Zaki, a developer, has a plot of 20-acre land near Klang town. He is considering whether to build a row of single story terrace houses or bungalow houses. He also has the option of not to proceed with the project. Given a favorable market, he estimate that he will earn a profit of RM60,000 if he builds single story terrace houses and RM800,000 if he builds bungalow houses. However, with an unfavorable market condition, he estimates that he will lose RM100,000 with the single story houses and RM400,000 with the bungalow houses. The probability of favorable market is 0.7.

Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15

a. If σM = 16%, calculate the variance of returns of securities A, B, and C.

b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C?

An investment company is considering investing into one of the following stocks with the risk and return characteristics given below:
Risk free rate = 5.1%    
Average market rate = 7%

Stock Exp. Rate Beta
A 18% 1,5
B 16% 1,3
C 18% 1,85
D 6% 0,9
E 5.5% 0,7
F 5.8% 0.7

Required:
1. Determine which stocks are overvalued and which are undervalued in comparison with market fair determination of required returns. Provide your reason why you think they are over or undervalued
2. Which stock is definitely better than which stock even without the calculations and why?
3. Which stock seems the best investment alternative and why?

Researchers wanted to compare the effectiveness of a water softener used with a filtering process with a water softener used without filtering. Ninety locations were randomly divided into two groups of equal size. Group A locations used a water softener and the filtering process, while group B used only the water softener. At the end of three months, a water sample was tested at each location for its level of softness. (Water softness was measured on a scale of 1 to 5, with 5 being the softest water.) The results were as follows.

group A

x₁ = 2.1
s₁ = 0.7

group B

x₂ = 1.7
s₂ = 0.4

Determine, at the 90% confidence level, whether there is a difference between the two types of treatments.

In Professor Krugman’s economics course, the correlation between the students’ total scores prior to the final exam and their final exam scores is r = 0.7. The pre-final-exam totals for all students in the course have a mean of 265 and a standard deviation of 45. The final exam scores have mean of 76 and standard deviation 9. Professor Krugman has lost Sam’s final exam, but knows that her total before the exam was 290. He decides to predict her final-exam score from her pre-exam total. Use the least-squares best-fit regression line to predict Julie’s final-exam score. Round your answer to one decimal place.

You may need to use the appropriate technology to answer this question.

A production line operation is tested for filling weight accuracy using the following hypotheses.

The sample size is 30 and the population standard deviation is σ = 0.7 Use α = 0.05.

What is the probability of making a type II error when the machine is overfilling by 0.4 ounces? (Round your answer to four decimal places.)

What is the power of the statistical test when the machine is overfilling by 0.4 ounces? (Round your answer to four decimal places.)

There are N symmetric firms in the industry, facing market demand
Q (p) = 250-p

Firms have a constant marginal cost of production of c = 10, and they compete in prices.
a) What are the Bertrand equilibrium price, output levels, and profits?
b) Suppose that the firms want to sustain the monopoly price using grim trigger strategies. Let each firm
produce a share of 1/N of the total demand under collusion. Calculate the critical discount factor as a function D (Delta) of N. Does collusion become easier or harder to sustain as N increases?
c) Suppose that the actual discount factor is = 0.7. How many firms can enter this industry without jeopardizing the cartel?

A steam power plant operates on a practical Rankine Cycle. The steam enters the turbine at 3 MPa and “648” K and is condensed in the condenser at a pressure of 46 kPa. You are assigned on a project to improve the thermal efficiency of this plant. a) Draw the schematic of the plant and determine the thermal efficiency of the practical cycle assuming that the efficiencies of pump and turbine are 0.75 and 0.7, respectively. ( b) Draw a TS diagram and show your suggestions for improving the thermal efficiency (i.e. increasing/decreasing temperature of steam entering into turbine, increasing/decreasing pressure of the boiler or condenser, and any other option). Show the effect of each case you suggest on a TS diagram. Discuss also the quality of steam in each case.

Question 6. There are two bidders in a sealed-bid, second-price auction. The object for sale has a common value. Each bidder, i = 1,2, receives a signal i that is independently and uniformly distributed on the interval [0, 1]. The true value of the object, v, is the average of the two signals,

v = (σ1 + σ2) / 2

(a) If bidder 1 gets the signal σ = 0.7, how much does he think the object is worth?

(b) Suppose that each bidder submits a bid equal to the expected value of the object (conditional on his signal). If bidder 1 submits the winning bid, what is the expected value of the object?

(c) What is the expected surplus for bidder 1 under the assumptions in (b)?

A company is considering different options with respect to the current asset policy. In all instances, the firms fixed assets will be $1,000,000 and the firm plants to use of debt ration of 70% (D/TA = 0.7). The market interest rate is 9% on all debt used (both short and long term). Two options are under consideration: Option 1 - hold current assets equal to 30% of projected sales. Option 2 - hold current assets equal to 60% of projected sales. The company forecasts it will earn 25% of sales before paying interest (EBIT = 0.25 * Sales) and projects to do $3,000,000 in sales. Finally, the federal and state tax rate is 35%. What is the ROE for each option?