Finance-AW-Q184

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ASSIGNMENT 1

 

 

Question 1

 

Table 1 shows the financial ratios for two different groups of firms; the most-admired firms (1) and the least-admired firms (2). The financial ratios are earnings before interest and taxes to total assets (EBITASS), return on total capital (ROTC), return on equity (ROE), return on assets (REASS) and market to book value (MKTBOOK).

 

Table 1: Financial Data for Most-Admired and Least-Admired Firms
 

Firm Group MKTBOOK ROTC ROE REASS EBITASS
1 1 2.304 0.182 0.192 0.377 0.158
2 1 2.703 0.206 0.205 0.469 0.210
3 1 2.385 0.188 0.182 0.581 0.207
4 1 5.981 0.236 0.258 0.491 0.280
5 1 2.762 0.193 0.178 0.587 0.197
6 1 2.984 0.173 0.178 0.546 0.227
7 1 2.070 0.196 0.178 0.443 0.148
8 1 2.762 0.212 0.219 0.472 0.254
9 1 1.345 0.147 0.148 0.297 0.079
10 1 1.716 0.128 0.118 0.597 0.149
11 1 3.000 0.150 0.157 0.530 0.200
12 1 3.006 0.191 0.194 0.575 0.187
13 2 0.975 -0.031 -0.280 0.105 -0.012
14 2 0.945 0.053 0.019 0.306 0.036
15 2 0.270 0.036 0.012 0.269 0.038
16 2 0.739 -0.074 -0.150 0.204 -0.063
17 2 0.833 -0.119 -0.358 0.155 -0.054
18 2 0.716 -0.005 -0.305 0.027 0.000
19 2 0.574 0.039 -0.042 0.268 0.005
20 2 0.800 0.122 0.080 0.339 0.091
21 2 2.028 -0.072 -0.836 -0.185 -0.036
22 2 1.225 0.064 -0.430 -0.057 0.045
23 2 1.502 -0.024 -0.545 -0.050 -0.026
24 2 0.714 0.026 -0.110 0.021 0.016

 

Your objective is to select the best of discriminating variables for forming the discriminant function that allow us to distinguish between the two different groups. Report your findings.
 
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Question 2

 

A Sample of 15 houses with similar square footage built by a particular housing developer throughout United States is selected and the heating oil consumption during the month of January is determined. It is believed that the average daily atmospheric temperature as measured in degrees Fahrenheit outside the house during that month and the amount of insulation as measured in inches in the attic of the house influence the heating oil consumption. The data is shown in Table 2.

 

Table 2 : Monthly heating oil consumption, atmospheric temperature and amount of attic insulation for random sample of 15 single-family houses.
 

House Monthly Consumption of Heating Oil (Gallons) Average Daily Atmospheric Temperature

()

Amount of Attic Insulation (Inches)
1 275.3 40 3
2 363.8 27 3
3 164.3 40 10
4 40.8 73 6
5 94.3 64 6
6 230.9 34 6
7 366.7 9 6
8 300.6 8 10
9 237.8 23 10
10 121.4 63 3
11 31.4 65 10
12 203.5 41 6
13 441.1 21 3
14 323.0 38 3
15 52.5 58 10

 

  1. Fit a model of monthly heating oil consumption and interpret it.
  2. How much proportion of monthly heating oil consumption that is explained in the model?
  3. Evaluate the appropriateness of fitted model in (a) by analysing the residual.
  4. What can you conclude from the multicollinearity of the predictors?

 

 

Question 3

 

A marketing manager of a financial institution is interested in determining the probability that a financial institution is being most successful given the size and FP of the financial institution.  Consider the data given in Table 3 for a sample of 12 most-successful (MS) and 12 least-successful (LS) financial institutions (FI).

 

Table 3: Data for Most Successful and Least Successful Financial Institutions.
 

Most Successful Least Successful
SUCCESS SIZE FP SUCCESS SIZE FP
1 1 0.58 2 1 2.281
1 1 2.80 2 0 1.06
1 1 2.77 2 0 1.08
1 1 3.50 2 0 0.07
1 1 2.67 2 0 0.16
1 1 2.97 2 0 0.70
1 1 2.18 2 0 0.75
1 1 3.24 2 0 1.61
1 1 1.49 2 0 0.34
1 1 2.19 2 0 1.15
1 0 2.70 2 0 0.44
1 0 2.57 2 0 0.86

 

The value of SUCCESS is equal to 1 for the most successful financial institution and is equal to 2 for the least successful institution. The value of SIZE is equal to 1 for the large financial institution and is equal to 0 for a small financial institution.

 

  1. Construct a contingency table between success and the size of the FI
  2. Compute
  3. Calculate
  4. Fit a logistic regression model of a financial institution is being most successful given the size of the financial institution.
  5. Fit a logistic regression model of a financial institution is being most successful given the size and FP of the financial institution.
  6. Interpret (d) and (e) and make a comparison between them.

 

Question 4

 

The financial analyst on an investment banking firm is interested in identifying a group of customer that have similarities in terms of income (RM thousand) and education (years). Table 4 contains income and education in years for six hypothetical subjects.

 

Table 4: Hypothetical Data

Subject Id Income

(RM thousand)

Education (years)
S1 5 5
S2 6 6
S3 15 14
S4 16 15
S5 25 20
S6 30 19

 

  1. Construct a similarity matrix containing Euclidean Distances.
  2. Determine the type of clustering technique to be used.
  3. Determine the number of clusters of the subjects and interpret your findings.

ASSIGNMENT 1

 

 

Question 1

 

Table 1 shows the average price for a number of foods in several cities in the United States. The main objective of this work is to form a measure of the Consumer Price Index (CPI). In particular, you need to form a weighted sum of the various food prices that would summarize how expensive or cheap are a given city’s food items. Use an appropriate statistical method to achieve the above objective. Justify your answer. Technique –Principle Component Analysis (Factors)

 

Table 1: Food Price Data

City Average Price (cents per pound)
Bread Burger Milk Oranges Tomatoes
Atlanta 24.5 94.5 73.9 80.1 41.6
Baltimore 26.5 91.0 67.5 74.6 53.3
Boston 29.7 100.8 61.4 104.0 59.6
Buffalo 22.8 80.6 65.3 118.4 51.2
Chicago 26.7 86.7 62.7 105.9 51.2
Cincinnati 25.3 102.5 63.3 99.3 45.6
Cleveland 22.8 88.8 52.4 110.9 46.8
Dallas 23.3 85.5 62.5 117.9 41.8
Detroit 24.1 93.7 51.5 109.7 52.4
Honolulu 29.3 105.9 80.2 133.2 61.7
Houston 22.3 83.6 67.8 108.6 42.4
Kansas City 26.1 88.9 65.4 100.9 43.2
Los Angeles 26.9 89.3 56.2 82.7 38.4
Milwaukee 20.3 89.6 53.8 111.8 53.9
Minneapolis 24.6 92.2 51.9 106.0 50.7
New York 30.8 110.7 66.0 107.3 62.6
Philadelphia 24.5 92.3 66.7 98.0 61.7
Pittsburgh 26.2 95.4 60.2 117.1 49.3
St. Louis 26.5 92.4 60.8 115.1 46.2
San Diego 25.5 83.7 57.0 92.8 35.4
San Francisco 26.3 87.1 58.3 101.8 41.5
Seattle 22.5 77.7 62.0 91.1 44.9
Washington DC 24.2 93.8 66.0 81.6 46.2

 

Question 2

 

Table 2 shows the financial ratios for a sample of 24 firms, the 12 most-admired firms and the 12 least-admired firms. The financial ratios are earnings before interest and taxes to total assets (EBITASS) and return on total capital (ROTC). Technique – Multiple Discriminant Analysis

 

Table 2: Financial Data for Most-Admired and Least-Admired Firms

Firm Number

(Dependent Variables)

Most-Admired Firm Number

(Dependent Variables)

Least- Admired
EBITASS

(Independent Variables)

ROTC

(Independent Variables)

EBITASS

(Independent Variables)

ROTC

(Independent Variables)

1 0.158 0.182 13 -0.012 -0.031
2 0.210 0.206 14 0.036 0.053
3 0.207 0.188 15 0.038 0.036
4 0.280 0.236 16 -0.063 -0.074
5 0.197 0.193 17 -0.054 -0.119
6 0.227 0.173 18 0.000 -0.005
7 0.148 0.196 19 0.005 0.039
8 0.254 0.212 20 0.091 0.122
9 0.079 0.147 21 -0.036 -0.072
10 0.149 0.128 22 0.045 0.064
11 0.200 0.150 23 -0.026 -0.024
12 0.187 0.191 24 0.016 0.026

 

  1. Determine the best set of factors that significantly differentiate between the two types of firms. Justify your answer.
  2. Use the answer from (a) to classify the future observations.

 

 

Question 3

 

A market analyst is interested in determining if type of firms (Most-Admired and Least- Admired) has an effect on the financial ratios (EBITASS and ROTC). The data is tabulated in Table 2. Use MANOVA to achieve the above objective. Interpret the result.

 

 

Question 4

 

The internal Revenue Service (IRS) is trying to estimate the monthly amount of unpaid taxes discovered by its auditing division. In the past, the IRS estimated this figure on the basis of the expected number of field-audit labour hours. In recent years, however, field-audit labour hours have become an erratic predictor of the actual unpaid taxes. As a result, IRS is looking for another factor with which it can improve the estimating equation. The auditing division does keep a record of the number of hours its computers are used to detect unpaid taxes. By using data in Table 3: Technique – Multiple Linear Regression

 

  1. Fit a more accurate estimating model for the unpaid taxes discovered for each month.
  2. Determine the significance of each predictor.
  3. Find and interpret the Coefficient of Determination.
  4. How much in unpaid taxes do they expect to discover in November?

 

Table 3: Data from IRS Auditing Records During the Last 10 Months

Month Field-Audit Labour Hours (00s Omitted) Computer Hours

(00s Omitted)

Actual unpaid Taxes Discovered

(millions of dollars)

January 45 16 29
February 42 14 24
March 44 15 27
April 45 13 25
May 43 13 26
June 46 14 28
July 44 16 30
August 45 16 28
September 44 15 28
October 43 15 27

 

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