An Electronic Version of This Exam Is Available on the Class Web Site

MAT116 Final Exam An electronic version of this exam is available on the class web site.

Directions: (1) This is an individual effort! All work you submit must reflect your own individual understanding. (2) You many not get discuss this exam with any person outside of the 7:45AM section of MAT116 (3) You may discuss the exam with fellow students in this section of 116 subject to the "Talking Only and Hands Behind Your Back" principle. This means any discussion of the problems may not include the sharing or viewing of any paper or electronic work/files or the use of any writing or recording devices. Literally, you can talk about what you're doing but you can't see each other's actual work or files. (4) Unless otherwise specified, carefully show all relevant work, formulas, explanations. Don't just put down a formula and then the answer. Pretend you're writing the exam for another 116 student…they need to see what you're doing and thinking. (5) The work must be wordprocessed and a final version printed for submission…no electronic files! (6) Clearly label and number each problem and its parts. (7) The exam is due on Monday, December 15 at 8AM. For every day, or portion of a day, that you are late, you will lose 15%.

The management of a company finds that 70% of factory assembly-line employees hired are satisfactory and 30% are unsatisfactory. Let S be the event that an employee is satisfactory. Let U be the event that an employee is unsatisfactory. The company has developed a test to help improve their hiring process. Let T be the event that a person passes the test, and let F be the event that they fail it. The probability that an employee passes the test given they are satisfactory is 90%. Also, the probability they will fail the test given they are an unsatisfactory employee is 80%. Find the probability that a randomly selected employee is satisfactory given that they have passed the test.

A bank loan is given to a borrower who has 6 years of business experience (Y) and a Graduate Degree (T). The economy is in a boom time(C). The full value of the loan is $2,500,000. The default value is $300,000. The foreclosure value is $1,800,000. Here is data from the DCOUNT command. All notation matches what we said and did in the project. (BR = BR Bank, CJ = Cajun Bank, DP = DuPont Bank).

Recall the overall success and failure probabilities to be P(S) = 0.464 and P(F) = 0.536.

BR Bank Data n(SBR) = 1,470 n(SBR Y) = 125 n(FBR) = 1,779 n(FBR Y) = 125 n(Y) = 250

Cajun Bank Data n(SCJ) = 962 n(SCJ T) = 325 n(FCJ) = 1,212 n(FCJ T) = 258 n(T) = 583

Dupont Bank Data n(SDP) = 1,386 n(SDP C) = 354 n(FDP) = 1,417 n(FDP C) = 291 n(C) = 645

Using only this data, and any other computations necessary from this data, determine whether or not the bank should foreclose or workout on this loan. Some of the conditional probabilities have already been computed for you. Others you will need to show and compute on your own. You must organize and briefly explain your steps along the way.

You deposit $400 per month into an account that pays 5% interest, compounded monthly and do so for 30 years in preparation for retirement. a. Your friend strikes it rich in the lottery and decides to deposit a lump sum of money into the same kind of account so that he has the same amount of money that you do at the end of the 30 years. How much does he need to deposit today to accomplish this? Do not use Excel for this problem (except to check your work). b. After 30 years, you both retire and ask your investment company to move the balance of the account to a safer investment that earns only 3.5% annual interest, compounded monthly. You also instruct them to send you equal monthly checks so that after 20 years, the account is empty. How much money do you receive every month? Do not use Excel for this problem (except to check your work). c. Use Excel to build an amortization table beginning at the time retirement starts showing the balance of the account for each month. Copy only the first 6 months of data as your answer. The table should include at least (i) interest earned for the month and (ii) the balance of the account after your check is paid to you. Go to the class web page and visit the Links portion of the site. There, you will find a file called FinalExamData.xls. Download this data, which gives three years of Disney stock data. You should assume a riskfree rate of 2.5% and an option period of 10 weeks. Also, assume a strike price of $23.20. a. Compute the weekly risk free ratio. Show all calculations. b. Use Excel to compute all of the normalized weekly ratios and report the first five of them as your answer to this question. You can just copy and paste the final results but do provide a brief explanation of how you got the normalized ratios. c. What is the annualized volatility of the stock assuming that you are going to use the volatility in the BlackSholes formula? Explain how you got your result. d. Use the BlackSholes formula to find a fair price for the option. You may use Excel and just report your final answer…not need to show all work or calculations on this one.

Still using the data from the FinalExamData.xls file, please answer the following. a. What are the mean and standard deviation of the original weekly ratios? (Not the normalized ratios!) b. Use Excel to produce a histogram of the weekly ratios. Copy the cleaned up graph into your final document. c. Assume that the weekly ratios are normally distributed with mean and standard deviation equal to those found in part (a) of this problem. Label the horizontal axis of graph with the mean and with at least three standard deviations in each direction away from the mean.

d. Once again assuming that the weekly ratios are normally distributed with mean and standard deviation equal to those found in part (a) of this problem, find the probability that a stock decreases in value between 5% and 6% over a oneweek period. Clearly explain how you get your answer, showing all relevant calculations along the way.