2.a. You are running a batch reactor. Each batch takes about four hours to run. You measure the purity of the batch four times in the last hour to ensure that it has stabilized. You want to monitor the results using an X-R chart. The data you have collected for the first 10 batches are given the table below. X1, X2, X3 and X4 are the four samples you pull from the batch in the last hour. Using all the data, find trial control limits for and R charts, construct the chart, and plot the data. (30 pts)

2.b. Is the process in statistical control? Identify out-of-control points. (30 pts)

a. Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

Exercise 11-27 (Algo) Cost Allocation: Direct Method (LO 11-2)

Required:

Compute the allocation of service department costs to producing departments using the direct method. (Do not round intermediate calculations.)

b. Assume that both Machining and Assembly work on just two jobs during the month of August: CM-22 and CM-23. Costs are allocated to jobs based on machine-hours in Machining and labor-hours in Assembly. The number of labor- and machine-hours worked in each department are as follows:

Required:
How much of the service department costs allocated to Machining and Assembly in the direct method should be allocated to Job CM-22? How much should be allocated to Job CM-23?

1. Stock Valuation: A stock has an initial price of $100 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $125. Compute the percentage total return, capital gains yield, and dividend yield.

Capital Gains = 125-100 = 25 and Dividend Yield = $2

            Total return percent = (25+2)/100 = 27/100 = 27%

            Capital Gain return = 25/100 = 25%

            Dividend Yield = 2/100 = 2%

2. Total Return: You bought a share of 4% preferred stock for $100 last year. The market price for your stock is now $120. What was your total return for last year?

Dividend = 4% of 100 = $4. The capital gain = 120-100 = 20

Total return for last year = $24 = 24%

3. CAPM - A stock has a beta of 1.20, the expected market rate of return is 12%, and a risk-free rate of 5 percent. What is the expected rate of return of the stock?

CAPM - Expected return of Stock = Rf + beta*(Rm - Rf) = 5 +1.2*(12-5) = 13.4%

4. WACC: The Corporation has a targeted capital structure of 80% common stock and 20% debt. The cost of equity is 12% and the cost of debt is 7%. The tax rate is 30%. What is the company's weighted average cost of capital (WACC)?

We*Re + Wd*Rd*(1-T) = 0.8*12 + 0.2*7*(1-0.3) = 10.58%

5. Flotation Costs: Medina Corp. has a debt-equity ratio of .75. The company is considering a new plant that will cost $125 million to build. When the company issues new equity, it incurs a flotation cost of 10%. The flotation cost on new debt is 4%. What is the initial cost of the plant if the company raises all equity externally?

125 million will be raised by issuing both debt and equity so that D/E remains 0.75.

D = 0.75E

E + 0.75E = 125

E = 71.43, D =125- 71.43 = 53.57

Initial cost of the plant will be = 125 + 71.43*0.10 + 53.57*0.04 = 125 + 9.2858 = 134.2858

1. Stock Valuation: A stock has an initial price of $100 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $125. Compute the percentage total return, capital gains yield, and dividend yield.

Capital Gains = 125-100 = 25 and Dividend Yield = $2

            Total return percent = (25+2)/100 = 27/100 = 27%

            Capital Gain return = 25/100 = 25%

            Dividend Yield = 2/100 = 2%

2. Total Return: You bought a share of 4% preferred stock for $100 last year. The market price for your stock is now $120. What was your total return for last year?

Dividend = 4% of 100 = $4. The capital gain = 120-100 = 20

Total return for last year = $24 = 24%

3. CAPM - A stock has a beta of 1.20, the expected market rate of return is 12%, and a risk-free rate of 5 percent. What is the expected rate of return of the stock?

CAPM - Expected return of Stock = Rf + beta*(Rm - Rf) = 5 +1.2*(12-5) = 13.4%

4. WACC: The Corporation has a targeted capital structure of 80% common stock and 20% debt. The cost of equity is 12% and the cost of debt is 7%. The tax rate is 30%. What is the company's weighted average cost of capital (WACC)?

We*Re + Wd*Rd*(1-T) = 0.8*12 + 0.2*7*(1-0.3) = 10.58%

5. Flotation Costs: Medina Corp. has a debt-equity ratio of .75. The company is considering a new plant that will cost $125 million to build. When the company issues new equity, it incurs a flotation cost of 10%. The flotation cost on new debt is 4%. What is the initial cost of the plant if the company raises all equity externally?

125 million will be raised by issuing both debt and equity so that D/E remains 0.75.

D = 0.75E

E + 0.75E = 125

E = 71.43, D =125- 71.43 = 53.57

Initial cost of the plant will be = 125 + 71.43*0.10 + 53.57*0.04 = 125 + 9.2858 = 134.2858

Based on the above answers explain how companies make financial decisions

Say that a sample of size 49 taken from a normally distributed population, has variance = 1. The sample has a mean of 0.49. Then, a 95% confidence interval for µ will be

A well-known brokerage firm executive claimed that 70% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 800 people, 67% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 70% at the 0.005 significance level.

The null and alternative hypothesis would be:

H0:p≥0.7H0:p≥0.7
H1:p<0.7H1:p<0.7

H0:μ=0.7H0:μ=0.7
H1:μ≠0.7H1:μ≠0.7

H0:μ≥0.7H0:μ≥0.7
H1:μ<0.7H1:μ<0.7

H0:p=0.7H0:p=0.7
H1:p≠0.7H1:p≠0.7

H0:p≤0.7H0:p≤0.7
H1:p>0.7H1:p>0.7

H0:μ≤0.7H0:μ≤0.7
H1:μ>0.7H1:μ>0.7

The test is:

left-tailed

two-tailed

right-tailed

The test statistic is:  (to 3 decimals)

The p-value is:  (to 4 decimals)

Based on this we:

Fail to reject the null hypothesis

Reject the null hypothesis

2) Test the claim that the proportion of men who own cats is significantly different than 60% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6

H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6

H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6

H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6

H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6

H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 20 people, 65% owned cats

The test statistic is:  (to 2 decimals)

The positive critical value is:  (to 2 decimals)

Based on this we:

Fail to reject the null hypothesis

Reject the null hypothesis

Lynch was the loan officer at First Bank. Patterson applied to borrow $25,000. Bank policy required that Lynch obtain a loan guaranty from Patterson’s employer, a milk company. The manager of the milk company visited the bank and signed a guaranty on behalf of the company. The last paragraph of the guaranty stated, “This guaranty is signed by an officer having legal right to bind the company through authorization of the Board of Directors.” Should Lynch be satisfied with this guaranty? Would he be satisfied if the president of the milk company, who was also a director, affirmed that the manager had authority to sign the guaranty? Explain.

Ralph owned a retail meat market. Ralph’s agent Sam, without authority but purporting to act on Ralph’s behalf, borrowed $7,500 from Ted. Although he never received the money, Ralph repaid $700 of the alleged loan and promised to repay the rest. If Sam had no authority to make the loan, is Ralph liable? Why?

A guest arrived early one morning at the Hotel Ohio. Clemens, a person in the hotel office who appeared to be in charge, walked behind the counter, registered the guest, gave him a key, and took him to his room. The guest also checked valuables (a diamond pin and money) with Clemens, who signed a receipt on behalf of the hotel. Clemens in fact was a roomer at the hotel, not an employee, and had no authority to act on behalf of the hotel. When Clemens absconded with the valuables, the guest sued the hotel. Is the hotel liable? Why?

You have recently been promoted to General Manager at Creekview Lodge, a 50 room hotel in Gatlinburg, Tennessee. You started working at the lodge in high school in the restaurant and after college, returned to Creekview as one of the assistant managers before being promoted to hotel manager. Recently, a 200-room hotel opened not far from Creekview Lodge, and although Creekview still maintains near 100% capacity there has been quite a bit of turnover. More than ten employees left to work for the larger hotel which boasted higher pay and better health insurance.

You were informed this morning by the front desk team that the latest customer survey results show a drop in the satisfaction rating for guest room cleanliness. The current report indicates that 73% of guests responded “completely satisfied”, 12% responded “satisfied”, 10% responded “neither satisfied nor unsatisfied”, and 5% responded “unsatisfied.” The housekeeping staff lost four employees to the new hotel, so although disappointed, you aren’t surprised by this news. Still, you could not remember a time that the hotel had received such a low satisfaction rating.

As manager of Creekview Lodge, what is your next step in addressing the problem?

A)Take immediate action and require that all rooms be inspected by the hotel manager (you) or an assistant manager before being made available to customers

D)Review the standards of performance and compare to current performance

Section A – Hotel Business in Hong Kong Question A1 Answer the below short questions (a) to (i) according to A Statistical Review of Hong Kong Tourism 2018, published by Hong Kong Tourism Board in June 2019.

a) What is the total number of visitor arrival to Hong Kong upon 2018? How many visitors stayed overnight?

b) Identify Hong Kong’s top THREE source markets of visitors’ arrival to Hong Kong in 2018.

c) Which month contained the highest visitor arrivals number in 2018?

d) Briefly describe the hotel performance in 2018.

e) Which hotel category noted a highest gain percentage in room occupancy compare with 2017?

f) State TWO districts which recorded the highest room occupancy rate in Hong Kong.

g) In 2017, which department in the hotel earn the second highest revenue and what is the total percentage.

h) Refer to the hotel room occupancy rate and average achieved hotel room rate in 2018, illustrate TWO indicators or messages reflected from those figures.

i) The percentage distribution of visitor arrivals by months 2018 were quite steady along the year, the range of percentage starting from 7.2% to 10.1%. If you were the manager of a hotel, try to briefly explain the reasons behind of the distributions. (For example: What is/are the factor(s) may affect the percentage of arrival on Dec 2018.)