(a) Derive Freundlich and Langmuir isotherm equations.

(b) An aqueous solution containing a valuable solute is colored by a small amount of an impurity. Before crystallization, the impurity is to be removed by adsorption on a decoloring carbon which adsorps only insignificant amount of the principal solute. Equilibrium data at constant temperature is as follows:

It is desired to reduce the color intensity to 10% of its original value (9.6)
(1) Find out Freundlich adsorption isotherm
(2) Determine the quantity of fresh carbon requirement per 100 kg of solution for a single stage operation.

An investor is considering the following three stocks to invest. Suppose that the current T-bill rate is 5% and the market rate of return is 13%

Which of the following statements is FALSE based on CAPM?

a) None of the alternatives is false.

b) If the investor puts equal amount of money in each of the three stocks, he/she is expected to earn 13% from the portfolio.

c) The current market price of stock B is such that it is expected to earn 15%. Therefore, the stock is currently undervalued.

d) On average, stock C moves in the same direction as the S&P 500 index.

e) Stock A is more risky than the market portfolio.

You are considering starting a company that manufactures racing bicycles. You are planning on financing your firm 40% equity and 60% debt. You estimate that your upfront costs will be $5M, and that you will earn an EBIT of $1M per year for the next 12 years. Lightning Bolt Bikes makes racing bicycles similar to the ones that you wish to manufacture. They have a CAPM equity beta of 1.9 and a debt to equity ratio of 0.7. The tax rate for both firms is 35%, the riskless rate is 3%, and the expected return on the S&P500 is 15% Cost of Debt 6%

What is your firm’s weighted average cost of capital?

What is the NPV of your proposed bicycle company using the WACC method?

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?