Boston Consulting Group Potential Test Free Practice Test igotanoffer.com Free BCG Potential Test Copyright © IGotAnOffer Ltd. How to make the most of this practice test (1/2) We have designed our tests to resemble the official BCG Potential Test as closely as possible. Here are a few tips to use this test as efficiently as possible: Do not print out the test. Remember, the BCG Potential Test is an online test. When you will be sitting the test in BCG offices, you will have to do the test on a computer screen and will not be allowed to print it. You should therefore get used to reading the questions and documents on a computer screen and working out your answers on scrap paper. If you print out the test and take notes directly on it, you will not experience the real test conditions. Do the whole test under real time conditions: you have 20 minutes to complete it. At the end of the 20 minutes, put your pen down, even if no one is there to ask you to. The reason this is important is that you need to track your progress across different sample tests. If you complete the test in varying durations you will have no way to know for sure if you are progressing or not. Check your answer sheet against the answer key. Mark your score for each of the questions: +3 points for correct answers, -1 point for incorrect answers, 0 points for questions not answered. Then calculate your total score. Your objective is to improve your score compared to the last sample test you tried. In fact, it is likely that your score in the first full test you solve will be fairly low (30+ points). This is completely normal, as you are still learning about the format of the test, and how to use your answering method within the time allocated. If you stick to the method, and review your answers carefully, you should see a quick improvement in your score. Copyright © IGotAnOffer Ltd. How to make the most of this practice test (2/2) Review the solutions in the answer key carefully and compare them with your notes, to see why you didn’t approach the question correctly in the first place. A careful review requires that you go through the steps given in the solution, pencil in hand, and re-do all the steps that aren’t obvious to you. This will take some time, but will prove invaluable to your progress. Do the test again Once you are comfortable with all the answers, you can move on to the next sample test. After going through all the available practice tests, you should return to the ones you have already done, and make sure that you can now solve them easily within the allocated time. When you do so, use blank scrap paper, so that you don’t get distracted by your previous notes, and feel like you are under real test conditions. Finally, we are here to answer any of your questions, so if you get stuck trying to understand the explanations in the answer key, just drop us a line at: support@igotanoffer.com. We’ll be happy to fill any gaps! Copyright © IGotAnOffer Ltd. Instructions Online case. During your recruiting process with BCG you will have to go through an online case. The purpose of this exercise is to test your analytical and logic skills as well as your business sense. Sample. This document is a sample of 10 questions put together by IGotAnOffer. Its purpose is to help you prepare for the actual online exercise you will have to complete. We recommend you take no more than 20 minutes to take this test. Each question is divided into 2 parts: • on the left, you will find the question itself • on the right, you will find the information you need to answer the question No calculator. This sample test has been designed to be completed without a calculator. However, we have worked with candidates in Israel and Russia who have been allowed to use a calculator when completing their test. We therefore advise you to contact your local HR at BCG to clarify whether you will be allowed to use a calculator or not during your actual test. If you find out that you are allowed to use a calculator, you should complete the test in about 16 minutes instead of the standard 20 minutes without a calculator. Scoring system. You should select one or more answers for each question. During the actual test you will be able to move onwards and backwards and change your prior answers so you should feel free to do the same here. For each right answer you will get +3 points, 0 points for no answer and -1 point for a wrong answer. Copyright © IGotAnOffer Ltd. BCG Potential Test – PayCo Question 1 What is the current cost per sale for PayCo assuming all lead sources have the same conversion rate? 1. 2. 3. 4. $39 / sale $44 / sale $49 / sale $54 / sale Doc 1 Doc 2 Doc 3 Current lead mix: cost per sale Case overview Current situation PayCo is a payments company that processes debit card and credit card transactions in the United States. PayCo’s clients are shops such as restaurants, bars, apparel shops, supermarkets, petrol stations, etc. Question x rents / 23debit and credit card The company machines to its clients. It earns a rental fee for the card machines as well as a small fee for each card transaction processed by their client. The company works with banks to acquire new clients. It purchases lists of businesses from them and calls them to sell card machines and services. PayCo purchases lists of leads at different prices from Alma Bank, Bingo Bank and Com Bank. Copyright © IGotAnOffer Ltd. Doc 4 Cost per lead ($) Share of total mix of leads (%) Alma Bank $5 30% Bingo Bank $3 60% Com Bank $6 10% Sales representatives call the leads to try and sell them card machines and services. The average conversion rate from lead to actual customer is about 10%. The conversion rate is driven by: 1. The quality of leads provided (lead needs service, can afford it, etc.) 2. The effort the sales agent puts in (time spent, skills, etc.) Sales representatives are organised in three teams (one per bank). Each lead is handled by one single sales representative. BCG Potential Test – PayCo Question 2 Which of the following statements would explain why the conversion rate changes from bank to bank: a. The number of representatives per team varies b. The sales representatives salaries and bonuses vary c. The type of business the lead is in varies d. The working hours of individual sales agents vary 1. 2. 3. 4. Option b Options a and b Options a, b and c Options b, c and d Doc 1 Doc 2 Doc 3 Current lead mix: cost per sale Case overview Current situation PayCo is a payments company that processes debit card and credit card transactions in the United States. PayCo’s clients are shops such as restaurants, bars, apparel shops, supermarkets, petrol stations, etc. Question x rents / 23debit and credit card The company machines to its clients. It earns a rental fee for the card machines as well as a small fee for each card transaction processed by their client. The company works with banks to acquire new clients. It purchases lists of businesses from them and calls them to sell card machines and services. PayCo purchases lists of leads at different prices from Alma Bank, Bingo Bank and Com Bank. Copyright © IGotAnOffer Ltd. Doc 4 Cost per lead ($) Share of total mix of leads (%) Alma Bank $5 30% Bingo Bank $3 60% Com Bank $6 10% Sales representatives call the leads to try and sell them card machines and services. The average conversion rate from lead to actual customer is about 10%. The conversion rate is driven by: 1. The quality of leads provided (lead needs service, can afford it, etc.) 2. The effort the sales agent puts in (time spent, skills, etc.) Sales representatives are organised in three teams (one per bank). Each lead is handled by one single sales representative. . BCG Potential Test – PayCo Question 3 Assuming PayCo buys leads from all three banks, what is the maximum conversion rate it could achieve? 1. 2. 3. 4. 10.5% 11.2% 11.8% 12.3% Doc 1 Doc 2 Doc 3 Doc 4 New lead mix: cost per sale Bank by bank analysis Conversion rate results Alma Bank is a large commercial bank from the East Coast of the US. Its clients are mainly restaurants and shops. After carrying out some research, your team finds out that the conversion rate actually differs between the three banks. Com Bank has got a similar list of clients to Alma Bank but is established on the West Coast of the US. PayCo needs to achieve its sales target by using 300,000 leads per year. Question 23 Bingo Bank x is /established in the Midwest and primarily serves Mom and Pop businesses. The team at PayCo has always assumed a similar conversion rate of 10% across all three banks. Copyright © IGotAnOffer Ltd. Conversion rate # of leads available per year Alma Bank 12% 100,000 Bingo Bank 8% 600,000 Com Bank 15% 80,000 BCG Potential Test – PayCo Question 4 What would be the average cost per sale for PayCo if it sourced leads from the three banks in a way that maximises sales? Doc 1 Doc 2 Doc 3 New lead mix: cost per sale Bank by bank analysis 1. 2. 3. 4. $35.0 / sale $37.5 / sale $39.9 / sale $39.6 / sale Doc 4 Conversion rate results Alma Bank is a large commercial bank from the East Coast of the US. Its clients are mainly restaurants and shops. After carrying out some research, your team finds out that the conversion rate actually differs between the three banks. Com Bank has got a similar list of clients to Alma Bank but is established on the West Coast of the US. PayCo needs to achieve its sales target by using 300,000 leads per year. Question 23 Bingo Bank x is /established in the Midwest and primarily serves Mom and Pop businesses. The team at PayCo has always assumed a similar conversion rate of 10% across all three banks. Copyright © IGotAnOffer Ltd. Conversion rate # of leads available per year Alma Bank 12% 100,000 Bingo Bank 8% 600,000 Com Bank 15% 80,000 BCG Potential Test – PayCo Question 5 Assume that the average annual revenue per customer for PayCo is $100, and that it chooses the mix of leads that maximises average conversation rate. What percentage difference in profit margin would result from this choice compared to a 10% conversion rate across all banks? 1. 2. 3. 4. 0.98% -0.98% 1.48% -1.48% Copyright © IGotAnOffer Ltd. Doc 1 Doc 2 Doc 3 Doc 4 New lead mix: impact on profits Bank by bank analysis Conversion rate results Alma Bank is a large commercial bank from the East Coast of the US. Its clients are mainly restaurants and shops. After carrying out some research, your team finds out that the conversion rate actually differs between the three banks. Com Bank has got a similar list of clients to Alma Bank but is established on the West Coast of the US. PayCo needs to achieve its sales target by using 300,000 leads per year. Question 23 Bingo Bank x is /established in the Midwest and primarily serves Mom and Pop businesses. The team at PayCo has always assumed a similar conversion rate of 10% across all three banks. Conversion rate # of leads available per year Alma Bank 12% 100,000 Bingo Bank 8% 600,000 Com Bank 15% 80,000 BCG Potential Test – PayCo Question 6 Assume that the average annual revenue per customer for PayCo is $100, and that it chooses the mix of leads that maximises average conversation rate. What would be the change in total profits compared to the current situation? 1. 2. 3. 4. $0.2M increase $0.2M decrease $0.3M increase $0.3M decrease Doc 1 Doc 2 Doc 3 New lead mix: impact on profits Bank by bank analysis Conversion rate results Alma Bank is a large commercial bank from the East Coast of the US. Its clients are mainly restaurants and shops. After carrying out some research, your team finds out that the conversion rate actually differs between the three banks. Com Bank has got a similar list of clients to Alma Bank but is established on the West Coast of the US. PayCo needs to achieve its sales target by using 300,000 leads per year. Question 23 Bingo Bank x is /established in the Midwest and primarily serves Mom and Pop businesses. The team at PayCo has always assumed a similar conversion rate of 10% across all three banks. Copyright © IGotAnOffer Ltd. Doc 4 Conversion rate # of leads available per year Alma Bank 12% 100,000 Bingo Bank 8% 600,000 Com Bank 15% 80,000 BCG Potential Test – PayCo Question 7 Which of the following quantities, in addition to the cost per lead, would you need in order to calculate the full cost per sale: a. Hourly wage of sales representative b. Number of leads processed per sales representative per hour c. Number of sales representatives in each team d. Number of sales managers in each team 1. 2. 3. 4. Option a Options a and b Options c Options c and d Doc 1 Doc 2 Doc 3 Sale representatives’ incentives Day to day Sale representatives’ compensation PayCo’s sales representatives work from 9am to 5pm from Monday to Friday 47 weeks a year. The sales representatives’ base salary starts at $40k and increases by about 5% per year for each additional year they stay with the company. Sales representatives are divided into three teams. Each team deals with one of the following lead sources: Alma Bank, Bingo Bank and Com Bank. Question x / 23 Every day, sales representatives receive a list of 85 leads from their respective bank and work through the list during the day. The list of leads they get are newly setup businesses which are likely to require debit and credit card payment processing services. Sales representatives simply cold-call the leads and try to convince them to sign up for PayCo services. Copyright © IGotAnOffer Ltd. Doc 4 In addition, sales representatives can receive $10 for each sale they make. The Head of Sales has noticed that sales representatives for Bingo Bank are much less motivated than their peers on average. After investigating, he found that these sales representatives have been consistently generating lower sales and receiving smaller bonuses than their peers. BCG Potential Test – PayCo Question 8 Which of the following statements would NOT solve the motivation problem of the sales representatives in the Bingo Bank team? 1. 2. 3. 4. Work with Bingo Bank to increase the quality of the leads purchased from them by PayCo Group sales representatives handling different banks in a single team and randomise the allocation of leads between them Keep sales representatives in different teams but rotate lead sources between them Increase bonuses to $20 per sale for all sales representatives Copyright © IGotAnOffer Ltd. Doc 1 Doc 2 Doc 3 Doc 4 Sale representatives’ incentives Day to day Sale representatives’ compensation PayCo’s sales representatives work from 9am to 5pm from Monday to Friday 47 weeks a year. The sales representatives’ base salary starts at $40k and increases by about 5% per year for each additional year they stay with the company. Sales representatives are divided into three teams. Each team deals with one of the following lead sources: Alma Bank, Bingo Bank and Com Bank. Question x / 23 Every day, sales representatives receive a list of 85 leads from their respective bank and work through the list during the day. The list of leads they get are newly setup businesses which are likely to require debit and credit card payment processing services. Sales representatives simply cold-call the leads and try to convince them to sign up for PayCo services. In addition, sales representatives can receive $10 for each sale they make. The Head of Sales has noticed that sales representatives for Bingo Bank are much less motivated than their peers on average. After investigating, he found that these sales representatives have been consistently generating lower sales and receiving smaller bonuses than their peers. BCG Potential Test – PayCo Question 9 Which of the following measures would best help the company to fully prevent sales representatives from agreeing unprofitable prices with future customers? 1. 2. 3. 4. Train sales representatives to negotiate better prices with leads Fine sales representatives when they give unprofitable prices Incentivise sales representatives to sell at higher prices with a different bonus system Set up an audit team that would check prices and validate contracts before they count towards sales representatives’ total sales Copyright © IGotAnOffer Ltd. Doc 1 Doc 2 Doc 3 Doc 4 Incentive structure Current issue Sales representatives are currently only incentivised based on the number of customers they manage to sell to. The head of finance of the group has noticed that the prices at which sales representatives agreed to provide PayCo’s services have decreased in the Question x / 23 past few months. The head of sales suspects that this might be due to sales representatives selling at increasingly lower prices to increase their bonus. Pricing When selling PayCo’s services, sales representatives negotiate a share of their customers’ future revenue. For debit cards, they usually agree a price of about 15 cents per future transaction processed for the client. For instance, if PayCo processes a debit card transaction for a sandwich at $5, they will receive 15 cents from the sandwich shop in exchange for their service. For credit cards, the price agreed is a percentage of the transaction instead of a fixed fee. This percentage is usually around 1.5%. The average split of debit and credit card transactions is 40-60 (debit – credit). Lately, sales representatives have been found to sell PayCo’s services at increasingly less profitable prices. BCG Potential Test – PayCo Question 10 Which of the following statements is supported by the information available to you? 1. 2. 3. 4. PayCo would achieve higher revenues if all transaction fees came from debit cards Credit card transactions contribute more to PayCo’s annual revenues than debit card transactions Leads from Alma Bank contribute more to PayCo’s revenues compared to leads from Bingo Bank None of the above / we lack sufficient information Doc 1 Doc 2 Doc 3 Doc 4 Incentive structure Current issue Sales representatives are currently only incentivised based on the number of customers they manage to sell to. The head of finance of the group has noticed that the prices at which sales representatives agreed to provide PayCo’s services have decreased in the Question x / 23 past few months. The head of sales suspects that this might be due to sales representatives selling at increasingly lower prices to increase their bonus. Pricing When selling PayCo’s services, sales representatives negotiate a share of their customers’ future revenue. For debit cards, they usually agree a price of about 15 cents per future transaction processed for the client. For instance, if PayCo processes a debit card transaction for a sandwich at $5, they will receive 15 cents from the sandwich shop in exchange for their service. For credit cards, the price agreed is a percentage of the transaction instead of a fixed fee. This percentage is usually around 1.5%. The average split of debit and credit card transactions is 40-60 (debit – credit). Lately, sales representatives have been found to sell PayCo’s services at increasingly less profitable prices. Copyright © IGotAnOffer Ltd. Structure of answer key Regular BCG Potential test answers IGotAnOffer special tips and detailed answer We have just introduced “IGotAnOffer special tips” to the Free BCG Potential test. This new feature aims to give some extra information based on our experience on the BCG Potential test, while the “Regular BCG Potential test answers” just provide you with the right answer. We want to know how useful you find these new features before rolling them out to our other BCG Potential tests. If you liked this free BCG Potential test, please take a few seconds to send us an email at contactus@igotanoffer.com and tell us how valuable you found the special tips. Thanks! Copyright © IGotAnOffer Ltd. Answer key Question 1 Correct answer: 1 This calculation can be broken down into two steps: 1.Calculate cost per lead 2.Calculate cost per sale The cost per lead needs to be calculated across all three banks, taking into account their total share of mix: $5 x 30% + $3 x 60% + $6 x 10% = $3.9 / lead The cost per sale can be calculated by dividing the cost per lead by the conversion rate: $3.9 / 10% = $39.0. The correct answer is therefore answer 1. Copyright © IGotAnOffer Ltd. Answer key Question 2 Correct answer: 4 The conversion rate depends on two drivers: the quality of leads provided and the effort put in by the sales agents. Each answer needs to be evaluated against the two drivers. Also note that each lead is handled by a single sales agent. a. Increasing the number of representatives can increase the volume of leads handled but not the conversion rate as each lead is dealt with by a single agent b. The sales agents’ salaries and bonuses directly influence the effort they put in and therefore the conversion rate c. The type of business the leads is in influences the quality of the lead. For instance, if the business is a van that sells ice cream, it probably will not accept debit cards and therefore is not a good potential lead d. The working hours of sales representatives directly impacts the effort they put in Therefore options b, c and d impact the conversion rate and so answer 4 is the correct answer. Copyright © IGotAnOffer Ltd. Answer key Question 3 Correct answer: 2 In order to maximise its conversion rate, PayCo needs to rank lead sources from the highest to the lowest conversion rates. It should then use as many leads from the first source before considering the second one: 1. Com bank 15%; 80,000 leads available 2. Alma bank 12%; 100,000 leads available 3. Bingo bank 8%; 600,000 leads available PayCo needs 300,000 leads per year to meet its target sales. To maximise the conversion rate, the lead mix should then be: 1. Com bank: 80,000 2. Alma bank: 100,000 3. Bingo bank: 120,000 The maximum conversion rate achievable is then: (15% x 80,000 + 12% x 100,000 + 8% x 120,000) / 300,000 = 11.2% The correct answer is therefore answer 2. Copyright © IGotAnOffer Ltd. Answer key Question 4 Correct answer: 3 The maximum sales target is the one that can be achieved by using the maximum conversion rate based on the available leads. The average cost per sale can be calculated as: the sum of the number of sales based on the number of leads per bank from question 3 and the conversion rate multiplied with the cost per sale per bank and divided by the total number of sales (weighed average). Sales per bank: 1. Alma bank: 100,000 leads x 12% = 12,000 sales 2. Bingo bank: 120,000 leads x 8% = 9,600 sales 3. Com bank: 80,000 leads x 15% = 12,000 sales For each bank, the cost per sale can be calculated by dividing the cost per lead by the conversion rate: 1. Alma bank: $5 / 12% = $41.7 2. Bingo bank: $3 / 8% = $37.5 3. Com bank: $6 / 15% = $40 Therefore the average cost per sale is: ((12,000 x $40) + (12,000 x $41.7) + (9,600 x $37.5)) / (12,000 +12,000 + 9,600) = $39.9 The correct answer is therefore answer 3. Copyright © IGotAnOffer Ltd. IGotAnOffer special tip It is quite common to have to use data from previous questions in the BCG Potential Test. Sometimes the data will come from a previous answer and sometimes from the previous document itself. Therefore it is critical that you understand every piece of data given in a previous question or calculated in a previous answer. Since this is an online test in order to avoid going back and forth on your screen we recommend to keep your notes in your draft paper very clear and highlight (e.g. by drawing a box around it) the key information that you think might be relevant in the coming questions. Answer key Question 5 Correct answer: 4 This question can be solved using a three-step approach: 1. Calculate the profit margin with a 10% conversion rate across all banks 2. Calculate the profit margin using the average cost per sale 3. Calculate the percentage difference between the two margins The cost per sale for 10% conversion rate is $39 according to Question 1. As a consequence, the current margin is ($100 - $39) / ($100) = 61% The average cost per sale is $39.9 according to Question 4. The profit margin would therefore become ($100 - $39.9) / ($100) = 60.1% The percentage difference is therefore (60.1% - 61%) / (61%) = -1.48% Copyright © IGotAnOffer Ltd. Answer key Question 6 Correct answer: 1 To calculate total profits in each situation we need to: 1. Calculate the number of customers: # of leads x conversion rate (A) 2. Calculate the revenues for all customers: (A) x $100 (B) 3. Calculate profits: (B) x profit margin for each situation Profits in the current situation are: • 300,000 x 10% x $100 x 61% = $(300,000 x 6.10) Profits with the maximum conversion rate are: • 300,000 x 11.2% x $100 x 60.1% = $(300,000 x 6.73) The difference between the two is therefore: • (300,000 x 6.73) – (300,000 x 6.10) = 300,000 x 0.63 = $189,000 ≈ $0.2M The correct answer is therefore answer 1. Copyright © IGotAnOffer Ltd. IGotAnOffer special tip Notice here how you can minimise the number of difficult calculations you are doing to answer the question. Instead of fully calculating profits in the current situation ($300,000 x 6.10) and profits in the new situation ($300,000 x 6.73) and then subtracting them, we factorised the two products into ($300,000 x 0.63). This enabled us to do one multiplication instead of 2. As you answer BCG Potential Test questions you should look for this type of opportunity to minimise the number of difficult calculations you have to make. Answer key Question 7 Correct answer: 2 The cost per sale calculated in previous questions only includes the cost related to the purchase of leads from the different banks. It does not include the cost related to the sales force. Calculating the full cost per sale would require knowing how much sales representatives cost per customer acquired. The different answers need to be evaluated against this criterion: a. The hourly wage of sales representatives would be helpful to calculate the cost of sales per customer acquired b. The number of leads processed per hour per agent would also be helpful, as it would allow you to calculate the cost allocation between the different leads c. The number of sales reps per team would not be helpful as each lead is handled by a single agent d. The number of sales managers would not help determining the sales cost per customer acquired Answer 2 is therefore the correct answer. Copyright © IGotAnOffer Ltd. Answer key Question 8 Correct answer: 4 The head of sales’ initial conclusion is that sales representatives handling Bingo Bank leads “have been consistently making less sales and getting lower bonuses than their peers”. Indeed, the conversion rate for leads from Bingo Bank is lower than that for other banks. The comment implies that, to increase sales representatives’ satisfaction, their bonus would need to be similar relative to their peers. However, if bonuses increase to $20 per sale for all sales representatives, the relative bonus obtained by sales representatives focused on Bingo Bank will not increase. Answer 4 would therefore not help solve the problem and is the correct answer. Copyright © IGotAnOffer Ltd. IGotAnOffer special tip Some questions are phrased negatively in the BCG Potential Test. For instance here you are asked to find which statement “would NOT solve the motivation problem…” Thinking in negative terms is harder than thinking in positive terms. We therefore suggest that you rephrase negative questions as positive ones. Here, you should ask yourself: ‘Would this initiative increase the Bingo Bank team’s motivation?’ Answer 4 is the only option that would not help to increase the motivation of Bingo Bank’s team. Answer key Question 9 Correct answer: 4 Answers 1 to 3 would all help decrease sales representatives’ tendency to sell at unprofitable prices. However, none of them would completely stop the trend: 1. Training sales representatives to give better prices could still result in sales representatives giving unprofitable prices in practice. 2. Giving a fine to sales representatives, while a good incentive, is not guaranteed to fully stop the trend. 3. Similarly, setting up a better incentives scheme is also not guaranteed to halt the trend. Answer 4 is the correct answer because it fully prevents sales representatives from selling at unprofitable prices via an external audit team. Copyright © IGotAnOffer Ltd. Answer key Question 10 Correct answer: 4 None of the first three options is completely accurate based on the information we have: 1. PayCo makes 15 cent for every debit card transaction and 1.5% for every credit card transaction. For every transaction higher than $10 PayCo therefore receives a higher fee from credit cards. We do not know the average transaction size and therefore cannot conclude. 2. We know that the debit / credit card split is 40% / 60%. However we do not know the average debit / credit card transaction size. As a consequence, we cannot conclude if answer 2 is correct or not. 3. We know that leads from Alma Bank are mainly restaurants and shops and that leads from Bingo Bang are mainly Mom and Pop businesses. However, we do not have any information on the volume and type of transactions these businesses make. We therefore cannot conclude that this statement is true. Copyright © IGotAnOffer Ltd. IGotAnOffer is not affiliated to the Boston Consulting Group. Use of “BCG”, “BCG Potential Test”, “BCG Test” or any other variations do not imply any affiliation with or endorsement by the Boston Consulting Group. The information provided on igotanoffer.com and its related products is for educational purposes only. It is provided on an "as is" basis with no warranties expressed or implied. The information is believed to be accurate, but is not guaranteed to be so. By reading this content, you agree to waive IGotAnOffer Ltd. of any liability from the action you may take as a result of using the information available on igotanoffer.com and its related products. Copyright © IGotAnOffer Ltd.