Fuzzy Analysis of Financial Risk Management Strategies for Sustainable Public-Private Partnership Infrastructure Projects in Ghana

1. Introduction

Achieving sustainable infrastructure development has been proven to be contending especially for developing economies. Developing nations such as Ghana are confronted with short-lived and poorly maintained public-sponsored infrastructure projects together with huge infrastructure deficit [1,2]. These limitations put a cap on the progress towards the attainment of sustainable development. The challenge is demonstrated in trafficked and congested transport networks, dilapidated school buildings, hospitals, and recreational centres, and polluted water supply among others [3,4]. In Ghana, the developmental challenges have worsened by rapid urbanization and high population growth rate [4]. The ever-increasing population demands eco-friendly and sustainable facilities and projects to meet the basic needs of life. However, the financial support from the Government of Ghana (GoG) is not enough to build and operate infrastructures for all the citizenry due to insufficient budgetary funds [5,6]. Recent COVID-19 recession and banking crisis in the country have impacted negatively on the flow of private investment into sustainable and environmentally-conscious development projects [7]. Project such as the extension of Accra-Tema Motorway including the eco-recreational parks, Ghana-Burkina Railway Interconnectivity, Installation of Lquid Waste Treatment Plant in Kotoku, Sogakope-Lome Transboundary Water Supply and Atuabo Natural Gas Processing Plant have been financed through the public-private partnership arrangements [8,9].

Nevertheless, these eco-friendly PPP projects have recorded monumental financial challenges. Scholarly works on financial challenges in Ghana together with project, and institutional reports from Ministry of Finance, Ghana, World Bank and African Development Bank position financial risks as the topmost obstacle to successful execution of sustainability-inspired and climate-friendly PPP projects. Financial risks such as rising costs of materials, operating the facilities, maintenance, and energy consumption, as well as lower than expected revenue from these projects pose threatening risks to the projects and financial investment returns for private financiers. Therefore, it is necessary that effective and sustainable financial measures are implemented to mitigate these negative consequences [10,11]. This study aims at analysing the financial risk management strategies for sustainable and eco-friendly PPP infrastructure projects in Ghana. The major significance of this article is twofold. The results provide relevant guiding measures on financial risks to assist PPP project managers and practitioners. The study could be an integral part of the strategies designed to improve organisational and project management processes on limiting financial losses for sustainable infrastructure development and future studies. The rest of the study presents literature review, methodology, the results from the data analysis, and conclusion.

2. Literature Review

2.1. Sustainable Public-Private Partnership Infrastructure Projects

Sustainable infrastructure development has become a well embraced concept in environmentally-conscious and social inclusion matters [12]. It requires a degree of environmental, social, and economic improvement to ensure the well-being of future generations [13]. Sustainable infrastructure development is embedded in the all the 17 goals of United Nation’s Sustainable Development Goals (SDGs) [14]. However, Villalba-Romero, et al. [15] explained that sustainable infrastructure development agenda could not achieved without the strong support private financiers who play paramount roles in shifting hitherto government-sponsored projects to public-private partnership (PPP) infrastructure projects. Fast-forward into the current and future PPP infrastructure development is the inclusion of environmental and social impact assessments of the projects together with net-zero and climate-friendly targets [16]. Similarly, the policies and programs of sustainability of renovating and improving the lifespan of existing PPP-built infrastructures are aimed at meeting the social needs of the society and preserve the environmental resources [17]. There is also a growing global recognition to consider the integration of sustainability and eco-friendly designs into infrastructure projects delivered through public–private partnerships (PPPs) [18]. The successful implementation of sustainable measures in infrastructural projects is considered as an important strategy for attaining sustainability [19].

2.2. Financial Risks in Sustainable PPP Infrastructure Projects

Prior and during the COVID-19 pandemic, financial risk has been recognised as a topical issue among PPP practitioners and financiers [20]. Financial risk is rated as a significant influencer of poor PPP infrastructure performance [21]. Financial risks encompass all the cashflow challenges related to the PPP infrastructure development [22]. They include rising loan interest charges, difficulty in soliciting for funds to build and maintain the PPP projects, additional construction budgeted costs, bloated operation and maintenance expenditure, low revenue from the project, poor investment returns to financiers and high market risks that emanates from unfavourable macroeconomic conditions. Akomea-Frimpong, et al. [23] identified fifty-four (54) topmost financial risks in relation to PPP projects. Among these 54 financial risks, financial charges associated with contractual loans was prominent followed by construction costs, inflation, and operation expenses. Osei-Kyei, et al. [24], study revealed the existence of shortage of funds to complete PPP projects in developing economies. Zhang, et al. [25], Xenidis and Angelides [26] and Yun, et al. [27] analysed the key variables that influence financial viability of PPP projects using credit worthiness of bond capital, the financial expertise of the project team, general prevailing economic conditions. The studies explored special purpose vehicles that undertook comparative analysis of project’s financial success. The analysis of the economic constraints of PPPs were analysed with the touch of both non-financial and economic models in transport, schools, hospitals, and playgrounds under the PPP arrangements. Prominent influencing factors that occasion financial difficulties are regulation-related with strict terms and caps on the amount that can be contracted and spent on PPPs [28,29]. The coronavirus pandemic also triggered lockdowns and compulsory restrictions putting on a strain on the usage of PPP infrastructures which are already in operation [30]. It has prompted revenue (cash inflow) crisis with PPP infrastructure operations closing with piling debts. However, it remains unexplored the multidimensional perspectives on measures to reduce the financial losses of PPP infrastructure projects.

3. Research Methodology

3.1. Questionnaire Survey Data

The starting point in designing the survey questionnaire was the search for the appropriate variables to be included in the survey. So, a review of existing literature was conducted using the terms “financial risk management strategies” and “sustainable and eco-friendly public-private partnership projects”. Scholarly literature from Web of Science, EBSCOhost, Scopus, Web of Science, and Google Scholar were retrieved and thoroughly analysed to extract data for the content of the survey questionnaire. These bibliographic databases are prominent in searching and extracting relevant literature for academic research in the Architecture, Engineering, and Construction research field. After thorough review of the articles retrieved with more emphasis on Ghana, forty-one (41) financial risk management strategies (FRMSs) were extracted from the literature. The 41 FRMSs were given to five experts (two senior academics and three practitioners who are knowledgeable in PPP projects) through pilot testing. The feedback received from the experts assisted in making changes to the variables to meet the PPP project-setting of Ghana. Some of the 41 variables were either deleted or merged with other variables reducing the number to twenty-three as shown in Table 1. Two sections included in the survey questionnaire were the profile of respondents (Section 1), and financial risk management strategies (Section 2). The variables (statements) in Section 2 were the items demonstrated in Table 1.

The targeted participant to respond to the statements in the surveys were practitioners and experts on PPP projects in Ghana. To participate in this study, a respondent must have taken a significant part in the construction and operation of a PPP project or PPP-related activity. Purposively, the respondents (participants) were selected were encouraged to nominate or recommend colleagues to be involved in the data collection process. In summary, a total of 403 participants were compiled with personal and career profiles. Emails were sent to the targeted participants but 334 responded to the emails and responded to the Qualtric links of the survey questionnaires attached to the emails. Upon thorough data cleaning, 283 surveys were accepted, and 51 responses were deleted due to failure to respond to the statements in the questionnaire. The 287 surveys were fully filled and analysed. This sample size (287 responses) is sufficient and it is supported by prior statistical models on the adequacy of sample size by Sunindijo and Kamardeen [31], Kotrlik and Higgins [32] and Cochran [33]. The mathematical equation is demonstrated as follows:

$$N=\frac{t^{2}X{s}^2}{d^2}$$

The N refers to the sample size, t is the significance level at 0.05 (5%) with a critical value of 1.96, s represents the estimated variance of deviation within the 5 points Likert scale, d is the points or scales on a Likert scale multiplied by a margin of error. Therefore, the expected sample size from this mathematical equation is supposed to be:

$$N=\frac{{1.96}^{2}X{1}^2}{{\left(5\mathrm{*}0.05\right)}^2}=61$$

The results from the mathematical formula of 61 respondents is lower than the accepted sample size of this study of 287 responses, confirming the sufficiency of the dataset. Table 2 demonstrates the description of the respondents.

3.2. Analysis of Data

Statistically, the dataset’s reliability was tested to ascertain the internal consistency of the data within the SPSS statistical software 29 (Statistical Package for the Social Sciences). With the aid of Cronbach Alpha (CA), a 0.872 CA score was realised for the reliability test, a reflection of the internal consistency of the multiple items in the questionnaire [34]. Further, the Shapiro-Wilk test was conducted to establish the nature of the normality of the data [35]. The outcomes of the analysis show p-values of less than 0.000, an indication of non-normal distribution of the dataset [36]. With this result, it settled the stage for the usage of non-parametric data analysis techniques of Kruskal-Wallis test together with Mann-Whitney U test [37,38]. These non-parametric statistical tools assisted in establishing the differences views of the participants of this study [39]. The two statistical techniques are commonly utilized to assess the significant differences in non-parametric datasets [40]. Three categories of data were analysis to determine the differences and criticality of the 287 datasets: PPP practitioners, PPP project types and PPP sectors.

Further, exploratory factor analysis (EFA) was used to extract principal factors from the 287 datasets. EFA explores the causal relationships between the latent variables and the measured items acting as common factor model [41]. In EFA, the fundamental tests to determine the reliability and validity of the model include Kaiser-Meyer-Olkin (KMO) that measures the sampling adequacy of the dataset. Its significance and adequacy are established by Bartlett’s Sphericity test. Communalities within the EFA analysis indicate the sum of loadings of the variance explained by a variable (or factor). With the rotation results showcasing the minimisation of variables to retain significant financial risk management variables.

Lastly, the data is analysed with fuzzy synthetic evaluation method. Linguistically, fuzzy logic theory rectifies the anomalies in complicated reasoning and vague terms that appear in subjective views on a subject into a more objective set of outcomes [42]. With fuzzy analysis, the subjective opinions can be operationalised and computed to ascertain desired results for decision making. Fuzzy synthetic evaluation (FSE) promotes the evaluation of diverse responses for decision-making based on different set of ranking criteria [43]. Previous studies such as Nguyen and Macchion [42] and Kukah, et al. [44] mentioned that FSE is appropriate the analysis of diverse factors (or criteria) in different fields. Within the construction project management literature, Xu, et al. [45], Wuni, Shen and Osei-Kyei [35] and Ekanayake, et al. [46] stated that FSE establishes weights and membership functions that ensures objective analysis of matters associated with the management of construction firms and projects. Additionally, Owusu-Manu, et al. [47] and Osei-Kyei, et al. [48] recounted the appropriateness of FSEs in choosing the critical factors in multi-criteria decision making scenarios. The FSE in this study is modelled as follows.

Step one: Establish the principal groups from the exploratory factor analysis, $PCFR=\left\{f_1, f_2, f_i,\dots f_m\right\}$.

Step two: Set a grading alternatives, $Gt=\left\{{gt}_1, {gt}_2, {gt}_3,\dots {gt}_e\right\}$ where: ${gt}_1$= Strongly disagree, ${gt}_2$= Disagree, ${gt}_3$= Neutral, ${gt}_4$= Agree and ${gt}_5$=Strongly agree.

Step three: Determine the weightings (W_i) of each of the financial risk management strategies and the principal groups using their mean scores.

Step four: Construct the fuzzy evaluation matrix from the principal groups:

$$R_i=\left[\begin{array}{ccccc}{X}_{11}& X_{12}& X_{13}& X_{14}& X_{15}\\ X_{21}& X_{22}& X_{23}& X_{24}& X_{25}\\ X_{31}& X_{32}& X_{33}& X_{34}& X_{35}\\ \dots & \dots & \dots & \dots & \dots \\ X_{m1}& X_{m2}& X_{m3}& \dots & X_{mt}\end{array}\right]$$

Where $R_i$ is the fuzzy evaluation matrix,

Step five: Undertake the fuzzy synthetic evaluation as:

$$D_i=W_i●R_i$$

Where$D_i$represents the FSE value, $W_i$is the weightings function, $R_i$is the membership functions of the principal groups and “●” is the fuzzy composite operator.

$$D_i=\left\{{wt}_1, {wt}_2, {wt}_3,\dots {wt}_m\right\}●\left[\begin{array}{ccccc}{X}_{11}& X_{12}& X_{13}& X_{14}& X_{15}\\ X_{21}& X_{22}& X_{23}& X_{24}& X_{25}\\ X_{31}& X_{32}& X_{33}& X_{34}& X_{35}\\ \dots & \dots & \dots & \dots & \dots \\ X_{m1}& X_{m2}& X_{m3}& \dots & X_{mt}\end{array}\right]$$

Step six: Calculate both criticality indexes of the entire dataset and each principal (group) factor using:

$$\mathrm{K}={\sum }_{\mathrm{i}=1}^5\mathrm{D}\mathrm{x}\mathrm{G}$$

Where$G=(\mathrm{1,2},\mathrm{3,4},5)$, the grading alternatives.

4. Results

4.1. Mean Scoring Analysis

In this section, the mitigating strategies on financial risks to increase the financial outcomes of sustainable and eco-friendly PPP projects are analysed. The criticality threshold varies in past studies of 2.5, 3, 4 and 4.5 [59]. In this analysis, the minimum of mean of 3.0 adopted based on the outcomes of the dataset and importance of the FRMSs in comparison with researches such as Babatunde, Opawole and Akinsiku [54] and Tang and Shen [60]. From the Table 3, 4 and 5, it is noticeable that almost all means of the FRMSs range from 3 to 5. These ratings provided by respondents presupposes that these critical financial risk management strategies of sustainable infrastructures in Ghana. Consequently, to assess the difference in perceptions held by the two main parties involved in PPP projects i.e., public, and private sectors, when it came to the ranking of the 23 identified FRMSs, Mann-Whitney U test (at 5% level of significance). The null hypothesis posited no difference in the perceptions of both sectors on FRMSs. As vividly demonstrated in Table 3 of the test results and it indicates statistically significant values that for all the identified FRMs. That means, the two sectors related to the PPP projects in Ghana hold different views about management strategies on financial risks to enhance sustainable infrastructures in the country within the PPP arrangements. In Table 4 and Table 5 tested differences in perspectives of four groups of PPP practitioners in Ghana and three groups of PPP project types with Kruskal-Wallis test. The aim was to depict the statistically significant differences in comparing the various groupings with results indicating statistical significance values at p-value of 0.050. Substantially, the null hypothesis of no differences in views of practitioners on FRMSs of sustainable and eco-friendly PPP projects in Ghana is rejected. This indicates that there are real differences in the perception of practitioners on the FRMSs. The expansive results in Table 5 buttresses the differing perspectives of participants on the financial risk management measures on project types: social, economic, and environmental PPP projects. The analysis was set on the null hypothesis that a project type will not trigger the adoption of a particular FRMS. However, the outputs of the Kruskal-Wallis test analysis give a different result where nineteen of the FRMSs recorded significant values less than 5% [17].

4.2. Factor Analysis

To examine the underlying relationships of the twenty-three (23) FRMSs, the exploratory factor analysis (EFA) technique was employed. Previously, studies such as Muhammad and Johar [61] and Rachmawati, et al. [62] have adopted EFA to assess the relationships between variables and given vivid explanations of the complex phenomena surrounding the variables in PPP research. Zhang [63] also argued that EFA is useful to condense bulky data into an abridged version. The preliminary statistical tests that were performed before conducting the EFA for the FRMSs (Chan et al., 2010). The KMO score was established from the analysis as 0.884 greater than the recommended threshold value of 0.60 used in existing literature [64]. The Bartlett’s test of Sphericity results include chi-square = 9268.672 with significance level = 0.000 approving the suitability of the survey data for the appropriate analysis on the 23 FRMSs in the FA [65,66]. Following these tests of the dataset, the extraction of the groups with principal component analysis (PCA) using a varimax rotation was undertaken and the outcome a six-factor solution shown in Table 6. The popularity of varimax rotation is known in the PPP research domain due to its simplification of the interpretation comparative to other rotation methods [67]. Table 6 shows the four-factor components producing eigenvalues more than 1.0 and explains 74.96% of the variances in the respondents given by the participants of the survey. The factor loadings of the variables indicate the portion a variable contributes to a principal component [34]. With the factor loadings and the eigenvalues of the groups, all the 23 FRMSs belong to a principal group, with factor loadings more than 0.7, the required threshold [68].

4.3. Fuzzy Synthetic Evaluation

From the results in Section 4.2 (factor analysis), the levels of fuzzy synthetic evaluation (FSE) can be drawn to further analyse the dataset on FRMS. The FSE involves the multi-factor and multi-level approach starting from the third level, the criticality of each of the items (FRMSs) in the four principal components (FRMSGs) are assessed [69,70]. This is followed by the second level analysis which determines the criticality of the principal components (FRMSGs). Finally, it is at the first level that the overall financial risk management strategies index is computed flowing from level two and three. To summarise the evaluation of the FSE as presented in Section 3.2, the following steps are applied:

a) Determine the weightings of the FRMSs and FRMSGs

Studies such as Chang, et al. [71] and Aghimien, Aigbavboa, Edwards, Mahamadu, Olomolaiye, Nash and Onyia [69] mentioned that the overall outcomes of the FSE analysis is dependent on the weights assigned to each of the FRMSs and FRMSGs. To compute the weightings, there are different types of techniques available in existing literature such as the mean normalisation method, the analytic hierarchy process, point allocation system, judgement method and unit weighting [72,73]. In this analysis, the mean scoring approach (using the overall mean criticality scores) is adopted due to its ability to transform and strengthen the stability of test data and the model [45,74]. The weightings of the FRMSGs and FRMSs are determined as follows:

$${\mathrm{w}}_{\mathrm{i}}=\frac{{\mathrm{M}\mathrm{C}\mathrm{S}}_{\mathrm{i}}}{{\sum }_{\mathrm{i}=1}^5{\mathrm{M}\mathrm{C}\mathrm{S}}_{\mathrm{i}}},0<{\mathrm{w}}_{\mathrm{i}}<1,\mathrm{a}\mathrm{n}\mathrm{d}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}}=1$$

${\mathrm{w}}_{\mathrm{i}}$ represents the weighting function of each of the FRMSs and the FRMSGs whiles ${\mathrm{M}\mathrm{C}\mathrm{S}}_{\mathrm{i}}$ demonstrates the mean criticality score of each of variables. $\mathrm{i}$ shows the scores on the 5-point Likert scale which is the grading scales. In summary, the weighting function is given as:

$${\mathrm{w}}_{\mathrm{i}}=\left\{{\mathrm{w}}_1,{\mathrm{w}}_2{, \mathrm{w}}_3{, \mathrm{w}}_4\dots \dots \dots \dots .,{\mathrm{w}}_{\mathrm{n}}\right\}$$

For instance, in Table 7, the mean score of FRMS2 is 4.73, and it is part of FRMSG1 which has a total mean criticality score of 32.30. Therefore, the weighting of FRMS2 was determined as:

$${\mathrm{w}\mathrm{t}}_{\mathrm{C}\mathrm{F}\mathrm{R}18}=\frac{4.73}{4.73+4.50+4.11+4.36+3.44+3.95+3.23+3.98}=\frac{4.73}{32.30}=0.146$$

Similarly, the same calculation was done for all the FRMSs as shown in Table 7. The weightings form the basis the determination of the membership functions. The computation undertook for the FRMSGs include the following:

$${\mathrm{w}\mathrm{t}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}1}=\frac{32.30}{32.20+27.91+17.31+11.76}=\frac{32.30}{89.28}=0.362$$

$${\mathrm{w}\mathrm{t}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}2}=\frac{27.91}{32.20+27.91+17.31+11.76}=\frac{27.91}{89.28}=0.313$$

$${\mathrm{w}\mathrm{t}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}3}=\frac{17.31}{32.20+27.91+17.31+11.76}=\frac{17.31}{89.28}=0.194$$

$${\mathrm{w}\mathrm{t}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}4}=\frac{32.30}{32.20+27.91+17.31+11.76}=\frac{17.31}{89.28}=0.132$$

b) Membership functions of the FRMSs and FRMSGs

The source of the membership functions (MFs) of the FRMSs is the percentage of the overall responses to the questionnaire survey dataset. As mentioned in Section 3.1, Likert-scale of the financial risk management strategies was set as: Strongly disagree (1), SiD; Disagree (2), Di; Neutral (3), Ne; Agree (4), Ag; and Strongly Agree (5), SiA. Therefore, to determine the MF of the FRMS4 (strategic green financing alliance), the responses of 2.40% rating on “Strongly disagree”, 6.60% on “Disagree”, 30.70% on “Neutral”, 38.30% on “Agree” and 22.00% on “Strongly agree” ratings from the 287 datasets. Therefore, the MF of FRMS4 is computed as:

$${\mathrm{M}\mathrm{F}}_{\mathrm{C}\mathrm{F}\mathrm{R}18}=\frac{0.024}{\mathrm{S}i\mathrm{D}\left(1\right)}+\frac{0.066}{\mathrm{D}i\left(2\right)}+\frac{0.307}{\mathrm{N}e\left(3\right)}+\frac{0.383}{\mathrm{A}g\left(4\right)}+\frac{0.220}{\mathrm{S}i\mathrm{A}\left(5\right)}$$

Giving a membership function of FRMS4 is (0.024, 0.066, 0.307, 0.383, 0.220). The rest of the MFs of FRMSs are calculated using the same approach. Further, the MFs of the FRMSGs (level 2) are obtained from the MFs of the FRMSs (level 3) and their weightings. This establishes the fuzzy evaluation matrix which is the combination of the membership functions of FRMSs and the weightings as:

$${\mathrm{D}}_{\mathrm{i}}={\mathrm{W}}_{\mathrm{i}}\mathrm{●}{\mathrm{R}}_{\mathrm{i}}$$

Where ${\mathrm{D}}_{\mathrm{i}}$ represents the FSE evaluation matrix, ${\mathrm{W}}_{\mathrm{i}}$is the weightings function, ${\mathrm{R}}_{\mathrm{i}}$is the fuzzy evaluation matrix and “●” is the fuzzy composite operator. Based on this explanation, the membership functions of the FRMSGs can be computed as:

$${\mathrm{D}}_{\mathrm{i}}=\left\{{\mathrm{w}}_1,{\mathrm{w}}_2,{\mathrm{w}}_{\mathrm{i}},\dots {\mathrm{w}}_{\mathrm{m}}\right\}\mathrm{●}\left[\begin{array}{ccccc}{\mathrm{X}}_{11}& {\mathrm{X}}_{12}& {\mathrm{X}}_{13}& {\mathrm{X}}_{14}& {\mathrm{X}}_{15}\\ {\mathrm{X}}_{21}& {\mathrm{X}}_{22}& {\mathrm{X}}_{23}& {\mathrm{X}}_{24}& {\mathrm{X}}_{25}\\ {\mathrm{X}}_{31}& {\mathrm{X}}_{32}& {\mathrm{X}}_{33}& {\mathrm{X}}_{34}& {\mathrm{X}}_{35}\\ \dots & \dots & \dots & \dots & \dots \\ {\mathrm{X}}_{\mathrm{m}1}& {\mathrm{X}}_{\mathrm{m}2}& {\mathrm{X}}_{\mathrm{m}3}& \dots & {\mathrm{X}}_{\mathrm{m}\mathrm{t}}\end{array}\right]$$

FRMSG1 had weights of ${\mathrm{w}\mathrm{t}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}4}=\left\{0.322,0.286,0.392\right\}$, and membership function of FRMSG4 of

$${\mathrm{R}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}4}=\left[\begin{array}{ccccc}0.010& 0.042& 0.244& 0.348& 0.355\\ 0.035& 0.094& 0.105& 0.453& 0.314\\ 0.000& 0.042& 0.087& 0.244& 0.627\end{array}\right]$$

Thus, the fuzzy evaluation matrix for the FRMSG4 is:

$${\mathrm{D}}_{\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}4}=\left\{0.322,0.286,0.392\right\}\mathrm{●}\left[\begin{array}{ccccc}0.010& 0.042& 0.244& 0.348& 0.355\\ 0.035& 0.094& 0.105& 0.453& 0.314\\ 0.000& 0.042& 0.087& 0.244& 0.627\end{array}\right]=(0.013,0.057,0.143,0.337,0.0450)$$

The same approach is applied to compute the fuzzy matrixes for FRMSG1, FRMSG2 and FRMSG3 as demonstrated in Table 8.

c) The criticality indexes of the principal groups and the entire dataset.

The combination of the fuzzy matrixes and the grade alternatives set from the overall outcomes of the financial risk management strategies on the Likert-scale of 1 to 5. In view of this, the criticality indices of the FRMSs are set as:

$${\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}}_{\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}=\sum _{\mathrm{i}=1}^5({\mathrm{D}}_{\mathrm{i}}\mathrm{x}{\mathrm{G}}_{\mathrm{i}})$$

Where ${\mathrm{G}}_{\mathrm{i}}=(\mathrm{1,2},\mathrm{3,4},5)$ on the ranging scale of the Likert concerning the total effectiveness of the financial risk management strategies, and ${\mathrm{D}}_{\mathrm{i}}$ is the Fuzzy evaluation matrix. Consequently, the critical factor groups were computed as:

$$\begin{gathered} \mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}1=\left(0.031,0.097,0.265,0.374,0.232\right)\mathrm{X}(1,2,3,4,5) \\ =(0.031*1+0.097*2+0.265*3+0.374*4+0.232*5)=\mathbf{3}\mathbf{.}\mathbf{679} \end{gathered}$$

$$\begin{gathered} \mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}2=\left(0.023,0.048,0.208,0.362,0.359\right)\mathrm{X}(1,2,3,4,5) \\ =(0.023*1+0.048*2+0.208*3+0.362*4+0.359*5)=\mathbf{3}\mathbf{.}\mathbf{985} \end{gathered}$$

$$\begin{gathered} \mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}3=\left(0.020,0.076,0.131,0.373,0.400\right)\mathrm{X}(1,2,3,4,5) \\ =(0.020*1+0.076*2+0.131*3+0.373*4+0.400*5)=\mathbf{4}\mathbf{.}\mathbf{058} \end{gathered}$$

$$\begin{gathered} \mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}4=\left(0.013,0.057,0.143,0.337,0.450\right)\mathrm{X}(1,2,3,4,5) \\ =(0.013*1+0.057*2+0.143*3+0.337*4+0.450*5)=\mathbf{4}\mathbf{.}\mathbf{154} \end{gathered}$$

The overall index of the FRMS was determined with the fuzzy matrices of FRMSGs and the sum weightings. First, the fuzzy evaluation matrix is computed from Table 7, the FRMSGs have weightings of ${\mathrm{W}}_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}\mathrm{i}}=(0.362,0.313,0.194,0.132)$ and Table fuzzy matrixes:

$${\mathrm{R}}_{\mathrm{O}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{G}\mathrm{i}}=\left[\begin{array}{ccccc}0.031& 0.097& 0.265& 0.374& 0.232\\ 0.023& 0.048& 0.208& 0.362& 0.359\\ 0.020& 0.076& 0.131& 0.373& 0.400\\ 0.013& 0.057& 0.143& 0.337& 0.450\end{array}\right]$$

Therefore, the overall financial risk management strategies matrix is computed as:

$${\mathrm{D}}_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{P}\mathrm{C}\mathrm{F}\mathrm{R}}={\mathrm{W}}_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{P}\mathrm{C}\mathrm{F}\mathrm{R}}\mathrm{●}{\mathrm{R}}_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{P}\mathrm{C}\mathrm{F}\mathrm{R}}$$

$${\mathrm{D}}_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{P}\mathrm{C}\mathrm{F}\mathrm{R}}=(0.362,0.313,0.194,0.132)\mathrm{X}\left[\begin{array}{ccccc}0.031& 0.097& 0.265& 0.374& 0.232\\ 0.023& 0.048& 0.208& 0.362& 0.359\\ 0.020& 0.076& 0.131& 0.373& 0.400\\ 0.013& 0.057& 0.143& 0.337& 0.450\end{array}\right]$$

= (0.024, 0.072, 0.205, 0.365, 0.333)

Then, the overall financial risk management strategies index is calculated as:

$$\begin{gathered} {\mathrm{O}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{F}\mathrm{R}\mathrm{M}\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}=\left(0.024,0.072,0.205,0.365,0.333\right)\mathrm{X}(\mathrm{1,2},\mathrm{3,4},5) \\ =(0.024*1)+(0.072*2)+(0.205*3)+(0.365*4)+(0.333*5) \\ =3.911 \end{gathered}$$

6. Practical and Research Implications of the Study

In recent past, Ghana has been experiencing challenges with its economic outlook together with budgetary shortages as reported by the Ministry of Finance and Bank of Ghana. Moreover, the COVID-19 economic recession has taken a large hit on the economic advances of the country affecting the funding of PPP projects [52,102]. Thus, the results of this are important to understand and equip project managers to devise measures to attract funding and management financial risks in these challenging times. Learning from the consequences of the pandemic and past funding challenges to infrastructure projects in the country, project managers and key stakeholders can institute project-based financial policies and budgets to either minimise or lower current project account deficits, stimulate favourable investment outcomes and promote inclusive financial management solutions that care of fluctuations in exchange rate, interest charge and inflation rates [103]. With increasing focus on net-zero, climate resilience and sustainability-based financial risk management measures, this study provides key measures to meet the economic sustainability targets. Further, the relevance of this study is in the mitigation of shortages of funds and the establishment of guiding practice framework to support the construction and management of PPP projects in Ghana. In addition, the study is important to multiple-stakeholder partners who take active part in the PPP financing and development in Ghana in understanding project financial reporting systems and governance structures. Effective project finance risk management policies coupled with investment successes increase the confidence investors have in PPP projects and will increase private investments into Ghana’s public project development.

Future studies should use this study as a guide to delve deeper into the risks on the economic sustainability of PPP projects and similar developing countries who share key developmental features like Ghana. In addition, the financial management of PPP infrastructures in Ghana can be facilitated by solutions from researchers using innovative technological software to develop project-focused financial risk management framework to guide PPP projects. The advancement of health and safety technology-based financial assessment and management are important to understand the challenges of construction workers. Drawing lessons from this study, studies must investigate into financial risk management measures to manage climate change, nature-based solutions, social inclusion, and environmentally inspired risks of PPP infrastructure initiation, development, and management.

7. Conclusion and Limitations

ThisThis study identified, assessed, and established the financial risk management strategies (FRMSs) for sustainable PPP project development. It undertook questionnaire survey of knowledgeable and experienced PPP experts in the Ghanaian economy. The data analysis was done with non-parametric tests (Kruskal-Wallis and Mann-Whitney U) in addition to factor analysis and fuzzy synthetic evaluation to analyse the differences between PPP practitioners, sectors, and project types. Statistically, the results showed no significant differences between the views of the various groups on mitigation strategies on financials risks of PPPs. The study also evaluated the criticality of the principal components of the FRMSs using exploratory factor analysis and fuzzy synthetic evaluation method. The findings include the promotion of sustainable funding, effective cost reduction strategies, inclusion of competent team members together with good leadership who are focused on ensuring the sustainable development of PPP projects. Also, the study established emerging technologies and regulations and strong financial alliances towards climate-resilient PPP projects.

Despite these relevant findings aimed at mitigating financial risks on sustainable infrastructures like schools, roads, and hospitals in the PPP contracts for Ghana’s socio-economic development, the study has some limitations which must be addressed. Limited categories of analysis were done in this study using project type, sector, and practitioner. Further studies must expand the scope to include but not limited to analysis on project size, the capital investment, project settings and external stakeholders to attain more multidimensional framework to countermeasure financial risks. With a limited sample size of responses from PPP practitioners in Ghana, the generalizability of the application of the findings is affected. Thus, caution must be exercised in the applications of the findings of the study taking into consideration the project setting and economic environment.