Question 1

a) For the data in Homework 2, Question 1, calculate the ANOVA table. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

b) Give a 95% confidence interval for the mean sale price for 2000 sq. ft. houses.

c)   Give a 95% prediction interval for the sale price of an individual 2000 sq. ft. house.

d)   For the data in Homework 2, Question 2, calculate the ANOVA table for the data. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

Question 2

A research firm collected data on a sample of n = 30 drivers to investigate the relationship between the age of a driver and the distance the driver can see. The data is given below:

Use SAS to fit a simple linear regression and answer the following questions:

a) Find the least squares estimate for the regression line Y_i = b₀ + b₁X_i + e_i.

b) Estimate the standard deviation of the error term e_i

c)   Test the null hypothesis that b₁ = 0, using α = 0.05. Is the model useful?

d)   Calculate R²? Explain what this means, and comment on whether or not it suggests the model is good.

e)   Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good.

f)    What would you expect the distance that a 50 year old driver can see to be?

g)   Give a 95% prediction interval for the distance that an individual 50 year old can see.

h) Give a 95% confidence interval for the mean distance that 50 year olds can see.

5. (a) Construct a 99% confidence interval for the mean height of the entire female/male SCC student body.

(b) What is the width of this interval?

(c) Write a sentence interpreting your confidence interval.

(d) Review your 93% and 99% confidence intervals above. Which is wider and why?

male Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

Use the heights from the SCC data to answer the following questions. Men are to use the male data, and women are to use the female data (only answer the questions for ONE set of data, not both).

2. State the following for the SCC sample male heights.

a. Sample size (n)

b. Sample mean (?̅)

c. Sample standard deviation (s

male Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

We have gathered the following information on Cheesecake Factory

• Current Dividend (Source – Yahoo!Finance) = $1.28
• Required Return (Estimated) = 8.9%
• Current EPS (Source – Yahoo!Finance) = $2.14
• Current Book Value Per Share (Source – Yahoo!Finance) = $13.24
• Current EBITDA per share (Source – Yahoo!Finance) = $5.25
• Current Debt per share = $2.80                Current Cash and Equivalents per share = $0.61
• Initial Growth Rate for H-Model (Estimated) = 9%
• Terminal Growth Rate for H-Model (Estimated) = 3%
• Time to Reach Terminal Growth Rate for H-Model (Estimated) = 10 years
• Forecasted Growth Rates (Estimated)
  • Year 1 = 6%
  • Year 2 = 9%
  • Year 3 = 12%
  • Year 4 = 6%
  • Year 5 = 4%
  • Years 6 through infinity = 3%
• Historical PE, PB and EV/EBITDA (Source – Morningstar and Gurufocus.com)
  • 5-Year Average = 19.8        4.1          9.3         
• Comparative PE, PB, and EV/EBITDA for S&P 500 (Source – Morningstar and estimate)
  • 19.2 (5-year avg = 19.6)                 3.7 (5-year avg = 2.9)      13.0 (5-year average 12.3)

1. Calculate the price for Cheesecake Factory using the
   1. H-Model
   2. Non-Constant Dividend Valuation Approach
   3. Relative valuation     
      1. Historical PE, PB, and EV/EBITDA
      2. Comparative PE, PB, and EV/EBITDA (Adjust S&P 500 to reflect Cheesecake Factory’s average discount or premium to the market over the past 5 years. Example, if the S&P 500 had an average PE over the past 5 years of 17.0 and your company had an average PE of 14, then your company has historically traded at 82.35% of the market average PE. Therefore, if the current S&P 500 PE is 17.7, your company should have a PE of 14.58 based on the comparative relative valuation to PE. Take the 14.58 times your firm’s EPS to get fair value using this method.)

A popular U.S. automobile manufacturer has​ 10,000 dealerships located throughout the country. The automobile manufacturer has multiple brands within its​portfolio: a value brand that caters to younger​ clientele, a moderate brand that caters to middle class customers and​ finally, a premium brand which is marketed to wealthy clientele. The​ company's leadership, located at corporate​ headquarters, is very interested in the relationship between the median salary of potential customers and the​ company's revenue.​ Specifically, the company is concerned that if potential​ customers' salaries continue to not increase in the​ future, the​company's revenue will remain​ stagnant, which will in turn steer away potential investors and shareholders. The​ company's research department recently collected data for analysis in order to support​ leadership's upcoming discussion with shareholders and investors about the​ company's future revenue forecast. Sales figures from a random sample of 1000 dealerships were collected. The research division also conducted statistical​ analysis, using data provided by the Bureau of Labor and​ Statistics, to calculate the median salary of people living in the vicinity of these​ 1,000 dealerships. The Dealership​ Number, State, Median​ Salary, Annual​Sales, Number of Vehicles​ Sold, Square Footage and Quality Award Winner data were collected for these 1000 dealerships.

We have an interest in finding out if the different dealerships sell different kinds of cars. Although our data set does not contain a lot of​ detail, one way to find such differences is by looking at the combination of Annual Sales and Number of Vehicles Sold for each dealership.

Find the median values of Annual Sales and Number of Vehicles Sold.

The median value for Annual Sales is ​$__ ,and the median value for Number of Vehicles Sold is ​$__.

Create two new indicator variables that indicate if a dealership has above median Annual Sales and above median Number of Vehicles Sold​ (so called​median-splits). In order to obtain the indicator variables with​ StatCrunch, use the following menu and option​ selections, where the expressions have the format​"Annual

​Sales">​xxx,

xxx being the calculated median value​ (same for Number of Vehicles​ Sold).

Data​ > Compute​ > Expression​ > Build Expression​ > Compute

Now create the contingency table of these two new indicator variables.

What values do you find on the diagonal of this contingency table​ (upper-left and​ lower-right cells)?

The value in the​ upper-left cell is__, and the value in the​ lower-right cell is __ .

What values do you find on the​ anti-diagonal of this contingency table​ (upper-right and​ lower-left cells)?

The value in the​ upper-right cell is __ , and the value in the​ lower-left cell is __ .

Based on this contingency​ table, what is the conditional probability of a dealership with above median Number of Vehicles Sold having above median Annual​Sales?

The conditional probability is__ .

Based on this contingency​ table, what is the conditional probability of a dealership with above median Number of Vehicles Sold having below median Annual​Sales?

The conditional probability is__.

How would you describe the events dealership having above median Number of Vehicles Sold and dealership having below median Annual​ Sales?

Independent

or

Disjoint

Make a scatterplot of Annual Sales against Number of Vehicles Sold. In order to obtain the scatterplot with​ StatCrunch, use the following menu and option selections.

Graph​ > Scatter Plot​ > Select X​ & Y variable​ > Compute

Describe the relationship between Annual Sales against Number of Vehicles Sold.

Required information

[The following information applies to the questions displayed below.]

Inner Secret T Shirt Company produces and sells one product. The following information pertains to each of the company’s first three years of operations:

Variable costs per unit:     

Manufacturing:     

Direct materials   $   27

Direct labor   $   15

Variable manufacturing overhead   $   5

Variable selling and administrative   $   3

Fixed costs per year:     

Fixed manufacturing overhead   $   600,000

Fixed selling and administrative expenses   $   170,000

During its first year of operations, O’Brien produced 97,000 units and sold 73,000 units. During its second year of operations, it produced 79,000 units and sold 98,000 units. In its third year, O’Brien produced 89,000 units and sold 84,000 units. The selling price of the company’s product is $73 per unit.

Required:

1. Assume the company uses variable costing and a FIFO inventory flow assumption (FIFO means first-in first-out. In other words, it assumes that the oldest units in inventory are sold first):

a. Compute the unit product cost for Year 1, Year 2, and Year 3.

b. Prepare an income statement for Year 1, Year 2, and Year 3.

2. Assume the company uses variable costing and a LIFO inventory flow assumption (LIFO means last-in first-out. In other words, it assumes that the newest units in inventory are sold first):

a. Compute the unit product cost for Year 1, Year 2, and Year 3.

b. Prepare an income statement for Year 1, Year 2, and Year 3.

3. Assume the company uses absorption costing and a FIFO inventory flow assumption (FIFO means first-in first-out. In other words, it assumes that the oldest units in inventory are sold first):

a. Compute the unit product cost for Year 1, Year 2, and Year 3.

b. Prepare an income statement for Year 1, Year 2, and Year 3.

4. Assume the company uses absorption costing and a LIFO inventory flow assumption (LIFO means last-in first-out. In other words, it assumes that the newest units in inventory are sold first):

a. Compute the unit product cost for Year 1, Year 2, and Year 3.

b. Prepare an income statement for Year 1, Year 2, and Year 3.

Value of an internationally traded product has different components with different magnitude. Would you please take a product that is produced in two different countries (e.g., USA and Canada), and discuss how the value of a product or service can be converted tin common currency without undervaluing or underestimating the product or service. Thanks.

Consider a T-bond maturing in March 2020 with coupon payments on September 1^st and March 1^st. Assume that the bond has $1000 par value, 10% coupon rate, and YTM = 12.5%. The bond is traded on December 13, 2013.

What is the Accrued Interest?

What is the full price?

What is the flat price?

Discuss how an exchange rate is determined and what South Africa can do to ensure that a depreciating currency does not affect economic growth. In your answer, look at a number of factors, which include the volume traded, the general economic conditions at the time of trade, and, where applicable, government mandates. [50 marks)