INTRODUCTION
The economic development and gradual opening of China’s
aviation market has grown increasingly rapidly. The throughput continues to
maintain its high growth. For example, the growth of China’s
air cargo has risen by 34.5% in the past 5 years; passenger throughput of Shanghai
airlines will reach 100,000,000 in 2015. Meanwhile, with the impact of the positive
factors, such as the stabilization in oil prices and the appreciation of Chinese
currency (Renminbi, namely, RMB), the operating environment of the aviation
industry is better than that in previous years. Therefore, an evaluation of
the profitability of airlines has become the core of research. To acquire and
retain customers in such a highly competitive market, it is of strategic importance
for Chinese airlines to understand the critical factors affecting their profitability.
The primary purpose of this study is to evaluate the profitability of Chinese
listed airlines according to these critical factors.
Among the dozens of contemporary comprehensive evaluation methods worldwide,
there are two general categories: subjective and objective weightsbased evaluation
methods. The former are mostly qualitative approaches, such as Analytic Hierarchy
Process (AHP) (Isaai et al., 2011) and the fuzzy
comprehensive evaluation method (Wang and Hu, 2000),
where the weights are retrieved from the subjective judgments of experienced
experts. In Grey Relation (Liou et al., 2011),
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) (Torlak
et al., 2011) and Principal Component Analysis (PCA) (Shan
et al., 2011), the indicator weights are determined either by the
indicator correlations or by the variation coefficient of the indicators. However,
when evaluating listed airlines as well as other social and economic henomena,
most scholars only use one evaluation method, such as the Factor Analysis (FA),
PCA, etc., (Yuan, 2013; Mao
et al., 2013; Zhang, 2012; Shi
et al., 2013; Qi et al., 2008).
Analytic Hierarchy Process (AHP) is a structured technique for dealing with
complex decisions. Rather than prescribing a “correct” decision, AHP
helps decision makers find one decision that best suits their goal and their
understanding of the problem. That is a process of organizing decisions that
people are contemplating. Cheng and Lu (2010) evaluated
tourism resources exploration potential of Zhangdu Lake wetland using the evaluation
index system based on AHP.
In enterprise profitability evaluation, the fuzziness of some factors makes
them difficult to evaluate but a comprehensive evaluation method based on fuzzy
mathematics can quantitatively evaluate the profitability of enterprises to
make up for the disadvantage of AHP. Wang et al.
(2011) built a set of environmental evaluation index system to develop the
circular economy for the iron and steel industry based on the ideas and theories
of circular economy.
In an incomplete and inaccurate profitability system, due to many complex factors
or inadequate data, multilevel gray evaluation expands the information sources
and improves the reliability of evaluation and analysis. In addition, Gray Relation
Analysis (GRA) between these two factors can quantitatively analyze the correlation
degree, which is more reasonable and more accurate. Lan
and Kai (2009) used multilevel gray evaluation method to evaluate the innovation
capability of hubandspoke enterprise clusters. They combined the advantages
of the analytic hierarchy process and the grey clustering method. The result
showed that their methodology was especially useful when there was partial information
and/or qualitative variables were used.
Ustinovichius and Simanaviciene (2010) studied the
sensitivity analysis for cooperative decision using TOPSIS. However, judging
from the ranking decisionmaking steps of Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS), TOPSIS has some inevitable drawbacks,
(a) In the real world, it is not practical to find the positive and the negative
ideal solutions. But these two solutions are the necessary boundaries of the
entire solution set, (b) In this method, the weight information is determined
in advance and the weight values are usually subjective, resulting in a certain
subjective arbitrary and (c) In the application, the new projects are likely
to cause TOPSIS reverse. Therefore, a more specific indepth analysis is always
in need afterwards.
Principal Component Analysis (PCA) uses an orthogonal transformation to convert
a set of observations of possibly correlated variables into a set of values
of uncorrelated variables. PCA is mostly used as a tool in exploratory data
analysis and for making predictive models (Shaw, 2003).
However, principal components are guaranteed to be independent only if the data
set is jointly normally distributed and if the PCA is sensitive to the relative
scaling of the original variables. FA is an improvement over the PCA, in that
it estimates how much of the variability is due to common factors. But Sternberg
(1977) proposed that in FA, each orientation is equally acceptable mathematically.
This means that all rotations represent different underlying processes but all
rotations are equally valid outcomes of standard factor analysis optimization.
Therefore, it is impossible to select the proper rotation using factor analysis
alone. In addition, more than one interpretation can be made of the same data
factored the same way; moreover, factor analysis cannot identify causality (Darlington
et al., 1973).
In summary, many mathematical methods can be applied in comprehensive evaluations
but the different focal points of these methods and the choice of methods may
lead to different evaluation results, even if they are based on the same data.
Both the theory and methods to evaluate the profitability of the airlines need
to be developed and improved. Therefore, the core issue is to study the profitability
of airlines, discuss the mechanism of airline profitability, the evaluation
system and the method used to enhance profitability. In order to evaluate airline
management and performance, this study presents a new approach to evaluate the
Chinese aviation industry, obtaining more comprehensive, objective and realistic
results.
METHODS
In order to evaluate and analyze the 12 listed airlines comprehensively and
scientifically, an integrated approach was applied. First of all, FA, PCA and
GRA were utilized to analyze and evaluate the profitability and three results
were retrieved, respectively. Second, KendallW was used for the consistency
test of these results. If they were consistent, the scores would be standardized
and summed up. The final ranks would be based on the summation of the standard
scores. If the results were not consistent, the three methods would be compared
pair wisely. The consistent methods would be sorted together. Then, the sample
data, the evaluation results and the nature of the methods would be analyzed
specifically and the objective, realistic and consistent methods would be selected
for the comprehensive evaluation. The followings are the detailed steps:
Step 1: 
Evaluate, respectively using FA, PCA and GRA 
Step 2: 
Test the consistency of the results by KendallW 
Step 3: 
Standardize the scores of each sample retrieved from each method and obtain
the standard score R_{ij}. (R_{ij} represents the standard
score of the sample in the method) 
Step 4: 
Calculate: 
Step 5: 
Rank according to the value of P_{i} 
RESULTS
Data and the index: The indicators were selected fully and scientifically
according to the financial theory, data availability and the specific issue
in this study. These indicators can reflect the profitability of the aviation
industry objectively and systematically. The five indicators for the comprehensive
evaluation and analysis of the 12 Chinese listed airlines were rate of return
on sale (X_{1}), profit rate of sales cost (X_{2}), operating
profit rate of cost (X_{3}), rate of return on total assets (X_{4})
and return on equity (X_{5}). SPSS14.0 MATLAB and EXCEL were the software
tools for FA, PCA and GRA. The sources came from the Sohu Annual Reports of
Financial Listed Companies in 2010 (Sohu, 2010).
Table 1: 
Standardized data of the profitability indicators of the
listed airlines 

Comprehensive evaluation and analysis of the profitability
• 
Factor analysis: Standardize the raw data, adjust the
mean of the indicators and the values of variance to 0 and 1, eliminate
differences between the dimensions of variables and obtain the following
data (Table 1) 
• 
Retrieve the eigenvalue and the variance contribution rate of each factor
with PCA in SPSS. According to the principle that the cumulative contribution
rate should be over 85% and were selected as the factors whose cumulative
were 89.43% 
• 
Obtain the factor loading matrix with the Varimax orthogonal rotation
matrix and then retrieve the scores of the factors by regression. Take the
ratio of the variance contribution rate of each factor to the cumulative
variance contribution rate of the remaining four factors as the weight.
Aggregate the weights and retrieve, which is the composite score of each
company: 
Principal component analyses:
• 
Standardize the raw data using SPSS to establish the correlation
matrix of variables R 
• 
Calculate the eigenvalues and the corresponding contribution rates of
R using SPSS (Table 2) 
According to the principle that the cumulative contribution rate should be
over 85%, the two factors and were extracted as:
where,
was the standardized X_{i}.
Table 2: 
Eigenvalue and contribution rate of the principal components
in PCA^{3} for the profitability evaluation of
Hainan airline 

Grey relational analysis
• 
Establish the reference sequence based on the maximum value
of each indicator. Standardize the raw data, that is, divide the maximum
value of each index for each company through this index value. If the profitability
of a listed company is highly correlated to this reference sequence, the
score of the company will be high; that is to say, the company has high
profitability 
• 
Take the indicators of the 12 listed airlines as the comparison sequence.
Calculate the “corresponding difference list” of each comparison
and reference sequence. The maximum corresponding difference is Δmax
= 1.57 and the minimum Δmin = 0 
• 
According to the actual situation of the transport industry, assume that
the discrimination coefficient is ξ = 0.5, calculate the correlation
coefficient δ_{i} (k) and the correlation degree σ_{i}
of x_{i}, the comparison sequence and x_{0} and the reference
sequence, by using the equation: 
and:
where, N is the number of indicators.
Specific calculation of the correlation degree is shown in Table
3. Hainan Airlines is used as the example. Four rank the companies based
on their correlation degrees.
Table 3: 
Calculation of the correlation degree of Hainan Airlines 

Table 4: 
Profitability Evaluation scores and ranks of the 12 listed
airlines and airports based on PCA, GRA and FA 

Evaluation scores and ranks in PCA, GRA and FA: The reason why the factor
scores of a company were negative was that the original data were standardized
and the average of the profitability indicators was addressed as zero. Therefore,
the negative profitability scores of an airline just indicated that the profitability
of the company was lower than the average performance. For the specific scores
and ranks in the three methods (Table 4).
Test of the evaluation results in KendallW: Kendall’s W that can
be used for assessing agreement among raters was used to examine the consistency
of the evaluation results of N objects from M methods. Kendall’s W ranges
from 0 (no agreement) to 1 (complete agreement) (Kendall
and Smith, 1939):
where, k denotes the number of evaluation methods, R^{2}_{0}
that of objects and R^{2}_{p} the sum of the rankings of these
objects.
The hypothesis was that H_{0} denoted the inconsistency of the rankings
and H_{1} the consistency.
To test if the statistic χ^{2} = m (n1)W approximated in a large
sample, determine if; if so, reject
and accept the hypothesis of the consistency among the x^{2}≥x^{2}_{α}
rankings.
According to Nonparametric tests in SPSS, the coefficient of concordance was
W = 0.954 and was approximate the significance probability of ASYMP, with sig
= 0.000<0.05.
Clustering analysis: Take the standard scores in the three methods as
the cluster indicators and cluster the 12 listed airlines with the Euclidean
Distance Method. According to the clustering dendrogram generated from the SPSS
14.0 package, these airlines can be divided into three groups. The first group
includes Xiamen Airport only. The second group includes 5 airlines, i.e., Baiyun
Airport, Sinotrans, Shanghai Airport, COHC and Shenzhen Airport. And the third
group includes 6 airlines, i.e., Hainan Airlines, Hainan Airlines (B Share),
China Southern Airlines, Shandong Air (B Share), Air China and Shanghai Airlines.
Two results can be generated. First, the clustering results of the profitability
were closely related to the main business of the airlines. It was obvious that
the profitability of the airports and the auxiliary companies was better than
that of the transport airlines.
In type 1, Xiamen Airport was principally engaged in the service of terminal
and ground facilities for domestic and international airlines. In the financial
crisis, this company took efforts to promote transit operations, the implementation
of the easilyaccessed channel and ad hoc adherent technologies. All
of these policies contributed to the development of the aviation market in Xiamen.
In type 2, the three major airports focused on transportation and the auxiliary
business. Sinotrans was engaged in the import and export goods, as well as in
the agency business of the transit of the international goods across the border.
The main business of COHC was oil services.
In type 3, the airlines are all engaged in the passenger and cargo transportations.
Their performance was poor in 2010 for the following reasons: (1) The global
financial crisis reduced the demand, (2) Oil prices increased dramatically,
(3) The tendency towards RMB appreciation slowed down and (4) A large purchase
of aircraft also increased the airline’s
respective financial burdens and depreciation costs.
Secondly, in the poor financial condition, the profitability of the airlines
is inversely proportional to the size of the company. In type 3, small companies,
namely, Hainan Airlines (B Share), Shandong Air (B Share) and Hainan Airlines
were rated better than large airlines such as China Southern Airlines, Air China
and Shanghai Airlines. The reason why is believed to be that the big companies
could not achieve similar economies of scale as compared to the small airlines,
as well as the cost amortization of the fixed.
CONCLUSION
As can be seen from the final evaluation results, the profitability of Xiamen
Airport ranked first in the aviation industry, which is consistent with the
actual condition. In this study, a comprehensive evaluation approach was proposed
based on the previous evaluation methods. This improvement overcomes the onesidedness
of a single method and the disadvantages of other methods and eliminates the
difference of various evaluation methods. This approach leads to the more objective,
comprehensive and realistic evaluation results. In particular, the final evaluation
scores can be clustered to obtain a more accurate classification. This model
can offer some suggestions and reference to various evaluations of the listed
companies. This way of choosing the benchmarking companies in the listed companies
is also a helpful tool to study the benchmarking companies and propose the improvement
policies for listed companies. The proposed method can not only be a comprehensive
analysis and evaluation of the profitability of the listed airlines but also
help the investors to understand the status and the weak points of the listed
Chinese airlines. The further research and discussion may include, (1) The study
of the profitability evaluations of the airlines and airports from various countries,
(2) The enrichment and the improvement of the evaluation theory and the methodology,
(3) The selection and contributions of the nonfinancial indicators in the profitability
evaluation and (4) The detailed recommendations and suggestions for the decision
makers, policy makers and airline companies.
The proposed method can not only be a comprehensive analysis and evaluation
of the profitability of the listed airlines but also help the investors to understand
the status and the weak points of the listed Chinese airlines. The further research
and discussion may include, (1) The study of the profitability evaluations of
the airlines and airports from various countries, (2) The enrichment and the
improvement of the evaluation theory and the methodology, (3) The selection
and contributions of the nonfinancial indicators in the profitability evaluation
and (4) The detailed recommendations and suggestions for the decision makers,
policy makers and airline companies.
^{1}Rate of return on sale (X_{1}), Profit rate of sales
cost (X_{2}), Operating profit rate of cost (X_{3}), Rate of return on total assets
(X_{4}) and Return on equity (X_{5})
^{2}China ocean helicopter corp
^{3}Principal component analysis
^{4}Y_{1} , Y_{2} ,…, Y_{3} are the five principal components
in PCA based on the data from Hainan airlines
^{5}Rate of return on sale (X_{1}) , Profit
rate of sales cost (X_{2}) , Operating profit rate of cost (X_{3}
) , Rate of return on total assets (X_{4}) and Return on equity (X_{5})
^{6}Principal component analysis
^{7}Gray relation analysis
^{8}Factor analysis
^{9}China ocean helicopter corp