(a) Calculate overall duration of all the assets.

(b) Calculate overall duration of all the liabilities.

(c) Calculate the leverage adjusted DGAP.

(d) Calculate overall change in values for all the assets for a 3% increase in interest rate.

(e) Calculate overall change in values for all the liabilities for a 3% increase in interest rate.

(f) Using the results from (d) and (e), compute the change in equity value for a 3% increase in interest rate.

(g) The director of Michael Bank wants to immunize the balance sheet completely by setting a new value of duration of all the assets. However, if it is impossible to change the duration of all the liabilities, and the top management does not want to change the total values of assets and liabilities. In that case, calculate a new value of duration of all the assets for the director so that immunization can be carried out.

A Pharmaceutical company produces three drugs: A, B, and C. It can sell up to 500 kg of each drug at the following prices (per kg):

Drug Sales price

A $10

B $15

C $25

The company can purchase the raw material at $7 per kg. Each kg of raw material can be used to produce either one kg of Drug A or one kg of Drug B. Assume cost of these operations is negligible. For a cost of $4 per kg processed, Drug A can be converted to 0.7 kg of Drug B and 0.3 kg of Drug C. For a cost of $5 per kg processed, Drug B can be converted to 0.9 kg of Drug C. Formulate this problem as a spreadsheet model and use Solver to determine the number of kgs of the raw material to purchase to make Drug A and Drug B, and the number of kgs of Drugs A and B to further process in order to maximize profit from selling the drugs subject to producing more than using each drug and max sales constraints.

Hint: Each operation in this problem has one input and one or more outputs, whereas each operation in the Production Process problem in Session 10 had one output but 1 or more inputs.   So in this problem, instead of "Production of 1 unit of" on the top, put the "Usage of 1 unit of" on the top, and put kgs of each drug to be produced on the left.   Consider the raw material to make Drug A different from that to make Drug B (call them RM1 and RM2). Instead of labour, there is cost.

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

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 15.20%.) 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 = 24.39%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

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

4. 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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Question 5

a) (1) X~Normal(mean=4, standard deviation=3), (2) Y~Normal(mean=6, standard deviation = 4), and (3) X and Y are independent, then, P(X+Y>13) equals (in 4 decimal places)

Answers options: a) 0.7257, b) 0.3341, c) 0.2743, d) 0.6759, e) none of these

b) Let X~Gamma(4, 1.2). Which of the following is possible R code for computing the probability that X < 2.6?

Answers options: a) dgam(2.6, 4, 1.2), b) pgamma(4, 1.2, 2.6), c) dgamma(2.6, 4, 1.2), d) pgamma(2.6, 4, 1.2), e) None of these

c) If X~Exponential(lambda=2.8), which of the following code computes P(X>2) correctly?

answers options: a) 1-dexp (2, rate=2.8), b) pexp(2, rate=2.8), c) 1-pexp(2, rate=2.8), d) dexp(2, rate=2.8)

d) If X has an Exponential distribution with mean 2.5, which of the following code computes P(X<3) correctly?  

Answers options: a) pexp(3, rate=2.5), b) dexp(3, rate=2.5), c) pexp(3, rate=0.4), d) dexp(3, rate=0.4), e) None of these

e) If X1, X2, ..., X100 are independent and identically distributed as Uniform (0,1), the probability that the average of these 100 random variables is less than 0.3 equals   , approximately? ( ). Answers options: a) 0.4586, b) 0.5414, c) 0.6406, d) 0.3594, e) None of these

a. About % of the area under the curve of the standard normal distribution is outside the interval z=[−0.3,0.3]z=[-0.3,0.3] (or beyond 0.3 standard deviations of the mean).

b. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.6404P(-b<z<b)=0.6404, find b.

b=

c. Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.6z=-1.6 and z=1.6z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?

Answer:  percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)

d. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.6 years, and standard deviation of 3.1 years.

If you randomly purchase one item, what is the probability it will last longer than 20 years?

e. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 224-cm and a standard deviation of 1.8-cm. For shipment, 27 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 223.6-cm and 224.2-cm.
P(223.6-cm < M < 224.2-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Digitone_Co is exploring to use air freight to transport lasers from China to Bulgaria. How much more or less they will have to pay if they shift from ocean to air transportation?

Assume the below numbers for this part (Assume no additional cost other than the ones mentioned below):

1. The total annual demand for headsets is 100000. The per unit cost is € 400.
2. The weight of each unit of the laser is 0.4 Kg.
3. Inventory holding cost is 11% per year.
4. Air rate is € 5/kg and it takes 4 days to transport the headsets from China to Bulgaria via air.
5. Ocean rate is € 0.3/kg and it takes 21 days to transport the headsets from China to Bulgaria via ocean.
6. There are 365 days in a year.

1. Enter the difference between the Cost of Ocean Transportation and the Cost of Air Transportation (Ocean Cost - Air Cost)?

HomeShop has a branch/local office in Japan. HomeShop sells 30000 units to customers in Bulgaria and 100000 units to customers in Japan. Profit per unit is € 89 (Ignore all other costs). All profits are repatriated from Japan. The corporate tax rate in Bulgaria is 40% and 32% in Japan.

2. With no Tax relief agreement in Japan, what are the total taxes that HomeShop has to pay in both countries?

3. Now assume that there is a possibility to use foreign tax credit (FTC) in Bulgaria. What will be the total taxes HomeShop has to pay in this scenario in both countries?

In 2016, the mean salary for all Ontario public employees in the School Board sector with salaries of at least $100,000 was 114.35 (in thousands of dollars), and the standard deviation was 15.67 (also in thousands of dollars). Let ??Xi be the salary of one randomly selected employee (denoted i), and let ?¯X¯ be the sample mean for a sample of 500 employees with salaries of at least $100,000 from the School Board sector.

(i) Which is larger: ?(??>116)P(Xi>116) or ?(?¯>116)?P(X¯>116)? Explain. (ii) Compute any probabilities possible with the given information.

(b) [6 pts] Suppose we know that ?(??>120)=?P(Xi>120)=a, where ?a is a constant. We define a new random variable ??Yi for each i, where ??Yi is equal to 1 if ??>120Xi>120 and is equal to 0 otherwise (??Xi is defined in part (a)). Also let ?=∑200?=1??W=∑i=1200Yi, where we assume that all the ??Yi’s are independent and have the same distribution.

What kind of distribution does ??Yi have (hint: it has a name)? What are the values of its parameter(s)? What kind of distribution does ?W have (it also has a name)? What are the values of its parameters? Explain in 1 sentence how you know ?W has this distribution.

(c) [6 pts] Suppose now that ?=0.3a=0.3. What is ?(?>70)P(W>70)? Use an appropriate approximation and correct for continuity. Give a clear interpretation (1 sentence).

The mayor of a city wants to see if pollution levels are reduced by closing the streets to the car traffic. This is measured by the rate of pollution every 60 minutes (8am 22pm: total of 15 mea- surements) in a day when traffic is open, and in a day of closure to traffic. Here the values of air pollution: With traffic: 214, 159, 169, 202, 103, 119, 200, 109, 132, 142, 194, 104, 219, 119, 234 Without traffic: 159, 135, 141, 101, 102, 168, 62, 167, 174, 159, 66, 118, 181, 171, 112 (a) Is this paired data or independent samples? (b) Construct the proper test to see if the pollution levels are reduced by closing the streets to the car traffic. Give the test statistic and the p-value. (c) Since the p-value depends on sample size, some people may wish to calculate an effect size which can be done dividing the absolute (positive) Standardize test statistic z by the square root of the number of pairs. R does not give the standardize test statistic in its output but it can be calculated using the p-value from the output and the following formula: abs (qnorm (pvalue))/2. According to Cohen's classification of effect sizes which is 0.1 (small effect), 0.3 (moderate effect) and 0.5 and above (large effect). What is the effect size from this test? (d) Compute a 95% confidence interval for the difference between the true pollution levels.

Ginny’s Restaurant Problem

Ginny is endowed with $10 million and is deciding whether to invest in a restaurant. Assume perfect capital markets with an interest rate of 6%.

1. List 4 perfect capital market assumptions.

1.   _ ______

2.   _ ______

3.     ______

4.   _ ______

2. Which investment option should Ginny choose?

Ginny is actively pursuing another business venture as a ticket scalper. She estimates that for a $2 million investment in inventory she can resell her tickets for $6 million over the next year (cash flows realized in exactly one year).  Assume the same 6% interest rate.

3. What is the NPV of the Ticket Brokering venture?
4. What is the new value of Ginny’s Corporation?
5. Suppose Ginny does not want to use her own $2 million to start the new venture. Instead, she wants to raise equity capital by issuing 100,000 new shares. What price will new investors be willing to pay?
6. How many shares will need to be sold to outside investors?
7. How will your answer differ if Ginny is not guaranteed to resell the tickets for $6 million?

(ix)      According to Ginny’s prospectus, cash flows from ticket sales (net of expenses) are expected to follow the following distribution:

What is the new value of Ginny’s Corporation?

(x)       What price will new investors be willing to pay for Ginny’s shares?

1) (note: Please also provide the excel formulas used to solve it )  You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 18 containers. Estimate the population standard deviation at a 90% level of confidence.

(Data checksum: 216.29)

Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer.

a) Find the sample standard deviation:

b) Find the lower and upper χ2 critical values at 90% confidence:
Lower:    Upper:

c) Report your confidence interval for σ (  ,  )

2) (note: Please also provide the excel formulas used to solve it )

If n=300 and p^=0.3, construct a 90% confidence interval about the population proportion. Round your answers to three decimal places.

Preliminary:

1. Is it safe to assume that n≤0.05n≤0.05 of all subjects in the population?
   • No
   • Yes
   
   
2. Verify nˆp(1−ˆp)≥10. Round your answer to one decimal place.
   
   nˆp(1−ˆp)=

Confidence Interval: What is the 90% confidence interval to estimate the population proportion? Round your answer to three decimal places.

< p <