Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows.

(a)

Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving (0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor?

ComputersFinancial     ManufacturingPharmaceuticals

What is the expected return percentage of the preferred market segment?

%

(b)

At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving (0.4), stable (0.4), and declining (0.2). What is the preferred market segment for the investor based on these new probabilities?

ComputersFinancial     ManufacturingPharmaceuticals

What is the expected return percentage of the preferred market segment?

%

(Problem 6)     In a popular day care center, the probability that a child will play with the computer is 0.45; the probability that he or she will play dress-up is 0.27; play with blocks, 0.18; and paint, 0.1. a) Construct the probability distribution for this discrete random variable.

b)         What is the Probability a child plays with a computer or paint

(Problem 7)     The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. Find the mean, variance, and standard deviation.

Can you make sure I answered it correctly

Given:

Mean: 1.3

Variance= -1.66

SD= 1.29

A company that manufactures and sells consumer video cameras sells two versions of their popular hard disk​ camera, a basic camera for ​$500​, and a deluxe version for ​$1200. About 55​% of customers select the basic camera. Of​ those, 30​% purchase the extended warranty for an additional ​$100. Of the people who buy the deluxe​ version, 50​% purchase the extended warranty. Complete parts a through d below. ​a) Sketch the probability tree for total purchases. Warranty 0.3 Basic and Warranty 0.165 Basic 0.55 No Warranty 0.7 Basic and No Warranty 0.385 Warranty 0.5 Deluxe and Warranty 0.225 Deluxe 0.45 No Warranty 0.5 Deluxe and No Warranty 0.225 ​(Type integers or​ decimals.) ​b) What is the percentage of customers who buy an extended​ warranty? 39​% ​(Type an integer or a​ decimal.) ​c) What is the expected revenue of the company from a camera purchase​ (including warranty if​ applicable)? The expected revenue from a camera purchase is ​$ nothing. ​(Type an integer or a​ decimal.) ​d) Given that a customer purchases an extended​ warranty, what is the probability that he or she bought the deluxe​ version? The probability is nothing. ​(Round to three decimal places as​ needed.)

(15pt) Assume that GDP (Y) is 5,000. Consumption (C) is given by the equation C = 1,200 +

0.3(Y – T) – 50r, where r is the real interest rate, in percent. Investment (I) is given by the

equation I = 1,500 – 50r. Taxes (T) are 1,000, and government spending (G) is 1,500. Here,

notice that C is negatively related to the real interest rate.

a)What are the equilibrium values of C, I, and r? (3pt)

b)What are the values of private saving, public saving, and national saving? (3pt)

c)Graphically illustrate the above loanable fund market. (Warning: since C is also a function of r,

do you think the supply curve remain vertical?) (3pt)

d)Now assume there is a technological innovation that makes business want to invest more. It

raises the investment equation to I = 2,000 – 50r. What are the new equilibrium values of C, I, and r? (3pt) Also, graphically illustrate this change on the graph you draw from part (c). (1pt)

e)How would you justify the fact that C is also negatively related to r? (2

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight-line over 6 years, but, in fact, it can be sold after 6 years for $606,000. 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 $1.70 per trap and believes that the traps can be sold for $7 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 12%.

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? (Do not round your intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

Suppose the risk-free rate is 3%. And the market interest rate is 5%. There are two stocks A and B. Both pay annual dividend per share of $2 and $3, respectively. The correlations (denoted as corr(x,y)) between their returns and the market return are corr(r1,rm) = 0.2 and corr(r2,rm) = 0.7, respectively. The standard deviations (denoted as σ) of their returns and the market return are σ 1 = 0.4, σ 2 = 0.6, and σ m = 0.3, respectively. (Note: The x and y above are two arbitrary random variables representing time series of returns.)

a. What are the returns (r1 and r2) for these two stocks from CAPM? (Hint: when you are computing beta, be aware that Cov(x,y)= corr(x,y)*σx*σy , Cov denotes covariance here.)

b. What are the prices of these two stocks if the dividend is not growing?

c. What are the Sharp ratios for these stocks and the market portfolio?

d. If 30% of my portfolio is stock A, the rest of it is stock B. What is the variance of my portfolio if E (r1 * r2) = 0.2? (Hint: Cov(x,y) = E(x*y) – E(x)*E(y))

Suppose the risk-free rate is 3%. And the market interest rate is 5%. There are two stocks A and B. Both pay annual dividends per share of $2 and $3, respectively. The correlations (denoted as corr(x,y)) between their returns and the market return are corr(r1,rm) = 0.2 and corr(r2,rm) = 0.7, respectively. The standard deviations (denoted as σ) of their returns and the market return are σ 1 = 0.4, σ 2 = 0.6, and σ m = 0.3, respectively. (Note: The x and y above are two arbitrary random variables representing time series of returns.)

a. What are the returns (r1 and r2) for these two stocks from CAPM? (Hint: when you are computing beta, be aware that Cov(x,y)= corr(x,y)*σx*σy , Cov denotes covariance here.)

b. What are the prices of these two stocks if the dividend is not growing?

c. What are the Sharp ratios for these stocks and the market portfolio?

d. If 30% of my portfolio is stock A, the rest of it is stock B. What is the variance of my portfolio if E (r1 * r2) = 0.2? (Hint: Cov(x,y) = E(x*y) – E(x)*E(y))

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.7 million. The equipment will be depreciated straight-line over 6 years, but, in fact, it can be sold after 6 years for $671,000. 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 $1.80 per trap and believes that the traps can be sold for $8 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 11%.

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? (Do not round your intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

2. A company that manufactures auto parts is weighing the possibility of investing in an FMC (Flexible Manufacturing Cell). This is a separate investment and not a replacement of any existing facilities. Management desires a good estimate of the distribution characteristics of the AW. There are 3 random variables. An economic analyst is hired to estimate the desired parameter, AW. She concludes that the scenario presented to her is suitable for Monte Carlo simulation because of the uncertainties and a direct approach is virtually impossible. The company has done a preliminary economic study and provided the analyst with the following estimates:

• Investment – Normally distributed with mean of $200,000 and SD of $10,000

• Life – Uniformly distributed with minimum of 5 years and maximum of 15 years

• Market Value at End of Life – $20,000 (single outcome, no uncertainty)

• Annual Net Cash Flow – $32,000 (0.5 probability) $40,000 (0.3 probability) $44,000 (0.2 probability)

• MARR – 10% All the elements subject to variation vary independently.

Use Monte Carlo simulation to compute E(AW). Start with 200 trials and increase in increments of 200 until you feel confident that a stable (steady state) value is reached. What is that value?PLEASE SHOW IN EXCEL WITH FORMULAS

A consumer has an income of $3,000. Wine costs $3 per glass, and cheese costs

    $6 per pound.

     a. (0.5 pt) Draw the consumer’s budget constraint with wine on the vertical axis.

                        (Make sure to label the axes.)

     b. (0.1 pt) What is the slope of the budget constraint?

    c. (0.1 pt) On the graph for part a, draw an indifference curve illustrating an optimum

                        bundle (point K).

     d. (0.4 pt) The consumer now gets a raise. So, her income increases from $3,000 to

                        $4,000.

                        → Show what happens if both wine and cheese are normal goods with

                               a new optimum bundle (point Q). What happens to the consumption of

                             wine and cheese?

                        → Then, show what happens if cheese is an inferior good with a new

                             optimum bundle (point R). What would happen to the consumption of wine

                             and cheese in this case?

     e. (0.3 pt) The consumer’s income is $3,000 again. However, the price of cheese has

                        risen from $6 to $10 per pound, while the price of wine remains $3 per

                        glass. Show what happens to the consumption of wine and cheese with a

                        new optimum bundle (point T).