weeks. By how many percent did the total cost of laptop A increase/decrease? 39.3: In the first week, the mark-up percentages of Laptop B and Laptop C were 65% and 120%, respectively. 30% of the total cost of all laptops sold was contributed to Maintenance Cost, which was two thirds of the Marketing Cost. 10% was distributed to Finance Cost and the remaining to Operation Cost. How much was Operation Cost in the first week? 39.4: Total Cost of Laptop B increased by 16% in the third week and its mark-up percentage was 50%. Calculate the gross profit of all B laptops sold in the third week?

PLEASE GO ON TO THE NEXT PAGE 40

Full Cases Case 40: Real Estate Broker

Jack works as real estate broker for a living, both for a domestic company and as a free-lancer. His monthly income structure is as follow: -

-

From company: o Fixed salary: $3,200 before income tax of 15% o Commission (not taxed): $450 for each of the first 3 successful contracts, 10% increase (compounded) for each additional successful contracts o Bonus (not taxed): varies Free-lance (not taxed): o Fixed amount charged per client: $580 o Commission: 3% the value of the real estate property traded

40.1: In January, Jack took charge of 11 company contracts and made 6 successful. What was his net income (after tax) from the company in January, given that his bonus was 2% of total commissions? 40.2: In the same month, Jack signed a number of free-lance contracts, two thirds of which were successful. The average value of each of these contracts was $75,000. Given that his total net income in January was $28,600. How many free-lance contracts did Jack sign? 40.3: In February, Jack made 5 company contracts and 4 free-lance contracts successful (he signed 12 free-lance contracts), each of which was $56,000 in average value. He received no bonus from the company that month due to some complaints from the clients. In order to keep his net income the same as last month, Jack had to increase the commission percentage of his free-lance contracts. What was the new commission percentage Jack charged for each of his freelance contracts in February?

PLEASE GO ON TO THE NEXT PAGE 41

Full Cases Case 41: Suit Tailoring

Zeiss Suit is a famous suit tailoring store for both men and women. Below is the price of each type of suit provided at Zeiss Suit:

Men Suit Quality Price per unit High £985 Medium £612 Low £385

Women Suit Quality Price per unit High N/A Medium £584 Low £310

41.1: In December 2011, Profit from medium quality suits (for both men and women) was £18,600. The Total number of medium quality suits sold was 55. Calculate the approximate Profit Margin of all medium quality suits sold. 41.2: Total number of all women’s suits sold in December was 96. Given that the ratio of high, medium and low quality women suits sold was 3 : 8 : 5. Revenue from women suits sold was £52,030. What was the price of a high quality women’s suit? 41.3: The Average mark-up percentage of a suit sold at Zeiss suit is 120%. General cost structure of a suit is as follows: Material – 35%, Labor: 40% (of which, 60% was paid to the tailors and 40% to salesmen and other workers), other Costs: the rest. In November 2011, 169 suits were made by 9 of the store’s tailors and sold out. On average, how much was a tailor approximately paid in that month? Assume that the number of suits of each type sold that month were quite similar.

PLEASE GO ON TO THE NEXT PAGE 42

Full Cases

Hurdle 12 Case 42: Betty’s Hair Salon

Betty owns a small hair salon. Below is its business data in the recent 3 months:

Revenue Expense

May $12,670 $5,420

June $9,810 $4,480

July $11,450 $5,180

42.1: In which month did Betty’s salon have the highest profitability (in %)? 42.2: Fixed cost per month is $1,280 and total variable cost per client is $10, both of which remained the same in all 3 months. The average price charged per client ordering service at Betty’s salon changed in June and July changed by how many percent compared to the previous month? 42.3: Betty is thinking about increasing the quality of her service, making the total variable cost per client increase by 15%. Her expectation is that the number of clients will double and all clients visiting the salon this month will get a 30% discount on their bills (compared to the number of clients and prices charged in July). How much profit/loss (in $) will Betty make in August?

PLEASE GO ON TO THE NEXT PAGE 43

Full Cases Case 43: Website Management

Jay works for a website company and is currently the project manager of 3 different websites: BooksOnline.com (selling books), EnglishTips.com (sharing English learning tips and selling practice tests) and GetEverything.com (a platform that offers online commercial stores to private individuals and organizations to sell anything). Here are some analytical data on the websites in May 2013:

BooksOnline.com EnglishTips.com GetEverything.com

Visits (thousands) 34.6 42.8 53.9

Unique visitors 7,395 12,590 10,470

Page views (thousands) 67 55 178

Conversion rate (%) 37 12 65

In which: -

Visits: total number of visits to the website Unique Visitors: number of unduplicated visitors (counted only once) to the website Page views: total number of pages viewed. Repeated views of a single page are counted. Conversion rate (%): the percentage of visitors (duplicated visitors are counted) who pay via Paypal to buy something on the website.

43.1: Which website has the highest number of page views per visit? Rank from highest to lowest. 43.2: For BooksOnline.com, the ratio of new visits to returning visits is 1 : 5. Of the number of new visits, 2/3 are people who never come back to the website. How many times on average does an unique returning visitor come back to the website after the first visit? (Note that a number of visitors visited the website the first time before May and came back in May, their visits in May are all counted as returning visits). 43.3: EnglishTip.com has not been doing very well based on the analytical data in May. Jay is thinking about ways to increase the number of page views per visit. He estimates that a 1% increase in number of page views per visit may bring the conversion rate up by 0.3%. In June, his ideas were implemented and some statistics were collected as follows: visits increased by 25%, the number of page views per visit was 1.68, average total value per Paypal bill was $8.5. How much revenue did EnglishTip.com generate in June 2013?

PLEASE GO ON TO THE NEXT PAGE 44

Full Cases Case 44: Mobile Ice-cream Store

By the end of the month, the owner of a mobile ice-cream store managed to gather the following data on his small business:

Type of icescream Cherry Vanilla Strawberry

# Sold per day

Unit Price

34 58 23

$2.5 $1.8 60 cents

Unit production cost $1.875 $1.17 $0.42

*Note: in calculating profit margin, only production cost is counted.

44.1: Calculate Share (%) in Revenue of each type of ice-cream. 44.2: Rank the profit margin of each type of ice-cream from highest to lowest 44.3: The owner of the store sees that vanilla ice-cream sells very well so he wants to double its profit margin by increasing the selling price and reducing the unit production cost. If the production cost is to be reduced by 20%, how many percent will the selling price have to be increased to achieve the owner’s target?

PLEASE GO ON TO THE NEXT PAGE 45

Full Cases

Hurdle 13

Case 45: Furniture Importer

Royal House is a famous European furniture importer in Japan. It retails to both consumers at showroom prices and distributes in bulk to other retailers at wholesale prices. Below is the price table for the 3 best-selling products at Royal House.

Product Name

Showroom price

Royal Sofa Vienna Bed Bassett Cabinet

$2,180 $3,850 $4,040

Discount for Wholesale (2050 items) 15% 10% 12%

Discount for Wholesale (5080 items) 18% 14% 15%

Discount for Wholesale (>80 items) 23% 20% 19%

45.1: In June, Royal House showroom sold 13 Royal Sofas, 8 Vienna Beds and 15 Bassett Cabinets. Total Showroom Revenue was $219,680. Calculate Share (%) in Showroom Revenue of each of the 3 best-selling products. 45.2: Also in June, Royal House wholesaled to 5 retailers at quantities as follows: Retailer # 1 2 3 4 5

Royal Sofa 80 55 30 150 35

Vienna Bed 45 75 0 0 60

Bassett Cabinet 0 100 40 0 90

How many percent of Royal House’s total revenue is from its wholesale revenue? 45.3: In July, Royal House launched a new type of bed: Manhattan Bed, whose showroom price is $4,620. For the Manhattan Bed, unit cost is 20% higher than that of the Vienna Bed and profit margin is 45%. For this new product, Royal House offers a 25% discount on wholesale of more than 80 items. A retailer wants to buy 100 beds but has not decided on which model. What type of bed, Vienna or Manhattan, would Royal House want to sell to this retailer?

PLEASE GO ON TO THE NEXT PAGE 46

Full Cases Case 46: Internet Providers

FHU, VCG, HTV are the 3 biggest market leaders in the Internet service market in Scotland. Below are their monthly data on the number of clients and fee charged per client of each type:

Internet provider

FHU VCG HTV

Average household clients (thousands) 250 120 67

Fee charged per household client Fixed for first 50Mb £12 £10 £5

Per next Mb £0.5 £1 £0.6

Average firm/org. clients (thousands) 32 19 42

Fee charged per firm/org. client Full price for unlimited Mb £540 £650 £420

46.1: What is their market share in the firm/org. internet market, given that the monthly market revenue is approximately £60 billion? 46.2: Adele’s family has 4 people, each of them estimated to consume 60Mb per month. Which Internet provider from the above 3 should they choose? 46.3: For all 3 companies, for every 1% increase in fee charged per firm/org. client they will lose 500 clients and for every 1% decrease they gain 200 clients. New fees charged per firm/org. client of FHU and HTV is £589 and $400 respectively. By how many percent will their monthly revenue from this type of client increase or decrease?

PLEASE GO ON TO THE NEXT PAGE 47

Full Cases Case 47: Stock market

Maya has $15 million to invest in stocks. She intends to buy 3 types of stock: ASP, SHN and MCG.

Stock

Current price

ASP SHN MCG

$13.5 $8.6 $21.3

Highest Expected Return (compared to current price) 30% 45% 75%

Highest Expected Loss (compared to current price) 15% 10% 55%

47.1: Maya buys 200,000 ASP stocks, 450,000 SHN stocks and 100,000 MCG stocks. In the best case scenarios of all three stocks, how much (in $) would she get in return? 47.2: Taking our best guess for return on each type of stock as the average between highest expected return and highest expected loss, and the possibilities for each scenario are 50/50, 30/70, 20/80 for ASP, SHN and MCG respectively. Which stock has the highest return? 47.3: Maya used all her money to buy ASP stocks at the price of $15 and cut loss at the highest expected loss point. She wants to use her leftover money to invest in SHN. What is the least amount of SHN stock Maya should buy in order to cover all her loss from the ASP investment when the return of SHN is maximum?

PLEASE GO ON TO THE NEXT PAGE 48

Full Cases

Hurdle 14

Case 48: Headphone Retailer

A headphone store in a small town retails only 3 types of headphones. Below is its last month’s business data:

Type of Headphone A B C

Unit Selling Price $45.5 $30 $95

Unit Variable Cost $13.5 $9 $21

Profit Margin 60% 55% 25%

48.1: Last month, the store made revenues of $13,650, $10,950 and $6,650 from selling headphones A, B, C, respectively. Calculate the total Fixed Cost of all 3 types of headphones. 48.2: The owner of the store wishes to increase his store’s revenue by 15% next month. However, the quantity sold of each type of headphone is not expected to pick up as there is no anticipatory increase in demand. The only way he can do that is to increase the unit selling price of headphone type B. By how many percent does the unit selling price of headphone type B need to be increased in order for the owner to achieve his goal? 48.3: Total Unit Cost per each headphone regardless of type is about to drop by 30% in the next month. If the new target Profit Margins for headphone type A, B and C are 65%, 70%, 50% respectively, what is the new unit selling price of each type of headphone?

PLEASE GO ON TO THE NEXT PAGE 49

Full Cases Case 49: Real Estate Broker

Johnny is a free-lance real estate broker. -

For each real estate contract, he charges his client a flat fee which is non-refundable. If the contract succeeds, the selling party will pay him 5% of the contract value and the buying party 1%.

49.1: In July 2013, Johnny made $45,500 in total revenue. His fixed amount of non-refundable fee charged per contract was $1,500 and the average value of each contract was $35,000. About 80% of the contracts were dealt successfully. What is the total number of contracts Johnny received in July 2013?

Johnny is about to enter into a number of contracts in the first week of September 2013. Below is data on these contracts: Contract No.# 1 2 3 4 5

Contract Value $49,000 $32,700 $78,900 $38,000 $125,000

Possibility of Success 90% 75% 80% 65% 50%

Fixed Non-refundable Fee $1,200 $850 1% of contract value $1,100 $2,000

49.2: Taking the best guess of Johnny’s income from a contract as the average income from that contract in both the cases of success and failure. Which contract has the highest best guess of income? 49.3: Only the first 3 contracts did actually succeed and the last 2 failed. How much did Johnny earn in that week?

PLEASE GO ON TO THE NEXT PAGE 50

Full Cases Case 50: French Teaching Center for Kids

A new French Teaching Center for Kids has just opened 3 months ago. Its upfront investment (including Rent, Equipment Cost, Operations Cost, Labor Cost, etc.) to open the center added up to $5.2 million.

Program

Number of classes

Basic Intermediate Advanced

15 20 10

Maximum number of students / class 10 15 10

Number of sessions / week 3 3 2

Fee charged per student for the whole program $1,800 $2,200 $2,900

Variable Cost per class session $350 $420 $550

*Note: each program lasts for 2 months.

50.1: Given that all provided data remain unchanged over the first year of operation and all classes of the center are always full, how long does it take the center to repay all the upfront investment cost to break even? 50.2: After breaking even, the center decides to increase the fee charged per student (regardless of program) by 15%. Assume that due to the increase in fee, each class now only has 80% of the maximum number of students per class. What is the center’s monthly revenue? 50.3: A Marketing event to attract more students to the center is proposed. It is projected that in 100 kid attendants to the event, 60 will register for a trial free course and then half of them will pay for a basic program. What is the Return (in %) of this Marketing event, given that it costs $650,000 and 2,840 kids attended the event. (Basic Program’s fee remains at $1,800)

PLEASE GO ON TO THE NEXT PAGE 51

Full Cases

Answer Key Hurdle 1 Case 1: Thailand Beer factory

1.1: Fixed Cost is $330 Because Revenue increases by $20 while Cost increases by $10 each year, Variable Cost is 50% of Revenue. Plugging back to the initial information, we find out that Fixed Cost is $330.

1.2: Profit in 2011 is - $230 (loss) Revenue:

$200

Fixed Cost:

$330 (from question 1.1)

Variable Cost: $100 (50% of Revenue)

1.3: 132% At the break-even point, Revenue = Fixed Cost + Variable Cost. We already know that Revenue is twice the Variable Cost, so in order to satisfy the above equation, Revenue must be twice the Fixed Cost also, which means Revenue must be $660. In 2010, 16% capacity generates $80 in Revenue. Thus, if the factory wants to generate $660 in revenue, it must produce at 132% capacity. This means that it is impossible to break even!

1.4: 71.43% Let P be the current price In previous questions, we know that VC is 50% Revenue which means VC per unit = 50% P At the current Price, Revenue = P * Units Sold

PLEASE GO ON TO THE NEXT PAGE 52

Full Cases Variable Cost = VC per unit * Units Sold = 50% * P * Units Sold Fixed Cost = 330 To break even,

Revenue = Variable Cost + Fixed Cost P * Units Sold = 50% * P * Units Sold + 330 50% * P * Units Sold = 330

(1)

If the price increases by 20%, Revenue = 1.2 * P * Units Sold Variable Cost = 50% P * Units Sold Fixed Cost = 330 To break even,

(1) and (2) number.

Revenue = Variable Cost + Fixed Cost

120% * P * Units Sold = 50% * P * Units Sold + 330 70% * P * Units Sold = 330 (2) the new units sold to break even equals 50/70 of (or 71.43%) the original

1.5: 88% With the new shift, the new full capacity increases by 50% compared to the original full capacity (3 shifts compared to 2 shifts) The original capacity to break even is 132% the original full capacity which is now 88% of the new full capacity (132% / 1.5)

1.6: 96% Previously, we calculated that Variable Cost is 50% of Revenue and found out 88% of full capacity is needed to break even. Now with the complexity of Over Time, we need to calculate that new Ratio. ⅓ (1 night shifts in the total of 3 shifts) of Labor Cost has an 50% increase. So Labor Cost increases by 50% x ⅓. Labor Cost is ½ of Var Cost. So Var Cost increases by 50% x 50% x ⅓ = ~ 8%.

PLEASE GO ON TO THE NEXT PAGE 53

Full Cases So now, Var Cost is actually 54% of Revenue (50% x 1.08). New equation for Break Even Revenue:

$660 equals 88% of the new full capacity

Revenue = Fixed Cost + Var Cost R

= 330 + .54 R

0.46 R

= 330

R

= ~ 720

$720 equals 96% capacity.

Case 2: Electronics Retailer

2.1:

Water purifier: $107,376; Cooker: $291,775; Air-conditioner: $297,953; Vacuum: $220,097; In this case, Cost = Selling Price / (Mark-up % + 100%) Annual Cost of Water purifier: $22,370 / 250% x 12 = $107,376 Annual Cost of Cooker: $66,865 / 275% x 12 = $291,775 Annual Cost of Air-conditioner: $84,420 / 340% x 12 = $297,953 Annual Cost of Vacuum: $53,190 / 290% x 12 = $220,097

2.2: Average Variable Cost per Air-Conditioner: $1,020.3; Average Variable Cost per Vacuum: $417.3 Average Variable Cost = (Total Cost - Fixed Cost) / Quantity Average Variable Cost per Air-Conditioner: ($297,953 - $200,000) / (8 x 12) = $1,020.3 Average Variable Cost per Vacuum: ($220,097 - $160,000) / (12 x 12) = $417.3

PLEASE GO ON TO THE NEXT PAGE 54

Full Cases

2.3: Water Purifier section’s expected average monthly Profit: $14,316.8 and +6.7% Cooker section’s expected average monthly Profit: $44,982 and +5.7% Provided that Cost x (Mark-up % + 100%) = Selling Price, then we have Profit = Cost x Mark-up % Current average monthly Profit of Water Purifier section: ($107,376 / 12) x 150% Expected average monthly Profit of Water Purifier section: ($107,376 / 12) x 160% = $14,316.8 % change in average monthly Profit of Water Purifier section: (160% - 150%) / 150% = 6.7% Current average monthly Profit of Cooker section: ($291,775 / 12) x 175% Expected average monthly Profit of Cooker section: ($291,775 / 12) x 185% = $44,982 % change in average monthly Profit of Cooker section: (185% - 175%) / 175% = 5.7%

Case 3: Dishwasher Producer

3.1: $456.30 Revenue of Medium dishwashers: ($1,483,350 / 25%) x 38% = $2,254,692 Selling price of one Medium dishwasher: $2,254,692 / 1,800 = $1,252 COGS of one Medium dishwasher: $1,252 / 270% = $456.30

3.2: Small 34%; Medium 37.1%; Large 28.9% Revenue of Large dishwashers: ($1,483,350 / 25%) x 37% = $2,195,358 Selling price of one Large dishwasher: $550 + ($550 x 185%) = $1,567.50 Quantity of Large dishwashers sold: $2,195,358 / $1,567.50 = 1,401

PLEASE GO ON TO THE NEXT PAGE 55

Full Cases Share in Quantity of Small dishwashers: 1,650 / (1,650 + 1,800 + 1,401) x 100% = 34% Share in Quantity of Medium dishwashers: 1,800 / (1,650 + 1,800 + 1,401) x 100% = 37.1% Share in Quantity of Large dishwashers: 1,401 / (1,650 + 1,800 + 1,401) x 100% = 28.9%

3.3: +21.95% in selling price; New mark-up percentage: 177% Old COGS per unit for Small dishwashers: ($1,483,350 / 1,650) / 250% = $359.60 New COGS per unit for Small dishwashers: $359.60 x 110% = $395.56 Expected quantity of Small dishwashers sold: (4,851 x 82%) x 34% = 1,353 Required price level to maintain Revenue: $1,483,350 / 1,353 = $1,096.30 Old selling price per unit of Small dishwashers: $1,483,350 / 1,650 = $899 Required % change in selling price: ($1,096.30 - $899) / $899 x 100% = 21.95% New mark-up % of Small dishwashers: ($1,096.30 - $395.56) / $395.56 x 100% = 177%

Case 4: Tea Retailing Stand

4.1: Honey Tea: 19.37%; Lemon Tea: 27.35% Expenses of Milky Tea = $16,500 x 79% = $13,035 Total Expenses = $13,035 / 23% = $56,674 Expenses of Honey Tea = $56,674 x 24.5% = $13,885 Profitability of Honey Tea = ($17,220 - $13,885) / $17,220 = 19.37% Expenses of Lemon Tea = $56,674 x 21.6% = $12,242 Profitability of Lemon Tea = ($16,850 - $ 12,242) / $16,850 = 27.35%

PLEASE GO ON TO THE NEXT PAGE 56

Full Cases 4.2: Milk Tea: $11.4; Honey Tea: $12.41; Lemon Tea: $15.83 Quantity of Milk Tea sold: ($56,674 x 23%) / $9 = 1,448 units Selling price per unit of Milk Tea: $16,500 / 1,448 = $11.4 Quantity of Honey Tea sold: ($56,674 x 24.5%) / $10 = 1,388 units Selling price per unit of Honey Tea: $17,220 / 1,388 = $12.41 Quantity of Lemon Tea sold: ($56,674 x 21.6%) / $11.5 = 1064 units Selling price per unit of Lemon Tea: $16,850 / 1064 = $15.83

4.3: -74 units New expense for Honey Tea: $56,674 x 26% = $14,735 Required Sales of Honey Tea to maintain profitability: $14,735 / 80.63% = $18,275 Extra quantity of units needed to be sold: $18,275 / ($12.41 + $1.5) - 1,388 = -74

Hurdle 2

Case 5: Dental Clinic

5.1: $218,725 Fixed Cost = Break-even Unit x (Selling price - Variable Cost) Fixed cost for Tooth Extractions: 6,500 x ($5 - $2.75) = $14,625 Fixed cost for Root Canals: 6,500 x ($28.50 - $19) = $61,750 Fixed cost for Fillings: 6,500 x ($25.90 - $14) = $77,350 Fixed cost for Cleanings: 6,500 x ($18 - $8) = $65,000 Total monthly Fixed Cost of St. Paul Dental Clinic:

PLEASE GO ON TO THE NEXT PAGE 57

Full Cases $14,625 + $61,750 + $77,350 + $65,000 = $218,725

5.2: $35,625 Revenue from Fee of Root Canals: 8,000 x $28.50 = $228,000 Gross Profit from Root Canals: $228,000 – (8,000 x $19 + $61,750) = $ 14,250 Gross Profit of the Clinic: $14,250 / 40% = $35,625

5.3: $7122.5 Net Profit Number of clients who had Fillings last month: ($94,850 - $77,350) / 14 = 1,250 Revenue from Fillings service: 1,250 x $25.90 = $32,375 Net Profit of Fillings service: $32,375 x $0.22 = $7122.5

Case 6: University Students Recruitment

6.1:

40%

As the Capture rate is 50%, the University needs to accept 8,000 domestic students in order to get 4,000 domestic students to actually enroll. 8,000 is 40% of 20,000.

6.2:

0.5%

As the Capture rate is 10%, the University needs to accept 10,000 international students in order to get 1,000 international students to actually enroll. 10,000 is 0.5% of 2,000,000.

6.3:

80%

As the highest Acceptance rate allowed is 50% and the Capture rate is 50%, the University needs to receive 16,000 domestic applications in order to accept 8,000 and finally get 4,000 domestic students enrolled. 16,000 is 80% of 20,000.

PLEASE GO ON TO THE NEXT PAGE 58

Full Cases

6.4:

1%

As the highest Acceptance rate allowed is 50% and the Capture rate is 10%, the University needs to receive 20,000 international applications in order to accept 10,000 and finally get 1,000 international students enrolled. 20,000 is 1% of 2,000,000.

6.5:

1.2%

Understand the Conceptual part: Since there is a limit on the Application Rate, to have enough students, the University has to raise the Acceptance Rate to higher than 50% for the Domestic group. To qualify for the ranking requirement, the University has to lower the Acceptance Rate for the International group. And to compensate for that, the University needs to attract more applications from the International group which means increasing the Application Rate for the International group. Detailed Calculation: Recall that with those Capture rates, 8000 and 10,000 applications (domestic and international, respectively) will be accepted to meet the enrollment goal. That is 18,000 in total. With 18,000 applications accepted, to maintain the 50% overall acceptance rate, there must be 36,000 applications in total. With only 60% of Application Rate, the number of domestic applications is 12,000 (= 20,000 * 60%). So there has to be 24,000 international applications. This means that the Application Rate for the International group is 1.2 % (= 24,000 / 2,000,000)

Case 7: Movie Cinema

7.1: $521.6 higher According to given facts, a 10% decrease in price will result in a 20% increase in demand. The new Revenue generated after the price change is:

PLEASE GO ON TO THE NEXT PAGE 59

Full Cases (30*1.2*10*0.9) + (350*1.2*8*0.9) + (70*1.2*6*0.9) + (600*1.2*5*0.9) = $7041.6 The old Revenue generated before the price change is: [(30*10) + (350 x 8) + (70 x 6) + (600 x 5)] = $6520 So the new Revenue is ($7041.6 - $6520) = $521.6 higher than the old Revenue.

7.2: $1,632 lower According to given facts, a 10% increase in price will result in a 20% decrease in demand. The new Revenue generated after the price change is: (100*0.8*12*1.1) + (500*0.8*10*1.1) + (200*0.8*7*1.1) + (1000*0.8*6*1.1) = $11,968 The old Revenue generated before the price change is: [(100*12) + (500 x 10) + (200 x 7) + (1000 x 6)] = $13,600 So the new Revenue is ($13,600 - $11,968) = $1,632 lower than the old Revenue.

Case 8: Milk Farm

8.1: 179,487 liters of Organic milk; 193,036 liters of Whole milk; 152,461 liters of Jersey milk Volume = Value / Price Queen Anne’s Volume of the organic milk market: ($1,200,000 x 35%) / $6.50 = 64,615.4 liters Total Volume of the organic milk market: 64,615.4 / 36% = 179,487 liters Queen Anne’s Volume of the whole milk market: ($1,080,000 x 34.8%) / $5.90= 63,701.7 liters Total Volume of the whole milk market:

PLEASE GO ON TO THE NEXT PAGE 60

Full Cases 63,701.7 / 33% = 193,036 liters Queen Anne’s Volume of the Jersey milk market: ($1,240,000 x 36.4%) / $7.75 = 58,240 liters Total Volume of the Jersey milk market: 58,240 / 38.2% = 152,461 liters

8.2: Organic milk market: $1,368,000; Whole milk market: $1,231,201; Jersey milk market: $1,413,600 Expected Revenue of Queen Anne from organic milk: (64,615.4 x 114%) x $6.50 = $478,800 (rounded) Expected Revenue of Queen Anne from whole milk: (63,701.7 x 114%) x $5.90 = $428,458 Expected Revenue of Queen Anne from Jersey milk: (58,240 x 114%) x $7.75 = $514,550 Total value of organic milk market: $478,800 / 35% = $1,368,000 Total value of whole milk market: $428,458 / 34.8% = $1,231,201 Total value of Jersey milk market: $514,550 / 36.4% = $1,413,600

8.3: Organic milk: -59.34%; Whole milk: -62.72%; Jersey milk: -56.88% Expected Revenue from organic milk: ($1,200,000 x 126.5%) x 35% = $531,300 Expected Revenue from whole milk: ($1,080,000 x 126.5%) x 34.8% = $475,438 Expected Revenue from Jersey milk: ($1,240,000 x 126.5%) x 36.4% = $570,940 New volume of organic milk: $531,300 / ($6.50 x 112%) = 72,981 liters New volume of whole milk: $475,438 / ($5.90 x 112%) = 71,949 liters New volume of Jersey milk: $570,640 / ($7.75 x 112%) = 65,742 liters

PLEASE GO ON TO THE NEXT PAGE 61

Full Cases % change in volume of organic milk: (72,981 - 179,487) / 179,487 x 100% = -59.34% % change in volume of whole milk: (71,949 - 193,036) / 193,036 x 100% = -62.72% % change in volume of Jersey milk: (65,742 - 152,461) / 152,461 x 100% = -56.88%

Hurdle 3

Case 9: Bungy Jump

9.1: $30.70 per Adult ticket; $14 per Child ticket Average monthly Revenue from Adults: ($30,000 + $28,500 + $29,300 + $26,000) / 12 = $9,483 Average monthly Revenue from Children: ($22,000 + $23,400 + $22,800 + $24,900) / 12 = $7,758 Ticket fee for Adult: $9,483 / (850 / 11 x 4) = $30.70 Ticket fee for Children: $7,758 / (850 / 11 x 7) = $14

9.2: Electricity: 23.66%; Maintenance: 15.17% Amount spent on Electricity per month: $9,483 x 0.37 = $3,509 Amount spent on Maintenance per month: $7,758 x 0.29 = $2,250 Total monthly Expense: ($9,483 + $7,758) x 0.86 = $14,827 Share of Electricity in Total monthly Expense: $3,509 / $14,827 x 100% = 23.66% Share of Maintenance in Total monthly Expense: $2,250 / $14,827 x 100% = 15.17%

9.3: It is not enough to obtain an annual profitability of 17% under current conditions. Total annual Revenue: ($30,000 + $28,500 + $29,300 + $26,000) + ($22,000 + $23,400 + $22,800 + $24,900) = $206,900

PLEASE GO ON TO THE NEXT PAGE 62

Full Cases Desired level of Profit: $206,900 x 17% = $35,173 Total annual Expense: $14,827 x 12 = $177,924 Real level of Profit: $206,900 - $177,924= $28,976

PLEASE GO ON TO THE NEXT PAGE 63

Full Cases Case 10: How to make use of Free Cash

10.1: Ranking from highest to lowest in terms of Return on Investment by dollar value: Stock - Real Estate - Bank - Bond We have assumed that Return on Investment is the dollar value average between the Best and Worst Scenarios. Thus, the RoI of each option is as follow: _ Bank: [(100 x 0.04) + (100 x 0.025)] / 2 = $3.25 million. (This option allows us to use 100% of the fund, which is $100 million) _ Bond: (100 x 0.6 x 0.1) / 2 = $3 million. (This option allows us to use a maximum of 60% of the fund) _Stock: [(100 x 0.25 x 0.8) + (-0.1 x 100 x 0.8)] / 2 = $6 million. (This option allows us 80% usage of the total fund) _Real Estate: [(100 x 0.2 x 0.5) + (-0.05 x 100 x 0.5)] / 2 = $3.75 million (This option allows us 50% usage of the total fund)

10.2: Ranking from highest to low in terms of Risk by dollar value: Stock - Real Estate Bond - Bank We know that Risk is the dollar value difference between the Best and Worst Scenarios. Thus, the Risk of each option is as follows: _Bank: (100 x 0.04) - (100 x 0.025) = $1.5 million _Bond: (100 x 0.6 x 0.1) - (100 x 0.6 x 0) = $6 million _Stock: (100 x 0.25 x 0.8) - (-0.1 x 100 x 0.8) = $28 million _Real Estate: (100 x 0.2 x 0.5) - (-0.05 x 100 x 0.5) = $12.5 million

10.3: Maximum percentage of fund used for Stocks would be 25%. Currently, with Real Estate the company loses (-0.05 x 100 x 0.5) = -$2.5 million in the Worst Scenario. The equation to calculate loss in Stocks in the Worst Scenario is (-0.1 x 100 x Y %),

PLEASE GO ON TO THE NEXT PAGE 64

Full Cases while Y% is the Maximum Usage of Fund percentage. In order for Lot of Cash Inc. not to lose more than $2.5 million in Stocks, Y % = -2.5 / -10 = 0.25 = 25%.

Case 11: The Laundromat

11.1: $1820 for dry cleaner, $1664 for washing machine. Total refund: $348.4 In 2011, there are 52 Sundays and 52 Fridays due to it being a leap year and the first day is a Saturday. Therefore Fred went to the Laundromat every Sunday and Friday of 2011. He spent (52 x $35) = $1820 on the dry cleaner and (52 x $32) = $1664 on the washing machine. He got ($1820 + $1664) x 10% = $348.4 as total refund.

11.2: Fred should not take the offer because: If he takes the offer, he would spend ($35 x 0.95 x 52) = $1729 on the dry cleaner and ($32 x 0.95 x 52) = $1580.8 on the washing machine. At the end of the year, he would get ($1729 + $1580.8) x 5% = $165.49 as total refund. Comparing the actual expense after refund Fred would spend on laundry in a year in both cases: ($1820 + $1664 - $348.4) = $3135.6 < ($1729 + $1580.8 - $165.49) = $3144.31

11.3: Save 63.74% on the dry cleaner and 68.54% on the washing machine. If he only goes one Sunday and one Friday per month, Fred has 4 kg of working clothes to dry clean and 12 kg of casual clothes to wash. He would spend 12 x $55 = $660 to dry clean and 12 x $45 = $540 on the washing machine in a year. This means that he would save ($1820 $660) / $1820 x 100 = 63.74% on dry cleaning and ($1664 - $540) / $1664 x 100 = 68.54% on washing.

PLEASE GO ON TO THE NEXT PAGE 65

Full Cases Case 12: Travel Agent

12.1: 6031 Adult tourists; 2585 Child tourists Quarterly Revenue from Domestic tours: $418,500 / 13.4% = $3,123,134 The total quantity of tourists from Domestic tours (X) can be represented in this equation: (X * 70% * $370) + (X * 30% * $345) = $3,123,134 ⇔ (25900 * X + 10350 * X) / 100 = 3,123,134 ⇔ 36250 * X = 312,313,400 ⇔

X = 8616 tourists

Quantity of adult tourists: 8616 x 70% = 6031 tourists Quantity of child tourists: 8616 x 30% = 2585 tourists

12.2: $3,765,223 on Adult tourists; $2,407,394 on Child tourists New price for an Adult on International tours: $855 x 114% = $ 974.70 New price for a Child on International tours: $820 x 114% = $934.80 Expected Revenue from International tours: $762,900 / 11% = $6,935,455 The total quantity of tourists from International tours (Y) can be represented in this equation: (Y * 60% x $974.70) + (Y * 40% x $934.80) = $6,935,455 ⇔ (58,482 * Y + 37,392 * Y) / 100 = 6,935,455 ⇔ 95,874 * Y = 693,545,500 ⇔ Y = 7234 tourists Allowed expenses for adult tourists on International tours: (7234 x 60% x $974.70) x 89% = $3,765,223 Allowed expenses for child tourists on International tours:

PLEASE GO ON TO THE NEXT PAGE 66

Full Cases (7234 x 40% x $934.80) x 89% = $2,407,394

Hurdle 4 Case 13: Cake Bakery

13.1: 25% Profit of Birthday Cake: ($25 x 18%) x 3,200 = $14,400 Profit of Wedding Cake: ($14,400 / 28%) x 25% = $12,857 Quantity of Wedding cakes sold: 3,200 x 2 / 5 = 1,280 units Profit per unit of Wedding cake: $12,857 / 1,280 = $10 Profitability of Wedding cakes: $10 / $40 x 100% = 25%

13.2: Birthday Cake: 47.9 %; Wedding Cake: 30.65%; Small Cake: 21.45% Revenue of Birthday Cake: $25 x 3,200 = $80,000 Revenue of Wedding Cake: $40 x 1,280 = $51,200 Quantity of Small Cake sold: 1,280 x 7 / 3 = 2,987 units Revenue of Small Cake: 2,987 x $12 = $35,844 Share in Revenue of Birthday Cakes: $80,000 / ($80,000 + $51,200 + $35,844) x 100% = 47.9% Share in Revenue of Wedding Cakes: $51,200 / ($80,000 + $51,200 + $35,844) x 100% = 30.65% Share in Revenue of Small Cakes: 100% - 47.9% - 30.65% = 21.45%

13.3: +30% in selling price Expected quantity of Small Cakes sold: 2,987 x 92% = 2,748

PLEASE GO ON TO THE NEXT PAGE 67

Full Cases Expected total profit: ($14,400 / 28%) x 1.2 = $61,714 Old profitability of Small Cakes: ($14,400 / 28% x 32%) / $35,844 x 100% = 46% Required revenue from Small Cakes: ($61,714 x 32%) / 46% = $42,931 New average price of Small Cakes: $42,931 / 2,748 = $15.60 % change in price of Small Cakes: ($15.60 - $12) / $12 x 100% = 30%

Case 14: Contract Factory

14.1: $50 million per VAS We know that for $800 million in Revenue from Manufacturing CF A receives $100 million from VAS. Thus for a $200 million contract it would receive an extra $25 million from VAS. We also know that the number of VAS per Manufacturing Contract is 0.5. Combine these two factors we can say CF A charges, on average, $50 million for one VAS.

14.2: $100 million per VAS Likewise for CF B, it makes $450 million in Revenue from VAS for every $900 million in Revenue from Manufacturing Contracts. Thus a $300 million Manufacturing contract will bring $150 million in Revenue from VAS. We also know that for CF B the number of VAS per Manufacturing Contract is 1.5. Thus, CF B charges $100 million per VAS. 14.3: 25% New dollar value for Other Sources’ Revenue will be $100 x 3 = $300 million, which boosts total Revenue up to $1.2 billion. Thus, its new market share is $300 / $ 1200 = 0.25 or 25%.

Case 15: Australian Burger King Chain

15.1: $190,151,520

PLEASE GO ON TO THE NEXT PAGE 68

Full Cases Annual wages expense on Cashiers: (300 x 8) x 30 x $8 x 52 = $29,952,000 Annual wages expense on Cooks: (300 x 12) x 49 x $7.70 x 52 = $70,630,560 Annual wages expense on Assistant Manager: (300 x 6) x 60 x $10.10 x 52 = $56,721,600 Annual wages expense on Shift Manager: (300 x 4) x 56 x $9.40 x 52 = $32,847,360 Total annual wages expense of Australian Burger King Chain: $29,952,000 + $70,630,560 + $56,721,600 + $32,847,360 = $190,151,520

15.2: +3.89% This year’s Sales of Australian Burger King Chain: $190,151,520/ 35% = $543,290,057 Next year’s new wages expense on Cooks: (300 x 12) x 49 x $8.20 x 52 = $75,216,960 Next year’s new wages expense on Assistant managers: (300 x 6) x 60 x $10.60 x 52 = $59,529,600 Next year’s new total wages expense of Australian Burger King Chain: $29,952,000 + $75,216,960 + $59,529,600 + $32,847,360 = $197,545,920 Next year’s Expected Sales of Australian Burger King Chain: $197,545,920 / 35% = $564,416,914 Corresponding % change in Sales of Australian Burger King Chain from this year to the next year: ($564,416,914 - $543,290,057) / $543,290,057 x 100% = +3.89%

15.3: 406 cooks New wages expense on Cashiers: (320 x 8) x 30 x $8 x 52 = $31,948,800 New wages expense on Assistant Managers: (320 x 6) x 60 x $10.10 x 52 = $60,503,040 New wages expense on Shift Managers: (320 x 4) x 56 x $9.40 x 52 = $35,037,184 Remaining wages for Cooks: 190,151,520 - 31,948,800 - 60,503,040 - 35,037,184 = $62,662,496

PLEASE GO ON TO THE NEXT PAGE 69

Full Cases Number of Cooks that can be paid with this amount of wages: $62,662,496 / $7.70 / 49 / 52 = 3,194 Number of Cooks that will have to be cut down on: (300 x 12) - 3,194 = 406

Case 16: Vehicle Dealer

16.1: New Vehicles: Revenue is $365,151,515; Selling price is $24,263 Used Vehicles: Revenue is $353,571,429; Selling price is $9,208 Sales of New Vehicles: $60,250,000 / 16.5% = $365,151,515 Average selling price per New Vehicles: $365,151,515 / 15,050 = $24,263 Sales of Used Vehicles: $39,600,000 / 11.2% = $353,571,429 Average selling price per Used Vehicles: $353,571,429 / 38,400 = $9,208

16.2: 14.07% Desired level of Net Profit: $39,600,000 x 118% = $46,728,000 New selling price: ($46,728,000 / 11.2%) / 39,720 = $10,504 % change in selling price to achieve the desired level of profit: ($10,504 - $9,208) / $9,208 x 100% = 14.07%

16.3: -25.93% Old amount of Expenses for New Vehicles division: $365,151,515 - $60,250,000 = $304,901,515 New amount of sales for New Vehicles: (15,050 x 108.5%) x ($24,263 / 1.5) = $264,131,062 New amount of Expenses for New Vehicles division: $264,131,062 x 85.5% = $225,832,058

PLEASE GO ON TO THE NEXT PAGE 70

Full Cases % change in Expenses for New Vehicles division: ($225,832,058 - $304,901,515) / $304,901,515 x 100% = -25.93%

Hurdle 5 Case 17: Software Shop

17.1: Month 1 - Month 3 - Month 2 Profitability of month 1: ($15,000 - $8,200) / $15,000 x 100% = 45.3% Profitability of month 2: ($16,500 - $10,400) / $16,500 x 100% = 36.96% Profitability of month 3: ($14,800 - $9,300) / $14,800 x 100% = 37.16%

17.2: -4.72% Average monthly revenue of this quarter: ($15,000 + $16,500 + $14,800) / 3 = $15,433 Average monthly expense of this quarter: ($8,200 + $10,400 + $9,300) / 3 = $9,300 Expected average monthly expense of next quarter: $9,300 / 1.15 = $8,087 Required level of average monthly Revenue of next quarter: $8,087 / 55% = $14,704 % change in average quarterly Revenue: ($14,704 - $15,433) / $15,433 x 100% = -4.72%

17.3: $51,855; 46.46% Average annual expense on Rental fee of the shop: ($15,433 x 12) x $0.28 = $51,855 Share of Rental fee in the Average annual expense of the shop: $51,855 / ($9,300 x 12) x 100% = 46.46%

Case 18: Airline Seating Options

PLEASE GO ON TO THE NEXT PAGE 71

Full Cases

18.1: 76% Currently 150 economy seats are filled, so the maximum number of business seats that can be filled to replace the space left is (200 – 150) / 1.5 = 33 seats. The number of business seats that should be filled in so that the Revenue stays the same (a) can be presented in this equation as: 50 * 100 = a * 200

a = 25 (seats), which is 76% of 33

18.2: 177 seats Since First Class seats obviously bring in much more revenue, the airline should put 4 First Class seats on every flight. Business seats also bring in more revenue so the airline should take full advantage of this and put 10 Business seats on every flight as well. The remaining seats will be Economy seats. The remaining number of Economy seats is 200 - (4 x 2) - (10 x 1.5) = 177 seats

18.3: $21,700 Demand for First Class seats is 4, which leaves 6 vacant First Class seats. These seats can be split back into 12 Economy seats to generate more revenue. Likewise, there will be 10 vacant Business seats. However, these will be more difficult to split since 1 Business seat = 1.5 Economy seat. Nevertheless, with the stated assumption, there should be an extra 15 Economy seats ready to be used. The original number of Economy seats would be 200 - (10 x 2) - (20 x 1.5) = 150 seats. Afterwards, with a total of 27 extra economy seats, there will be 177 Economy seats, along with 4 First Class seats and 10 Business seats. Revenue = (4 x 500) + (10 x 200) + (177 x 100) = $21,700.

Case 19: Plumbers

19.1: 2.47% for Downtown Installation; 12.11% for Suburb Maintenance; 6.8% for Commercial Repair

PLEASE GO ON TO THE NEXT PAGE 72

Full Cases Since Domestic / Commercial and Downtown / Suburb are dependent groups, the total number of Downtown + Suburb cases must equal the number of Domestic + Commercial cases. Number of Downtown Installation cases:

14 + 15 - 9 = 20 cases

Number of Suburb Maintenance cases:

160 + 240 - 302 = 98 cases

Number of Commercial Repair cases:

220 + 160 - 325 = 55 cases

Percentage of Downtown Installation cases:

20 / (29 + 400 + 380) x 100% = 2.47%

Percentage of Suburb Maintenance cases: 12.11%

98 / (29 + 400 + 380) x 100% =

Percentage of Commercial Repair cases:

55 / (29 + 400 + 380) x 100% = 6.8%

19.2: +19.04% Expected number of Downtown Repair cases: 325 + (380 x 25%) = 420 cases Previous number of monthly Downtown cases:

325 + 14 + 160 = 499 cases

Expected number of monthly Downtown cases:

420 + 14 + 160 = 594 cases

% change in number of monthly Downtown cases: (594 - 499) / 499 x 100% = 19.04%

19.3: 48.4% for Maintenance cases; 39.2% for Suburb cases Expected number of Suburb Maintenance cases: 98 - (55 x 30%) = 81.5 cases New share of Maintenance cases: (302 + 81.5) / (29 + 400 + 380 - 55 x 30%) x 100% = 48.4% New share of Suburb cases: (9 + 81.5 + 220) / (29 + 400 + 380 - 55 x 30%) x 100% = 39.2%

Case 20: Ship Building Company

20.1: Shipwrights on ship A earn 18.46% more than those on ship B

PLEASE GO ON TO THE NEXT PAGE 73

Full Cases Wages per shipwright on ship A: ($3,250,000 x 35%) / 310 = $3,670 Wages per shipwright on ship B: ($2,530,000 x 30%) / 245 = $3,098 Shipwrights on ship A earn more than those on ship B by: ($3,670 - $3,098) / $3,098 x 100% = 18.46%

20.2: 0.45 for ship A; 0.30 for ship B Expected total payment for ship A: ($3,670 x 310) x $5.20 = $5,916,040 Gross Profit Margin of ship A: ($5,916,040 - $3,250,000) / $5,916,040 x 100% = 0.45 Expected total payment for ship B: ($3,098 x 245) x $4.75 = $3,605,300 (rounded) Gross Profit Margin of ship B: ($3,605,300 - $2,530,000) / $3,605,300 x 100% = 0.298 or 0.30

20.3: Ship A is more profitable and less efficient in its usage of the workforce Agreed purchase price of ship A: $7,800 x 600 = $4,680,000 Profitability of ship A: ($4,680,000 - $3,250,000) / $4,680,000 x 100% = 30.56% Ratio between shipwrights’ wages and Profit: ($3,670 x 310) : ($4,680,000 - $3,250,000) = 0.8 : 1 Agreed purchase price of ship B: $7,800 x 450 = $3,510,000 Profitability of ship B: ($3,510,000 - $2,530,000) / $3,510,000 x 100% = 27.92% Ratio between shipwrights’ wages and Profit: ($3,098 x 245) : ($3,510,000 - $2,530,000) = 0.775 : 1

Hurdle 6 Case 21: Stuffed Toys Retailer

21.1: Teddy Bear: $655,000; Donald Duck: $552,000; Lion King: $568,500

PLEASE GO ON TO THE NEXT PAGE 74

Full Cases Fixed Cost of Teddy Bear: ($25.50 x 50,000) - ($12 x 50,000) - FC = $20,000 ⇔ FC = ($25.50 x 50,000) - ($12 x 50,000) - $20,000 = $655,000 Fixed Cost of Donald Duck: ($19.90 x 50,000) - ($8.50 x 50,000) - FC = $18,000 ⇔ FC = ($19.90 x 50,000) - ($8.50 x 50,000) - $18,000 = $552,000 Fixed Cost of Lion King: ($22 x 50,000) - ($10.20 x 50,000) - FC = $21,500 ⇔ FC = ($22 x 50,000) - ($10.20 x 50,000) - $21,500 = $568,500

21.2: +23.38% Old break-even level of Unit Sales of Teddy Bear: $655,000 / ($25.50 - $12) = 48,519 Old break-even level of Dollar Sales of Teddy Bear: 48,519 x $25.50 = $1,237,235 New Fixed Cost of Teddy Bear: $655,000 x 85% = $556,750 New Variable Cost of Teddy Bear: $12 x 1.35 = $16.20 New break-even level of Unit Sales of Teddy Bear: $556,750 / ($25.50 - $16.20) = 59,866 New break-even level of Dollar Sales of Teddy Bear: 59,866 x $25.50 = $1,526,583 % change in break-even level of Dollar Sales of Teddy Bear: ($1,526,583 - $1,237,235) / $1,237,235 x 100% = 23.38%

21.3: +6.36% Cost of Production for Lion King at Unit Sales of 75,000: ($10.20 x 75,000) + $568,500 = $1,333,500 Required level of Sales to obtain desired profitability: $1,333,500 / 76% = $1,754,605

PLEASE GO ON TO THE NEXT PAGE 75

Full Cases Required selling price to obtain desired level of Sales: $1,754,605 / 75,000 = $23.40 % change in selling price to obtain desired profitability at Unit Sales of 75,000: ($23.40 - $22) / $22 x 100% = 6.36%

Case 22: Cost Management of a Gas Station

22.1: $2,243,400 Average monthly Cost of Operation for the gas station: ($159,000 + $8,550 + $23,560 + $131,100 + $8,420 + $21,280 + $176,700 + $8,680 + $23,560) / 3 = $186,950 Average annual Cost of Operation for the gas station: $186,950 x 12 = $2,243,400

22.2: Increase by 11.8% The estimation indicates that the gas station should be able to achieve a Gross Profit Margin of 0.44 on any given month with the Sales level of March. However, the average cost is just an indicator of what Sales should at least be in order to achieve the GPM of 0.44 because the cost of production rises and falls according to the Gas price / Electricity bill and the quantity of Gas sold by the station. This is good for reference purposes, but its reliability is fairly low and the gas station should not take it as a figure to aim for. Sales of the gas station in March: ($176,700 + $8,680 + $23,560) / 0.7 = $298,486 We will use the average cost of operation to work out the required level of Sales in order to achieve a Gross Profit Margin of 0.44 because we are looking for the minimum level of Sales that the gas station would need to obtain. Minimum level of Sales to obtain the desired Gross Profit Margin: $186,950 / 0.56 = $333,839 Sales in April should increase by: ($333,839 - $298,486) / $298,486 x 100% = 11.8% 22.3: 65,000 gallons per month The gas station will break even when:

PLEASE GO ON TO THE NEXT PAGE 76

Full Cases ($3.80 x Unit Sales) - Cost of Operation - $60,000 = 0 Again, we will use the average monthly Cost of Operation to tackle this question as it is the easiest approach. We have: ($3.80 x Unit Sales) - $186,950 - $60,000 = 0 ⇔ $3.80 x Unit Sales = $246,950 ⇔ Unit Sales = $246,950 / $3.80 ⇔ Unit Sales ≈ 65,000 gallons per month

Case 23: Cable TV and Internet Services

23.1: Cable TV market share: 39.4%; Household Internet market share: 43.1% Total Income of the Cable TV market: $230,400,000 + $144,360,000 + $130,152,000 + $79,788,000 = $584,700,000 SCTV’s market share, by Income, in the Cable TV market: $230,400,000 / $584,700,000 x 100% = 39.4%

Total Income of the Household Internet market: $110,942,400 + $57,744,000 + $62,832,000 + $25,779,600 = $257,298,000 SCTV’s market share, by Income, in the Household Internet market: $110,942,400 / $257,298,000 x 100% = 43.1%

23.2: The number of Cable TV subscribers of SCTV this year and last year: 3,200,000 and 3,128,055 The number of Cable TV subscribers of HTVC this year and last year: 2,406,000 and 2,117,958

PLEASE GO ON TO THE NEXT PAGE 77

Full Cases

Cable TV: SCTV’s number of subscribers this year: $230,400,000 / 12 / $6 = 3,200,000 SCTV’s number of subscribers last year: ($230,400,000 / 102.3%) / 12 / $6 = 3,128,055

HTVC’s number of subscribers this year: $144,360,000 / 12 / $5 = 2,406,000 HTVC’s number of subscribers last year: ($144,360,000 / 113.6%) / 12 / $5 = 2,117,958

Household Internet: SCTV’s number of subscribers this year: $110,942,400 / 12 / $2.90 = 3,188,000 SCTV’s number of subscribers last year: ($110,942,400 / 102.3%) / 12 / $2.90 = 3,116,325

HTVC’s number of subscribers this year: $57,744,000 / 12 / $2.5 = 1,924,800 HTVC’s number of subscribers last year: ($57,744,000 / 113.6%) / 12 / $2.5 = 1,694,366

23.3: 8.33% lower in Cable TV fee and 6.9% lower in Household Internet fee Next year’s expected Income from Cable TV of SCTV: $230,400,000 x 107% = $246,528,000 Next year’s expected number of subscribers: 3,200,000 x 116% = 3,712,000 Intended Cable TV fee of SCTV next year: $246,528,000 / 12 / 3,712,000 = $5.50 Required % change in Cable TV fee: $0.5 / $6 x 100% = 8.33%

PLEASE GO ON TO THE NEXT PAGE 78

Full Cases Next year’s expected Income from Household Internet of SCTV: $110,942,400 x 107% = $118,708,368 Next year’s expected number of subscribers: 3,188,000 x 116% = 3,698,080 Intended Household Internet fee of SCTV next year: $118,708,368 / 12 / 3,698,080 = $2.70 Required % change in Household Internet fee: $0.2 / $2.90 x 100% = 6.9%

Case 24: Bus Service Provider

24.1: Child fare: 23.14%; Adult Fare: 66.07%; Senior Fare: 10.79% Total Revenue of the bus company: ($90 x 14,000) + ($135 x 26,700) + ($70 x 8,300) = $5,445,500 Share of the Monthly Child fare: ($90 x 14,000) / $5,445,500 x 100% = 23.14% Share of the Monthly Adult fare: ($135 x 26,700) / $5,455,500 x 100% = 66.07% Share of the Monthly Senior fare: ($70 x 8,300) / $5,455,500 x 100% = 10.79%

24.2: Net Profit: $1,573,145; Profitability: 28.89% Gas expense of the company last month: $5,445,500 x 0.32 = $1,742,560 Total expense of the company last month: $1,742,560 / 45% = $3,872,355 Net Profit of the company last month: $5,445,500 - $3,872,355= $1,573,145 Profitability of the company last month: $1,573,145 / $5,445,500 x 100% = 28.89%

24.3: Net Profit: +50.4%; Profitability: 42.3%

Total expense of the company this month: $3,872,355 / 1.2 = $3,226,962

PLEASE GO ON TO THE NEXT PAGE 79

Full Cases Total Revenue of the company this month: ($90 x 14,000 x 115%) + ($135 x 26,700) + ($65 x 8,300) = $5,593,000 Net Profit of the company this month: $5,593,000 - $3,226, 962 = $2,366,038 % change in Net Profit of the company: ($2,366,038 - $1,573,145) / $1,573,145 x 100% = 50.4% Profitability of the company this month: $2,366,038 / $5,593,000 x 100% = 42.3%

Hurdle 7

Case 25: Casio Calculators Retailer

25.1: FX 970G: $86; FX 950ii: $98.20 Total Revenue from the three brands: ($89 x 153,800) / 32% = $42,775,625 Selling price of FX 970G calculators: ($42,775,625 x 30.3%) / 150,700 = $86 Selling price of FX 950ii calculators: ($42,775,625 x 37.7%) / 164,200 = $98.20

25.2: Gross Profit Margin: 0.628; Net Profitability: 20.93% Gross Profit per FX 970G calculator: $86 - $32 = $54. Gross Profit Margin of FX 970G brand: ($86 - $32) / $86 = 0.628 Net Profitability of FX 970G brand: $18 / $86 x 100% = 20.93%

25.3: $0.51 COGS per FX 900ES calculator: $4,351,300 / 153,800 = $28.29 Gross Profit per FX 900ES calculator: $89 - $26.50 = $62.50 Total expense spent per FX 900 ES calculator: $62.50 x 72% = $45

PLEASE GO ON TO THE NEXT PAGE 80

Full Cases Amount of expense spent per FX 900ES for every dollar of Sales: $45 / $89 = $0.51

Case 26: Cosmetics Retailer

26.1: Avon: Sales growth from Jan-Apr to May-Aug: (4,300 - 4,850) / 4,850 x 100% = -11.34% Sales growth from May-Aug to Nov-Dec: (4,680 - 4,300) / 4,300 x 100% = 8.84% Shiseido: Sales growth from Jan-Apr to May-Aug: (4,950 - 4,820) / 4,820 x 100% = 2.7% Sales growth from May-Aug to Nov-Dec: (4,760 - 4,950) / 4,950 x 100% = -3.8% L’Oreal: Sales growth from Jan-Apr to May-Aug: (4,150 - 3,770) / 3,770 x 100% = 10.1% Sales growth from May-Aug to Nov-Dec: (4,540 - 4,150) / 4,150 x 100% = 9.4% Overall: Sales growth from Jan-Apr to May-Aug: (13,400 - 13,440) / 13,440 x 100% = -0.3% Sales growth from May-Aug to Nov-Dec: (13,980 - 13,400) / 13,400 x 100% = 4.3%

26.2: Avon: $21.86; Shiseido: $26.40; L’OReal: $31.64 Total value of Sales from Avon’s products: $1,080,000 x 28% = $302,400 Average selling price of Avon’s products: $302,400 / (4,850 + 4,300 + 4,680) = $21.86 Total value of Sales from Shiseido’s products: $1,080,000 x 35.5% = $383,400 Average selling price of Shiseido’s products: $383,400 / (4,820 + 4,950 + 4,760) = $26.40 Total value of Sales from L’Oreal’s products: $1,080,000 x 36.5% = $394,200

PLEASE GO ON TO THE NEXT PAGE 81

Full Cases Average selling price of L’Oreal’s products: $394,200 / (3,770 + 4,150 + 4,540) = $31.64

26.3: +50.85% Expected Sales of Thorakao in the next period: $1,080,000 x 40% = $432,000 Expected Sales from Avon’s products: (4,850 x 88%) x ($21.86 + $5) = $114,640 (rounded) Expected Sales from Shiseido’s products: (4,820 x $26.40) x 108% = $137,430 (rounded) Required Sales from L’Oreal’s products: $432,000 - ($114,640 + $137,430) = $179,930 Required Unit Sales of L’Oreal’s products: $179,930 / $31.64 = 5,687 units % change in Unit Sales of L’OReal’s products compared to last year’s same period: (5,687 -3,770) / 3,770 x 100% = 50.85%

Case 27: Hoa Vien Restaurant

27.1: Medium Yellow: 265.38%; Medium Black: 309.09%; Large Yellow: 200%; Large Black: 238.46% Mark-up percentage for Medium Yellow: $4.75 / (0.8 + 0.5) x 100 – 100% = 265.38% Mark-up percentage for Medium Black: $4.5 / (0.6 + 0.5) x 100 – 100% = 309.09% Mark-up percentage for Large Yellow: $6 / (1.5 + 0.5) x 100 – 100% = 200% Mark-up percentage for Large Black: $5.5 / (1.125 + 0.5) x 100 – 100% = 238.46%

27.2: Yellow: 80 small glasses; 99 medium glasses; 118 large glasses Black: 65 small glasses; 75 medium glasses; 85 large glasses Profit: 1630.25

PLEASE GO ON TO THE NEXT PAGE 82

Full Cases You can solve for results using three simultaneous equations as below: For Yellow beer: 0.5S + 0.8M + 1.5L = 297 3S + 4.75M - 6L = 0 S - 2M + L = 0

For Black beer: 0.5S + 0.8M + 1.5L = 220 2S + 4.5M - 5.5L = 0 S - 2M + L = 0

Revenue: (80 x 3) + (99 x 4.75) + (118 x 6) + (65 x 2) + (75 x 4.5) + (85 x 5.5) = $2353.25 Cost: (112.5 + 148.5) + 297 + (220 x $0.75) = $723 Profit = Revenue - Cost = $1630.25

27.3: 3.6% Total broken glasses: 5 small, 6 medium and 3 large The biggest percentage that profit can increase by is when all glasses broken are New revenue: (80 x 3) + (99 x 4.75) + (118 x 6) + (60 x 2) + (69 x 4.5) + (82 x 5.5) + (14 x 8) = $2 411.75 New profit = New revenue - Cost = $1688.75 Biggest possible percentage: ($1688.75 - $1630.25) / 1630.25 x 100 = 3.6%

Case 28: Light bulbs producer

28.1: $1.98 per unit

PLEASE GO ON TO THE NEXT PAGE 83

Full Cases Break-even Unit Sales of Type 1: $720,000 / $25 = 28,800 Equation to find Variable Cost of Type 1: (28,800 x $25) - (28,800 x VC) - $150,000 = 0 ⇔ $720,000 - $150,000 = 28,800 x VC ⇔ VC = $570,000 / 28,800 = $19.8

28.2: $8.50 per unit Sales of Type 2 light bulb at given Unit Sales: 10,000 x $20 = $200,000 Equation to find Variable Cost of Type 2: $200,000 - (10,000 x VC) - $120,000 = -$5,000 ⇔ $200,000 - $120,000 + $5,000 = 10,000 x VC ⇔ VC = $85,000 / 10,000 = $8.50

28.3: +5.4% Current Variable Cost of Type 3: ($18 x 18,000) - (18,000 x VC) - $115,000 = $50,000 ⇔ $324,000 - $115,000 - $50,000 = 18,000 x VC ⇔ VC = $159,000 / 18,000 = $8.83 New Variable Cost of Type 3: $8.83 x 105% = $9.30 Old break-even level of Unit Sales of Type 3: $115,000 / ($18 - $8.83) = 12,541 New break-even level of Unit Sales of Type 3: $115,000 / ($18 - $9.30) = 13,218 % change in break-even level of Unit Sales of Type 3: (13,218 - 12,541) / 12,541 x 100% = +5.4%

PLEASE GO ON TO THE NEXT PAGE 84

Full Cases

Hurdle 8

Case 29: Basketball shoes

29.1: 170 pairs of domestic shoes, 102 pairs of oversea shoes. Break even unit = Fixed Cost / (Selling Price - Variable Cost) Domestic shoes: $850 / [25 – 25 x (60% + 20%)] = 170 Foreign shoes: $900 / [32 – 32 x (50% + 50% x 15% + 15%] = 102

29.2: Foreign shoes generate $844.4 more in profit than Domestic shoes Domestic shoes profit: [(196 x $25) x 20%] - $850 = $130 Foreign shoes profit: [(213 x $32) x 27.5%] - $900 = $974.4

29.3: Break-even Revenue: $2,944 New cost per pair of Foreign shoes = $32 x 50% + $32 x 50% x 9% + $32 x 15% = $22.24 New break-even unit: $900 / ($32 - $22.24) = 92 pairs Break-even Revenue: 92 pairs x $32 = $2,944

Case 30: Cereal Manufacturer

30.1: Honey Bee:

43,200 boxes to break even; Profit: $36,250; Profitability: 7.6%

Choco Chimp: 43,549 boxes to break even; Profit: $53,640; Profitability: 11% Fruit Frenzy:

43,200 boxes to break even; Profit: $68,750; Profitability: 13.7%

PLEASE GO ON TO THE NEXT PAGE 85

Full Cases

30.2: Second quarter’s Profit of Honey Bee: - $57,000 (Loss); of Choco Chimp: - $37,523 (Loss) and Fruit Frenzy: - $20,600 (Loss) Expected Sales of each brand in the Second Quarter are as follows: Honey Bee : $477,750 x 112% = $535,080 Choco Chimp: $490,680 x 112% = $549,562 Fruit Frenzy : $501,350 x 112% = $561,512

Expected quantity sold of each brand in the Second Quarter are as follows: Honey Bee : $535,080 / 9.75 = 54,880 Choco Chimp: $549,562 / 9.40 = 58,464 Fruit Frenzy : $561,512 / 9.25 = 60,704

Expected Profit of each brand in the Second Quarter are as follows: Honey Bee: $535,080 – ($270,000 + $130,000 + $3.5 x 54,880) = - $57,000 (Loss) Choco Chimp: $549,562 – ($270,000 + $130,000 + $3.2 x 58,464) = - $37,523 (Loss) Fruit Frenzy: $561,512 – ($270,000 + $130,000 + $3 x 60,704) = - $20,600 (Loss)

This would be a bad decision because Chopper Cereal would have to suffer losses across all three brands. The reason for this is that the increase in Fixed Cost exceeds the increase in Sales that the directors expected, leading to a Loss and as a result, negative Profitability.

30.3: New Profitability of Honey Bee: 11.5%; of Choco Chimp: 14.8% and Fruit Frenzy: 17.9% New Selling Price per unit of each brand in the Second Quarter are as follows:

PLEASE GO ON TO THE NEXT PAGE 86

Full Cases Honey Bee: $9.75 x 0.85 = $8.30 Choco Chimp: $9.40 x 0.85 = $7.99 Fruit Frenzy: $9.25 x 0.85 = $7.90

Expected Sales of each brand in the Second Quarter are as follows: Honey Bee: $477,750 x 1.22 = $582,855 Choco Chimp: $490,680 x 1.22 = $598,630 Fruit Frenzy: $501,350 x 1.22 = $611,647

Expected Profit of each brand in the Second Quarter are as follows: Honey Bee: ($70,224 - $56,250) x ($8.30 - $3.50) = $67,075 Choco Chimp: ($74,922 - $56,367) x ($7.99 - $3.20) = $88,879 Fruit Frenzy: ($77,424 - $55,102) x ($7.9 - $3) = $109,378

New Profitability of each brand as a result of price drop: Honey Bee: ($67,075 / $582,855) x 100% = 11.5% Choco Chimp: ($88,879 / $598,630) x 100% = 14.8% Fruit Frenzy: ($109,378 / $611,647) x 100% = 17.9%

The price drop proved to be more effective than the advertising campaign, at least on paper. It did not require extra spending and thus would not hold back the improvement on Sales and Profitability. However, if the expectation on Sales increase was wrong, Chopper might experience a significant drop in Profitability as well, but not as much as they would if the advertising campaign were to happen.

Case 31: Fertilizer Manufacturer

PLEASE GO ON TO THE NEXT PAGE 87

Full Cases

31.1: Selling price of Type A is $59.90 and B is $44.90 0.19 cents for Type A and 0.16 cents for Type B

Selling price of Type A: $13,597,300 / 227,000 = $59.90 Proportion of sales that goes to profit of Type A: $2,584,000 / $13,597,300 = 0.19 cents for every dollar of Sales Selling price of Type B: $12,033,200 / 268,000 = $44.90 Proportion of sales that goes to profit of Type B: $1,925,312 / $12,033,200 = 0.16 cents for every dollar of Sales

31.2: $5,463,150 for Type A and $4,876,528 for Type B

Cost of producing one unit of Type A fertilizer: $59.90 / 245% = $24.45 Gross Profit of Type A fertilizer: $13,597,300 - ($24.45 x 227,000) = $8,047,150 Amount of expense spent on Type A fertilizer: $8,047,150 - $2,584,000 = $5,463,150

Cost of producing one unit of Type B fertilizer: $44.90 / 230% = $19.52 Gross Profit of Type B fertilizer: $12,033,200 - ($19.52 x 268,000) = $6,801,840 Amount of expense spent on Type B fertilizer: $6,801,840 - $1,925,312 = $4,876,528

31.3: +9.36% for Type A; +8.9% for Type B New cost of production per unit of Type A fertilizer: $24.45 x 116% = $28.36 Intended selling price of Type A fertilizer: $28.36 + ($28.36 x 155%) = $72.30

PLEASE GO ON TO THE NEXT PAGE 88

Full Cases Required quantity sold to obtain desired Revenue: ($13,597,300 x 132%) / $72.30 = 248,250 units % change in quantity sold to correspond with the given conditions: (248,250 - 227,000) / 227,000 x 100% = 9.36%

New cost of production per unit of Type B fertilizer: $19.52 x 116% = $22.64 Intended selling price of Type B fertilizer: $22.64 + ($22.64 x 140%) = $54.40 Required quantity sold to obtain desired Revenue: ($12,033,200 x 132%) / $54.40 = 291,982 units % change in quantity sold to correspond with the given conditions: (291,982 - 268,000) / 268,000 x 100% = 8.9%

Case 32: Carpet Factory

32.1: $1,915,292.70 Revenue from Persian carpets: (12,760 x 28.5%) x $189.50 = $689,135.70 Revenue from Arabian carpets: (12,760 x 29.2%) x $154.50 = $575,655 Revenue from Indian carpets:

(12,760 x 30.3%) x $168.25 = $650,502

Total Revenue from all three models: $689,135.70 + $575,655 + $650,502 = $1,915,292.70

32.2: Persian carpet: $37.90; Arabian carpet: $27.86; Indian carpet: $25.14 Fixed Cost of Production for Persian carpets: $689,135.70 x 55% = $379,025 Break-even point for Persian carpets: (2,500 x $189.50) - (2,500 x Variable Cost) - $379,025 = 0 ⇔ 2,500 x ($189.50 - Variable Cost) = $379,025 ⇔ Variable Cost = $189.50 - ($379,025 / 2,500)

PLEASE GO ON TO THE NEXT PAGE 89

Full Cases ⇔ Variable Cost = $37.90 Fixed Cost of Production for Arabian carpets: $575,655 x 55% = $316,610 Break-even point for Arabian carpets: (2,500 x $154.50) - (2,500 - Variable Cost) - $316,610 ⇔ 2,500 x ($154.50 - Variable Cost) = $316,610 ⇔ Variable Cost = $154.50 ($316,610 / 2,500) ⇔ Variable Cost = $27.86 Fixed Cost of Production for Indian carpets: $650,502 x 55% = $357,776 Break-even point for Indian carpets: (2,500 x $168.25) - (2,500 x Variable Cost) - $357,776 = 0 ⇔ 2,500 x ($168.25 - Variable Cost) = $357,776 ⇔ Variable Cost = $168.25 - ($357,776 / 2,500) ⇔ Variable Cost = $25.14

32.3: Persian carpets: 61.2%; Arabian carpets: 71.85%; Indian carpets: 71.5% Desired level of Profit from Persian carpets: ($893,200 x 30.5%) x 112% = $305,117 This level of profit is achieved when: (2,500 x selling price) - (2,500 x $37.90) - ($379,025 x 96%) = $305,117 ⇔ 2,500 x (Selling price - $37.90) = $305,117 + $363,864 ⇔ Selling price = ($668,981 / 2,500) + $37.90 = $305.50 Required % change in selling price: ($305.50 - $189.50) / $189.50 x 100% = 61.2% Desired level of Profit from Arabian carpets: ($893,200 x 29%) x 112% = $290,111 This level of profit is achieved when: (2,500 x selling price) - (2,500 x $27.86) - ($316,610 x 96%) = $290,111

PLEASE GO ON TO THE NEXT PAGE 90

Full Cases ⇔ 2,500 x (selling price - $27.86) = $290,111 + $303,946 ⇔ Selling price = ($594,057 / 2,500) + $27.86 = $265.50 Required % change in selling price: ($265.50 - $154.50) / $154.50 x 100% = 71.85% Desired level of Profit from Indian carpets: ($893,200 x 31.5%) x 112% = $315,121 This level of Profit is achieved when: (2,500 x selling price) - (2,500 x $25.14) - ($357,776 x 96%) = $315,121 ⇔ 2,500 x (selling price - $25.14) = $315,121 + $343,465 ⇔ Selling price = ($658,586 / 2,500) + $25.14 = $288.57 Required % change in selling price: ($288.57 - $168.25) / $168.25 x 100% = 71.5%

Hurdle 9

Case 33: Cooking Oil Retailer 33.1: Fixed Cost: $1,280,000; Olive oil’s Profit: $1,056,074; Peanut oil’s Profit: $759,774 Fixed cost of production for the three oils = Revenue – (Variable Cost x Quantity) - Profit ⇔ Fixed Cost = (200,000 x $19.90) – (200,000 x $7.75) - $1,150,000 = $1,280,000 Quantity produced & supplied of Olive oil: 200,000 / 35% x 28.2% = 161,143 units Profit / Loss of Olive oil: (161,143 x $24.50) – (161,143 x $10) - $1,280,000 = $1,056,074 Quantity produced & supplied of Peanut oil: 200,000 / 35% x 36.8% = 210,286 units Profit / Loss of Peanut oil: (210,286 x $15) – (210,286 x $5.30) - $1,280,000 = $759,774

33.2: -15.64% in Profit; New Profitability 21.94% Current quantity produced & supplied of Olive oil: (200,000 + 161,143 + 210,286) x 29% = 165,714 units

PLEASE GO ON TO THE NEXT PAGE 91

Full Cases New Profit of Olive oil: (165,714 x $24.50) – (165,714 x $11.40) - $1,280,000 = $890,853 % change in profit of Olive oil: ($890,853 - $1,056,074) / $1,056,074 x 100% = -15.64% New Profitability: $890,853 / (165,714 x $24.50) x 100% = 21.94%

33.3: +5.33% Old Profitability of Peanut oil: $759,774 / (210,286 x $15) x 100% = 24.1% Desired level of profitability: 25.3% New quantity produced & supplied of Peanut oil: (200,000 + 161,143 + 210,286) x 34.5% = 197,143 units Total cost of production at this level of supply: (197,143 x $5.30) + $1,280,000 = $2,324,858 Required level of Sales / Revenue to achieve desired level of profitability: $2,324,858 / 74.7% = $3,112,260 Required price level to obtain the Revenue above: $3,112,260 / 197,143 = $15.80 % change in price level: ($15.80 - $15) / $15 x 100% = 5.33%

Case 34: Eggs Retailer

34.1: Duck eggs: 0.6 : 1; Quail eggs 0.71 : 1 Total profit of three kinds of eggs: ($118,800 x 0.22) / 38.5% = $67,886 Expense on duck eggs: $47,025 - ($67,866 x 27.5%) = $28,356 Expense / Revenue ratio of duck eggs: $28,356 / $47,025 = 0.6 / 1 Expense on quail eggs: $80,080 - ($67,886 x 34%) = $56,999 Expense / Revenue ratio of quail eggs: $56,999 / $80,080 = 0.71 / 1

PLEASE GO ON TO THE NEXT PAGE 92

Full Cases 34.2: $0.21 Selling price of quail eggs: $80,080 / 9,100 = $8.80 / dozen = $0.73 / egg Profitability of quail eggs is 29% because its Expense / Revenue ratio is 0.71 / 1 Thus, the dollar profit gained on each quail egg sold would be: $0.73 x 29% = $0.21

34.3: Profit: +45%; Share in total Profit: 39.87% New selling price of a dozen duck eggs: ($47,025 / 8,250) x 110% = $6.27 New expense on duck eggs: $28,362 / 1.15 = $24,663 New profit from duck eggs: ($6.27 x 8,250) - $24,663 = $27,065 Old profit from duck eggs: $47,025 - $28,362 = $18,663 % change in profit of duck eggs: ($27,065 - $18,663) / $18,663 x 100% = 45% New share in total profit of duck eggs: $27,065 / $67,886 x 100% = 39.87%

Case 35: Kayak Rentals 35.1: $11.90

Total rental hours for each kayak to break-even: $75,000 / ($15 x 20) = 250 hours Variable Cost of each single kayak is best presented by the following equation: ($15 x 20 x 250) - (20 x VC x 250) - $15,500 = 0 ⇔ 20 x 250 x VC = $59,500 ⇔ VC = $11.90

35.2: 5 double kayaks

PLEASE GO ON TO THE NEXT PAGE 93

Full Cases Again, we have to find the total variable cost in order to work out the number of double kayaks via the variable cost per unit. Thus, total variable cost of double kayak equals: ($25 x 500 x quantity) - (500 x $8 x quantity) - $18,000 = $10,000 ⇔ ($12,500 x quantity) - ($4,000 x quantity) = $38,000 ⇔ $8,500 x quantity = $38,000 ⇔ Quantity = $38,000 / $8,500 ≈ 5

35.3: Single Kayak: 18.51% and Double Kayak: 62%

Total hours working at full capacity: 100 x 24 = 2,400 hours Profit / Loss of single kayak at maximum capacity: (20 x 2,400 x $15) - (20 x 2,400 x $11.90) - $15,500 = $133,300 Profitability of single kayak when working at full capacity for 100 days: $133,300 / (20 x 2,400 x $15) x 100% = 18.51%

Profit / Loss of double kayak at maximum capacity: (5 x 2,400 x $25) - (5 x 2,400 x $8) - $18,000 = $186,000 Profitability of double kayak when working at full capacity for 100 days: $186,000 / (5 x 2,400 x $25) x 100% = 62%

Hurdle 10

Case 36: Rice Growing Plant

PLEASE GO ON TO THE NEXT PAGE 94

Full Cases 36.1: Plant C has the most productive of 409.72 kg / ha.

Profitability of Plant A: 325 / 0.8 = 406.25 kg / ha Profitability of Plant B: 240 / 0.65 = 369.23 kg / ha Profitability of Plant C: 295 / 0.72 = 409.72 kg / ha

36.2: Selling price per kg of rice in Plant A is 9.5% higher than that of rice in Plant B

Profit per kg of rice in Plant A: ($1830 x 0.8) / 325 = $4.50 Selling price per kg of rice in Plant A: $4.50 / 18.5% = $24.30 Profit per kg of rice in Plant B: ($1,640 x 0.65) / 240 = $4.44 Selling price per kg of rice in Plant B: $4.44 / 20% = $22.20 Selling price per kg of rice in Plant A is higher than that of rice in Plant B by: ($24.30 - $22.20) / $22.20 x 100% = 9.5%

36.3: $26.40

Selling price per kg of rice in Plant C would be best calculated using this equation: (Revenue - Cost of Production) / Revenue = Gross Profit Margin ⇔ 295) = 0.38

[(Selling price x 295) - (Variable Cost x 295) - (Fixed Cost)] / (Selling price x

⇔

1 - [(14 x 295) + 700] / (Selling price x 295) = 0.38

⇔

$4,830 / (Selling price x 295) = 0.62

⇔

Selling price = ($4,830 / 0.62) / 295 = $26.40

PLEASE GO ON TO THE NEXT PAGE 95

Full Cases Case 37: TFG Travel

37.1: 8,616 tourists of adult and child tourists

Quarterly Revenue from all Domestic tours: $418,500 / 13.4% = $3,124,134 The total number of tourists (X) can be represented by this equation: (X x 70% x $370) + (X x 30% x $345) = $3,123,134 ⇔ (25,900 x X + 10,350 x X) / 100 = 3,123,134 ⇔ 36,250 x X = 312,313,400 ⇔ X = 8,616 tourists Number of adult tourist: 8,616 x 70% = 6,031 tourists Number of child tourist: 8,616 x 30% = 2,585 tourists

37.2: $3,764,585 for adult tourists; $2,407,727 for child tourists

New price for an Adult on International tours: $855 x 114% = $974.40 New price for a Child on International tours: $820 x 114% = $934.80 Expected Revenue from International tours: $762,900 / 11% = $6,935,455 The total number of tourists (Z) can be represented by this equation: (Z x 60% x $974.40) + (Z x 40% x $934.80) = $6,935,455 ⇔ (58,464 x Z + 37,392 x Z) / 100 = 6,935,455 ⇔ 95,856 x Z = 693,545,500 ⇔ Z = 7235 tourists Total expenses for adult tourists on International tours:

PLEASE GO ON TO THE NEXT PAGE 96

Full Cases (7235 x 60% x $974.40) x 89% = $3,764,585 Total expenses for child tourists on International tours: (7235 x 40% x $934.80) x 89% = $2,407,727

Case 38: Imported Fruit Shop

38.1: $6.8

Mark-up percentage formular = (selling price – cost) / cost Here we have: ($17 – Cost) / Cost = 150%

$17 – Cost = Cost x 1.5

$17 = 2.5 x Cost

Cost = $17 / 2.5 = $6.8

38.2: 267.6%

Cost per 1 kg of grapes type A is $6.8

Cost per 1 kg of grapes type B is $3.4

If a customer buys 1 kg of grapes type A and 1 kg of grapes type B, he has to pay ($17 + $20.5) = $37.5; cost = $6.8 + $3.4 = $10.2 The mark-up percentage of 2 types combined = (37.5 - 10.2) / 10.2 = 267.6 %

38.3: $304.08

For 1 kg of Grapes type B: ($20.5 – cost) / cost = 2.5

$5.86

Revenue earned = 90% x (18 x $17 + 12 x $20.5) = $496.8 Profit earned = $496.8 – (18 x $6.8 + 12 x $5.86) = $304.08

PLEASE GO ON TO THE NEXT PAGE 97

Full Cases

Hurdle 11

Case 39: Andy’s Laptop Distributor

39.1: 29 Old price of laptop C: $19,500 / 6 = $3,250 New price of laptop C: $3,250 x 1.1 = $3,575 Number of laptop C sold in the last week: $103,675 / $3,575 = 29

39.2: Decreased by 17%

We have the equation: mark-up percentage = (selling price – cost) / cost For Laptop A: selling price = $27,880 / 34 = $820 In the first 2 weeks: 45% = ($820 – old cost) / old cost In the last 2 weeks: 70% = ($820 – new cost) / new cost

old cost = $565 new cost = $482

So, price of laptop A decreased by: ($565 – $482) / $482 = 17%

39.3: $5,900

In the first week: the total cost of all laptops sold were: Total cost of Laptops A: $27,880 / 1.45 = $19,228 Total cost of Laptops B: $18,370 / 1.65 = $11,133 Total cost of Laptops C: $19,500 / 2.20 = $8,864 Total Cost of all laptops sold: $19,228 + $11,133 + $8,864 = $39,335

PLEASE GO ON TO THE NEXT PAGE 98

Full Cases Operation Cost = (100% - 30% - 45% - 10%) x $39,335 = 15% x $39,335 = $5,900

39.4: $6,457

Old cost of Laptop B in the first 2 weeks: $11,133 / 11 = $1,012 New cost of Laptop B in the third week: $1,012 x 1.16 = $1,174 Mark-up percentage = 50%

new selling price = $1,174 x 1.5 = $1,761.

Gross profit of all laptops B sold in the third week: ($1,761 - $1,174) x 11 = $6,457

Case 40: Real Estate Broker

40.1: $5,768

Net income after tax from company in Jan = $3,200 x 0.85 + ($450 x 3 + $450 x1.1 + $450 x1.12 + $450 x 1.13) x1.02 = $5,768 40.2: 11 free-lance contracts were signed

Jack’s income from free-lance contracts in Jan = $28,600 - $5,768 = $22,832 Let X be the number of free-lance contracts Jack signed in Jan, we have the equation: X x 580 + 2/3 x X x 75,000 x 3% = 22,832

580 x X + 1,500 x X = 22,832

X = 11

40.3: 7.4%

Net income after tax from company in Feb = $3,200 x 0.85 + $450 x 3 + $450 x 1.1 + $450 x 1.12 = $5,110

PLEASE GO ON TO THE NEXT PAGE 99

Full Cases Let Y be the new commission percentage Jack charged for each of his free-lance contracts in February, we have the equation: 5,110 + 580 x 12 + 4 x 56,000 x Y = 28,600

224,000Y = 16,530

Y = 7.4%

Case 41: Suit Tailoring

41.1: 56.6%

Average price of a medium quality suit = (£612 + £584) /2 = £598 Approximate revenue of all medium quality suits sold = £598 x 55 = £32,890 Approximate profit margin of all medium quality suits sold = 18,600 / 32,890 = 56.6%

41.2: £817

Number of high quality women’s suits sold in Dec = 96 / 16 x 3 = 18 Number of medium quality women’s suits sold in Dec = 96 / 16 x 8 = 48 Number of low quality women’s suits sold in Dec = 96 / 16 x 5 = 30 Price of a high quality women’s suit = (£52,030 – 48 x £584 – 30 x £310) / 18 = £817

41.3: £1,261

Average price of a suit sold at Zeiss = (£985 + £612 + £385 + £817 + £584 + £310) / 6 = £615.5 Approximate revenue in Nov 2011 = £615.5 x 169 = £104,020 Approximate total cost = £104,020 / 2.2 = £47,282

PLEASE GO ON TO THE NEXT PAGE 100

Full Cases Average salary paid to each tailor = (£47,282 x 0.4 x 0.6) / 9 = £1,261

Hurdle 12 Case 42: Betty’s Hair Salon

42.1: May

Profitability in each month is: May: (12,670 – 5,420) / 12,670 = 57.22%

Highest profitability

June: (9,810 – 4,480) / 9,810 = 54.33% July: (11,450 – 5,180) / 11,450 = 54.76%

42.2: June compared to May: price increased by 0.33% July compared to June: price decreased by 4.2%

Number of clients each month is: May: (5420 – 1,280) / 10 = 414 June: (4,480 – 1,280) / 10 = 320 July: (5,180 – 1,280) / 10 = 390 Average Price charged per client each month: May: $12,670 / 414 = $30.6 June: $9,810 / 320 = $30.7 July: $11,450 / 390 = $29.4 June compared to May: price increased by (30.7 – 30.6) / 30.6 = 0.33%

PLEASE GO ON TO THE NEXT PAGE 101

Full Cases July compared to June: price decreased by (30.7 - 29.4) / 30.7 = 4.2%

42.3: Make a profit of $5,802.4

Revenue in August: 390 x 2 x $29.4 x 70% = $16,052.4 Expense in August: $1,280 + 390 x 2 x $10 x 115% = $10,250 Betty will make a profit of ($16,052.4 - $10,250) = $5,802.4

Case 43: Website Management

43.1: GetEverything.com – BooksOnline.com – EnglishTip.com

Number of pages viewed per visit = Page views / Visits For BooksOnline.com: 67 / 34.6 = 1.94 For EnglishTip.com: 55 / 42.8 = 1.29 For GetEverything.com: 178 / 53.9 = 3.3

43.2: 8.7

In May, the number of new visits = 34,600 / (1+5) x 1 = 5,767 – this number includes the first and only one visit or visitors who never come back to the website and the first time of returning visitors who come back to the website after their first visit. The number of visitors who visit the website the first time in May and never come back = 5,767 /3 x 2 = 3,845. The number of returning unique visitors to the website in May = 7,395 – 3,845 = 3,550

PLEASE GO ON TO THE NEXT PAGE 102

Full Cases The average number of time a returning unique visitor come back to the website after their first visit = (34,600 – 3,845) / 3550 = 8.7

43.3: $95,497.5

Number of visits in June = 42,800 x 1.25 = 53,500 Number of pages viewed per visit increased by (1.68 – 1.29) / 1.29 = 30% New conversion rate = 12% + 0.3% x 30 = 21% Revenue generated = 21% x 53,500 x $8.5 = $95,497.5

Case 44: Mobile Ice-cream Store

44.1: Cherry: 41.8%; Vanilla: 51.4%; Strawberry: 6.8%

Total Revenue per day = $2.5 x 34 + $1.8 x 58 + $0.6 x 23 = $203.2 Share in Revenue of Cherry = ($2.5 x 34) / $203.2 = 41.8% Share in Revenue of Vanilla = ($1.8 x 58) / $203.2 = 51.4% Share in Revenue of Strawberry = ($0.6 x 23) / $203.2 = 6.8%

44.2: Vanilla – 35%

Strawberry – 30%

Cherry – 25%

Profit margin of Cherry = ($2.5 - $1.875) / $2.5 = 25% Profit margin of Vanilla = ($1.8 - $1.17) / $1.8 = 35% Profit margin of Strawberry = ($0.6 - $0.42) / $0.6 = 30%

PLEASE GO ON TO THE NEXT PAGE 103

Full Cases 44.3: 73%

New targeted profit margin = 35% x 2 = 70% Profit margin = profit / price = (price – cost) / price = 1 – (cost/ price) margin) x price price = cost / (1-profit margin)

cost = (1 – profit

Let X be the current selling price, so current cost = (1 - 35%) x X = 0.65 x X New cost = 0.65 x X x 80% = 0.52 x X New selling price = 0.52 x X / (1-70%) = 1.73 x X So, selling price has to be increased by (1.73 x X – X) / x X = 73%

Hurdle 13

Case 45: Furniture Importer

45.1: Royal Sofa: 13%, Vienna Bed: 14%, Bassett Cabinet: 28%

Share of Royal Sofa = $2,180 x 13 / $219, 680 = 13% Share of Vienna Bed = $3,850 x 8 / $219, 680 = 14% Share of Bassett Cabinet = $4,040 x 15 / $219, 680 = 28%

45.2: 90%

Wholesale Rev from Retailer 1 = 80 x $2,180 x 82% + 45 x $3,850 x 90% = $298,933

PLEASE GO ON TO THE NEXT PAGE 104

Full Cases Wholesale Rev from Retailer 2 = 55 x $2,180 x 82% + 75 x $3,850 x 86% + 100 x $4,040 x 81% = $673,883 Wholesale Rev from Retailer 3 = 30 x $2,180 x 85% + 40 x $4,040 x 88% = $197,798 Wholesale Rev from Retailer 4 = 150 x $2,180 x 77% = $251,790 Wholesale Rev from Retailer 5 = 35 x $2,180 x 85% + 60 x $3,850 x 86% + 90 x $4,040 x 81% = $558,031 Total Wholesale Rev = $298,933 + $673,883 + $197,798 + $251,790 + $558,031 = $1,980,435 Share of wholesale Rev in total Rev = $1,980,435 / ($219, 680 + $1,980,435) = 90%

45.3: Vienna Bed

Unit cost of Manhattan Bed = $4,620 x 55% = $2,541 Unit cost of Vienna Bed = $2,541 / 1.2 = $2,117.5 Profit if the retailer takes 100 Vienna Beds = ($3,850 x 80% - $2,117.5) x 100 = $96,250 Profit if the retailer takes 100 Manhattan Beds = ($4,620 x 75% - $2,541) x 100 = $92,400 Thus, Royal House would want to sell Vienna Beds to this retailer for a higher profit.

Case 46: Internet Providers 46.1: FHU: 28.8%; VCG: 20.6%; HTV: 29.4%

FHU’s share = 32,000 x £540 / £60,000,000 = 28.8% VCG’s share = 19,000 x £650 / £60,000,000 = 20.6% HTV’s share = 42,000 x £420 / £60,000,000 = 29.4%

PLEASE GO ON TO THE NEXT PAGE 105

Full Cases 46.2: FHU (for cheapest fee)

Total Mb consumed by everyone in Adele’s family in a month = 240Mb If using FHU, monthly fee = £12 + 190 x £0.5 = £107 If using VCG, monthly fee = £10 + 190 x £1 = £200 If using HTV, monthly fee = £5 + 190 x £0.6 = £119

46.3: FHU: Rev decreases by 6.3%; HTV: Rev decreases by 2.5%

For FHU: % increase in price = (£589 - £540) / £540 = 9%

they lose 4,500 clients.

New Rev = (32,000 – 4,500) x £589 = £16,197,500 Old Rev = 32,000 x £540 = £17,280,000 Rev decreases by (£17,280,000 - £16,197,500) / £17,280,000 = 6.3% For HTV: % decrease in price = (£420 - £400) / £420 = 5%

they gain 1000 clients.

New Rev = (42,000 + 1,000) x £400 = £17,200,000 Old Rev = 42,000 x £420 = £17,640,000 Rev decreases by (£17,640,000 - £17,200,000) / £17,640,000 = 2.5%

Case 47: Stock market 47.1: $4,149,000 Return = 200,000 x $13.5 x 30% + 450,000 x $8.6 x 45% + 100,000 x $21.3 x 75% = $4,149,000

47.2: ASP ASP’s best guess for return = 30% x 50% - 15% x 50% = 7.5%

PLEASE GO ON TO THE NEXT PAGE 106

Full Cases SHN’s best guess for return = 45% x 30% - 10% x 70% = 6.5% MCG’s best guess for return = 75% x 20% - 55% x 80% = -29%

47.3: 1,202,887 stocks Highest expected loss point of ASP = $13.5 x 0.85 = $11.5 The amount that Maya loses from ASP investment = ($15 - $11.5) x ($15 million / $15) = $3.5 million She is left with $11.5 million she can buy ($11.5 million / $8.6) = 1,337,209 SHN stocks at most. Let A be the lowest number of SHN stocks that Maya should buy, we have the equation: A x $8.6 x 1.45 = $15 million

A = 1,202,887 stocks.

Hurdle 14

Case 48: Headphone Retailer

48.1: $6,570

For headphone type A: Number of unit sold = $13,650 / $45.5 = 300 (units) Total Cost = $13,650 x 40% = $5,460 Total Fixed Cost = $5,460 – 300 x $13.5 = $1,410 With similar calculation steps, Total Fixed Cost for Headphone type B and C is $1,642.5 and $3,517.5 Total Fixed Cost = $1,410 + $1,642.5 + $3,517.5 = $6,570

PLEASE GO ON TO THE NEXT PAGE 107

Full Cases 48.2: 42.67%

Expected Revenue for next month = ($13,650 + $10,950 + $6,650) x 115% = $35,937.5 Expected Revenue from Headphone Type B = $35,937.5 - $13,650 - $6,650 = $15,637.5 New Selling price per headphone type B = $15,637.5 / ($10,950 / $30) = $42.8 % increase in price = ($42.8 - $30) / $30 = 42.67%

48.3: Type A: $36.4; type B: $31.5; type C: $99.75

For headphone type A: New Total Unit Cost = $45.5 x 40% x 70% = $12.74 New Unit Selling Price = $12.74 / 35% = $36.4 With similar calculation steps, new Unit Selling Price for headphone type B and C is $31.5 and $99.75

Case 49: Real Estate Broker

49.1: 14 contracts

Let X be the total number of contracts Johnny received in July 2013. We have the equation: X x $1,500 + X x 80% x $35,000 x 6% = $45,500

X = 14

49.2: Contract No.5 has the highest best guess of income

PLEASE GO ON TO THE NEXT PAGE 108

Full Cases Best guess of income of each contract is as follows: - Contract No.1: ($1,200 x 10%) + [(1,200 + $49,000 x 6%) x 90%] = $3,846 - Contract No.2: ($850 x 25%) + [($850 + $32,700 x 6%) x 75%] = $2,321.5 - Contract No.3: ($789 x 20%) + [($789 + $78,900 x 6%) x 80%] = $4,576.2 - Contract No.4: ($1,100 x 35%) + [($1,100 + $38,000 x 6%) x 65%] = $2,582 - Contract No.5: ($2,000 x 50%) + [($2,000 + $125,000 x 6%) x 50%] = $5,750

49.3: $10,841

His actual earnings that week = ($1,200 + $49,000 x 6%) + ($850 + $32,700 x 6%) + ($78,900 x 1%) + $1,100 + $2,000 = $10,841

Case 50: French Teaching Center for Kids

50.1: 8.7 months

Monthly Revenue = (10 x 15 x $1,800/2 - $350 x 12) + (20 x 15 x $2,200/2 - $420 x 12) + (10 x 10 x $2,900/2 - $550 x 8) = $596,360 Number of months to break even = $5.2 million / $596,360 = 8.7 months

50.2: $547,560

New Monthly Revenue = (15 x 10 x 80% x $1,800 x 115% /2 - $350 x 12) + (20 x 15 x 80% x $2,200 x 115% /2 - $420 x 12) + (10 x 10 x 80% x $2,900 x 115%/2 - $550 x 8) = $547,560

PLEASE GO ON TO THE NEXT PAGE 109

Full Cases 50.3: 236%

Number of new kids registering for a basic program through the marketing event = $2,840 x 30% = 852 Return (in %) of the event = 852 x $1,800 / $650,000 = 236%

***

We hope this practice package is helpful in your preparation for the Problem Solving Test. If you have not done so, please visit our website for free in-depth theories and practice on the Problem Solving Test (breakdown by question types).

http://www.mconsultingprep.com/problem-solving-test/how-to-prepare

PLEASE GO ON TO THE NEXT PAGE 110