Bankruptcy Prediction: Statistical Analysis

This assignment involves analyzing the relationship between various financial ratios (PS, TS, TC, TL, TA, WC, OE) and the likelihood of a company going bankrupt. Students perform hypothesis testing to determine if statistically significant differences exist between financially sound companies and those facing bankruptcy. The analysis utilizes p-values and alpha levels to draw conclusions about the predictive power of different financial indicators.

Statistics For Managerial Decisions
Assignment 2
[Pick the date]
Student Name

Question 1
ASX Companies
1. Crown Resorts Limited
2. Tabcorp Holdings Limited
(a) The quarterly opening values for the ASX companies
 For the above values, the stem and leaf pot
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(b) The combined graph as relative frequency histogram for CWN and frequency polygon for
TAH
0 to less
than 2 2 < 4 4 < 6 6 < 8 8 < 10 10 < 12 12 < 14 14 < 16 16 < 18
0
5
10
15
20
25
30
35
Relative frequency histogram and Frequency
Polygon
Opening Quarterly Price)
Relative frequency
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(c) The name of five ASX listed companies and their respective market capitalization for the
year 2016 is shown below:
Village Roadshow
Tatts Group
Star Entertainment Group
Aristocrat Leisure
Tasracing
0 1 2 3 4 5 6
Bar Chart : Market Capitalization 2016
Market Capitalization(Billion Australian Dollars)
Company NAME
(d) As per the data available from the Australia,, Crown Resorts seems to be a hold or buy
but definitely not a sell.
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Source: http://markets.theaustralian.com.au/shares/CWN/crown-resorts-limited
However, on account of the takeover planned by the company over the Tatts group, TAH have
been upgrades and hence most of the big brokerage houses are bullish on this counter
Source: http://www.theaustralian.com.au/business/companies/tabcorp-market-valuation-boosted-
by-tatts-takeover-approval/news-story/26e07dac51dd9e46dd2c5625c9b6bc95
My views are also aligned in favour to investing in TAH on account of the merger gains.
However, one needs to be cautious on the reaping of synergies so that profitability can swell and
share price can appreciate.
Question 2
Given set of data
(a) Computation of mean, first quartile and third quartile and mean (Hillier, 2006)
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5

6

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Result
(b) Computation of standard deviation, range and coefficient of variation (Hillier, 2006)
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Result
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(c) Box and whisker pot
CBA NAB ANZ WBC
-0.50
0.50
1.50
2.50
3.50
4.50
5.50
Box - Whisker Plot: Annual dividend
(d) There has been criticism of the lending practices followed by banks in Australia which
has caught the eye of APRA and hence in view of this increase in credit risk, APRA has
decided to bring in extra capital cushion by making changes in the Tier 1 capital
requirement which has been increased by 100 basis points. This would in turn have an
adverse impact on the interest margins of the banks.
Question 3
(a)After considering the proportion of the respective offers made for given grades, it would be
fair to conclude that best student for most popular discipline is “Engineering and Related
Technologies.” Proportion of students in “Engineering and Related Technologies” is given
as 30%.
(b) Probability needs to be computed for the case where a randomly selected Australian
student is studying in discipline “Society and Culture” with an ATAR score of 80 or less than
8.
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Favourable outcomes (ATAR score 80 or less than 80) = = (2814+ 2807+3806+5030 ¿=14,457
Total number of expected outcomes = 221060
Value of probability = Favourable outcomes/ Total number of expected outcomes
= 14457/221060 = 0.0654
(c)After considering the proportion of the respective offers made for given grades, it would be
fair to conclude that “Education” discipline is representing highest proportion of the students
along with the lowest ATAR grades. Proportion of students in “Education” is given as
7.30%.
(d) “Health” is the discipline which possess majority of the Australian student from “NO
ATAR / Non – Yr 12” background. The main reasons for this may be due to the inclination
that such students would have towards physical health as there focus is not towards
education. As a result, it is natural for these students to make attempts to build career in the
same field as their interest.
Question 4
(a) Total weeks = 52 weeks
1st week has started = 4th January 2016
The below highlighted table represents amount of rainfall on each week and the mean value and
standard deviation
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Weekly rainfall - Poisson distribution
There are 135 days on which rainfall has been reported.
Mean = 135 /52 = 2.596
(i) Probability (in one week- no rainfall reported) (Lind, Marchal and Wathen, 2012)
Input:
γ=2.596 , x=0 ,
P={ e−2.596 ( 2.596 )0
0 ! } = 0.0745
(ii) Probability (in a week – 2 or higher than 2 days rainfall reported) (Taylow and Cihon,
2004)
P ( x> ¿2 )=?
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P ( x> ¿2 ) =1−P(x <2)
From z table
P ( x<2 )=0.6299
Hence,
P ( x> ¿2 )=1− ( 0.6299 )
P ( x> ¿2 )=0.37
(b) Weekly rainfall - Normal distribution
From above table: mean of rainfall amount = 12.48
Standard deviation of rainfall amount = 14.58
Standard error of rainfall amount = 14.58 / (sqrt(52)) = 2.021
(i) Probability (in a week- rainfall amount is fall between 8 mm to 16 mm)
P ( 8< x <16 )=P ( Z1< Z <Z2 )
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Z1 =( 8−12.48
2.021 )=−2.22∧Z2= ( 16−12.48
2.021 )=1.74
¿ P ( −2.22< z< 1.74 )
From z table
¿ P ( −2.22< z< 1.74 )
¿ 0.9459
(ii) “Amount needs to be determined when 12% of the weeks have that amount of rainfall
or greater.”
Total amount of rainfall = x mm (Assumption)
Probability (x > z) = 12%
(z) value with the help of excel function: NORMSINV () is computed as -1.174. (Taylow and
Cihon, 2004)
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Now,
( x−12.48
2.021 )=−1.174
X =10.10 mm
Hence, the amount of rainfall has determined as 10.10 mm.
Question 5
(a) For the independent variables the normality plots are highlighted below (Medhi, 2001):
The above normality plots on the whole have a linear trend even though there are some values
which do tend to deviate but these are essentially outliers. Hence, they can be assumed as
normal.
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(b) 95% confidence interval has been determined by using mean value and confidence level
(95%) and is summarized below (Harmon, 2011) .
(a) The respective hypotheses are shown below:
(i) NP/TA
p value = 0.2065
Alpha = 5%
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Fails to reject null hypothesis because p is greater than alpha and hence, “no statistically
significant difference for those entities which go bankrupt and those which do not”
(2) PS TS
p value = 0
alpha = 5%
Reject null hypothesis because p value is lesser than alpha and hence, “there is a statistically
significant difference between those entities which go bankrupt and those which do not.”
(3) TC TS
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p value = 0
alpha = 5%
Reject null hypothesis because p value is lesser than alpha and hence, “there is a statistically
significant difference between those entities which go bankrupt and those which do not.”
(4) TL TA
The p value from the above table = 0.0005
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alpha = 5%
Null hypothesis would be rejected as p value is lower than level of significance. The conclusion
can be drawn is that there is a statistically significant difference between those entities which go
bankrupt and those which do not.
(5) WC TA
p value = 0.0007
alpha = 5%
Reject null hypothesis because p value is lesser than alpha and hence, “there is a statistically
significant difference between those entities which go bankrupt and those which do not.”
(6) OE TL
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p value = 0.1248
alpha = 5%
Fails to reject null hypothesis because p is greater than alpha and hence, “no statistically
significant difference for those entities which go bankrupt and those which do not (Shi and Tao,
2008)”
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Reference
Fehr, F. H. and Grossman, G. (2003). An introduction to sets, probability and hypothesis testing.
3rd edn. Ohio: Heath.
Harmon, M. (2011) Hypothesis Testing in Excel - The Excel Statistical Master. 7th edn. Florida:
Mark Harmon.
Hillier, F. (2006) Introduction to Operations Research. 6th edn. New York: McGraw Hill
Publications.
Lind, A.D., Marchal, G.W. and Wathen, A.S. (2012) Statistical Techniques in Business and
Economics. 15th edn. New York : McGraw-Hill/Irwin.
Medhi, J. (2001) Statistical Methods: An Introductory Text. 4th edn. Sydney: New Age
International.
Shi, N. Z. and Tao, J. (2008) Statistical Hypothesis Testing: Theory and Methods. 3rd edn.
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Singapore : World Scientific.
Taylor, K. J. and Cihon, C. (2004) Statistical Techniques for Data Analysis. 2nd edn.
Melbourne: CRC Press.
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