Knowledge-Based Systems 26 (2012) 288–293
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Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys
Multicriteria decision-making based on goal programming and fuzzy analytic hierarchy process: An application to capital budgeting problem Yu-Cheng Tang a,⇑, Ching-Ter Chang b a b
Accounting Department, National Changhua University of Education, Taiwan Department of Information Management, Chang Gung University, Taiwan
a r t i c l e
i n f o
Article history: Received 24 April 2010 Received in revised form 15 August 2011 Accepted 10 October 2011 Available online 25 October 2011 Keywords: Capital budgeting Fuzzy analytic hierarchy process Goal programming Decision-making Sensitivity analysis
a b s t r a c t Our objective in this paper is to develop a decision-making model to assist decision-makers and researchers in understanding the effect of multiple criteria decision-making on a capital budgeting investment. This decision-making model helps decision-makers with reducing decision-making time and choosing a suitable decision alternative for a capital budgeting investment within the companies’ goals, constraints and strategies. The methods utilized in this paper are goal programming (GP) and fuzzy analytic hierarchy process (FAHP). We demonstrate a case study of the capital budgeting investment by using these two methods in a small car rental company. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Capital budgeting decision-making is one of the most demanding responsibilities of top management [21,12]. An increasing number of companies have struggled to justify strategic technology investments using traditional capital budgeting systems [2]. The existing accounting-based decision-making models (such as discounted cash flow (DCF)) are said to be no longer adequate to help evaluate investments in technological innovation, mainly because of the strategic, intangible nature of the benefits involved [13,22]. When business decisions are made, they involve not only consideration of information which is quantifiable in numerical terms (e.g. financial information), but also consideration of subjective (e.g. non-financial information) opinions [27,2,1]. Such subjective considerations are naturally expressed in linguistic rather than in numerical terms [14]. Therefore, we realized that non-financial information needs to be quantified in order to integrate it with numerical information. This research will focus on how to integrate financial and nonfinancial information in the company’s constraints, goals and strategies. The methodologies presented within this research are goal programming (GP) and fuzzy analytic hierarchy process (FAHP) which address the problem of capital budgeting in uncertain environments. ⇑ Corresponding author. Tel.: +886 4 7232105x5621; fax: +886 4 7211150. E-mail address:
[email protected] (Y.-C. Tang). 0950-7051/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2011.10.005
Capital budgeting is primarily concerned with sizable investments in long-term assets. Investment decisions deal with the funds raised in financial markets which are employed in productive activities to achieve the firm’s overall goal, in other words, how much should be invested and what assets should be invested are the main objectives. Therefore within this research it is assumed that the objective of the investment or capital budgeting decision is to achieve the company’s goals and to stay within its constraints. GP normally deals with conflicting objective measures. Each of these measures is given a goal or target value to be achieved. FAHP provides a relatively more complete description of decision-making process involving the subjective and imprecise judgments of decision makers [4]; [17]; [11]. The methods are divided into two steps. Firstly, financial and other objectives along with a company’s goals, constraints and strategies are formulated as important selection criteria. A set of decision alternatives (DAs) as preliminary outcomes will be sifted by using GP from financial information. Secondly, subjective opinions elicited from decision-makers (DMs) are transformed into fuzzy comparison matrices (for the details of FAHP also refer to Chang [8], Tang [23]). A simple practical preference ranking method (synthetic extent method) is investigated to rank alternatives in a multiplicative aggregation process. The extent analysis method has been employed in quite a number of applications, such as capital measurement [5], budget allocation [23], assets selections and investment [6,7,24] and for more detail refer to Wang et al. [26]. However, disadvantages have also
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been pointed out, such as an inability to derive the true weights from a fuzzy or crisp comparison matrix [26]. This research will utilize the formulation of a degree of possibility for comparing two triangular fuzzy numbers as proposed in Zhu et al. [30]. One aspect of the FAHP method within this research is the prevalence of and allowance for incompleteness in the judgements made by DMs. For example, if a DM is not willing or is unable to specify the preference judgements, s/he is able to omit a judgement in the form of a pairwise comparison between two DAs. The rest of the paper is organized as follows. Section 2 describes the details of the used cars selection problem. Section 3 proposes GP procedures and the synthetic extent method of the FAHP. Section 4 illustrates the results of the used cars selection problem. The conclusion is provided in Section 5.
2. Identification of the used cars selection problem The case study concerns a small car hiring company and their choice of type of fleet cars to be adopted. This choice is an important investment decision, with a large proportion of their budgets being tied up in their final choice. In order to find out which are the most important criteria used by the DMs, two interview phases are implemented, semi-structured and structured interviews. The semi-structured interview within this research was designed to identify all the relevant issues affecting the decisionmaking (e.g. the company’s goals, constraints and objectives, etc.). It was difficult to discover all these issues in the beginning until the DMs were reassured. In this phase, the semi-structured interview shows that there are two constraints (i.e., five cars can be chosen each time and the total size of engines are limited to under 8000cc); two goals (i.e., to minimize the cost of suitable cars and to minimize the cars’ age and mileage); four pieces of objective information (i.e., size of engine, price, car age and mileage). There
Table 1 Pairwise comparisons between criteria based on the DM’s opinions.
are six subjective criteria identified by this company’s DMs, i.e., ‘‘Equipment, Comfort, Car Parts and Components, Customer Demand, Safety, and Image’’, denoted as C1, C2, . . . , C6, respectively. Apart from those constraints, goals and criteria, the semi-structured interviews also identified ten type of most commonly used cars, denoted herein A01 ; A02 ; . . . ; and A010 , respectively (see Appendix A). They are the initial DAs in this case study. After we identified their constraints, goals and objectives, we utilized the GP methodology to obtain the DAs. With respect to the AHP’s pairwise comparison method, we still needed to explain a lot to the DMs as it is difficult for people to understand the judgment matrices in the first time. Therefore, in the second phase of interviews, the DMs were asked to indicate their preferences between pairs of criteria, and then between pairs of DAs over the different criteria. In this phase, a DM can leave a judgement out without giving any judgement on the fuzzy comparison matrix. The results from the second phase of interview are shown in Tables 1 and 2. 3. Proposition of GP procedures and the synthetic extent method of the FAHP 3.1. First step: introduction of the procedure of GP GP is an important technique for allowing DMs to consider several objectives in finding a set of acceptable solutions. It has been accomplished with various methods such as Lexicographic (Preemptive), Weight (Archimedean), and MINIMAX (Chebyshev) achievement functions [18]. It can also be said that GP has been, and still is, the most widely used technique for solving multi-criteria decision-making problems. The purpose of GP is to minimize the deviation between the achievement of goals, fi(Y), and their acceptable aspiration levels, gi. A mathematical expression for the standard version of GP is given below. (GP) method
Minimize
n P
jfi ðYÞ g i j;
i¼1
C1 C2 C3 C4 C5 C6
C1
C2
C3
C4
C5
C6
1 1/3 9 – – 1/3
3 1 3 9 9 –
1/9 1/3 1 9 9 –
– 1/9 1/9 1 1 9
– 1/9 1/9 1/9 1 1/7
3 – – 1 7 1
subject to Y 2 F;
where fi(Y) is the linear function of the ith goal, Y is a 1 N vector of decision variables and gi is the aspiration level of the ith goal. The oldest and still most widely used form of achievement function for GP is represented as follows. (GP-achievement)
Minimize
n P i¼1
Table 2 a to f: Comparisons between DAs over the different criteria.
ðF is a feasible setÞ;
þ
di þ di ; þ
subject to f i ðYÞ di þ di ¼ g i ;
(a) C1
A1
A2
A3
A4
A5
(b) C2
A1
A2
A3
A4
A5
A1 A2 A3 A4 A5
1 – – – 1/5
– 1 1/7 3 1/5
– 7 1 5 1/5
– 1/3 1/5 1 1/5
5 5 5 5 1
A1 A2 A3 A4 A5
1 8 8 7 –
1/8 1 – – 1/5
1/8 – 1 8 1/5
1/7 – 1/8 1 1/5
– 5 5 5 1
(c) C3
A1
A2
A3
A4
A5
(d) C4
A1
A2
A3
A4
A5
A1 A2 A3 A4 A5
1 1/7 3 – 5
7 1 1/5 – –
1/3 5 1 1/5 1/5
– – 5 1 –
1/5 – 5 – 1
A1 A2 A3 A4 A5
1 3 1/3 5 –
1/3 1 – 5 1/5
3 – 1 5 –
1/5 1/5 1/5 1 1/5
– 5 – 5 1
(e) C5
A1
A2
A3
A4
A5
(f) C6
A1
A2
A3
A4
A5
A1 A2 A3 A4 A5
1 8 – 7 –
1/8 1 – 1 1/3
– – 1 8 1/3
1/7 1 1/8 1 1/3
– 3 3 3 1
A1 A2 A3 A4 A5
1 7 5 9 –
1/7 1 1/7 – 6
1/5 7 1 8 1/6
1/9 – 1/8 1 1/6
– 1/6 6 6 1
Y 2 F;
for i ¼ 1; 2; . . . ; n;
ðF is a feasible setÞ;
where di (i = 1, 2, . . . , n) are additional continuous variables. 3.2. Second step: construction of the FAHP comparison matrices The aim of any FAHP method is to elucidate an order of preference on a number of DAs, i.e., a prioritised ranking of DAs. Central to this method is a series of pairwise comparisons, indicating the relative preferences between pairs of DAs in the same hierarchy. It is difficult to map qualitative preferences to point estimates, hence a degree of uncertainty will be associated with some or all pairwise comparison values in an FAHP problem [28]. By using triangular fuzzy numbers (TFNs), via the pairwise comparisons made, the fuzzy comparison matrix X = (xij)nm is constructed. The pairwise comparisons are described by values taken from a pre-defined set of ratio scale values as described in Saaty [19]. The ratio comparison between the relative preference of elements
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indexed i and j on a criterion can be modeled through a fuzzy scale value associated with a degree of fuzziness. Then an element of X, xij (comparison of ith DA with jth DA with respect to a specific criterion) is a fuzzy number defined as xij = (lij, mij, uij), where mij, uij and lij are the modal-value, the upper bound and the lower bound values of a fuzzy number xij, respectively. To keep the reciprocal nature of the fuzzy comparison matrix X, the fuzzy number is also satisfied with lij ¼ u1 ; mij ¼ m1 ; uij ¼ l1 [24]. ji ji ji There are various operations upon TFNs, the relevant reference can be referred to in Kaufmann and Gupta [15].
0
Si ¼
m X
M jC i
" n Y m X
j¼1
#1 MjC i
ð1Þ
;
i¼1 j¼1
where represents fuzzy multiplication and superscript 1 represents the fuzzy inverse. The concepts of synthetic extent can also be found in Chang [8], Tang [23], Tang and Beynon [24]. The degree of possibility of two fuzzy numbers M 1 P M 2 is defined as:
h i VðM1 P M 2 Þ ¼ sup minðlM1 ðxÞ; lM2 ðyÞÞ ; xPy
ð2Þ
VðM1 P M 2 Þ ¼ 1 iff m1 P m2 ; VðM2 P M 1 Þ ¼ hgtðM1 \ M2 Þ ¼ lM1 ðxd Þ;
where iff represents ‘‘if and only if’’ and d is the ordinate of the highest intersection point between the lM1 and lM2 TFNs (see Fig. 1) and xd is the point on the domain of lM1 and lM2 where the ordinate d is found. The term hgt is the height of fuzzy numbers on the intersection of M1 and M2. For M1 = (l1, m1, u1) and M2 = (l2, m2, u2), the possible ordinate of their intersection is given by the expression (2). The degree of possibility for a convex fuzzy number can be obtained from the use of Eq. (3)
VðM 2 P M 1 Þ ¼ hgtðM 1 \ M 2 Þ ¼
l1 u 2 ¼ d: ðm2 u2 Þ ðm1 l1 Þ
ð3Þ
The degree of possibility for a convex fuzzy number M to be greater than the number of k convex fuzzy numbers Mi (i = 1, 2, . . . , k) can be given by the use of the operation max and min [10] and can be defined by:
VðM P M 1 ; M 2 ; . . . ; Mk Þ ¼ V½ðM P M 1 Þ and ðM P M 2 Þ and . . . and ðM P Mk Þ ¼ min VðM P Mi Þ; i ¼ 1; 2; . . . ; k: 0
Assume that d ðAi Þ ¼ min VðSi P Sk Þ, where k = 1, 2, . . . , n; k – i and n is the number of criteria as described previously. Then a weight vector is given by:
0
ð4Þ
0
The vector W is normalised and denoted by:
W ¼ ðdðA1 Þ; dðA2 Þ; . . . ; dðAm ÞÞ:
ð5Þ
One point of concern, highlighted in this paper is when two elements (fuzzy numbers – M1 and M2) say (l1, m1, u1) and (l2, m2, u2) in a fuzzy comparison matrix satisfy l1 u2 > 0 then V(M2 P M1) = hgt(M1 \ M2) = lM2 ðxd Þ, with lM2 ðxd Þ given by Zhu et al. [30]:
(
lM2 ðxd Þ ¼ 3.2.1. Value of fuzzy synthetic extent Let C = {C1, C2, . . . , Cn} be a criteria set, where n is the number of criteria and A = {A1, A2, . . . , Am} is a DA set where m is the number of DAs. Let M1C i ; M 2C i ; . . . ; M m C i be values of extent analysis of ith criteria for m DAs where i = 1, 2, . . . , n and all the M jC i (j = 1, 2, . . . , m) are TFNs. The value of fuzzy synthetic extent (Si) with respect to the ith criteria is defined as:
0
W 0 ¼ ðd ðA1 Þ; d ðA2 Þ; . . . ; d ðAm ÞÞ:
l1 u2 ðm2 u2 Þðm1 l1 Þ
l1 6 u2 ;
0
others:
ð6Þ
In Zhu et al. [30] this fuzziness is influenced by a d (degree of fuzziness) value, where mij lij = uij mij = d. That is, the value of d is a constant and is considered an absolute distance from the lower bound value (lij) to the modal value (mij) or the modal value (mij) to the upper bound value (uij). However, when the modal value (mij) is greater than 1 and the degree of fuzziness is greater than mij 1 then the lower bound value lij will be less than 1 or less than 0. It implies that the lower bound value lij is meaningless with the fuzzy scale value mij greater than 1. To remove this potential of conflict, a restraint on the lij value needs to be set up at 1. This argument assumes that the fuzziness in a preference judgement (mij – 1) does not include the possibility of reversal in the direction of the preference initially implied. There is no limit on the upper bound of the fuzzy scale value. 3.2.2. The use of sensitivity analysis to decide the degrees of fuzziness It is required to have a suitable degree of fuzziness for the fuzzy numbers. In this paper, the use of sensitivity analysis to decide the degrees of fuzziness will be elucidated. We firstly consider the judgements made between the criteria based on the DM. There are six lines in Fig. 2 which represent the weight values associated with the different criteria. In Fig. 2 the numbers (with criteria) on the d-axis represent the degree of fuzziness appearance points with respect to each criterion. For example the degree of fuzziness d up to 1.17 (on Fig. 2 d-axis), shows that C5 has the absolute dominant preference. This means that Safety is an important criterion to be considered when the DM makes decisions and the weight value is 1. After d reaches 1.17, the criterion C4 has weight. The next criterion is C3 which has weight as d approaches 1.32, etc. The values of d at which the criteria (or DAs) have positive weight values (non-zero) are hereafter referred to as appearance points. For the fuzzy comparison matrix with judgements between criteria (see Fig. 2), all the six criteria have positive weights when d is greater than 3.45. This means that if d is less than 3.45 some criteria have no positive weights. Zahir [29] discussed this aspect within the traditional AHP, suggesting that the DM does not favour one criterion (or DA) and ignore all others, but rather places the criteria (or DAs) at various levels. Besides, pairwise comparisons are made between criteria (or DAs) then it is expected that all weights should have positive values. It is suggested therefore that it is useful to choose a minimum workable degree of fuzziness. The
1
C5
0.5
0
Fig. 1. The comparison of two fuzzy numbers M1 and M2.
1.17 1.32 C4 C3
2.5 C1
2.8 C2
3.45 C6
δ
5
Fig. 2. The weights obtained from pairwise comparisons between criteria for d ? 5.
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expression minimum workable degree of fuzziness is defined as the largest of the values of d at the various appearance points of criteria (or DAs) on the d-axis. When considering the final results, the domain of workable d is expressed as dT, and is defined by the maximum of the various minimum workable degrees of fuzziness throughout the problem, that is here dT ¼ max dTc ; dT1 ; dT2 ; . . . ; dTn1 ; dTn where the subscript T is the maximum of the minimum workable d values in the n + 1 (Tc matrix) fuzzy comparison matrices.
(a) C1 1 A4 0.5
0
0.67
1.67
A3 , A2
3.15
A1
(b) C2 1
δ 5
4
A5
A4
4. The results of the used cars selection problem
0.5
4.1. The results of first step obtained from the GP Two goals of the problem are given as to minimize the cost of suitable cars and to minimize the cars’ age and mileage. Other constraints are given as: (i) to find five suitable cars out of these ten cars; (ii) the total size of engine is limited to under 8000cc; (iii) the total price is limited to under 12,000 pounds. From these two goals we know that the smaller the value of goals, the better the achievement. Thus, we can set two goals of the problem g1 and g2 to be zero corresponding to the above goals þ þ Minimize d1 þ d2 ; subject to A01 ; A02 ; A03 ; . . . and A010 ; 2A01 þ 1:5A02 þ 3A03 þ 2A04 þ 2A05 þ 3A06 þ 3A07 þ 1:5A08 þ 3:5A09 þ þ 3A010 d1 ¼ g l1 ðAgeÞ: 0 9500A1 þ 4000A02 þ 45000A03 þ 30000A04 þ 25000A05 þ 25000A06 þ þ 35000A07 þ 4000A08 þ 28000A09 þ 9300A010 d2 ¼ g l2 ðMileageÞ: 0 0 0 0 0 0 0 0 0 A1 þ A2 þ A3 þ A4 þ A5 þ A6 þ A7 þ A8 þ A9 þ A10 ¼ 5ð5 carsÞ: 1995A01 þ 1995A02 þ 1600A03 þ 1600A04 þ 1000A05 þ 1600A06 þ 1600A07 þ 1400A08 þ 1995A09 þ 1600A10 < 8000 ðSize of engineÞ: 19995A01 þ 4500A02 þ 2000A03 þ 3000A04 þ 1500A05 þ 1850A06 þ 2500A07 þ 3500A08 þ 14000A09 þ 5000A010 4.5 and the results on
0
0.35 0.62
3.65
4.5
A2 A3
A5
A1
(c) C3 1
δ5
A5 0.5
0 0.18 0.56
(d) C4 1
A3
1.18
A1
δ5
2.45
A2
A4
A4 0.5
0
0.63
1.55 1.66
2.8
A2
A1
A5
A3
δ5
(e) C5 1 A4 0.5
0 0.12
δ5
1.81 1.815 2.4
A2
A3
A5
A1
(f) C6 1 A4 0.5
0
0.85
A2
1.2
A3
2.14
A5
4.5 δ 5
A1
Fig. 3. a to f: Comparisons between DAs over six criteria.
weights should possibly only be considered in the workable d region. The use of minimum workable degree of fuzziness is intended to exclude values of d at which there are no positive weights for the DAs. However the use of a workable value of d is not to be strictly enforced. In Table 3, the final results show that the most preferred car is the Ford (A4), and then the Volkswagen (A2), the Daewoo (A3), the Proton (A5) and the Vauxhall (A1), which is the least preferred car in the DM’s mind. From the comparison between the criteria in Table 3, the most preferred criterion out of the six criteria is Safety. It means that the DMs care about safety more than other criteria. The results in Table 3 also can be compared with Tables 1 and 2a–f. For example, the weight value of C6 is the least of the weights in Table 3. Comparing with Table 1, apart from C6 having extreme preferences to C4, C6 has no preference in relation to other criteria.
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Table 3 The sets of weight values for all fuzzy comparisons matrices using the 1–9 scale and the final results over d = 4.5 based on the DM’s opinions. DM
Weight values for DAs
DAs
A1
A2
A3
A4
A5
C1 C2 C3 C4 C5 C6 Final results
0.1741 0.0024 0.2226 0.1802 0.1228 0.0021 0.1421
0.2340 0.3097 0.1869 0.2547 0.2804 0.2631 0.2513
0.2345 0.2924 0.2400 0.1879 0.1590 0.2449 0.2109
0.2628 0.3275 0.1043 0.2843 0.2872 0.3053 0.2509
0.0946 0.0680 0.2462 0.0929 0.1507 0.1847 0.1447
Ranking orders
Weight values for criteria
0.1295 0.1006 0.2067 0.2148 0.2811 0.0674
[A4, A2, A3, A5, A1]
Also the DM made no opinions on C2 and C3 when they are compared with C6. For the comparisons between DAs over C2, A5 has the least weight (0.0924) in Table 3. This also can be examined in Table 2b. In Table 2b, the DM made one no opinion on A5 to A1 and three 1/5 when A5 compare to A2, A3 and A4. Other results shown in Table 3 can also be examined by this way. The results also can be compared with Figures. In Fig. 2, C5 is the dominate criterion and can be examined in Table 1. In Table 1, C5 has greatest preference compared with other criteria, in that C5 has two extremely preferred (9s), one equally preferred (1) and one very strongly preferred (7). The rest of the preference ranking order in Fig. 2 is C4, C3, C1, C2 and C6 respectively. In Table 1, C4 has two 9s and one 1. C3 also has greater preference than other criteria, as it has one 9 and one 3. This pattern continues in Fig. 3a–f compared with Tables 2a–f. The consistency can be examined by this way. 5. Conclusions The aim of this research is to investigate the application of the methods of the goal programming (GP) and the fuzzy analytic hierarchy process (FAHP) of multi-criteria decision making (MCDM), within a capital budgeting case study. In this research, GP is proposed to solve the financial information, such as the company goals, constraints, or other company’s strategy. FAHP is to deal with the imprecise judgements made by decision makers (DMs). The redefinition of the degree of fuzziness associated with the preference judgements made allows the change of imprecision (fuzziness) to be succinctly reported. The issue of imprecision is reformulated in this study, which further allows a sensitivity analysis on the preference weights evaluated to changes in the levels of imprecision.
In this research, the goals are represented as numerical data. The scales used within this FAHP are verbal definitions and explanations of the integer (1–9) scale. If we use fuzzy AHP methodology then all the numerical data will be assessed into verbal assessment inputs. Ghosh and Roy [11] mentioned that AHP does not consider the relevant constraints and multiple conflicting goals. The verbal data’s limitations also can be referred to Cho [9]. They also mentioned that GP combined with the AHP can prove to be a flexible tool to reach the company’s goals and constraints. This research is focused on integrating the numerical and nonnumerical information. Therefore, either FAHP or GP cannot stand alone to deal with both numerical and non-numerical information. This also can be referred to Badri [3]. Badri pointed out the drawbacks of using AHP alone and proposed that AHP and GP are combined to cover the limitations. Relevant references also can be referred to Tsai [25], Ravisankar and Ravi [16]. From the academic point of view, the model provided in this research can deal with the DMs consideration of the company’s goals, constraints, strategies and with imprecise judgements simultaneously. It also provides a high tolerance for ambiguity and a well-ordered sense of priorities. From the practical point of view, this research involved a field study and collection of data from semi-structured interviews, structured interviews and a questionnaire. It displays the integration of theory and practicality. The other contributions of this paper are saving decision-making time for decision makers – by using GP, and eliciting the subjective opinions from decision makers – by using FAHP, etc. Future research associated with the FAHP include, from the MCDM point of view, those developments with the traditional AHP. These include the appropriateness of the 9-unit scale (integer values one to nine), which within AHP is still an ongoing issue. The effect of using a different 9-unit scale within FAHP would further elucidate the sensitivity analysis issues.
Appendix A 1. Information table for car selection case study Type
Central locking Electric windows Power steeling Automatic Air condition 5 Doors Airbags Antilock braking system
BMW 3 Series Touring p p p p p p p p
Honda Vauxhall Civic Merit p p p p p p p
p p p p p p p
Volkswagen Daewoo Ford Honda Proton Polo Lanos Fusion New Persona Civic p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p
Toyota Celica
Fiat Punto
p p p p p p p p
p p p p p p p p
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Appendix A (continued) Type
BMW 3 Series Touring p Impact protection system p Anti-theft devices Image Metalic green Size of engine (cc) 1995 Insurance* 10 Price (£) 19,995 Car age (years) 2 Car mileage 9500
Honda Vauxhall Civic Merit Red 1995 7 4500 1.5 4000
Metallic blue 1600 8 2000 3 45,000
Volkswagen Daewoo Ford Honda Proton Polo Lanos Fusion New Persona Civic p p p p Red Black Blue Silver Green 1600 7 3000 2 30,000
1000 6 1500 2 25,000
1400 9 3500 1.5 4000
1600 7 2500 3 35,000
1600 11 1850 3 25,000
Toyota Celica p p Metallic blue 1995 6 14,000 3.5 28,000
Fiat Punto Black 1600 9 5000 3 9300
* The insurance has groupings from 1-20, depending on each car, for example, a Proton Persona is in group 11. A lower insurance grouping attracts a lower insurance premium cost. The higher the grouping the more expensive the insurance cost.
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