The grade point averages (GPA) of 18 randomly selected college students are used to estimate the mean GPA of the college students. The GPAs from the sample are as follows:

2.3       3.3       2.6       1.8 0.2 3.1       4.0       0.7 3.1

2.3       2.0       3.1       3.4       1.3       2.6       2.6 3.7 2.2

1. (5 points) Is it justified to use of the standard normal distribution to construct the confidence interval? Explain.
2. (10 points) If the population is assumed to be normally distributed, construct a 98% confidence interval for the population mean GPA. Show your work in detail and use 3 decimal digits.

You are given the following three stocks and you have been asked to propose a portfolio for a wealthy client. The client wants either a 2 asset (A-B, B-C, or A-C) or a 3 asset(A-B-C) portfolio. In any case, the portfolios must be equal weighted. Which of the four portfolios do you suggest to the client? Why? Show your work step by step.

1. You are given the following three stocks and you have been asked to propose a portfolio for a wealthy client.  The client wants either a 2 asset (A-B, B-C, or A-C) or a 3 asset(A-B-C) portfolio. In any case, the portfolios must be equal weighted.  Which of the four portfolios do you suggest to the client? Why?

Show your work step by step.

HW 7 16. Madison would like to form a portfolio between Microsoft (Ticker: MSFT) and a bond index fund. The following table shows the performance of the two assets in each state of the economy.

Prob. MSFT(%) Bond(%)

Recession           0.1     -40       12

Normal               0.7     20        6

Boom                 0.2     50        -2

Suppose the standard deviation of Microsoft is 23.24% and the standard deviation of the bond fund is 3.92%. Madison will form a portfolio which invests 40% into Microsoft and 60% into the bond fund.What is the standard deviation and sharpe ratio of the portfolio if risk-free rate is 4%?

Below is the income statement of a publicly-traded biotech company from 2004 until 2007:

The company’s stock was trading for $2 in 2004 and is now trading for $7. Are investors irrational? Should the stock be sold short? Is it possible for a company in the biotech business to be worth something even though it has no current sales? What can justify the billion-dollar values of technology companies which have yet to earn any profits?

Five years ago, a company was considering the purchase of 65 new diesel trucks that were 14.73% more fuel-efficient than the ones the firm is now using. The company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If the company manages to save on fuel costs, it will save $1.875 million per year (1.5 million gallons at $1.25 per gallon). On this basis, fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, the firm would save $2.025 million in total if he buys the new trucks).

Consider two possible forecasts, each of which has an equal chance of being realized. Under assumption #1, diesel prices will stay relatively low; under assumption #2, diesel prices will rise considerably. The 65 new trucks will cost the firm $5 million. Depreciation will be 25.44% in year 1, 38.22% in year 2, and 36.45% in year 3. The firm is in a 39% income tax bracket and uses a 11% cost of capital for cash flow valuation purposes. Interest on debt is ignored. In addition, consider the following forecasts:

Forecast for assumption #1 (low fuel prices):

Required: Calculate the percentage change on the basis that an increase would take place from the NPV under assumption #1 to the probability-weighted (expected) NPV.

Answer% Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Further Information (solution steps):

• Step (1): Calculate the annual expected price of diesel per gallon under each assumption, based on the probabilities outlined in the inputs section.

• Step (2): Using the annual expected fuel prices calculated in step (1), determine the increase in annual savings created by the proposed efficiency for each assumption.

• Step (3): Find the increased cash flow after taxes (CFAT) for both forecasts, based on the annual increase in fuel savings determined in step (2) as the increase in earnings before depreciation and taxes (EBDT), and the starting point from which profit is calculated for each assumption. As part of this step, you must establish annual depreciation (remember: depreciation is a noncash charge).

• Step (4): Considering the increased annual CFAT produced in step (3), calculate the NPV of the truck purchases for each assumption, based on the discount rate (cost of capital) indicated in the inputs section

• Step (5): In view of the outcomes produced in step (4), estimate the combined NPV weighed by the probability of each assumption.

• Step (6): Finally, calculate the percentage difference hypothesizing that an increase took place starting from the NPV for assumption #1 to the combined NPV worked out in step (5).

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6.3 million. The equipment will be depreciated straight-line over 6 years, but, in fact, it can be sold after 6 years for $519,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.20 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 40%, and the required rate of return on the project is 10%.

Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV

Given​ Barbara's estimated​ Cobb-Douglas utility​ function, ​U(q 1​, q 2​) = q 1^0.2 q 2^0.8​, for​ CDs, q 1​, and​ DVDs, q 2​, derive her Engel curve for movie DVDs. Illustrate in a figure. Let p be the price of ​ DVDs, $1.00 be the price of​ CDs, and Y be income. ​Barbara's Engel curve for movie DVDs is

Y= ? (Please provide answer)

​(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts.​E.g., a subscript can be created with the​ _ character.)

1. If the variance of ONLY one asset in a two-asset portfolio changes, what other metric changes?
   1. Weight of the asset whose variance changes
   2. Covariance between the two assets in the portfolio
   3. Variance of the other asset
   4. All of the above
   5. None of the above

2. Given the following calculate the geometric mean yield for the entire holding period:

1. 7.2%
2. 7.3%
3. 7.4%
4. 7.5%
5. 0%

3. Using the information below, calculate the expected return:

1. 17.2%
2. -2.2%
3. 17.4%
4. -2.5%
5. 17.6%

4. Which of the following would cause the Security Market Line to pivot upward:

1. A pharmaceutical company receives FDA approval for a new drug
2. Real growth rate of the economy declines
3. The expected rate of inflation increases
4. All of the above
5. None of the above

5. Given the following, calculate the covariance of returns for these two assets:

1. 0.01%
2. 0%
3. -0.01%
4. 0.05%
5. -0.05%

6. Calculate the standard deviation of a portfolio comprised of the following two assets that have a correlation coefficient of 0.5:

1. 2.8%
2. 2.9%
3. 3.0%
4. 3.1%
5. -2.2%

7. Suppose the standard deviations of each asset increases by 30% of their original values but the correlation coefficient does not change. What happens to the portfolio standard deviation?
   1. It also increases by 30%
   2. It increases by more than 30%
   3. It increases by less than 30%
   4. It decreases by 30%
   5. I don’t know, but this class is awesome!

8. What is the efficient frontier?
   1. The set of portfolios the represent the best combination of risk and return
   2. The set of portfolios that dominate all other portfolios
   3. The set of portfolios from the MVP to the maximum-risk portfolio
   4. All of the above
   5. None of the above

9. Which is not included in the efficient frontier?
   1. Stocks
   2. Bonds
   3. Real Estate
   4. The risk-free asset
   5. Artwork

The diagram shows a mass after it slides down the inclined plane. There is a static
friction coefficient of 0.5 and a kinetic friction coefficient of 0.3 between the box
and the incline. The angle of the incline is 30 degrees , and the box has a mass of 4
kg . The starting height at the top of the ramp is 0.8 meters (and the distance along
the ramp is 1.6 meters ).
A) Prove, with numbers, that the box, if let go from rest at the top of the ramp
*will* start to slide down?
B) Calculate the magnitude of the energy “lost” due to the work done by friction
(in Joules).
C) Calculate the speed of the box at the bottom of the ramp (in m/sec).