For each question on a multiple-choice test, there are five possible answers of which exactly one is correct for each question. Assume there are 10 questions on the test and a student selects one answer for each question at random. Let X be the number of correct answers he or she gets.

a) How is X distributed? (Specify the values of the corresponding parameters).

b) Find P(X < 6) and P(X = 6). c) Find E(X) and V ar(X).

2. Suppose that a basketball player makes a free throw 60% of the time. Let X equal the number of free throws that this player must attempt to make a total of 3 shots. Assume independence among attempts,

a) How is X distributed? (Specify the values of the corresponding parameters)

b) Find P(X = 6).

c) Find E(X) and V ar(X). 2 3.

A factory puts biscuits into boxes of 100. The probability that a biscuit is broken is 0.03. Find the probability that a box contains 2 broken biscuits using Poisson approximation.

4. (20 pts) Let X have the p.d.f: f(x) = 3x 2 2 for −1 ≤ x ≤ 1 and f(x) = 0 for otherwise . a) Find P(X > 0.5). b) Find E(X). 3 c) Find the c.d.f F(x). d) Find π0.5. 4

5. (10 pts) Suppose that a system contains a certain type of component whose time, in years, to failure is given by X. The random variable X is modeled nicely by the exponential distribution with mean time to failure θ = 3. Find: a) P(X ≥ 4). b) Given that the component has been in operation for 2 years, find the conditional probability that it will last for at least another 4 years. 5

6. (8 pts) If X ∼ N(−10, 25), find: a) P(X ≤ 0) b) P(−15 ≤ X ≤ −5) c) P(X ≤ 20) d) π0.4.

7. (6 pts) If Z ∼ N(0, 1), find the values of z such that: a) P(Z > z) = 0.3. b) P(|Z| ≤ z) = 0.4. 6

8. (21 pts) Jim sells blueberry bushes to his customers when they are at least 18 inches tall. He wants to know how long it will take each of his blueberry bushes to grow tall enough to sell. To get an estimate of this time, he selects ten plants at random and records the number of days each one takes to grow from a seed into an 18 inch tall plant. 96, 98, 97, 101, 98, 95, 100, 95, 98, 101. Find the values of the following statistics a) Sample mean ¯x b) Sample median ˜x. c) Sample mode and sample range. d) Sample variance and sample standard deviation.

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, , for Stock B ( = 10.60%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 25.58%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

   Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

   Is it possible that most investors might regard Stock B as being less risky than Stock A?

   1. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   4. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   
   
   -Select-IIIIIIIVVItem 4

3. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.

   Stock A:

   Stock B:

   Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?

   1. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   3. In a stand-alone risk sense A is less risky than B. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   4. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   5. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.

Advertising on Facebook: Unlimited Potential

With 800 million active members, Facebook is a global social network of unprecedented size—and untold potential revenue. Users are familiar with the advertisements in the right-hand margins. Big names, such as Walmart and PepsiCo, post ads, as do smaller companies. What users may not realize is that advertisers can use personal information and connections within Facebook to refine the targeting of ads. For example, women who change their relationship status to “engaged” will suddenly start seeing ads from local caterers, planners, wedding-gown stores, photographers, and so on.

Facebook recently surpassed Google as the most visited site in the United States. Facebook's “self-service” ads consist of a small photo and some text. An advertiser establishes a daily budget—there is no minimum—using Facebook's ad-creation tool. When the advertiser has spent the day's entire budget, Facebook stops running the ad. If money is left over, the advertiser can roll it over to the next day's budget. Advertisers pay either every time a user views the ad or every time a user actually clicks on the link in the ad to open the company's Web site.

Facebook members can become “fans” of an advertiser's Facebook page or can reply to an invitation to a company-sponsored event through Facebook. But as with other media, consumers have a deep mistrust of Web advertising as a credible source of information. With ads on Facebook becoming omnipresent, click-through rates (CTRs) have fallen to about 0.3 percent from close to 3 percent. Some Facebook users find the ads off-putting—or worse—because advertisers can target them so precisely. But Dan Rose, the vice president for business development at Facebook, predicted that the quality of the ads would improve as more companies use the system.

Facebook requires the text and photo in an ad to be relevant to what is being advertised. However, Facebook does not review ads before they are posted. The only review system is user feedback. If a user reports an ad as misleading, offensive, uninteresting, irrelevant, repetitive, or “other,” Facebook deletes the ad from that user's page. The more people ask for an ad to be removed, the less likely Facebook is to allow it be posted on other people's pages.

Some observers predict that Facebook will transform Web advertising and even the advertising industry itself. And just as in the real world, in the virtual world people are much more likely to value the opinions of their friends more than those of people—or advertisers—they don't know.

Questions for Critical Thinking

1. Why do advertisers continue to post ads on Facebook, even though the click-through response rate is so low?

2. How does Web advertising affect consumer behavior? Does it help build customer relationships or not?

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Python Programming

This assignment will give you practice with interactive programs, if/else statements, collections, loops and functions.

Problem Description
A small car yard dealing in second hand cars needs an application to keep records of cars in stock. Details of each car shall include registration(rego), model, color, price paid for the car (i.e. purchase price) and selling price. Selling price is calculated as purchased price plus mark-up of 30%. For example, Toyota Corolla bought for $20,000 will have the selling price of 20000 * (1 + 0.3) = 26000.

Task Requirements
Imagine you have been invited to develop a menu driven python application to manage records of cars in stock. Based on the problem description, starter program (code template) has been provided. Investigate the provided starter program. There are four scripts(application.py, caryard.py, cars.py and vehicle.py). Driver function(main) is defined in the appliction.py, which imports caryard module(caryard.py). Caryard declares all the core functions (buy, sell, search, etc. …) for supporting the car yard business. The caryard module imports cars module(cars.py), and the cars module in turn imports the vehicle that include a definition of a Car class.
Program is executed by loading and running the application.py. The important work of interconnecting and wiring of modules and functions have been already been done. However, most of these functions, although declared and wired up in the program are not yet implemented. Your task is to implement these functions. There are eleven (11) tasks to be completed described next within the modules:

1. application.py
• Task 1: implement menu ()

2. caryard.py
• Task 2: implement buy_car ()
• Task 3: implement sell_car ()
• Task 4: implement search_car ()
• Task 5: implement list_all_cars ()

3. cars.py
• Task 6: implement addCar (rego, model, color, price)
• Task 7: implement removeCar (rego)
• Task 8: implement all_cars ()
• Task 9: implement search(rego)

4. vehicle.py
• Task 10: implement the Car class
• Task 11: UML model of a Car class

Description of Program functions:

Program displays a menu on execution. Five menu options are available to allow the user to buy, sell, search, show all cars, and exit program respectively. Program functionality and screen output for each of the menu option when selected by the user follows:

Program menu on execution:



Option 1 (Buy a car): User enters 1. Note the error message for duplicate car rego

 
Option 2 (Sell a car): User enters 2. Note the error message for invalid car rego, and the sell price which is a (30%) mark-up of purchase price.

Option 3 (Search): User enters 3

Option 4 (Show all): User enters 4

Option 5 (Exit Program): User enters 5

Luangwa Mineral Resources is a State Owned Enterprise (SOE) that was in past managed parastatal before being privatize after liberalization of the Zambia economy. The privatization of the firm was decided because the firm had been run down and was not performing well as expected. Further the firm accrued huge liabilities and was running losses consistently. After being privatized the new owners (majority shareholders 75%) re capitalized the firm by investing $160 million to improve operation and clear outstanding debts. The new Board of Directors brought in goods expertise and knowhow which greatly improved the way the company was managed. The company was turned around within Three years and become profitable and as a result government was able to receive its share of profits. The company remained profitable until a regime changed policy that now required government to own majority share in a bid to accrue more benefits for the state. The changes in policy meant the minority foreign investors could not control decision making within the company as now government took more control of the affairs. The Government appointed a new board and new management took over. The company in a span of four years since these changes has reached a stage where it is now failing to meet its obligations. It has accrued huge debts and has started making losses due to poor decision making regards operations. Audits reports indicated that miss application of resources to non-value adding activities, poor cash flow management, over employment and abuse of company resources and board members (Chairperson) and management staff. It was reported that in previous quarter the board had spent $1.0 million on workshops, travel allowances and meetings alone much of the money obtained through an overdraft with a local bank. This was done at the expense of procuring a critical component of the production process that only costed $150,000. Consequently production was shut down for six months. This has led to wide spread uproar in the media and among concerned stakeholders and the company’s board and corporate governance system has been questioned. Among the many expectations from stakeholders is the effectiveness of the board through composition of members, integrity and ethical values of board members and ability to critically analyses the company’s long term sustainability Required: i. Discuss the objective and importance of Corporate Governance in general to the operations of an organization. (6 Marks) ii. Identify and discuss the Agency Problem issues in this case study that may have led to the current situation how this can be rectified. (10 Marks) iii. Discuss how Corporate Finance can be applied in guaranteeing the company’s long term financial sustainability while balancing wealth maximsation.

Bank Balance Sheet (Note: Use this information for all three problems)

Appendix 23A

Item                             Amount            Duration       Interest Rate       

Cash-type Securities       $50m                1.2 year             2.25%

Commercial Loans          $100m             2.4 years           4.50%

Mortgages                     $350m             8.0 years           6.50%

Core Deposits                $270m             1.0 year             2.00%

Notes Payable                $180m             2.0 years           4.50%

APPENDIX 23A.1-

Change E= -(Da-kDl) * A * Change R/ 1 +R

Change E= Change in FI Net Worth

Da- Duration of asset portfolio

Dl- Duration of liability portfolio

K- Ratio of an FI's liabilties to assets

A- Size of FI's Asset portfolio

Change R/1+R- Shock to interest rates

3. Off-Balance sheet futures hedge (Use balance sheet information above, 8 points)

T-Bond futures contracts for the delivery of $100,000 face value are trading at 102-16, and have a duration of 9.50 years. This problem is based on the material in Appendix 23A: Hedging with Futures Contracts.

a. What is the total dollar price of each futures contract (P_F)?

b. For this bank to achieve complete immunization, solve for F (total dollar value of futures contracts to immunize). Note: We don’t know the number of contracts yet or a specific interest rate change, so that information should not be used to solve for the dollar value F. Use only the information provided above to solve for F.

c. Using F from part b above, solve for the number of T-Bond futures contracts needed by this bank to hedge the interest rate risk (round to the nearest whole number of contracts).

d. Explain in a full essay what risk this bank faces, what position this bank would take on the T-Bond futures contracts to hedge against the interest rate risk it faces, why it would take that position, and graph that position in a fully-labeled futures payoff diagram.

Assume average interest rates rise from the original level of 6.0% to 7.50%.

e. Calculate the on-balance sheet change in the bank’s value (ΔE), and specify the sign (positive or negative)

f. Calculate the off-balance sheet change in the value of the futures contracts (ΔF), and specify if it’s a gain or loss.

g. Assume you are a financial analyst and risk management specialist for the bank above. Write a full, complete, and convincing essay (executive summary) of at least several complete paragraphs to your company’s CEO that summarizes the main conclusions from this third problem, and specifically refer to your numerical results from parts e and f.

Consider the following information on Huntington Power Co.
Debt: 4,000, 7% semiannual coupon bonds outstanding, $1,000 par value, 18 years to maturity, selling for 102 percent of par; the bonds make semiannual payments.
Preferred Stock: 10,000 outstanding with par value of $100 and a market value of 105 and $10 annual dividend.
Common Stock: 84,000 shares outstanding, selling for $56 per share, the beta is 2.08

The market risk premium is 5.5%, the risk free rate is 3.5% and Huntington’s tax rate is 32%.

Huntington Power Co. is evaluating two mutually exclusive project that is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and decided to apply an adjustment factor of +2.1% to the cost of capital for both projects.

Project A is a five-year project that requires an initial fixed asset investment of $2.4 million. The fixed asset falls into the five-year MACRS class. The project is estimated to generate $2,050,000 in annual sales, with costs of $950,000. The project requires an initial investment in net working capital of $285,000 and the fixed asset will have a market value of $225,000 at the end of five years when the project is terminated.

Project B requires an initial fixed asset investment of $1.0 million. The marketing department predicts that sales related to the project will be $920,000 per year for the next five years, after which the market will cease to exist. The machine will be depreciated down to zero over four-year using the straight-line method (depreciable life 4 years while economic life 5 years). Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. The project will also require an addition to net working capital of $150,000 immediately. The asset is expected to have a market value of $120,000 at the end of five years when the project is terminated.

Use the following rates for 5-year MACRS: 20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%

1. Calculate WACC for the firm

2. What is the appropriate discount rate for project A and project B?

3. Calculate project A’s cash flows for years 0-5

4. Calculate project B’s cash flows for year 0-5

5. Calculate NPV, IRR and PI for project A

6. Calculate NPV, IRR and PI for project B

7. Which project should be accepted if any and why?

8. What is the NPV profile’s crossover rate (incremental IRR)?

9. By just considering the crossover rate, and without recalculating NPV or IRR, which project would you select if the appropriate discount rate for both projects is 8% and why?

Kaelea, Inc., has no debt outstanding and a total market value of $153,000. Earnings before interest and taxes, EBIT, are projected to be $9,500 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 20 percent higher. If there is a recession, then EBIT will be 30 percent lower. The company is considering a $45,300 debt issue with an interest rate of 5 percent. The proceeds will be used to repurchase shares of stock. There are currently 5,100 shares outstanding. Assume the company has a market-to-book ratio of 1.0.

a. Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued, assuming no taxes. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b. Calculate the percentage changes in ROE when the economy expands or enters a recession, assuming no taxes. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to the nearest whole number, e.g., 32.)

  
Assume the firm goes through with the proposed recapitalization and no taxes.

c. Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

d. Calculate the percentage changes in ROE for economic expansion and recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Assume the firm has a tax rate of 35 percent.

e. Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued. Also, calculate the percentage changes in ROE for economic expansion and recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

f. Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. Also, calculate the percentage changes in ROE for economic expansion and recession, assuming the firm goes through with the proposed recapitalization. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)