Masters in Management QUANTITATIVE ANALYSIS FOR BUSINESS Sample Final Mock Examination Please read the instructions below carefully: - The exam is 120 minutes long. 0 There are 2 sections equally weighted (50 points each). Each part within each section has equal weight. 0 As this is a sample exam, I have included questions from each of the 3 topics: Decision Theory, Forecasting and Risk Analysis but your actual exam will only contain 2 topics (randomly assigned). 0 The use of a simple scientific calculator is allowed, the use of a personal computer is not allowed. 0 If you get stuck on a question, move on to others in order to collect credit and get the best use out of your exam time. There is no negative marking. o For your answers, please use the space provided. If you need more space, please use the extra sheets provided. If you need still more paper, please ask. If you use extra sheets, please write your name and question number on the extra sheets and make sure they are in the right order when you hand in the exam. 0 Make explicit any assumptions underlying your answers, interpret your results and justify your answers, conclusions and recommendations. However please make sure you show your working, as you may be eligible for partial credit. 0 In grading, importance will be attached to the clarity and conciseness of your answers. Good luck! Question 1: A customer has approached Caja Madrid, a bank, asking for a 100,000 one-year loan at a 12% interest rate (principal and interest repayable after one year). The bank has to decide whether or not to grant the loan. If Caja Madrid does not approve this loan application, the 100,000 will be invested in government bonds that earn a 6% annual return. Historical data shows that the bank approved one thousand similar loans in the past and that only 50 customers defaulted on their loan (5%). If this customer defaults on the loan, the bank will lose the entire 100,000. a) (5 points) Assuming the bank is risk-neutral, what should Caja Madrid do? Please draw a decision tree. b) (5 points) Taking risk into consideration (ie the likelihood of defaulting), what would be your recommendation to Caja Madrid?As mentioned before, historical information shows that, on average, 5% of the customers default on their loan. However, a closer look reveals that the bank is 90% confident that this number is between 4% and 6% c) (5 points) How does this range affect your analysis and recommendation? For the remainder of the analysis, you can assume that the average number of defaults equals 5%. Caja Madrid is considering hiring a credit rating agency, which would be able to predict whether or not a particular customer is likely to default on a loan or not.d) (5 points) Suppose the credit rating agency would be able to predict defaults with perfect accuracy. What is the maximum that Caja Madrid should be willing to pay in order to obtain this information, i.e. to know for sure whether or not the customer will default before approving or rejecting the loan? The credit rating agency charges the bank 1% of the principal for performing a credit check. For this fee, it will do a detailed check on the credit history of the customer and provide a recommendation to the bank, either "favourable" or "unfavourable". The bank has used the services of this agency before, and past experience indicates that unfortunately, the recommendation was sometimes wrong. In fact, for 20% of the loans on which a customer had defaulted, the agency had provided a favourable recommendation! Moreover, some loans that had received a negative recommendation were repaid without any problem. Of all loans that were repaid, 5% actually received a negative recommendation from the agency. The bank was worried about these statistics, and was wondering whether it would be worthwhile to pay 1,000 to the agency to perform a credit check. Charalampos, is an employee at the bank. He argued that a recommendation made by the agency was not trustworthy. He argued that a negative recommendation could be useful, since it apparently has a low error associated with it, namely 5%, but a favourable recommendation is not to be trusted, given the 20% error rate. e) (5 points) Do you agree with Charalampos' reasoning? Question 2: 3) Below are the key descriptive statistics on the variable, Advertising Expenses. Calculate a 95% confidence interval for the mean of advertising expenses. Advertising Expenses Mean 23105.26316 Standard Error 1962.953284 Median 24000 Mode 25000 Standard Deviation 6556.314996 Sample Variance 7321052632 Kurtosis 0.169793834 Skewness -0.01 1 91 1 1 65 Range 35000 Minimum 5000 Maximum 40000 Sum 439000 Count 1 9 Answer: Here is the line fit for the previous part: Advertising Expenses Line Fit Plot $19,000 Sales $14,000 $9,000 $0 $10,000 $20,000 $30,000 $40,000 $50,000 Advertising Expenses To improve upon the above explanatory relationship, a multiple regression trying to explain sales by all the other independent variables, i.e. year, population, advertising expenses and previous year has been done below. Regression Statistics Multiple R 0.994833 R Square 0.989693 Adjusted F 0.986749 Standard E 314.273 Observatic 19 ANOVA df SS MS F Regressio 4 1.33E+08 33194680 336.0891 Residual 14 1382745 98767.5 Total 18 1.34E+08 Coefficient andard Err t Stat P-value Intercept 11121.02 8427.834 1.319558 0.208156 Year 169.5104 88.54661 1.914363 0.076237 Population -0.058827 0.084523 -0.695988 0.497828 AdvertisingE-09 Previous \\ 0.276927 0.009577 28.91637 6.93E-14 c) Give an interpretation of your observations related to the diagnostics. Answer:d) In view of the large intercept in part c, the regression was re-run forcing the intercept at zero. The below results were obtained. Give an interpretation of the results. Regression Statistics Multiple R 0.999835 R Square 0.99967 Adjusted F 0.932937 Standard I 321.9443 Observatic 19 ANOVA df SS MS F Regressio 4 4.71E+09 1.18E+09 11360.51 Residual 15 1554722 103648.2 Total 19 4.71E+09 Coefficient:andard Err t Stat P-value Intercept 0 #N/A #N/A #N/A Year 54.42569 15.67463 3.472216 0.003413 Population 0.052626 0.003266 16.11213 7.04E-11 Advertising009 13.44494 9.01E-10 Previous \\ 0.272211 0.009102 29.9077 8.7E-15 Answer:e) Give an estimate of the sales in year 13 if the population size estimate would have been 113,000 and the advertising expenditure would have been $10,000. Answer: Question 3 The International Masters in Business Administration is the flagship program of IE Business School'. Not only is the program training the future business leaders, but it is also generating important operating prots that fund other activities of the school such as research. The number of IMBA applications at IE Business School has been increasing for a number of years and given the consistently high performance in the FT rankings, the IMBA office expects this trend to continue next year. True to its mission to improve practice through education, IE Business School is considering expanding its November intake for the IMBA program from ve streams of 65 students to six streams. This is an expensive proposal and before committing to it, Christos, a newly appointed manager at the IMBA ofce, was asked to do some analysis. Christos came up with the following numbers. Cost and revenue The costs associated with the IMBA program are about 2.5M per intake year plus another 1M per stream, while the net revenue to the IMBA ofce amounts to 30,000 per student. Applications IE Business School received 2000 applications last year, representing a 5% increase from previous years, and it is expecting next year to receive about 2100 applications. The quality of these applications varies widely, but it is expected that 630 applicants (approximately 30% of the total) exhibit the academic and leadership qualities necessary to be given an offer. From the candidates given an offer, historically, 58% 1 This exercise is entirely ctional and is to be used for pedagogical purposes only. It is not indented to be an accurate reection of reality and it is in no way endorsed by IE Business School. enrolled to the program. Needless to say, there is substantial uncertainty on all these figures. Christos summarized this information in the spreadsheet of table 1. Based on this analysis. and given the prestige of expanding the program, the IMBA ofce concluded that it is probably a good idea to proceed with the sixth stream because it will generate an extra 212,000. a) Do you agree with this analysis? IE Business School Five Streams Six Streams Revenue per student 30.000 30000 Cost per stream 1.000.000 1.000.000 Fixed costs 2.500.000 2.500.000 High quality applications 630 530 Accepted applicants enrolled 58% 53% Potential students 365.4 355.4 Places per stream 65 65 Number of streams 5 6 Capacity 325 390 Number of students enrolled 325.0 365.4 Revenue 9.750.000 10.952.000 Cost 6 7.500000 3.500.000 Prcrt 2,250,000 2,462,000 Table 1: Profitability of the MBA programme Table 1: Profitability of the MBA programme To understand the value better, Christos decided to do some more analysis. Based on past experience, the number of high quality applications is most likely to be 630 but it could be as low as 510 and or as much as 750. The percentage of offers converted to enrolment is less uncertain, between 56%60%, because it eon be managed effectively by the MBA ofce through 'overbooking' and through creating waiting lists. Given these ranges the sensitivity analyses are shown in figure 2. One-Way Sensitivity - No of applicants 3.500.000 3.000.000 2,500.000 2.000.000 1.500.000 1,000,000 500.000 0 510 530 550 570 590 610 630 650 670 690 710 730 750 No of applicants Five Streams """ Six Streams Values in million euros One-Way Sensitivity - Accepted students enrolled 2.800.000 2,600,000 2,400,000 2,200.000 2,000.000 56.00% 57.00% 58.00% 59.00% 60.00% 56 of accpected students enrolled Values In mlllon euros Five Streams ----- Six Streams Figure 2: Sensitivity Analysis b) On the basis of the sensitivity analysis (gure 2), what can you conclude? Christos decided that in order to make a more informed decision he needed to do a simulation. c) Can you give him advice on what distributions to use for the uncertain inputs? Please give exact recommendations and explain the rationale behind your choices. After performing the simulation Christos plotted the histograms of the protability in figure 3. d) Describe, compare and explain the shape of these distributions. Specifically, try to explain why both probability density charts exhibit a spike at the very right. e) Based on the histograms of figure 3, should Christos recommend to the IMBA office to choose five or six streams? Please make an explicit recommendation (based on this analysis) and justify your reasoning.Histogr... 0.00 2.25 4... 90.... 5 .. 12 .... 36.... 50.... 4.0 3.5- Profit / Five Streams 3.0 Minimum -E3289778.1757 Maximum