You are a banker and are confronted with a pool of loan applicants, each of whom can be either low risk or high risk. There are 600 low-risk applicants and 400 highrisk applicants and each applicant is applying for a $100 loan. A low-risk borrower will invest the $100 loan in a project that will yield $150 with probability 0.8 and nothing with probability 0.2 one period hence. A high-risk borrower will invest the $100 loan in a project that will yield $155 with probability 0.7 and nothing with probability 0.3 one period hence. You know that 60% of the applicant pool is low risk and 40% is high risk, but you cannot tell whether a specific borrower is low risk or high risk. You are a monopolist banker and have $50,000 available to lend. Everybody is risk neutral. The current riskless rate is 8%. Each borrower must be allowed to retain a profit of at least $5 in the successful state in order to be induced to apply for a bank loan. You have just learned that 1,000 loan applications have been received after you announced a 45% loan interest rate. You can satisfy only 500. What should be your optimal (profit-maximizing) loan interest rate? Should it be 45% (at which you must ration half the loan applicants) or a higher interest rate at which there is no rationing?

Suppose that T-bills currently have a rate of return of 2%. As- sume that borrowing is possible at the risk free rate. You are risk averse and you are considering constructing a portfolio consisting of T-bills and one of the two risky assets: Stock A or Stock B. You did the following scenario analysis on stocks A and B

Events Bull Market Normal Market Bear Market

Probability Stock Aís return 0.3 50%
0.5 18%
0.2 -20%

Stock Bís return 10%
20%
-15%

1. (a) Compute the expected rate of return and the standard deviation for Stock A and Stock B.

2. (b) Based on the information you have so far, which of the two risky assets, Stock A or Stock B, would you choose to be included in your portfolio with T-bills? Explain.

3. (c) Your friend is considering the same problem but she is more risk averse than you. Should she arrive at a di§erent conclusion than you? Ex- plain.

4. (d) Suppose that you start your portfolio with $1 million and also your portfolio target risk (std dev) is 10% (this is your portfolio from part (b)), how many dollars will you invest in T-bills? What is your port- folioís expected return? Show your work.

2.a. You are running a batch reactor. Each batch takes about four hours to run. You measure the purity of the batch four times in the last hour to ensure that it has stabilized. You want to monitor the results using an X-R chart. The data you have collected for the first 10 batches are given the table below. X1, X2, X3 and X4 are the four samples you pull from the batch in the last hour. Using all the data, find trial control limits for and R charts, construct the chart, and plot the data. (30 pts)

2.b. Is the process in statistical control? Identify out-of-control points. (30 pts)

China's Galanz built a new complex at the expected cost of 2 billion yuan in order to produce 12 million air-conditioning units annually. The site was completed in 2004.
1 Make the following assumptions:

•The actual investment cost is either 1.9, 2.0, or 2.1 billion yuan, with respective probabilities of 0.25,0.50, and 0.25.
•The plant operates for 15 years, with the salvage value being either 50 million, 0, or-100 million(remediation costs) yuan at that time, with probabilities of 0.20,0.50, and 0.30, respectively.
•Finally, the net cash flow resulting from operations and sales is 60 yuan per unit. The number of units sold in each year is either 9 (0.1), 10 (0.2), 11 (0.3), or 12 (0.4) million. The figures in
parentheses represent the probabilities of the given level of production.

Assume that these are the only relevant cash flows and the interest rate is 18% per year.

a) Find an expression for the present worth (PW).

b) Find the expected value of the PW(if possible).

c) Find the standard deviation of the PW(if possible).

d)Find Pr(PW >0) (if possible).

e)Perform 200 simulations, and find the sample mean, standard deviation, as well as the probability that the investment will have a positive PW (point & interval estimates). Finally, summarize your process (which will naturally include all the appropriate steps) and results

Suppose the production function is written as follows: 0.5 0.5 ?=? ?

Suppose that saving rate (s) is 0.3, population growth rate (n) is 0.05, and capital depreciation rate (d) is 0.05. (note: when you write your equations, be careful to distinguish capitalized characters and non- capitalized characters!) 3-1.

(5%) Derive the per-capita production function (i.e. ? = ? and ? = ?). ?? 3-2.

(5%) Write down the key equation of the Solow model on capital accumulation per capita. Then, impute key parameter values. (you do not have to derive the key equation)

(15%) Draw a key graph for the Solow model. (hint: ? on y-axis and ? for x-axis. Then draw per- capita production function. You also need to draw two additional curves derived from the capital accumulation equation) 3-4.

(5%) What is the steady-state level of per-capita capital? Solve the model and obtain the number. What is the economic growth rate when the economy is under the steady-state? 3-5. (10%) Suppose at the first period of the economy, ? = 4. What happens to the economy? Use a graph to show your answer.

(10%) Suppose the economy now has higher population growth rate. What happens to the steady state? What happens to the economic growth rate? Discuss with a graph

1. Selected activities and other information are provided for Patterson Company for its most recent year of operations.

   						Expected Consumption Ratios
   Activity		Driver		Quantity		Wafer A		Wafer B
   7.   Inserting dies		Number of dies		2,500,000		0.7		0.3
   8.  Purchasing materials		Number of purchase    orders		2,400		0.2		0.8
   1.  Developing test programs		Engineering hours		12,000		0.25		0.75
   3.  Testing products		Test hours		20,000		0.6		0.4
   ABC assignments						$150,000		$150,000
   Total overhead cost								$300,000

   Required:

   1. Form reduced system cost pools for activities 7 and 8. Do not round interim calculations. Round your final answers to the nearest dollar.

   Inserting dies cost pool	$
   Purchasing cost pool	$

   2. Assign the costs of the reduced system cost pools to Wafer A and Wafer B. Do not round interim calculations. Round your final answers to the nearest dollar.

   Wafer A	$
   Wafer B	$

   3. What if the two activities were 1 and 3? Repeat Requirements 1 and 2.

   Form reduced system cost pools for activities 1 and 3.

   Do not round interim calculations. Round your final answers to the nearest dollar.

   Developing test programs cost pool	$
   Testing products cost pool	$

   Assign the costs of the reduced system cost pools to Wafer A and Wafer B.

   Wafer A	$
   Wafer B	$

You are a banker and are confronted with a pool of loan applicants, each of whom can be either low risk or high risk. There are 600 low-risk applicants and 400 highrisk applicants and each applicant is applying for a $100 loan. A low-risk borrower will invest the $100 loan in a project that will yield $150 with probability 0.8 and nothing with probability 0.2 one period hence. A high-risk borrower will invest the $100 loan in a project that will yield $155 with probability 0.7 and nothing with probability 0.3 one period hence. You know that 60% of the applicant pool is low risk and 40% is high risk, but you cannot tell whether a specific borrower is low risk or high risk. You are a monopolist banker and have $50,000 available to lend. Everybody is risk neutral. The current riskless rate is 8%. Each borrower must be allowed to retain a profit of at least $5 in the successful state in order to be induced to apply for a bank loan. You have just learned that 1,000 loan applications have been received after you announced a 45% loan interest rate. You can satisfy only 500. What should be your optimal (profit-maximizing) loan interest rate? Should it be 45% (at which you must ration half the loan applicants) or a higher interest rate at which there is no rationing?

You are a banker and are confronted with a pool of loan applicants, each of whom can be either low risk or high risk. There are 600 low-risk applicants and 400 highrisk applicants and each applicant is applying for a $100 loan. A low-risk borrower will invest the $100 loan in a project that will yield $150 with probability 0.8 and nothing with probability 0.2 one period hence. A high-risk borrower will invest the $100 loan in a project that will yield $155 with probability 0.7 and nothing with probability 0.3 one period hence. You know that 60% of the applicant pool is low risk and 40% is high risk, but you cannot tell whether a specific borrower is low risk or high risk. You are a monopolist banker and have $50,000 available to lend. Everybody is risk neutral. The current riskless rate is 8%. Each borrower must be allowed to retain a profit of at least $5 in the successful state in order to be induced to apply for a bank loan. You have just learned that 1,000 loan applications have been received after you announced a 45% loan interest rate. You can satisfy only 500. What should be your optimal (profit-maximizing) loan interest rate? Should it be 45% (at which you must ration half the loan applicants) or a higher interest rate at which there is no rationing?