article review in financial management

Financial planning behaviour: a systematic literature review and new theory development

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• Published: 03 October 2023
• Volume 29 , pages 979–1001, ( 2024 )

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• Kingsley Hung Khai Yeo 1 ,
• Weng Marc Lim 1 , 2 , 3 &
• Kwang-Jing Yii 1  

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Financial resilience is founded on good financial planning behaviour. Contributing to theorisation efforts in this space, this study aims to develop a new theory that explains financial planning behaviour. Following an appraisal of theories, a systematic literature review of financial planning behaviour through the lens of the theory of planned behaviour (TPB) is conducted using the SPAR-4-SLR protocol. Thirty relevant articles indexed in Scopus and Web of Science were identified and retrieved from Google Scholar. The content of these articles was analysed using the antecedents, decisions, and outcomes (ADO) and theories, contexts, and methods (TCM) frameworks to obtain a fundamental grasp of financial planning behaviour. The results provide insights into how the financial planning behaviour of an individual can be understood and shaped by substituting the original components of the TPB with relevant concepts from behavioural finance, and thus, leading to the establishment of the theory of financial planning behaviour, which posits that (a) financial satisfaction (attitude), (b) financial socialisation (subjective norms), and (c) financial literacy, mental accounting, and financial cognition (perceived behavioural controls) directly affect (d) the intention to adopt and indirectly shape, (e) the actual adoption of financial planning behaviour, which could manifest in six forms (i.e. adoption of cash flow, tax, investment, risk, estate, and retirement planning). The study contributes to establishing the theory of financial planning behaviour, which is an original theory that explains how different concepts in behavioural finance could be synthesised to parsimoniously explain financial planning behaviour.

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Introduction

Background of financial planning.

Personal financial planning is critical to maintaining a healthy financial status and fulfilling future financial needs (Mahapatra et al. 2019 ). In essence, personal financial planning is a process of managing personal wealth to obtain economic satisfaction (Kapoor et al. 2014 ). This encompasses six areas of financial planning, namely cash flow planning, tax planning, investment planning, risk management, estate planning, and retirement planning (Altfest 2004 ). Ideally, comprehensive financial planning should involve all six areas. However, the specific life stage of an individual, such as retirees, and life realities, such as retrenchment, may dictate the primary focus and/or relevance of these areas. For example, retirees might not be actively engaged in tax planning, and a retrenched worker might not be in a position to engage in investment planning. More importantly, personal financial planning is a profound concept that theoretically reflects and practically safeguards individuals’ financial resilience, and thus, it can be understood from two unique lenses: academic and practice.

From an academic perspective, the field of personal finance is interdisciplinary; it covers a wide range of areas, including economics, family studies, finance, information technology, psychology, and sociology (Schuchartdt et al. 2007 ). Different disciplines have varied theories that play a supporting role in understanding individuals’ financial behaviour and money management (Copur and Gutter 2019 ). However, the theories explaining personal finance are often borrowed rather than created, a situation that is common for emerging interdisciplinary fields (Murray and Evers 1989 ) such as personal finance (Lyons and Neelakantan 2008 ), which encompasses close to 250 publications only in Scopus by the end of 2022. Footnote 1

From a practice standpoint, Palmer et al. ( 2009 ) argued that it is necessary to develop financial planning for each individual that can deal with the uncertainty of the economic environment. Hanna and Lindamood ( 2010 ) echoed that personal financial planning can provide individuals sufficient economic benefits such as increasing wealth, preventing financial loss, and smooth consumption. Footnote 2 However, many individuals lack sufficient financial capability, skills, and knowledge to be able to effectively manage their personal finances (Chen and Volpe 1998 ).

Problems and importance of financial planning

Over time, the society is facing increasing challenges of high living expenses and various financial difficulties given the constant development of complexity in financial matters (Baker et al. 2023 ; Mahapatra et al. 2019 ). Individuals’ ability to manage their personal finances and financial affairs has been gaining attention across the world, wherein being financially healthy gets prioritised by individuals in their lives (e.g. changing investment approach and contributing more to retirement savings to hedge against inflation; Personal Capital 2022 ).

Birari and Patil ( 2014 ) state that individuals should practice and gain basic financial skills to manage their expenditures and acquire well-developed planning to avoid being in financial difficulties. Many factors may lead to irrational financial behaviours from individuals—for example, excess consumption, aggressive trading, lack of savings, and retirement planning. However, one of the major root causes that propels irrational financial behaviour as well as the many financial difficulties that people encounter is inarguably the lack of financial literacy (Organization for Economic Cooperation and Development 2020 ).

According to the Organization for Economic Cooperation and Development ( 2013 ), financial literacy consists of financial knowledge, skill, attitude, awareness, and behaviour to make a rational financial decision and achieve individual financial well-being. In other words, financial literacy is the ability to utilise knowledge and skills to manage financial matters effectively (Pailella, 2016 ; Tavares et al. 2023 ).

Noteworthily, financial behaviour in individuals’ daily lives cannot be separated from financial literacy. Tan et al. ( 2011 ) state that the process of personal financial planning requires individuals to acquire not only cognitive ability but also financial literacy. According to Ali et al. ( 2014 ), financial literacy should be given serious attention from individuals because it is able to affect their welfare. Indeed, financial literacy has been proven to have a positive impact on financial planning. Specifically, individuals who lack financial literacy will often end up in debt (Lusardi and Tufano 2009 ) and will most likely increase their financial burden (Gathergood 2012 ). By having sufficient relevant information, individuals can analyse their financial situation and make decisions wisely.

Gaps and necessity to theorise financial planning behaviour

As mentioned, extant understanding of financial planning is mainly derived from borrowed theories. While this practice remains acceptable, it is important that new theories are developed to enrich understanding of financial planning, particularly from a behavioural perspective, as the issue of good or poor financial planning is dependent on the individual and his or her financial planning behaviour. With the maturity of the literature on financial planning, the time is now opportune to engage in new theory development (Kumar et al. 2022 ).

The need for theory development is further accentuated as there is a notable lack of theory development in explaining financial planning behaviour. Noteworthily, existing frameworks and models remain piecemeal and do not fully cover the whole spectrum of financial planning. After an appraisal of theories related to financial planning (“ Evolution of theories ” Section), the theory of planned behaviour (TPB) has been found to be the most suitable theory on parsimonious grounds (i.e. the capability and capacity of the theory’s core components to act as an organising frame) and its track record of theory spinoffs (e.g. the theory of behavioural control; Lim and Weissmann 2023 ) to explain an individual’s financial planning behaviour. Therefore, an integration of the respective antecedents, decisions, and outcomes (ADO) to form a new, holistic theory is required to document the complexity and the extent of considerations required to explain financial planning behaviour. Such an integration can and will be pursued via a systematic literature review (Lim et al. 2022a , b ).

Goals and contributions of this study

The goal of this study is to establish a formal theory to explain financial planning behaviour. To do so, a systematic literature review is conducted, wherein the SPAR-4-SLR protocol is adopted to guide the review process, whereas the antecedents, decisions, and outcomes (ADO) framework (Paul and Benito 2018 ) and the theories, contexts, and methods (TCM) framework (Paul et al. 2017 ) are adopted and integrated to analyse the findings of the review—a best practice demonstrated and recommended by Lim et al. ( 2021 ). In doing so, this study makes two noteworthy contributions.

From a theoretical perspective, the integrated framework contributes to integrate fragmented knowledge and reduce the production of isolated knowledge on financial planning behaviour. In addition, the framework clarifies the state of existing insights and empowers the discovery of new insights on financial planning behaviour. Certainly, insights gathered from a well-structured framework can provide a better start to add to existing knowledge and increase growth in the field (Kumar et al. 2019 ; Lim et al. 2022a , b ). More importantly, the nomological structure of the framework also enables the study to establish a new theory called the theory of financial planning behaviour , which can act as a multi-dimensional behavioural guideline that involves planning, developing, and assessing the operation of cash flow, tax efficiency, investment planning, risk management, estate planning, and retirement planning within an individual.

From a practical standpoint, the insights from the study are expected to contribute to future financial service professionals gaining advantages in the understanding of financial planning behaviour in catering to the future needs of the public. Additionally, policymakers would benefit from utilising the information to effectively provide financial education programs to enhance individuals’ financial well-being. Further implications for this study focusing on consumers and managers are also discussed towards the end of this study.

Theoretical background

Evolution of theories.

Over the past decades, several theories have been used by researchers on financial planning and the determining factors that influence it. The evolution of theories relating to financial planning is based on the concept of behavioural finance. These theories remain important in financial planning research (Asebedo 2022 ; Overton 2008 ). The most well-known theory related to behavioural finance is the TPB (Ajzen 1991 ). It has been widely used on different research topics to predict and explain individuals’ behaviour or the insufficient control of their behaviour (Ajzen 1985 , 1991 , 2002 ). Noteworthily, the TPB is an extension of the theory of reasoned action, which suggested that human behaviour is determined by the intention to perform a certain behaviour, whereby the intention can be determined by attitudes and subjective norms (Fishbein and Ajzen 1975 ).

In addition, Maslow’s ( 1943 ) hierarchy of needs has been used by Chieffe and Rakes ( 1999 ) to identify and rate the different segments of financial services best suited to each level of income group. The hierarchical approach of this theory provides a framework that explains different financial planning services related to each income group. According to Xiao and Noring ( 1994 ) and Xiao and Anderson ( 1997 ), the notion of Maslow’s hierarchy of needs clearly explains an individual’s financial needs in the form of a hierarchy. The framework of a hierarchical form of financial planning indicates that individuals would only strive for a high level of financial needs after a lower level of financial needs is met. It is recommended for individuals to fulfil their needs step by step to avoid facing financial difficulties.

Another theory that has been applied to financial planning is the life-cycle hypothesis (Modigliani and Brumberg 1954 ), which is an economic theory that explains an individual’s saving and spending behaviour throughout their lifetime. The theory also points out that individuals want to have smooth consumption by saving more if their income increases and borrowing more when their income ceases. Shefrin and Thaler ( 1988 ) state that individuals mentally place their assets into three different accounts, which are current income, current assets, and future income. According to Modigliani and Brumberg ( 1954 ), this theory assumes that individuals will fully utilise their utility for future consumption and aim to accumulate savings and resources for future consumption after retiring. The model explains that individuals’ consumption and saving decisions are formed from a life-cycle perspective. Such individuals will begin with low income when they start working, and their income will slowly increase until it reaches a peak level. Taking a behavioural enrichment (or behaviourally realistic) perspective of the life-cycle theory, Shefrin and Thaler ( 1988 ) state that the behavioural life-cycle hypothesis includes mental accounting, self-control, and framing, which represent three important behavioural features that are usually missing in the economic perspective of the traditional life-cycle theory. The authors mention that individuals use mental accounting to control their propensity to spend on their assets. The willingness to spend is usually related to their current income. According to Warneryd ( 1999 ), individuals usually have a specific method to mentally allocate their expenditures into different accounts. In addition, the marginal propensity to save and consume will be different in each account. According to Shefrin and Thaler ( 1988 ), individuals may face difficulties in controlling their spending, and thus, these individuals may form personal behavioural incentives and constraints. For example, individuals would possess the intention to save and create assets when constraints are available. They also explain that individuals’ preferences are not fixed but vary depending on the constantly changing economic environment and social stimuli (Duesenberry and Turvey 1950 ; Katona 1975 ). Furthermore, the life-cycle theory faces some challenges while explaining individuals’ behaviour, such as assuming that individuals will act rationally, be consistent, and make wise intertemporal choices throughout their lifetime (Deaton 2005 ). The life-cycle theory explains that individuals’ saving decisions are based on their preferences for either present or future consumption. The theory also assumes that individuals determine a desirable age of retirement and level of consumption to fully utilise their utility throughout their lifetime.

Prospect theory is an economic theory that assumes individuals treat losses and gains differently, showing how an individual decides among several choices that involve uncertainties (Kahneman and Tversky 1979 ). This theory explains that their decisions are easily affected by psychological factors and that they are logical decision-makers. However, when individuals decide on whether to purchase or not, they are most likely affected by their cognitive biases. The theory also postulates that making losses will cause a larger emotional impact on individuals rather than a comparable amount of gain. Thus, individuals will prefer choosing the option with perceived gains. For example, individuals would prefer the option of a sure gain instead of a riskier option with a chance of receiving nothing or making a loss. Hence, the theory summarises that individuals are mostly loss averse when they face several choices. Individuals are more sensitive towards losses and would most likely prefer avoiding losses and prefer sure wins. This can be explained by the fact that the emotional impact of losses on an individual is greater than an equivalent gain.

The financial capability model is another prominent theory. Financial capability, which has been gaining prominence across the globe, is defined as the capability and skills of individuals to make rational and effective judgements on managing their financial resources (Noctor et al. 1992 ). Nowadays, individuals have been urged to ensure that they acquire sufficient resources for their retirement and provide a financial safeguard for any sudden occurrence. According to Atkinson et al. ( 2007 ), the financial capability model has been studied and is related to individuals’ financial behaviour, attitude, and knowledge. The researchers identified five different components under the financial capability model: (1) making ends meet (managing personal financial resources, i.e. individuals who have acquired financial knowledge skill sets can finance their resources well and meet financial goals); (2) keeping track (managing money, i.e. planning and recording personal daily expenses to avoid overspending); (3) planning ahead (this helps individuals to be future oriented, i.e. always planning and managing their financial resources to be prepared for any financial uncertainties in the future); (4) choosing products (accumulating resources and managing different assets’ risks, i.e. making a rational decision in choosing financial products and diversifying risks); and (5) staying informed (being updated and studying financial matters in the current market and economy, i.e. individuals have to be eager to keep track on financial matters happening in the market, such as changes in the overnight policy rate (OPR) and stock market movement).

After a review of all the theories (Table 1 ), the TPB has been found to be the most suitable theory to serve as a foundational lens for a review on financial planning behaviour with the aim of establishing a new theory in this field. Unlike the other theories (e.g. Maslow’s hierarchy of needs, life-cycle hypothesis including behavioural life-cycle hypothesis, financial capability model, prospect theory), the TPB is an adaptable yet parsimonious theory that has a track record of spinning off new theories (e.g. the theory of behavioural control; Lim and Weissmann 2023 ). Noteworthily, the TPB can be applied to financial behaviours (Bansal and Taylor 2002 ; East 1993 ; Xiao and Wu 2006 ), wherein the three antecedents of the TPB (attitude, subjective norms, and perceived behavioural control) are found to be associated with intention and contribute to financial behaviour (Shim et al. 2007 ; Xiao et al. 2007 ). Unlike other theories, the mediating effect of financial literacy, which provides an important lens to understand good and poor financial planning, can be applied to the TPB to explain an individual’s intention on financial behaviour. More importantly, it is necessary to understand how the TPB can further explain individuals’ behaviour before examining financial literacy through a behavioural approach. The theory assumes that intention is the best factor to predict an individual’s behaviour, which, in turn, is examined by attitude and social normative perceptions towards an individual’s behaviour (Montano and Kasprzyk 2015 ). Furthermore, individuals’ experiences normally affect their financial decision-making and the way they manage their personal finances. Therefore, financial literacy can be explained as an individual’s confidence and capability to make full use of their financial knowledge (Huston 2010 ) and manage financial matters (Lusardi and Mitchell 2014 ), which they would have perceived control over. In this regard, the theory can be applied to examine how the financial literacy process works on each individual. Moreover, Lusardi and Mitchell ( 2014 ) explain that the favour of financial literacy is more than that of financial capability, where individuals are responsible for their own financial decisions. Hence, financial literacy acknowledges the perceived control of individuals on their financial decisions. That being said, an individual will only show positive financial behaviour when they perceive the value of their behaviour based on their attitude. Therefore, financial behaviour will not be decided based on their financial knowledge but based on their attitude, which is the main component of this theory. In other words, the evaluation of financial knowledge will be better captured through the components of the TPB (e.g. perceived behavioural control), though conceptual contextualisation is necessary to better resonate with the financial planning behaviour of individuals. To aid this task, the next section provides a deeper discussion to understand the fundamental tenets of the TPB.

Theorisation of the theory of planned behaviour

According to Xiao ( 2008 ), the TPB is one of the best and most suitable theories related to financial behaviour that studies and predicts human behaviour. In essence, the TPB is an extension of the theory of reasoned action, which initially posits that attitude and subjective norms shape the intention to perform a behaviour, which, in turn, predicts the actual performance of that behaviour (Ajzen 1991 ). However, behavioural intention does not always translate into behavioural performance (Lim and Weissmann 2023 ), which is the main reason why the TPB was proposed to overcome the limitation of the theory of reasoned action, with the inclusion of perceived behavioural control in the TPB as a mechanism to recognise the volitional control that individuals possess in translating or not translating behavioural intention into behavioural performance (Ajzen 1991 , 2002 ).

Perceived behavioural control can be expressed as follows: Given an individual’s available resources and choices, how easy or hard it is to display a certain behaviour or act in a certain way? In this regard, the performance of an individual’s behaviour depends on his or her ability to act on said behaviour (Ajzen 1991 ). The TPB posits that the perceived control on certain behaviour will be greater when the individual has greater resources (social media, money, time) and choices (Lim and Weissmann 2023 ). Indeed, several researchers have found that perceived behavioural control has a positive relationship with intention and behaviour (Fu et al. 2006 ; Lee-Patridge and Ho 2003 ; Mathieson 1991 ; Shih and Fang 2004 ; Teo and Pok 2003 ).

Subjective norms can also be used to predict individual behavioural intention. As one of the original components of the theory of reasoned action, subjective norms refer to social influence and the social environment affecting an individual’s behavioural intention (Fishbein and Ajzen 1975 ). It is defined as an individual’s perception of the possibility that social agents approve or disapprove a behaviour (Ajzen 1991 ; Fishbein and Ajzen 1975 ). It focuses on everything around individuals, such as social networks, cultural norms, and group beliefs. This is known as a direct determinant of behavioural intention in the theory of reasoned action and the TPB. Through the lens of subjective norms, an individual is said to be willing to perform a certain behaviour even though he or she does not favour performing such behaviour while being under social pressure and social influence (Venkatesh and Davis 2000 ). Kuo and Dai ( 2012 ) state that as subjective norms become more positive, an individual’s behavioural intention to perform or act on a certain behaviour becomes more positive. Several studies have shown a significant relationship between subjective norms and intention (Chan and Lu 2004 ; May 2005 ; Teo and Pok 2003 ; Venkatesh and Davis 2000 ). Sharif and Naghavi’s ( 2020 ) research on family financial socialisation also finds that the behaviour of acquiring relevant norms and information on financial socialisation is associated with subjective norms. The informational subjective norms are known to predict perceived information. Ameliawati and Setiyani ( 2018 ) mention that subjective norms in the TPB represent financial socialisation. Their study describes subjective norms as financial socialisation to research the influence of financial management behaviour. In addition, the research of Jamal et al. ( 2015 ) on the effects of social influence and financial literacy on students’ saving behaviour used the TPB to develop the model. The author uses subjective norms to represent the social pressures influencing students’ intentions to save. It analyses the influences of parents and peers on the impact on the students’ saving behaviour. Hence, subjective norms have a significant effect on the intentions of individuals towards financial planning behaviour.

Attitude has been identified as a construct that guides an individual’s intention, which results in them acting on a particular behaviour. In essence, attitude can be defined as the evaluation of the positive and negative effects on individuals performing an act or behaviour (Fishbein and Ajzen 1975 ), and by extension, reflects the individual’s belief in certain behaviours or acts that contribute positively or negatively to a person’s life (Ajzen and Fishbein 2000 ). There are two components of attitude: the attitude towards a physical object (money, savings, pension) and the attitude towards behaviour or performing a certain act (using savings or money to practice financial planning). Keynes ( 2016 ) and Katona ( 1975 ) state that most individuals possess positive attitudes towards personal saving. Many studies have determined a significant relationship between attitudes and intention (Lu et al. 2003 ; Ramayah et al. 2020 ; Wu and Chen 2005 ). Therefore, attitude can be one of the most important factors to determine and predict human behaviour (Ajzen 1987 ). According to Xiao ( 2008 ), the more favourable the attitude of an individual on performing a behaviour, the easier it is for the individual to perform the behaviour and the stronger the behavioural intention. Further understanding of an individual’s attitude can help to predict their intention and behaviour.

Intention can be defined as an individual’s perception of performing a particular act or behaviour (Fishbein and Ajzen 1975 ). In this regard, intention is said to produce a direct effect on an individual’s behaviour as it signals the willingness of an individual to act (Ajzen 1991 ). The TPB explains that the degree of intentions that are converted into behaviour is determined by the amount of volitional control. Behaviour such as saving money is not considered as full volitional control given the lack of resources and opportunities able to affect the capability to perform the behaviour. While individuals can control their behaviour, their actual behaviour can easily be predicted by their intention accurately, but this does not prove that the measure of correlation is perfect between intention and behaviour (Fishbein and Ajzen 1975 ). Moreover, strong bias always exists in individuals, where they will overestimate the possibility of acting on desired behaviour and underestimate the possibility of acting on undesired behaviour. This can cause inconsistencies between intention and behaviour (performing an actual action) (Ajzen et al. 2004 ). Behaviour and intention will show high correlation whenever the interval time between them is low (Fishbein and Ajzen 1981 ). Yet, intention is known to change over time, and thus, if the interval between intention and behaviour is greater, the possibility of change in intention is higher (Ajzen 1985 ).

Behaviour refers to an observable response to a specific target (Fishbein and Ajzen 1975 ). In essence, the performance of a given behaviour is a direct outcome of the intention to perform that behaviour as well as an indirect result of attitude, subjective norms, and perceived behavioural control (Ajzen 1991 ), as discussed above.

The TPB has been widely used in different fields of research over the past decades: medicine (Hagger and Chatzisarantis 2009 ; McEachan et al. 2011 ), marketing and advertising (King et al. 2008 ; Yaghoubi and Bahmani 2010 ), tourism and hospitality (Han 2015 ; Quintal et al. 2010 ), information science (Lee 2009 ; Shih and Fang 2004 ), and, last but not least, human behaviour (Kobbeltvedt and Wolff 2009 ; Perugini and Bagozzi 2001 ). All the studies listed above have concluded on the positive and significant effect of attitude, subjective norms, and perceived behavioural control on an individual’s intention to act on behaviour. In the financial context, Shih and Fang ( 2004 ) apply the TPB to an individual’s financial decisions regarding internet banking. The study concludes that the TPB can be successfully applied to understand an individual’s intention to use internet banking. Lau et al. ( 2001 ) and Lee ( 2009 ) also apply the TPB to study investors’ intentions on online banking and trading online. To provide a more accurate account for financial planning behaviour, a systematic literature review is conducted and reported in the next sections.

Methodology

Study approach: systematic literature review.

This study conducts a systematic literature review to develop comprehensive insights into financial planning behaviour based on the TPB. As mentioned above, the TPB is the extension of the theory of reasoned action, and it strongly posits that an individual’s behaviour is determined by the three factors (attitude, subjective norms, and perceived behavioural control) and is backed by their behavioural intention (Ajzen 1991 ).

A systematic literature review is known as a ‘research synthesis’, an extensive process of summarising primary research based on an explicit research question, where it attempts to identify, select, synthesise, and assess all the evidence by providing answers to the research question (Donthu et al. 2021 ; Lim et al. 2022a , b ). In this regard, systematic literature reviews not only summarise and synthesise existing knowledge but also facilitate knowledge creation (Kraus et al. 2022 ; Mukherjee et al. 2022 ). Moreover, systematic literature reviews gathered eligible and pertinent evidence based on a preset criterion to answer a specific research question, and thus, a transparent and explicit systematic methodology can be used for systematic literature reviews to analyse and reduce biases (Harris et al. 2014 ; Paul et al. 2021 ).

Systematic literature reviews can be conducted through various methods. Generally, systematic literature reviews can be domain-based, theory-based, and method-based (Palmatier et al. 2017 ; Paul et al. 2021 ). In this study, a theory-based review was used for new theory development. Specifically, the theory-based review is chosen over the other approaches because it serves the purpose of analysing a specific role played by a theory in a given field. One of the examples given by Hassan et al. ( 2015 ) is the role of the TPB in the field of consumer behaviour. In this study, the TPB was applied to financial planning behaviour.

Study procedure: SPAR-4-SLR

Few protocols exist for systematic literature reviews. The most common protocol used by researchers in conducting systematic literature reviews is the preferred reporting items for systematic reviews and meta-analysis (PRISMA) by Moher et al. ( 2009 ). PRISMA is a comprehensive protocol that helps researchers to develop systematic literature reviews. It gathers and reports decisions that researchers have justified from their reviews. However, an uprising protocol was proposed by Paul et al. ( 2021 ) to address the existing limitations of PRISMA, namely the Scientific Procedures and Rationales for Systematic Literature Reviews protocol or the SPAR-4-SLR protocol. As shown in Fig.  1 , the protocol consists of three stages and six sub-stages, followed by sequences.

Assembling This stage constitutes the (1a) identification and (1b) acquisition of literature that is yet to be synthesised.

Arranging This stage entails the (2a) organisation and (2b) purification of literature in the stage of being synthesised.

Assessing This stage reflects the (3a) evaluation and (3b) reporting of literature that has been synthesised.

Review process

Systematic reviews assembling, arranging, and assessing the literature according to the SPAR-4-SLR protocol are expected to: (1) provide significant insights and (2) stimulate nuanced agendas for knowledge advancement in the review domain. Substantially, by providing such significant insights and agendas using the SPAR-4-SLR protocol, (1) the review is comprehensively justified for logical and pragmatic reasons, and (2) each stage and sub-stage is reported with full transparency.

The researchers begin with assembling in the (1a) identification stage, identifying the research domain and research question. The research domain of this study is behavioural finance with a specific focus on financial planning. The research question of this study is ‘How can the TPB be contextualised to develop a theory of financial planning behaviour?’ Thus, academic articles selected should focus on financial planning (i.e. the focus of this review) and the TPB (i.e. the theory contextualised for this review). The source quality was established based on Scopus or Web of Science indexing in line with Paul et al. ( 2021 ). Moving on to the (1b) acquisition stage, the search mechanism will rely on Google Scholar, which is free and can be easily accessed for article search. Footnote 3 The search period will begin from 2000 to 2020 (20 years) as most articles on the TPB and financial planning behaviour started to appear in the early 2000s. Related articles searched between these years are included in this study. The search was conducted multiple times with different keywords based on American and British spelling as well as different combinations: (1) ‘financial planning’ + ‘theory of planned behavior’, (2) ‘financial planning’ + ‘theory of planned behaviour’, (3) ‘personal financial planning’ + ‘theory of planned behavior’, and (4) ‘personal financial planning’ + ‘theory of planned behaviour’. Footnote 4

Next, the researchers move onto arranging in the (2a) organisation stage, wherein the organising code for this study is ADO and TCM, which rely on the suggested frameworks used, the ADO framework (Paul and Benito 2018 ; Pansari and Kumar 2017 ) and the TCM framework (Paul et al. 2017 ). Refer to Fig.  2 for the overview of ADO on the insights of the TPB on financial planning behaviour and its supporting TCM. In the (2b) purification stage, the articles gathered are filtered in this process. The researchers decided which articles to include and exclude from the study. The criteria to exclude articles in this stage include duplicate articles, irrelevant articles, inaccessible articles, and lastly, non-journal-title articles; 41 articles were excluded based on the criteria, and 30 articles proceeded to the next stage.

The state of the art of the antecedents, decisions, and outcomes of financial planning behaviour and its supporting theories, contexts, and methods

Finally, the researchers move into assessing in the (3a) evaluation stage, which involves the analysis and the agenda proposal. The study utilised content analysis, a methodical approach for coding and interpreting textual data from the selected articles to draw meaningful conclusions (Kraus et al. 2022 ). This systematic technique, which was executed by one author (a doctoral scholar) and cross-validated by another author (a senior academic) with an intercoder reliability of ± 95% and differences clarified and resolved, enabled the researchers to identify, categorise, and analyse patterns within the text, contributing to a comprehensive understanding of the subject matter (Patil et al. 2022 ). The theory development and future research agenda were formulated through conceptual extrapolation and sensemaking (i.e. scanning, sensing, and substantiating) (Lim and Kumar 2023 ). This process entailed critically examining the existing theories, extracting key concepts, and extrapolating these to propose new research directions. Thus, this study provided a roadmap for future studies, fostering further evolution in the field of financial planning behaviour. In the (3b) reporting stage, the reporting conventions used include figures, tables, and words. No ethical approval is required since the review is based on accessible secondary data (journal articles), which can be accessed by anyone with subscription (Lim et al. 2022a , b ).

Profile of TPB and financial planning behaviour research

The systematic review of 30 articles covered different insights into the existing research of the TPB and financial planning behaviour, covering the six components of financial planning (i.e. cash flow planning, tax planning, risk management, investment planning, estate planning, and retirement planning) (Fig.  2 ). Appendix 1 summarises the articles in Appendix 2 based on the approaches of Paul and Mas ( 2019 ) and Harmeling et al. ( 2016 ). The articles are classified based on author citations, years, number of citations, methods, sample, related financial planning components and variables, and lastly findings. The findings of each article briefly explained how the construct of the TPB is a predictor or shows a significant effect on financial planning behaviour.

Based on this review, which begins from 2000 to 2020, the past two decades of research in the field of behavioural economics (later known as behavioural finance) have been on continuously identifying and explaining an individual's finances from an extended social science perspective, which includes psychology and sociology. Behavioural finance can be defined as the field of study where psychological factors affect an individual's financial behaviour (Shiller 2003 ). The combination of the TPB and financial planning has proven to be impactful with over 3000 citations among the 30 articles. The articles utilised four different methods: the quantitative approach ( n  = 24), the qualitative approach ( n  = 3), the mixed method approach ( n  = 1), and the conceptual approach ( n  = 2).

Lastly, the TPB (i.e. attitude, subjective norms, perceived behavioural control, and behavioural intention) has been found to be a good predictor of financial planning behaviour (i.e. cash flow planning, tax planning, risk management, investment planning, estate planning, and retirement planning) and possesses positive relationships with each component of financial planning. For example, the TPB was found to be positively related to the intention to invest, mental budgeting behavioural intention, influencing savings and investment, and the intention to prevent risky credit behaviour, among others.

Contextualising the TPB for financial planning behaviour

Table 2 and Fig.  3 show the contextualisation of the TPB for financial planning behaviour, leading to the establishment of the theory of financial planning behaviour. Pansari and Kumar ( 2017 ) suggest the use of such a table to compare and explain each construct of the framework. The table, which leverages the findings from the review depicted in Fig.  2 , clearly illustrates how the TPB can be contextualised to explain financial planning behaviour. Attitude can manifest as financial satisfaction, wherein individuals who are dissatisfied, not fully satisfied, or wish to be more satisfied with their financial state will develop a positive disposition towards financial planning. Subjective norms can manifest as financial socialisation, wherein individuals learn about societal expectations of financial planning when they socialise with others (e.g. family, friends, work colleagues). Perceived behavioural control can manifest as financial literacy, mental accounting, and financial cognition, wherein the effect of financial satisfaction and financial socialisation is mediated through financial literacy, which may be shaped by the capability to perform mental accounting and the capacity for financial cognition. These factors can collectively shape the individual's intention to engage in financial planning, which, in turn, motivates the actual behaviour of engaging in financial planning, which can take six forms, namely cash flow planning, tax planning, investment planning, risk management, estate planning, and retirement planning.

Visual representation of contextualising the TPB into the theory of financial planning behaviour

Reflections and ways forward

Behavioural decision-making has been one of the most significant research interests for economists over the past decades. Past researchers (Xiao and Wu 2006 ; East 1993 ; Bansal and Taylor 2002 ) have applied the TPB to financial behaviour. The three antecedents of the TPB (attitude, subjective norms, and perceived behavioural control) were found to be associated with the intention of an individual and contribute to financial behaviour (Shim et al. 2007 ; Xiao et al. 2007 ). Unlike other theories, the mediating effect of financial literacy can be applied to the TPB to explain financial behaviour intentions. The variables of mental accounting and financial cognition were not frequently used by the researchers in the study of financial planning, while in this study, both variables are positioned as relevant components of perceived behavioural control in the TPB.

The concept of mental accounting has been extensively studied in the research area of psychology on financial decisions (Mahapatra and Mishra 2020 ). However, past studies on mental accounting in financial planning are insufficient. The formation and influences of mental accounting as a cognitive process—which consists of the concepts of current income, current assets, and future income as well as mental budgeting—play an important role in the personal financial planning process to each individual. It serves as a guideline in the process of financial planning and provides useful insights. Budgeting plays a key role in managing the financial life of an individual in terms of short-term (e.g. prioritising spending in different categories) and long-term (e.g. setting aside money for investment and future use) financial planning.

Previous research has applied mental accounting with the theory of the behavioural life-cycle model. Shefrin and Thaler ( 1988 ) mentioned that people mentally divide their incomes into current income, current assets, and future income, where the marginal propensity to consume (MPC) for each account is relatively different. Mental accounting is helpful and crucial for individuals to plan for their future financial needs so that they can deal with any unexpected financial difficulties in the future. However, there are still gaps to fill to come out with optimal financial decisions. Therefore, given the need of individuals for personal financial planning, it is necessary to apply mental accounting to each individual by determining their spending and saving tendencies.

Moreover, the 2008 global financial crisis and the COVID-19 pandemic have also taught the world painful lessons; the need for financial literacy and cash flow control has been highlighted and considered by the public. A study conducted by Shahrabani ( 2012 ) on the effect of financial literacy and intention to control personal budget concludes that individuals with high levels of financial knowledge and literacy can influence the intention to have budgetary control. The study shows a positive relationship between the intention to budget and financial knowledge. Selvadurai and Siraj ( 2018 ) study financial literacy education and retirement planning in Malaysia. The authors mention that mental accounting is closely related to financial literacy education. Financial literacy can enhance mental accounting as it affects the behaviour of an individual in planning their savings and expenditure. In particular, individuals who acquire financial literacy education are most likely able to control their expenditure by not spending more than their income, which results in having sufficient savings in the long run. The relationship between mental accounting and financial literacy has been proven to be indispensable.

Cognitive ability also plays an important role in financial literacy as it entails understanding financial knowledge and the ability to perform with available resources. While the relationship between financial cognition and financial literacy is strong, individuals can use their cognitive abilities to solve financial problems. Yet, the cognitive biases exist and influence financial decision-making. Agarwal and Muzumder ( 2013 ) state that individuals with no cognitive ability are most likely to face difficulties while making financial decisions. Also, individuals must at least acquire good memory skills, conceptual ability, and financial sophistication to be involved in financial activities. According to Fu et al. ( 2010 ), understanding the attitude of an individual enables one to predict their intentions and behaviour. This could also influence the formation of their attitude. Lusardi and Mitchell ( 2014 ) mention that cognitive abilities are a significant component of financial literacy to determine desirable financial decision-making. In the case of financial literacy, a link between cognitive abilities and the adaptability of financial decision-making has been studied extensively in the field of personal finance. An individual must acquire cognitive skills to make a sound financial decision in an effortless way, which consists of the ability to recall and utilise financial knowledge (memory) and to implement various numerical operations (numeracy) (Chirstelis et al. 2010 ; McArdle et al. 2009 ). Three variables were discussed under the model of financial cognition: financial attitude, risk attitude, and financial knowledge.

Based on the information mentioned above, the mediating effect of financial literacy on mental accounting and financial cognition is indispensable. Policymakers and researchers should work on improving financial literacy and forming positive financial behaviours. Several studies have proven that financial literacy has slowly become a significant component of rational financial decision-making and that it also provides implications for financial behaviour. Individuals or families with higher levels of financial literacy will have an advantage compared to others and higher wealth accumulation as they have the knowledge and skills to participate in financial activities (Schmeiser and Seligman 2013 ). Past studies have proven that financial literacy plays a remarkable role in determining financial outcomes in terms of the components of financial planning (Hilgert et al. 2003 ). Hence, the need for financial literacy in financial planning is indispensable, and it should be considered by individuals as it affects their welfare.

However, no one has attempted to contextualise the TPB and financial planning with the variable of mental accounting and financial cognition with the mediating effect of financial literacy to understand and determine financial behaviour. Thus, this new theory clarifies the conceptualisation and operationalisation of the theory of financial planning behaviour between the variables of mental accounting and financial cognition, and, most importantly, the mediating effect of financial literacy. However, the new theory, in its present and encompassing form, has yet to be tested empirically, and therefore, this warrants future research across different financial products across countries and populations to establish its generalisability.

Discussion and conclusion

This study developed a new theory called the theory of financial planning behaviour using the TPB of Ajzen to understand the financial behaviour of individuals in managing their personal finances. This study examines how the TPB can be contextualised into a theory that more relevantly explains financial planning behaviour. The theoretical background section of this study presents a comprehensive review of the evolution of theories as well as theorisation for the TPB. With a systematic review of the literature, it can be concluded that the constructs of the TPB can be contextualised to better explain financial planning behaviour—that is, the review results showed how different concepts and factors affect the financial planning of an individual by substituting the original components of the TPB with financial variables. Moving on, this study concludes with an articulation of its implications for academics, consumers, and managers.

Implications for academics

The main theoretical contribution of this study is the establishment of the theory of financial planning behaviour. Noteworthily, this new theory represents a noteworthy attempt to demonstrate how a grand theory such as the TPB can be contextualised and thus transformed into a new theory that resonates with realities in the field, in this case, financial planning. The systematic literature review methodology has also proven itself as a useful approach to source for scholarly evidence to offer preliminary support for the new theory.

Another noteworthy contribution is the extrapolation of perceived behavioural control, which answers the call by Lim and Weissmann ( 2023 ) to identify or source for new forms of behavioural control, going beyond the traditional psychological conceptualisation of self-efficacy. Through this study, three types of perceived behavioural control were revealed: financial literacy, mental accounting, and financial cognition. Moreover, the interdependent relationships between these three forms of perceived behavioural control were also identified and theorised, wherein the capability of mental accounting and the capacity for financial cognition shape the financial literacy of the individual, which, in turn, mediates the effects of financial satisfaction (attitude) and financial socialisation (subjective norms) on that individual’s intention and actual behaviour to engage in financial planning.

For researchers seeking to apply the theory of financial planning behaviour in a study, they might operationalise the variables in the following way. Financial satisfaction, financial socialisation, and financial literacy could be assessed using the scales validated by Madinga et al. ( 2022 ). Financial cognition and mental accounting, being somewhat newer constructs in the literature, might require the development of new scales, which could be validated through exploratory and confirmatory factor analysis. For data analysis, researchers might employ a structural equation modelling (SEM) approach to test the relationships between these constructs, as SEM allows for the simultaneous examination of multiple relationships among observed and latent variables. This technique also enables researchers to test the mediating role of financial literacy in the relationship between financial satisfaction, financial socialisation, and financial planning behaviour, thereby assessing the robustness of the proposed theory. If researchers are interested in examining the moderating effects of certain variables (e.g. age, education, or household income), they could use moderation analysis to determine whether the strength or direction of these relationships varies under different conditions.

To this end, the theory of financial planning behaviour should serve as a useful foundational theory to understand a myriad of individual financial planning behaviour such as cash flow planning, tax planning, investment planning, risk management, estate planning, and retirement planning. In this regard, future research is encouraged to explore for new mechanisms that can positively influence or strengthen the variables espoused by the new theory, such as financial satisfaction (e.g. mechanisms that can prompt individuals to evaluate their financial satisfaction—e.g. advertising), financial socialisation (e.g. platforms to encourage individuals to socialise within a financial setting—e.g. metaverse and social media groups), and financial literacy (e.g. ways to enhance mental accounting capability and financial cognition capacity). Nonetheless, this study does not discount the possibility of discovering additional attitudinal, normative, and control variables, which could lead to possible extensions to the theory of financial planning behaviour, as in the case witnessed by TPB. Thus, the new theory herein is intended to inspire new ideas, not to limit them.

Implications for consumers

This study reaffirms the importance of financial planning to safeguard financial resilience in individuals' daily lives. Adopting financial planning entails endless benefits for consumers who do so. Noteworthily, it is important to determine short-term and long-term financial goals and to achieve them via financial planning. Having these goals in mind can provide a sense of direction and purpose in life.

This study is important for all consumers who wish to make ideal financial decisions. Consumers may adopt better cash flow management by implementing financial planning to have a stable financial flow. A cash flow plan can provide an estimation of future income and expenses to achieve financial efficiency and create an emergency fund. Hence, implementing financial planning may help to relieve financial stress and plan for future needs.

Also, consumers can not only gain monetary benefits but also improve their financial literacy. The world has slowly become more financialised, where financial products have developed rapidly and become more complex (Kumar et al. 2023 ; Goodell et al. 2021 ), which requires consumers to be financially literate before making ideal financial decisions (She et al. 2023 ; Bannier and Schwarz 2018 ). Thus, financial institution managers and policymakers are working on improving the financial literacy of consumers and forming positive financial behaviour.

Indeed, financial literacy is a significant component of rational financial decision-making, and it also provides implications towards financial behaviour. Individuals or families with higher levels of financial literacy will have an advantage compared to others as well as higher wealth accumulation as they have the knowledge and skills to participate in financial activities.

Crucial to developing financial literacy is the capability to do mental accounting and the capacity for financial cognition. That is to say, consumers must seek financial education, be it formally or informally, so that they are able to identify and evaluate the different options for financial planning. Similarly, consumers should allocate adequate resources (effort, time) to think about financial planning, which is not a low but rather high involvement process.

Implications for managers

Promoting financial planning has always been a major challenge for financial managers. The newly established theory of financial planning behaviour emerging from the grand TPB can be put into practice by authorities. The findings of this study can be used by financial managers to understand the financial planning behaviour of consumers.

Based on the results and implications of past studies, introducing financial planning behaviour can benefit banks as well as investment and insurance companies that aim to promote consumer financial well-being. It can provide insights into how different factors affect the intention and adoption of financial planning.

Financial literacy needs to be considered as it is an important mediating factor that influences the intentions and behaviour of consumers. For example, whenever a bank introduces financial products to a prospect, that bank must ensure that the prospect is financially literate or else provide sufficient financial knowledge before the prospect develop a financial plan or purchase any financial product from that bank. This is to ensure that their customers possess knowledge of and clarity on the program or product.

In addition, financial institution managers are encouraged to focus on factors (i.e. mental accounting, financial cognition, financial socialisation, financial satisfaction, and financial literacy) that influence customer behaviour towards financial planning before implementing financial programs. For example, understanding the budgeting styles and minimum level of financial satisfaction of customers may help to develop relevant and applicable financial plans for them. Consider a middle-aged client, John, who has recently experienced a job loss. John is feeling uncertain about his financial future and seeks advice from a financial advisor. The financial advisor, following the theory of financial planning behaviour, would first evaluate John's financial literacy level to assess his understanding of financial products and concepts. Then, the advisor would use the theory's constructs such as mental accounting (how John organises his finances and prioritises spending), financial cognition (how John understands his financial situation), and financial satisfaction (how content John is with his current financial state) to develop a comprehensive financial plan. For instance, the financial advisor may realise that John's financial cognition is low, indicating a lack of understanding of the severity of his financial situation. Therefore, to improve his financial cognition, the advisor would emphasise financial education and assist John in developing better mental accounting habits, such as setting up separate 'pots' for his savings, expenses, and investments. This approach is aligned with promoting financial literacy and ensuring the client's knowledge and clarity on his financial plan, which are aspects underscored in our theory.

Implications for policymakers

The findings of this study serve to inform and guide policymaking in significant ways. Policymakers play a crucial role in shaping the financial landscape that influences financial planning behaviour. A key aspect is the importance of financial literacy, which suggests that national education policies should incorporate financial education from early learning stages. Special focus should be given to underprivileged and marginalised communities, who may lack access to financial literacy resources. This might involve legislation mandating financial institutions to fund these education programs as a part of their corporate social responsibility.

This study also illuminates the role of mental accounting and financial cognition in financial planning behaviour. This could inspire policymakers to collaborate with technology developers to create user-friendly digital tools and applications that promote mental accounting practices. Such initiatives should be supported by national policies encouraging technological innovation in the financial sector.

Furthermore, the impact of financial satisfaction on financial planning behaviour underscores the need for regulation in financial advertising. Policymakers should ensure that financial advertising does not create unrealistic expectations that lead to dissatisfaction, and transparency should be mandated, with severe penalties for institutions found to be misleading consumers.

Moreover, the study's findings encourage the creation of financial socialisation platforms. Policies should support the development of both online and offline platforms for learning, sharing, and discussing financial planning strategies and experiences. Policymakers should work with technology companies, local communities, and financial institutions to ensure these platforms are safe, accessible, and inclusive.

Lastly, the responsibility of policymakers extends to the protection of citizens from unfair financial practices. Legislation should ensure transparency in financial markets, particularly regarding fees, interest rates, and risks associated with financial products. Policymakers may also consider mandating financial counselling for complex financial decisions, such as mortgages or large investments, to increase financial satisfaction.

Limitations and future research directions

Notwithstanding the contributions of this study, several limitations exist that may pave the way for future research.

First, financial planning behaviour remains in the infant stage and thus the newly established theory was limited to available evidence. In this regard, this study does not discount the possibility of extending the theory of financial planning behaviour in enriching ways, such as by adding new dimensions of the original TPB components (e.g. additional forms of perceived behavioural control).

Second, the theory of financial planning behaviour has not been empirically examined in its entirety. Thus, future research is encouraged to adopt or adapt this newly established theory in empirical investigations to ascertain its reliability, validity, and generalisability.

Third, the systematic literature review herein was limited to a single theoretical lens (TPB). As indicated through the theoretical foundation discussion, multiple theories exist to explain financial planning behaviour. In this regard, it is important to acknowledge that the development of theories in this area is continuously evolving. As other theories mature, it would be beneficial for future research to consider conducting similar reviews using those theories, to provide a more comprehensive understanding of financial planning behaviour. This could potentially uncover novel insights and lead to the development of new frameworks that could more holistically explain individuals' financial behaviours.

Fourth, the outcomes of financial planning have not been theorised. While the assumption is that good financial planning results in financial resilience, further investigation is needed to empirically verify this assumption. Further exploration of other possible outcomes is also encouraged, both at the micro-level (e.g. life satisfaction, quality of life) and at the macro-level (e.g. country happiness and financial strength).

Fifth, the relationships in the theory of financial planning behaviour are inherently linear. Nonetheless, as experience in financial planning accumulates over time, this study does not discount the possibility of a cyclical loop that reinforces the said relationships. In this regard, future research that extrapolates the theory through a longitudinal perspective is also encouraged.

Sixth, the research landscape of financial behaviour is broad and includes other aspects such as financial counselling and financial therapy. Although these areas were not covered in this study, they may be relevant in the context of the TPB and could contribute to a more comprehensive understanding of financial behaviours. Thus, future research could consider investigating these areas using the TPB, which could also include other related theories, as a guiding theoretical framework. The expansion of search terms in subsequent studies would allow for a more diverse exploration of financial behaviours, potentially enhancing the generalisability and applicability of the findings. Furthermore, it may also reveal a broader range of factors influencing financial planning behaviour and related areas. Hence, researchers are encouraged to extend the current study by exploring the use of TPB alongside related theories in different areas of financial behaviour.

In closing, while this study viewed financial planning within the context of behavioural finance, it is crucial to underscore the fact that financial planning is a distinct profession with its own body of literature. Financial planning transcends the boundary of understanding and predicting individual financial behaviours. It encompasses a broad spectrum of activities, from cash flow management to estate planning, which are geared towards enhancing an individual's economic satisfaction. Each of these areas possesses a unique set of complexities and necessitates a specialised set of knowledge and skills. The profession of financial planning is dedicated to addressing these complexities and enhancing individuals' financial well-being. Our exploration of financial planning behaviour through behavioural finance should be seen as a facet of the broader, multi-dimensional discipline of financial planning. Future research should therefore endeavour to add to the rich and varied literature of financial planning to offer a more holistic and nuanced understanding of financial behaviour.

Based on a search for “personal finance” in the “title, abstract and keywords” and the subject area of “business, management and accounting” in Scopus on 25 December 2022.

Smooth consumption refers to consumption that balances or optimises spending and saving during different life phases to achieve the greatest overall standard of living (Morduch 1995 ).

Instead of Scopus or Web of Science, which are subscription-based, Google Scholar was used as the search mechanism because it is free to use and thus more accessible. Source quality can still be maintained by referring to Scimago Journal Ranks, which relies on Scopus, and Web of Science Master Journal List, albeit manually. With the journal lists acting as a cross-check mechanism and without the need for bibliometric data, Google Scholar is deemed to be adequate for the search and review. This practice is similar to that of existing reviews (e.g. Lim and Weissmann 2023 ; Lim et al. 2021 ).

Unlike Scopus or Web of Science, which use search string, Google Scholar use search keywords.

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Appendix 1: Articles on financial planning behaviour and TPB

• NA not available, TPB theory of planned behaviour.

Appendix 2: List of articles reviewed

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Xiao, J.J. and Wu, G. (2008). Completing debt management plans in credit counseling: An application of the theory of planned behavior. Journal of Financial Counselling and Planning 19(2): 29–45.

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Yeo, K.H.K., Lim, W.M. & Yii, KJ. Financial planning behaviour: a systematic literature review and new theory development. J Financ Serv Mark 29 , 979–1001 (2024). https://doi.org/10.1057/s41264-023-00249-1

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A multidimensional review of the cash management problem

• Francisco Salas-Molina   ORCID: orcid.org/0000-0002-1168-7931 1 ,
• Juan A. Rodríguez-Aguilar 2 &
• Montserrat Guillen 3  

Financial Innovation volume  9 , Article number:  67 ( 2023 ) Cite this article

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In this paper, we summarize and analyze the relevant research on the cash management problem appearing in the literature. First, we identify the main dimensions of the cash management problem. Next, we review the most relevant contributions in this field and present a multidimensional analysis of these contributions, according to the dimensions of the problem. From this analysis, several open research questions are highlighted.

Introduction

Cash managers must make daily decisions about the number of transactions between cash holdings and any other type of available investment asset. On the one hand, a certain amount of cash must be kept for operational and precautionary purposes. On the other hand, idle cash balances may be invested in short-term assets such as interest-bearing accounts or treasury bills for profit. Since Baumol ( 1952 ), several cash management models have been proposed to address the cash management problem(CMP).

Keynes ( 1936 ) initially identified three motives for holding cash: the transaction motive, the precautionary motive and the speculative motive. Other authors have added other motives for holding cash, such as the agency motive (Jensen 1986 ) or tax motive (Foley et al. 2007 ). More recently, other authors have highlighted other determinants of corporate cash policies (e.g., Gao et al. ( 2013 ) and Pinkowitz et al. ( 2016 )). As a result, the first objective of this study is to review the literature related to CMP from an economic and financial perspective, derived from the analysis of the main motives for holding cash.

While most cash management literature stems from the seminal paper by Baumol ( 1952 ), many cash management works approach CMP from a decision-making perspective. Our second objective is to review the literature related to CMP from a decision-making perspective, considering models proposed by different researchers to deal with cash when the ultimate goal is to elicit a cash management policy, namely, a temporal sequence of transactions between accounts.

To the best of our knowledge, only three surveys on cash management have been published since the 1950s. Gregory ( 1976 ) covered the beginning of the cash management literature including the important works by Baumol ( 1952 ) and Miller and Orr ( 1966 ). Ten years later, Srinivasan and Kim ( 1986 ) extended the analysis to models not considered by Gregory ( 1976 ). Finally, da Costa Moraes et al. ( 2015 ) reviewed several stochastic models since the 1980s. However, there is a lack of taxonomy for classifying models and identifying open research questions in cash management.

Within the context of CMP, from a decision-making perspective, we propose a taxonomy based on the main dimensions of the cash management problem: (i) the model deployed, (ii) the type of cash flow process considered, (iii) the particular cost functions used, (iv) the objectives pursued by cash managers, (v) the method used to set the model and solve the problem, and (vi) the number of accounts considered. These six dimensions provide a sound framework to classify the cash management models proposed in the literature. Here, we focus on the most relevant models in terms of number of citations. For a comprehensive review, we refer interested readers to Gregory ( 1976 ), da Costa Moraes et al. ( 2015 ) and Srinivasan and Kim ( 1986 ).

Our taxonomy helps researchers use a common framework to establish cash management areas. In addition, our multidimensional analysis enhances the understanding of the cash management problem, making it easier to identify open research questions. Note that the multidimensional framework described in this paper is not limited to the six dimensions mentioned above. Researchers may extend the number of dimensions, thereby enriching the analysis of the cash management problem.

The remainder of this paper is organized as follows. In " Motives for holding cash and related literature " in section, we consider the main motives for holding cash and review the literature related to CMP from an economic and financial perspective. In " A multidimensional taxonomy of the cash management problem " in section, we introduce and motivate the six dimensions of the CMP that define our taxonomy proposal. In " A review of the main contributions to the cash management problem " in section, we review the most relevant contributions to CMP from a decision-making perspective. Next, " A multidimensional analysis of the cash management problem " in section, we perform a comparative analysis of alternative cash management models that are directly linked to " Open research questions in cash management " in section, which identifies several open research questions in cash management. Finally, " Concluding remarks " in section concludes the paper.

Motives for holding cash and related literature

In this section, we consider the main motives for holding cash and review the literature related to CMP from an economics and finance perspective. We first consider the three motives for holding cash, initially identified by Keynes ( 1936 ), as follows:

The transaction motive, which is the need for cash for the current transaction of personal and business exchanges.

The precautionary motive, which is the desire for security as the future cash equivalent of a certain proportion of total resources acts as a financial reserve.

The speculative motive or the object of securing profit from knowing better than the market what the future will bring forth. The goal is to take advantage of future investment opportunities.

Later, Jensen ( 1986 ) argued that managers tend to accumulate cash rather than increase payouts to shareholders because of agency motives. Cash holdings may act as a buffer to cover eventual bad management decisions. One possible reason for this behavior is information asymmetry. Information is distributed asymmetrically throughout the organization; thus, managers usually have an advantage over shareholders in handling specific events because of information asymmetry (Eisenhardt 1989 ; Dierkens 1991 ). In addition, managers have an incentive to make the company bigger when compensation is linked to the size of the company, even when the company has poor investment opportunities. The motive for holding cash stems from the financial implications of agency theory (Jensen and Meckling 1976 ; Fama 1980 ; Fama and Jensen 1983 ; Eisenhardt 1989 ). In this theory, the firm is viewed as a set of contracts among the factors of production, in which each one is motivated by self-interest (Fama 1980 ). Consequently, the relationship between corporate managers (including cash managers) and owners presents friction due to conflicts of interest. The concept of agency costs defined by Jensen and Meckling ( 1976 ) is derived from an agency relationship in which managers and owners present divergences that result in monitoring costs, bonding costs to avoid certain actions, and other residual losses. One of these divergences relates to cash holdings. For example, consider that cash outflows to shareholders in the form of dividends reduce resources under managers’ control.

Kaplan and Zingales ( 1997 ) investigated the relationship between sensitivity of investment to cash flow and financing constraints, expressed as the differential cost between internal and external finance. They found that even though investment is sensitive to cash flow for the vast majority of firms analyzed, investment-cash flow sensitivities do not increase monotonically with the degree of financing constraints. Most of the firms analyzed could increase their investment if they choose to do so, thus providing further evidence of the agency motive for holding cash. Contrary to what was thought before, the authors concluded that higher sensitivities cannot be interpreted as evidence that firms are more financially constrained.

Leland ( 1998 ) argued that the key insight by Jensen and Meckling ( 1976 ) is that the firm’s choice of risk may depend on capital structure, hence challenging the Modigliani and Miller ( 1958 , 1963 ) assumption that investment decisions are independent of capital structure. Consequently, Leland ( 1998 ) proposed integrating both approaches to derive the optimal capital structure of a firm. The model reflects the interaction of different cash flow policies, namely, financing decisions and investment risk strategies. When investment policies are chosen, agency costs appear as a critical element in the model.

Further evidence of the agency motive for holding cash can be found in Dittmar et al. ( 2003 ), Pinkowitz et al. ( 2006 ), Dittmar and Mahrt-Smith ( 2007 ) and Harford et al. ( 2008 ). More recently, but still within the context of agency theory, Tran ( 2020 ) emphasized how external factors, such as the economic cycle, including the eventual financial crisis, affect cash holdings. The author found that the 2008 global financial crisis decreased the controlling effect of shareholder rights on corporate cash holdings, regardless of any control agency mechanism. Following a similar line of research, Tekin ( 2020 ) and Tekin et al. ( 2021 ) examined whether an agency cost explanation is valid for cash holdings during and after the financial crisis. During a financial crisis, agency costs tend to be higher than usual and the agency motive for holding cash is greater. The authors assessed the role of governance in cash management in 26 Asian developing countries and found that firms with poor governance increased their cash levels after the financial crisis. They concluded that cash holdings had a substitution effect on governance due to changes in managers’ risk aversion perceptions.

Cash management relates to financial constraints. The impact of financial restrictions on optimal cash holdings in the context of a financial crisis was considered by Tekin and Polat ( 2020 ), who compared firms in a highly regulated market with firms in a relatively unregulated market in the United Kingdom. The authors found that less-regulated firms had a faster adjustment of cash over the period 2002-2017. However, these firms decreased their cash adjustment speed more than highly regulated firms did during the financial crisis. Using a sample of firms from 26 developing Asian economies from 1991 to 2016, Tekin ( 2022 ) recently showed that financially constrained firms increased their cash levels more than financially unconstrained firms after the 2008 global financial crisis. In summary, exogenous shocks such as financial crises represent an important external factor in cash management.

Conversely, Foley et al. ( 2007 ) identify the tax motive for holding cash. More precisely, they found that the U.S. corporations, that would incur tax consequences associated with repatriating foreign earnings, hold higher levels of cash. Bates et al. ( 2009 ) showed that the average cash-to-assets ratio for U.S. industrial firms doubled from 1980 to 2006. They argue that the precautionary motive for cash holdings plays an important role in explaining the increase in cash ratios. From an analysis of the literature, Bates et al. ( 2009 ) summarized two additional motives for holding cash:

The agency motive, which is the need for cash derived from conflicts of interest among managers and owners.

The tax motive, which is the desire to avoid tax consequences associated with repatriation of foreign earnings.

Gao et al. ( 2013 ) analyzed a sample of public and private U.S. firms during the period 1995-2011 to conclude that public firms hold more cash than private firms. By examining the drivers of cash policies for each group, the authors attribute this difference to the much higher agency costs in public firms. Using a similar period (1998–2011), Pinkowitz et al. ( 2016 ) showed that U.S. firms held more cash on average than similar foreign firms. However, they argued that country characteristics had negligible explanatory power for the differences in cash holdings between U.S. firms and their foreign twins. Graham and Leary ( 2018 ) included the historic perspective in the analysis by studying average and aggregate cash holdings of companies in the U.S. from 1920 to 2014. Corporate cash holdings doubled in the first 25 years of the sample before returning to 1920 levels by 1970. Since then, the average and aggregate patterns have diverged.

Interest rates and environmental and health motives have recently been included in cash holding analyses. Gao et al. ( 2021 ) highlighted a non-monotonic relation between corporate cash and both real and nominal interest rates in both aggregate and firm-level data. The authors argue that these results imply that interest rates are unlikely to be the cause of the recent increase in corporate cash. Tan et al. ( 2021 ) compared cash holdings before and after the Environmental Inspection Program in China during the period 2014-2018 for manufacturing firms included and non-included in the program. The results suggest that this environmental program enhanced cash management efficiency because firms included in the program accumulated less cash. Finally, Alvarez and Argente ( 2022 ) focused on the impact of COVID-19 in household’s cash management behavior, considering the choice of means of payment and the average size and frequency of cash withdrawals. The authors used data on ATM (automated teller machine) cash disbursements in Argentina, Chile, and the U.S. to show that the intensity of the virus increased transaction costs.

A multidimensional taxonomy of the cash management problem

Cash flow management concerns the efficient use of a company’s cash and short-term investments (Gregory 1976 ). Cash is then viewed as a stock, a buffer, such as an inventory of wheat or bolts. Holding cash has a cost because of it being idle but, at the same time, transferring idle money to alternative investments is also costly. How much money should companies keep to operate efficiently? Identifying an appropriate answer to this question is the main goal of CMP. However, several aspects and dimensions must be considered to establish the boundaries of the problem. Hereafter, we focus on the main dimensions of the cash management problem, defining a cash management problem taxonomy to classify past research and identify open research questions.

Cash management models

In an attempt to solve CMP, several cash management models have been proposed to control cash balances based on a set of levels or bounds. CMP was first proposed from an inventory control perspective by Baumol ( 1952 ) in a deterministic manner. Later, Miller and Orr ( 1966 ) followed a stochastic approach, assuming that cash balance changes are random. Many other models have been developed based on these two seminal works. Most previous models assume a set of bounds to control cash balances; however, alternative configurations are also suitable.

Cash flow process

Cash flow statistical characterization is also a key issue in understanding cash management. Separation between inflows and outflows, or receipts and disbursements, is the basic breakdown, but a more detailed separation can be helpful when trying to extract patterns from data. In this sense, Stone and Miller ( 1981 , 1987 ) suggest the utility of problem structuring, or breaking down a problem into different subproblems, to appropriately handle cash flow forecasting as a key task in cash management. In addition, common assumptions on the statistical properties of cash flows include (i) normality, meaning that its values are centered around the average following a Gaussian distribution; (ii) independence, meaning that its values are not correlated with each other; and (iii) stationarity, meaning that its mean and variance are constant with time. However, little empirical evidence on the statistical properties of cash flow has been provided, with the exception of Mullins and Homonoff ( 1976 ), Emery ( 1981 ), Pindado and Vico ( 1996 ).

Costs in cash management

The main objective of managing cash is to keep the amount of available cash as low as possible while still keeping the company operating efficiently. Additionally, companies may place idle cash in short-term investments (Ross et al. 2002 ). Thus, the cash management problem can be viewed as a trade-off between holding and transaction costs. On the one hand, holding costs are usually opportunity costs due to idle cash that can be allocated to alternative investments. Holding too much cash is inefficient but holding too little may result in high shortage costs. On the other hand, transaction costs are associated with the movement of cash from/into a cash account into/from any other short-term available asset, such as treasury bills and other marketable securities. In summary, if a company tries to keep balances too low, holding costs will be reduced, but undesirable situations of shortage will force the sale of available marketable securities, thereby increasing transaction costs. By contrast, if the balance is too high, low trading costs will be incurred due to unexpected cash flow, but the company will carry high holding costs because no interest is earned on cash. Therefore, the company must optimize its target cash balance.

Desired objectives

In cash management literature, the focus is typically placed on a single objective, namely, cost. Except for Zopounidis ( 1999 ), Salas-Molina et al. ( 2018 ), cash management and multi-criteria decision-making are not usually linked concepts in financial literature. However, risk management is an important task in decision-making, and since different cash strategies entail different degrees of risk, a quantitative approach to measure risk is required. Furthermore, due to the different degrees of risk that firms are willing to accept, risk preferences are also an important issue for decision-makers.

Solving the cash management problem

Cash management poses a general optimization problem, namely, determining a policy that optimizes objective functions. However, several different techniques have been used to solve this optimization problem, ranging from mathematical programming, such as dynamic programming (Eppen and Fama 1968 ; Penttinen 1991 ) and control theory methods Sethi and Thompson ( 1970 ), to approximate techniques such as genetic algorithms (Gormley and Meade 2007 ; da Costa Moraes and Nagano 2014 ). An important question regarding alternative solvers is the optimality of solutions, which is a desired objective, but must be balanced with computational and deployment costs.

Managing multiple bank accounts

In cash management literature, cash management systems with multiple bank accounts have received little attention from the research community, with the exception of Baccarin ( 2009 ). However, cash management systems with multiple bank accounts are a rule, rather than an exception, in most firms.

Once the six main dimensions of the CMP are established, namely, models, cash flow, costs, objectives, solvers and number of accounts, we are in a position to review the most relevant cash management models proposed in the literature.

A review of the main contributions to the cash management problem

Although the advancement of a specific research topic is gradual rather than sharp, the history of CMP is long enough to distinguish at least two main periods: the classical period up to 2000 and the modern period from 2000 onwards. Since the initial inventory approach to CMP by Baumol ( 1952 ), the classical period is characterized by the common two-assets framework, linear cost functions, and the minimization of cost as the single goal of cash managers. However, a multidimensional approach to CMP emerges with Baccarin ( 2009 ), who considered cash management systems with multiple bank accounts and non-linear cost functions. We argue that this change in perspective and implied complexity gives rise to a new period in the study of CMP. In the following sections, we present a review of the most relevant works on CMP from Baumol ( 1952 ) to Baccarin ( 2009 ) and consider the most recent contributions. We respect the authors’ notations and clarify issues regarding notation when necessary for comparison purposes.

Baumol ( 1952 )

The inventory control approach to the cash management problem was introduced by Baumol ( 1952 ). The author expected that inventory theory and monetary theory would learn from one another. However, several important assumptions were made to, using the exact Baumol’s words, abstract from precautionary and speculative demands. The most important was that transactions were perfectly foreseen and occurred in a steady stream. Baumol assumed that an outflow of T dollars occurred for a given period in a steady stream. To offset these outflows, inflows can be obtained by borrowing or withdrawing from an investment at a cost of i dollars per dollar per period. An additional assumption is made by considering that these withdrawals are performed in many C dollars, evenly spaced in time, with a fixed cost of b dollars (see Fig. 1 ).

The Baumol model

Under these constraints, cash managers make T / C withdrawals for a given period, and the total cost is given by

where the first part of the equation is the number of transactions multiplied by the unitary fixed cost of each transaction and the second part is the average cash balance multiplied by the cost of holding this balance. Then, the goal for cash managers is to choose C such that Eq. ( 1 ) is minimized. Setting the derivative of the total cost with respect to C to zero, we obtain the value of C that minimizes ( 1 ) as follows:

The steady stream of payments and absence of receipts during the relevant period make this model impractical in many real applications. It was “only a suggestive oversimplification,” in the author’s own words. However, the first step in the inventory control approach to the cash management problem was performed. Interestingly, Baumol also envisioned the inherent task of forecasting cash flow by stating that with sufficient foresight, if receipts can meet payments, savings in the use of cash can be achieved.

Summarizing, Baumol ( 1952 ) initiated the inventory approach to the cash management problem proposing a deterministic model with uniform cash flows, with the objective of minimizing fixed transaction and holding costs for a single bank account using analytical methods.

Tobin ( 1956 )

Tobin argued that cash requirements depend inversely on the interest rate for a given volume of transactions, governed by the lack of synchronization of receipts and disbursements. The higher the lack of synchronization, the higher the need for transaction balances. However, there is no need to hold a cash balance. Instead, cash managers have the opportunity to maintain balances in assets with higher yields, such as bonds or marketable securities. When cash is needed, these assets could be shifted to cash again for payments. Consequently, it is likely that the amount of cash held for transaction purposes is inversely related to the interest rates of such alternative assets.

Given an interest rate r , the problem is to find the relationship between what is held in cash and what is held in alternative assets to maximize interest earnings, net of transaction costs. At the beginning of each period \(t=0\) , an amount Y is held by the cash manager that is uniformly disbursed until the end of period \(t=1\) when no cash is available, as shown in Fig. 2 . Thus, the total transaction balance is \(T(t)=Y(1-t)\) with \(0 \ge t \ge 1\) . However, this total T ( t ) can be divided between cash C ( t ) and bonds B ( t ) such that \(T(t)=C(t)+B(t)\) , where B ( t ) yields interest r per time period. Three different questions are then faced by Tobin: (i) given r and a fixed number n of transactions, determine the optimal timing and amounts to be held in cash and bonds; (ii) given r but a variable number n of transactions, determine the optimal \(n^*\) ; and (iii) how does \(n^*\) depends on r ?

The Tobin model

Considering transaction x between bonds and cash, the transaction cost is given by \(a + b \cdot x\) , with \(a,b >0\) . Then, for the general case, Tobin proves that the average number of bonds is given by

where \(n \ge 2\) and \(r \ge 2b\) . In order to determine the optimal number of transactions, the next profit function is maximized:

that is a decreasing function of n . Then, the optimal number of transactions \(n^*\) is greater than two when \(1/12 Y r (1 - 2b/r)^2 \ge a\) holds true. Finally, the relationship between the optimal number of transactions \(n^*\) and interest rate is given by Eq. ( 3 ). Since \(B_n\) is an increasing function of n , and \(n^*\) directly varies with r , the optimal proportion of bonds also directly varies with r ; consequently, the proportion of cash inversely varies with  r for sufficiently high rates.

Smith ( 1986 ) proposed a Dynamic Baumol-Tobin Model of Money Demand . However, this Baumol-Tobin model is more closely related to the Constantinides and Richard ( 1978 ) model than with the initial proposals by Baumol ( 1952 ) and Tobin ( 1956 ). More recently, Mierzejewski ( 2011 ) followed Tobin’s approach, according to which companies hold cash as a behavior towards risk, to propose a theoretical model of equilibrium in cash-balance markets, which is beyond the scope of this thesis.

Summarizing the above, the Tobin ( 1956 ) model is also a deterministic model dealing with a uniform cash flow such as the Baumol ( 1952 ) but incorporating the interest rate as a key parameter. In addition, Tobin considered not only fixed costs, but also variable transaction costs between two alternative assets, namely, bonds and cash. The goal was to minimize costs, and an analytical solution was provided.

Miller and Orr ( 1966 )

Miller and Orr introduced the stochastic cash balance problem by relying on the fact that the cash balance does not fluctuate steadily but rather irregularly for many companies, resulting in an impractical application of the Baumol model. Miller and Orr developed a simple model following an opposite approach to Baumol by considering stochastic cash flows. From a predictability point of view, Miller and Orr shifted from the perfect knowledge of cash flows in Baumol model to cash flows generated by a stationary random walk, from a deterministic approach to completely stochastic cash flows. They considered cash flows to be characterized as a sequence of independent and symmetric Bernoulli trials. They supposed that the cash balance will either increase or decrease by m dollars with probability \(p=1/2\) . The main features of this approach are independence, stationarity, zero-drift, and the absence of regular swings in cash flows. Moreover, they ignored shortages and variable transaction costs.

In their first attempt to deal with the corporate cash management problem, they assumed that companies seek to minimize the long-term average costs of managing the cash balance under a simple policy. This policy sets a lower bound, zero, and an upper bound, h , where cash balance is allowed to wander between the lower and upper levels. We say that the Miller and Orr ( 1966 ) is a Bound Based Model (BBM). Apart from the cash balance, the model also assumes the existence of a second asset of any kind, such as interest bearing assets or marketable securities grouped in a portfolio of investments that are easily transformed into cash at the company’s convenience. The policy implies that, when the upper bound reaches a withdrawal transfer, the balance is restored to a target level of z . Similarly, when the cash balance reaches zero, a positive transfer will be made to restore the balance to z , as shown in Fig. 3 .

The Miler-Orr model

Although Miller and Orr set the lower limit to zero in their work, in practice, a real cash manager should set the lower limit above zero for precautionary motives. This lower limit represents a safety cash buffer, and its selection depends on the level of risk the company is willing to accept. This model variation can be found in (Ross et al. 2002 ), which sets a lower limit l and an upper bound h . When h is reached, a withdrawal transfer is performed to restore the balance to the target level of z . Similarly, when the cash balance reaches l , a positive transfer is made to restore the balance to z . Formally, the transfer occurring at time t , \(x_t\) , is elicited by comparing the current cash balance, \(b_{t-1}\) , with the lower and upper bounds:

To obtain the limits, once the cash manager sets the lower limit l , the optimal values of the policy parameters h and z are derived from the expected cost per day over any planning horizon of T days, given by

where E ( c ) is the expected cost per day, E ( N ) is the expected number of transfers during the planning period T , \(\gamma\) is the cost per transfer, E ( M ) is the average daily cash balance, and v is the daily interest rate earned on the portfolio as the opportunity cost of idle cash. By letting \(Z=h-z\) , the problem can be stated in terms of the variance of the net cash flow as:

where the first part of the equation is the transfer cost term, and the second part is the holding cost term. The average cash balance is \((h+z)/3\) . Hence, the optimal parameters are given by

or in terms of the original parameters

The equivalent equations for the case of a lower bound ( l ) distinct from zero can easily be derived, as presented in Ross et al. ( 2002 ), to obtain

The major implication and main novelty of this model in comparison to the Baumol model is the presence of the observable variance of the net daily cash flow. As in the case of the Baumol model, the greater the transfer cost ( \(\gamma\) ), the higher the target cash balance ( z ), and the greater the daily interest rate ( v ), the lower the target cash balance ( z ). However, the greater the uncertainty of the net daily cash flow, measured by \(\sigma ^2\) , the higher the target cash balance ( z ), and the higher the difference between the lower bound ( l ) and the higher bound ( h ). This represents the first step towards a more practical approach to the corporate cash management problem because common sense shows that the greater the uncertainty, the greater the chance that the balance will drop below the lower bound.

Several extensions of the model have been considered to incorporate systematic drift in the cash balance and to allow for more than one portfolio asset with different transfers and holding costs. Despite the assumption of the totally stochastic mechanism of cash flow, the authors pointed out the presence of both stochastic and deterministic, or at least highly predictable, elements in cash flow, such as payroll disbursements or dividend payments. However, they argued that the gains from exploiting any cash flow patterns are by no means sufficiently large to offset the added costs of model development and implementation.

In summary, Miller and Orr ( 1966 ) was the first stochastic cash management model proposed in the literature. They introduced the concept of bounds or control limits, which are directly linked to the statistical properties of cash flows and are assumed to be random walks. Only fixed transaction costs were considered, and analytical solutions were provided for a single objective and cash account.

Eppen and Fama ( 1969 )

A variation of the Miller and Orr ( 1966 ) model was introduced by Eppen and Fama ( 1969 ) following a dynamic programming approach. However, it was a previous publication (Eppen and Fama 1968 ) which provided a complete analysis of the effect of variations in transfer, holding, and penalty costs on the optimal policies. The Eppen-Fama model is a generalization of the stochastic Miller-Orr model, in which transfer costs contain both fixed and variable components. They showed that if transfer costs have a fixed cost as well as a cost, proportional to the amount transferred, the optimal strategy is in the form of two limits ( u ,  d ) and two return points ( U ,  D ), one for each limit. In this model, when the cash balance reaches the upper bound ( d ), it is immediately restored to the upper return point ( D ), and when it reaches the lower bound ( u ), it is restored to the lower return point ( U ), as shown in Fig.  4 .

Eppen-Fama model representation with two return points

Following the Markovian approach, they assumed that the probability mass function of the transitions between different possible states is known and stationary. This assumption implies the process of discretization of the cash balance. At any point in time, the cash balance can be in one of N possible states, \(i=1,2,...N\) , each representing a discrete level of cash balance. The lowest level occurs in state 1 and the highest in state N , and each successive level differs by some constant R , for example 1000 €.

For the general case, two cost functions are defined. First, the transfer cost ( \(t_{i}^{k}\) ) caused by moving the cash balance from state i to state k :

where \(K_u\) and \(c_u\) are the fixed and variable components of a positive cash movement, respectively, and \(K_d\) and \(c_d\) are the fixed and variable components of a negative cash movement, respectively. Second, the holding or penalty cost ( L ( k )) associated with starting a period in state k can be defined as follows:

where \(c_p\) is the marginal penalty cost per period per R unit of cash, \(c_h\) is the marginal holding cost per period per R unit of cash, say 1000 €, and M is the minimum cash balance that must be maintained because of any condition required by banks. In the absence of this restriction, M is usually set to zero as the minimum cash balance required to be held in the bank account.

Recall that Miller and Orr ( 1966 ) suggests the use of two or three bounds. To account for fixed and variable transaction costs, Eppen and Fama ( 1968 ) proposed the use of four bounds. From an experimental perspective, the authors pointed out that higher dispersion in the probability distribution caused the outer bounds u and d and the return points U and D to be further away from zero. Therefore, in practical applications, it is highly recommended to carefully estimate the probability distribution, particularly in extremes. Moreover, when both the probability distribution and cost function are symmetric about zero, the optimal policies are symmetrical.

In summary, several interesting contributions on the practical side of the corporate cash balance problem were made by Eppen and Fama under the assumption of cash flow following a random walk. They considered both fixed and variable transaction costs, resulting in a policy based on four bounds aimed at minimizing costs. They proposed linear programming as a solver in Eppen and Fama ( 1968 ) and dynamic programming in Eppen and Fama ( 1969 ) for a single cash bank account.

Daellenbach ( 1971 )

Daellenbach proposes an improvement to the Eppen and Fama ( 1969 ) model, claiming that his model is a generalization of the Eppen-Fama model to situations where bank account overdrafts are not possible, and using two different sources of short-term funds, namely, marketable securities and short-term loans. Furthermore, in contrast to previous models, the probability distribution of cash flows is not necessarily stationary and the length of the review period may vary from period to period. Again, a decision about the adjustment of the cash balance must be made; however, in this model, an allocation decision about either marketable securities or borrowing transactions is also necessary. A dynamic programming approach was proposed for labeling periods in the planning horizon as \(n=N\) for the first period and \(n=1\) for the last period. Three state variables were then considered to describe the cash balance situation:

\(B_n\) or the cash balance at the beginning of period n carried forward from \(n+1\) .

\(Z_n\) or the borrowing balance at the beginning of period n carried forward from \(n+1\) .

\(S_n\) or the marketable securities balance at the beginning of period n carried forward from \(n+1\) .

If \(X_n\) and \(Y_n\) denote transactions in the form of borrowings or marketable securities, respectively, and \(R_n\) is the sum of uncontrollable cash transactions in period n with the probability density function \(f_n(r_n)\) , the following balance equation is used to link period \(n-1\) to period n :

subject to:

meaning that, (i) the initial cash balance before any adjustment has to be non-negative; (ii) the outstanding borrowing balance cannot be below zero; and (iii) marketable securities cannot be sold short.

According to the previous equations, the state variable set for the cash position at the beginning of period n , prior to any cash balance adjustment, is denoted by \(\Omega _n=(B_n,Z_n,S_n)\) , the decision variables are \((X_n,Y_n)\) , the total cost is the sum of (i) fixed and variable transaction costs for borrowing, (ii) fixed and variable transaction costs for marketable securities, (iii) interest cost on borrowings, (iv) returns on marketable securities (note that this is a negative cost or a benefit), and (v) penalty costs for cash shortages. These costs can be summarized as follows:

where \(H_1(X_n)\) is the borrowing cost function computed as

where \(b_{1}^{-}, b_{1}^{+}\) is the variable borrowing transaction costs for cash increases (+) and decreases (-), \(H_2(Y_n)\) is the marketable securities cost function computed as

where \(b_{2}^{-}, b_{2}^{+}\) are variable marketable security transaction costs for cash increases (+) and decreases (-), respectively; \(c_{1n}\) is the interest cost on ending loan balances; \(c_{2n}\) is the return on ending marketable securities holdings; \(L_n(B_n)\) is the expected cost of cash shortage incurred at the end of period n computed as:

where \(c_{3n}\) is the penalty for negative ending cash balances in period n .

Considering alternative funding sources, such as borrowings and marketable securities, introduces additional considerations on priorities based on feasible permutations of the cost coefficients as follows:

Case 1. If \(-b_{2}^{-}+c_2 \le -b_{1}^{-}+c_1 \le b_{1}^{+}+c_1 \le b_{2}^{+}+c_2\) , then borrowing transactions are preferred over marketable securities.

Case 2. If \(-b_{1}^{-}+c_1 \le -b_{2}^{-}+c_2 \le b_{2}^{+}+c_2 \le b_{1}^{+}+c_1\) , then marketable security transactions are preferred over borrowing.

Case 3. If \(-b_{2}^{-}+c_2 \le -b_{1}^{-}+c_1 \le b_{2}^{+}+c_2 \le b_{1}^{+}+c_1\) , then borrowing transactions are preferred over marketable securities for cash withdrawals, and marketable securities are preferred over borrowing for cash procurements.

Case 4. If \(-b_{1}^{-}+c_1 \le -b_{2}^{-}+c_2 \le b_{1}^{+}+c_1 \le b_{2}^{+}+c_2\) , then marketable securities are preferred over borrowing transactions for cash withdrawals, and borrowings are preferred over marketable securities for cash procurements.

Case 5. If \(-b_{2}^{-}+c_2 \le b_{2}^{+}+c_2 \le -b_{1}^{-}+c_1 \le b_{1}^{+}+c_1\) , then borrowing transactions are preferred over marketable securities for cash withdrawals, and marketable securities are preferred over borrowings for cash procurements.

As a result, the Daellenbach model can be regarded as an extension of the Eppen and Fama ( 1968 , 1969 ) model, but with four return points: \(\{U_{1n},D_{1n}\}\) denote the use of borrowings as the source of funds, and \(\{U_{2n},D_{2n}\}\) denote the use of marketable securities as the source of funds. The optimal policy gives preference to the source of funds dictated by the previous five cases based on the cost coefficients. If either constraint ( 19 ) or ( 20 ) prevents the completion of the transaction, then use the return point relevant to the other source of funds.

Subsequently, Daellenbach ( 1974 ) pointed out an important issue by posing the following general question: Are cash management models worthwhile? The objective was to determine the upper bounds of potential savings that could be realized by applying cash management models. In this study, a variant of the model in Daellenbach ( 1971 ) is proposed to consider fixed and variable transaction costs. In addition, a deterministic shortage cost function that charges negative cash balances at the end of the day is defined instead of the previous stochastic one. The main criticism of cash management models is based on the assumption of perfectly predictable cash flows. Any cost estimate based on perfect predictions will provide optimistic lower bounds for the actual cost incurred, which corresponds to determining what the optimal policy would have been given the actual cash flow. Using random normal simulations, the author estimated the upper bounds obtained by this variant of his cash management model on the performance of a hypothetical cash manager. The author concluded that the benefits of cash management optimization models were, in most cases, highly uncertain and offered a very small economic return.

In summary, Daellenbach ( 1971 ) used dynamic programming to provide a solution to the CMP as a set of control bounds but considered two available sources of funds, namely, marketable securities and short-term loans. In addition, the usual assumption on stationary cash flow was relaxed and fixed and variable transaction costs were considered as objectives to minimize.

Stone ( 1972 )

The use of forecasts and smoothing in control-limit models for cash management was proposed by Stone ( 1972 ). In this work, Stone first reviewed the assumptions of the Baumol ( 1952 ) and Miller and Orr ( 1966 ) models and pointed out a series of limitations of these models in real-world cash management situations. Stone argued that cash flows are neither completely certain, uniform, and continuous (as they are in the Baumol model) nor completely unpredictable (as they are in the Miller-Orr model). Most firms can forecast their cash flows. This is the first time that the concept of forecasting cash flows has been a key input to any cash management model. The author focused on the generally attempted tasks performed by cash managers. They usually:

Look ahead when buying and selling securities to incorporate data from their cash forecasts.

Smoothen cash flows by coordinating security maturities with predicted cash needs.

Buy the highest yielding securities subject to portfolio and liquidity constraints.

Maintain cash balances sufficient to meet banking requirements.

From these tasks, Stone derived the idea of including both forecasts and maturing securities in his model. The operation of this control-limit model is based on the ability to buy and sell securities of different maturities to reduce transaction costs by smoothing cash flows and thereby reducing the number of transactions. It is assumed that the current cash balance, \(CB_0\) , is known, and that a forecast of the net cash flow, \(E(C_t)\) , that will occur on each day t over the next k days is available. The expected level of cash balances k days from now is the sum of the current level of cash balances and the sum of k daily net cash flow. This can be expressed as

Alternatively, if the sum of net cash flows over the next k days is lumped into a single figure, the last equation can be rewritten as:

Next, a number of simple rules are proposed to be followed by cash managers to return to the desired target balance TB , based on two sets of control limits as shown in Fig. 5 . One set is defined by \(h_1\) and \(h_0\) as the upper and lower control limits for initiating considerations of a transactions. The other set is defined by \(h_1-\delta _1\) and \(h_0+\delta _0\) as the upper and lower limits, respectively, and determine if a transaction will actually be made.

Structure of the Stone model with two sets of limits

The set of rules followed by cash managers to operate the model are summarized as follows.

If the current cash balance \(CB_0\) is inside the control limits defined by \(h_1\) and \(h_0\) , no action is taken.

If the control limits \(h_1\) and \(h_0\) are exceeded, the forecasts over the next k days is considered to decide whether a transaction should be made.

If the expected cash balance in the next k days, \(E(CB_k)\) , exceed the control limits defined by \(h_1-\delta _1\) and \(h_0+\delta _0\) , a transaction is made to return the expected cash balance to the target level TB in k days.

No action is taken otherwise.

The innovation introduced by the Stone model is that when a transaction is made, the model returns the expected level of balance to the target level in k days rather than immediately returning the current balance to the target. Furthermore, the actual cash balance is the target plus the net cumulative forecast error. As \(K_t\) is the number of transactions to be made, these rules can be represented mathematically as follows:

Since the cash policy is fixed for a period of k-days, the use of forecasts forces the cash manager to monitor errors for k days after a transaction has occurred. However, the impact of the predictive accuracy of the forecasts on the policy performance was not evaluated. It is expected that a better prediction will lead to better policies, as hypothesized in Gormley and Meade ( 2007 ), and consequently, an evaluation of the impact of predictive accuracy is a mandatory step. Furthermore, efforts to improve predictive accuracy have associated costs that must be compared to the savings obtained to decide if further efforts are worthy. The impact of cash flow forecasts is an ongoing issue in cash management, which we address in Question 1, as we consider it a crucial challenge.

For the selection of the model parameters, no particular procedure was specified by Stone, although some suggestions were made, namely, not to treat them as fixed parameters, but rather adjust them as necessary. Simulation and the practitioner’s judgment were suggested as the best approaches to parameterization. The involvement of cash managers in the process of parameter selection was considered an advantage of this method. An alternative approach to deal with cash flow uncertainty was followed by Hinderer and Waldmann ( 2001 ) who developed a rigorous mathematical framework to include varying environmental factors in the cash manager decision-making process.

In summary, Stone was the first to formally develop a cash management model using forecasts as a key input. Consequently, they assume that cash flows are predictable to some extent. Several studies on daily cash flow prediction (Stone and Wood 1977 ; Stone and Miller 1981 ; Miller and Stone 1985 ; Stone and Miller 1987 ) represent an important contribution to cash management literature. However, the lack of a formal procedure to determine the set of parameters (bounds) of the look-ahead procedure, rather than the mere suggestion of using simulations, has become a serious limitation. No cost function was considered by Stone.

Constantinides and Richard ( 1978 )

Although Neave ( 1970 ) showed that the Eppen and Fama ( 1969 ) model was not optimal, Constantinides and Richard ( 1978 ) proved the existence of optimal simple policies for discounted costs when net cash flow followed a Wiener process. They studied the case of fixed and variable transaction costs and linear holding and penalty costs and used impulse control techniques to find sufficient conditions for an optimal policy defined by parameters \(d \le D \le U \le u\) . Similar to other bound-based models, control actions are only taken whenever the cash level either rises above u or falls below d money units.

Instead of the discrete time framework considered in Eppen and Fama ( 1968 ), Eppen and Fama ( 1969 ), Girgis ( 1968 ), Neave ( 1970 ), Constantinides and Richard assumed that decisions are made continuously over time. Moreover, they assumed that demand over any length of time is generated by a Wiener process, meaning that it is normally distributed with both the mean and standard deviation proportional to the length of time considered. However, they followed the impulse control approach of Bensoussan and Lions ( 1975 ) which was later extended by Richard ( 1977 ). This control technique is based on control actions taken at stochastic stopping times.

The problem formulation was similar to that used in previous studies on cash management. The cash balance at time t is defined as \(x=x(t)\) and it is charged with a holding/penalty cost \(C(x)={\text {max}} \{hx,-px\}\) , with \(h,p>0\) . The transaction cost of changing the cash level from \(x_0\) to \(x_1\) is

with \(k^+, k^-, K^+, K^- >0\) , such that a zero-control action incurs a fixed cost.

In addition, the cumulative demand for cash in interval [ t ,  s ], denoted by D ( t ,  s ), is independent and normally distributed with mean \(E[D(t,s)]=\mu (s-t)\) and variance \({\text {var}}[D(t,s)]=\sigma ^2(s-t)\) , where \(\mu\) and \(\sigma ^2\) are constants. Thus, the cumulative demand is given by

Where, w is a Wiener process in \(\mathbb {R}\) with zero drift and a diffusion coefficient of one. However, the use of diffusion processes to represent the cash holding evolution is not new (Miller and Orr 1966 ).

In this framework, cash managers continuously observe cash levels and perform control actions when necessary. At any stopping time \(\tau _i\) , the applied control \(\phi _i\) , is a random variable that is independent of the future state of the system. An impulse control policy v is represented as a sequence of stopping times and controls, \(v=[\tau _1,\phi _1; \tau _2,\phi _2; \ldots ]\) . If \(x(\tau _i^-)\) denotes the cash level at the stopping time \(\tau _i\) before the control action \(\phi _i\) is applied, and \(x(\tau _i)\) denotes the cash level after the control action, then the state equations of the cash level when policy v is applied are given by

when \(0 \le t < \tau _i\) , with \(x(0^-)=x_0\) , and:

when \(\tau _i \le t < \tau _{i+1}^-\) , with \(i \ge 1\) . Given a policy v and an initial cash balance \(x(0^-)=x_0\) , the expected total cost from time zero to infinity, discounted to time zero, is

where \(\beta\) denotes the discount rate. The final goal is to choose policy \(v^*\) such that \(J_{x_0}(v^*) \le J_{x_0}(v)\) , \(\forall v \in \Omega\) , where \(\Omega\) is the class of all impulse control policies.

Let \(V(x)=J_{x}(v)\) be the expected total cost from time t to infinity discounted to time t and conditional on the cash level \(x(t^-)=x\) . Note also that \(V(x)\ge 0\) since all costs are non-negative. There are only two possible alternatives for cash managers: taking no control action or making the most convenient transaction in terms of future costs. By applying dynamic programming and assuming that the subsequent decisions are also optimal, V ( x ) must satisfy

From this, the following theorem is derived.

Suppose that \(h>\beta k^-\) and \(p>\beta k^+\) hold true, then , an optimal policy exists for the cash management problem. This policy is simple and is given by

Note that the previous theorem implies that, if \(h<\beta k^-\) , it will never be optimal to reduce the cash level as long as \(K^->0\) . Similarly, if \(p<\beta k^+\) , it will never be optimal to increase the cash level, as long as \(K^+>0\) . If both conditions, \(h<\beta k^-\) and \(p<\beta k^+\) hold, the optimal policy prescribes no intervention. In the special case of \(h<\beta k^-\) and \(p>\beta k^+\) , it is optimal to increase the cash level, but not optimal to decrease the cash level. They then deal with an inventory problem in which the control action \(\xi (x)\) is constrained to be non-negative.

This model was later extended to the case of quadratic holding-penalty costs in Baccarin ( 2002 ) and to a multidimensional cash management system and general cost functions in Baccarin ( 2009 ), when cash balances fluctuate as a diffusion process. Premachandra ( 2004 ) also used a diffusion process to propose a more generalized version of the Miller-Orr model which relaxes most of its restrictive assumptions. The Wiener process is also a diffusion process (Itô 1974 ).

In summary, in addition to considering continuous cash flows, the most important contribution of the Constantinides and Richard ( 1978 ) model is Theorem 1 , which provides the necessary conditions to avoid the triviality of the cash policy. Furthermore, it represents the origin of several recent studies (Baccarin 2002 ; Premachandra 2004 ; Baccarin 2009 ) on cash management. However, the strong assumption of modeling cash flows as a diffusion process represents a serious limitation when dealing with empirical non-Gaussian cash flows.

Penttinen ( 1991 )

Penttinen presented myopic and stationary solutions for linear costs using a logistic distribution as the probability density function of random cash demand. Myopic one-period solutions have been suggested to avoid computational difficulties in multi-period applications with a large number of discrete states. In contrast to Constantinides and Richard ( 1978 ), Penttinen chose a discrete time framework because common planning and control practices in most organizations are typically performed in discrete intervals.

His main goal was to analyze the amount of suboptimality in myopic solutions. Thus, the problem formulation considers a stochastic cash balance in which demand \(\delta\) is a random variable. The amount of cash at the beginning of each period n is denoted by x and the cash balance after a control action is taken is denoted by y ( x ). The author considers the transaction costs \(a_n(y-x)\) as

where \(K_n,Q_n,k_n,q_n \ge 0\) . In addition, the retained and penalty costs \(m_n(y)\) charge the cash level y at the beginning of each period according to

Finally, the holding and shortage costs \(l_n(z)\) charge the cash level z at the end of each period. Here, the amount of cash remaining is given by \(z = y - \delta\) and the optimal balance at this point is zero because any positive balance is subject to a holding cost and any negative balance to a shortage cost:

The expected holding and shortage costs are given by the following loss function:

which is the convolution of \(l_n(y-\delta )\) with the probability density function \(\phi _n(\delta )\) . Then, the optimal discounted value of future costs at the beginning of period n is:

where \(\alpha\) is a discount factor, and \(*\) denotes convolution. Note that, when \(\alpha =0\) , the dynamic model is called a myopic model. The optimal policy of this general convex model is given by

where \(t \le T \le U \le u\) defines a transaction rule in the form of a simple policy \(y_n(x)\) such that

Penttinen introduced logistic distribution to ease calculations. In this case, the optimal myopic policy is given by

The reorder point t and disposal point u are derived numerically from T and U from Eqs. ( 42 ) and ( 43 ). To this end, an iterative procedure is presented to compute solutions that are expected to achieve rapid convergence. Different empirical results show the proportionality of policy parameters t , T , U , and u with the shortage cost ratio; thus, the higher the shortage cost, the higher the reorder and disposal points.

In contrast, stationary solutions are based on the assumption that each period possesses the same cost functions, and that cash demand is independent and identically distributed. Then, Penttinen presented additional empirical results on the amount of suboptimality between myopic and stationary solutions in the case of no fixed costs. His results show that the stationary model leads to slightly more cautious ordering policies.

In summary, it is important to highlight the assumption of the logistic distribution within the commonly used family of Gaussian cash flows to better represent empirical cash flows. Penttinen also assumed fixed and linear transaction costs to derive, by dynamic programming, two kinds of optimal policies, namely, myopic (minimizing short-term costs) and stationary (minimizing long-term costs). He considered both a single objective and single bank account in this proposal.

Gormley and Meade ( 2007 )

Gormley and Meade claimed the utility of cash flow forecasts in the management of corporate cash balances and proposed a Dynamic Simple Policy (DSP) to demonstrate that savings can be obtained using cash flow forecasts. They suggested the use of an autoregressive model as a key input for their model. However, gains in the forecast accuracy over the naive model are scant. Gormley and Meade expected that savings from using a non-naive forecasting model would increase if there were more systematic variations in cash flow and, consequently, higher forecast accuracy. If this hypothesis is correct, then the savings produced by a better forecasting model are expected to be significantly higher than those obtained by the naive forecasting model.

In their approach to the corporate cash management problem, Gormley and Meade used an inventory control stochastic model in which cash balances were allowed to move freely between two limits, as shown in Fig. 6 : the lower ( D ) and the upper balance limit ( V ). When the cash balance reaches any of these limits, a cash transfer returns to the corresponding rebalance level ( d ,  v ), as shown in Fig. 6 . Thus, the management of the cash balance over a period T is determined by a set of policy parameters or limits for the instant  t that can be extended \(\tau\) days ahead: \(D_{t+\tau }\) is the lower balance limit at time \(t+\tau\) , \(V_{t+\tau }\) is the upper balance limit at time \(t+\tau\) , \(d_{t+\tau }\) is the lower rebalance level at time \(t+\tau\) , and \(v_{t+\tau }\) is the upper rebalance level at time \(t+\tau\) .

The Dynamic Simple Policy of Gormley-Meade

The transfers for any prediction horizon are determined by

where \(\tilde{O}_{t+\tau -1}\) is the predicted opening balance at time \(t+\tau -1\) , \(\hat{w}_{t+\tau |t}\) is the predicted cash flow for \(t+\tau\) using a model that has been trained up to time t . In this model, \(D_{t+\tau } \le d_{t+\tau } \le v_{t+\tau } \le V_{t+\tau }\) and the following continuity function holds:

The expected cost over horizon T is given by the following objective function:

where the transfer cost function \(\Gamma\) is defined as

The notation used by the expected and transfer cost functions is as follows: h is the holding cost per money unit of a positive cash balance at the end of the day; u is the shortage cost per money unit of a negative cash balance at the end of the day; \(\gamma _{0}^{+}\) is the fixed cost of transfer into account; \(\gamma _{0}^{-}\) is the fixed cost of transfer from account; \(\gamma _{1}^{+}\) is the variable cost of transfer into account; \(\gamma _{1}^{-}\) is the variable cost of transfer from account; \(I_{\tilde{O}_{t+\tau }>0}\) is a boolean variable that equals one if \(\tilde{O}_{t+\tau }>0\) is true, zero otherwise; \(I_{\tilde{O}_{t+\tau }<0}\) is a boolean variable that equals one if \(\tilde{O}_{t+\tau }<0\) is true, zero otherwise.

The authors used genetic algorithms to solve the CMP, that is, to estimate the parameters \(\{D_{t+\tau }, d_{t+\tau }, v_{t+\tau }, V_{t+\tau }\}\) from \(\tau =1, \ldots , T\) . Moreover, because the model accepts forecasts as its main input, a cash flow autoregressive forecasting model was developed. To this end, a Box-Cox transformation (Box and Cox 1964 ) was used to achieve the normality of the real cash flow dataset used in this study.

In summary, Gormley and Meade ( 2007 ) proposed a cash management model that uses forecasts as a key input. Surprisingly, they did not refer to the work by Stone ( 1972 ) on the use of forecasts in cash management. They proposed evolutionary algorithms to derive cash policies within the usual context of fixed and linear transaction costs and a single objective. This solving procedure was recently followed in da Costa Moraes and Nagano ( 2014 ).

Chen and Simchi-Levi ( 2009 )

The concept of K-convexity was first used by Neave ( 1970 ) to show that the Eppen and Fama ( 1969 ) model may not be optimal. When fixed costs exist for both inflows and outflows, Chen and Simchi-Levi ( 2009 ) used the concept of (K,Q)-convexity by Ye and Duenyas ( 2007 ) to characterize the optimal policy in the stochastic cash balance problem. Their approach was closely related to inventory control, in that they used common inventory terminology rather than that usually employed in cash management research. For example, they speak about order and return rather than increase or decrease in cash transactions.

They considered a general cost function with holding and transaction costs. A transaction decision must be made at the beginning of each period. Let x be the cash balance at the beginning of period n before a decision is made and let y be the cash balance after a transaction is made. Transaction cost is computed as follows:

where \(K\ge 0\) , \(Q\ge 0\) , and \(k+q\ge 0\) , assuming that \(k\ge q\) ; that is, the positive variable transaction cost is greater than or equal to the negative variable transaction cost.

In contrast, the holding cost in time period n is described as a general cost function \(l_n(z)\) , which depends on the inventory level at the end of day z which, in turn, depends on the stochastic cash flow \(\xi _n\) . Therefore, the expected holding or penalty cost in period n is given by

In this study, the stochastic cash balance problem is formulated as a dynamic program, where \(C_n(x)\) is the cost-to-go function at the beginning of a period when there are n periods left in the planning horizon, and the initial inventory level is x :

where \(\gamma \in (0,1]\) denotes the discount factor.

They built a process to obtain the optimal policy based on the concept of ( K ,  Q )-convexity (Ye and Duenyas 2007 ) of the recursive function \(C_n(x)\) . A real value function is called ( K ,  Q )-convex for \(K,Q \ge 0\) . If for any \(x_0\) , \(x_1\) with \(x_0 \le x_1\) and \(\lambda \in [0,1]\) , the following condition holds:

We refer the interested reader to Chen and Simchi-Levi ( 2009 ) for further details on the properties of ( K ,  Q )-convex functions and for proof that the cost-to-go function \(C_n(x)\) is a ( K ,  Q )-convex function. However, several additional definitions are required to derive the optimal policy.

where \(t_n \le t'_n \le T_n\) and \(u'_n \le U_n \le u_n\) . Based on the previous definitions and assuming \(K>Q \ge 0\) , it is optimal to set the cash level \(y_n(x)\) after a decision is made according to

In summary, Chen and Simchi-Levi ( 2009 ) followed a sequential decision-making approach using dynamic programming to minimize the total expected costs over the planning horizon. They proposed a model based on bounds, without assuming any particular density function for cash flows, but rather a general one. However, no practical application has been provided to illustrate the model using a real case.

Baccarin ( 2009 )

To the best of our knowledge, quadratic holdings and penalty costs have been considered for the first time in Baccarin ( 2002 ). Furthermore, a general multidimensional approach to the cash management problem was first introduced by Baccarin ( 2009 ) using generalized cost functions and providing theoretical results for two bank accounts. Baccarin considered cash management systems with multiple bank accounts, in which cash balances fluctuate as a homogeneous diffusion process in \(\mathbb {R}^n\) . They formulated the model as an impulse control problem with unbounded cost functions and linear costs.

The optimization problem considers an n -dimensional Wiener cash flow process \(W_t\) that determines the dynamics of cash balances x ( t ) in the absence of any control action using the following Ito stochastic differential equation:

where \(b(x), \sigma (x) \in W^{1,\infty } (\mathbb {R}^n)\) . Then, an impulse control strategy within a continuous time framework is a sequence of control actions \(\xi _i\) at time \(t_i\) to form policy \(V=\{\xi _1,t_1; \ldots \xi _i,t_i; \ldots \}\) with \(t_i \le t_{i+1}\) . Subsequently, given policy V , the controlled process y ( t ) is defined as follows:

where \(\alpha _t = {\text {max}}\{n|t_n \le t\}\) . Holding costs are given by function f ( y ) and transaction costs by function \(C(\xi )\) , which is assumed to be lower semicontinuous and unbounded from above when \(|\xi |\rightarrow \infty\) . These holding and transaction cost functions satisfy the following inequalities:

As a result, each control policy V has an associated cost

where \(\gamma >0\) is the discount rate and \(\chi _{t_i < \infty } = 1\) if \(t_i<\infty\) , and zero otherwise. The problem is then to minimize \(J_x(V)\) over the set A of admissible controls V . The optimal control is obtained by dividing \(\mathbb {R}^n\) into two complementary regions: a continuation set, where the system evolves freely, and an intervention set, where the system is controlled in an optimal manner.

In summary, Baccarin ( 2009 ) provided a sound theoretical framework for cash management systems with multiple bank accounts within a continuous time framework with general cost functions and a single objective, namely, cost. Cash flows are assumed to follow a Wiener process, and the numerical solution to the optimization problem can be obtained by the finite element method, as described in Cortey-Dumont ( 1985 ), Boulbrachene ( 1998 ), which considers a discrete approximation of the continuous framework described above.

Recent contributions: the operation’s research perspective

In this section, we refer to several recent cash management works (after 2000) that deserve a mention because of some interesting characteristics. In this sense, Hinderer and Waldmann ( 2001 ) formally introduced the concept of environmental uncertainty in CMP by providing a rigorous mathematical framework and exploring different cases of cash flow processes. Premachandra ( 2004 ) used a diffusion process as in Baccarin ( 2009 ) to propose a generalized version of the Miller and Orr ( 1966 ) model. Baccarin ( 2002 ) also considered quadratic holding costs for the first time in the cash management literature. Bensoussan et al. ( 2009 ) extended the model by Sethi and Thompson ( 1970 ) by applying a stochastic maximum principle to obtain the optimal cash management policy.

Melo and Bilich ( 2013 ) proposed an Expectancy Balance Model to minimize combined holding and shortage costs in an attempt to deal with uncertainty. This model considers the existence of both deterministic flows, which are known in advance, and stochastic flows, grouped into intervals of occurrence. Recently, da Costa Moraes and Nagano ( 2014 ) proposed the use of genetic algorithms, as in Gormley and Meade ( 2007 ) and particle swarm optimization to solve the CMP using the Miller and Orr ( 1966 ) model. They provide numerical examples using Gaussian cash flows for both solvers within the structure of a single bank account and two alternative investment accounts.

Salas-Molina et al. ( 2018 ) proposed a multi-objective approach to the CMP by considering not only the cost but also the risk of alternative policies using the Miller and Orr ( 1966 ) model and compromise programming (Zeleny 1982 ; Yu 1985 ; Ballestero and Romero 1998 ). They proposed the use of the standard deviation (and upper semi-deviation) of daily costs as a measure of risk. The third goal (stability) was proposed in Salas-Molina et al. ( 2020 ). In Salas-Molina et al. ( 2017 ), the authors showed that forecasting accuracy is highly correlated to cost savings in cash management when using forecasts and the Gormley and Meade ( 2007 ) model. The authors used different cash flow forecasters based on time-series features. A similar approach, based on machine learning was proposed by Moubariki et al. ( 2019 ) and Salas-Molina ( 2019 ), developed a machine-learning approach to fit cash management models to specific datasets.

Herrera-Cáceres and Ibeas ( 2016 ) proposed a model predictive control approach in which a given cash balance function is used as a reference trajectory to be followed by means of the appropriate control actions. In this proposal, cash managers aim to minimize deviations from a reference trajectory instead of minimizing any cost function. In contrast, Schroeder and Kacem ( 2019 ), Schroeder and Kacem ( 2020 ) described online algorithms to deal with interrelated demands for cash flows without making any assumptions about the probability distribution of cash flows. Finally, a formal approach to managing cash with multiple accounts based on the graph theory was proposed by Salas-Molina et al. ( 2021 ).

A multidimensional analysis of the cash management problem

In the following section, we summarize the main cash management models presented in the literature according to the six dimensions introduced in Section 3, as shown in Tables  1 and  2 .

Models. The use of Bound-Based Models (BBM), whose policies are determined by a set of level or bounds, is a common pattern. From the initial inventory approach to the CMP by Baumol ( 1952 ), most models have attempted to derive optimal policies within the framework of some simple policy, typically employing constant cash balance bounds. A slight departure of this framework was considered by Stone ( 1972 ) and Gormley and Meade ( 2007 ) to introduce forecasts as key inputs to a BBM model. A more practical approach was followed by Archer ( 1966 ) to focus on the statistical exploration of data to deal with the lack of synchronization of inflows and outflows. Recently, Baccarin ( 2009 ), Bensoussan et al. ( 2009 ) and Schroeder and Kacem ( 2020 ) proposed models without relying on bounds.

Cash flow process. A wide variety of cash flow processes have been considered in the literature, ranging from the uniform and perfectly known cash flow in Baumol ( 1952 ) and Tobin ( 1956 ), to purely stochastic behavior in Miller and Orr ( 1966 ), Eppen and Fama ( 1969 ), Constantinides and Richard ( 1978 ), Premachandra ( 2004 ), Baccarin ( 2009 ), da Costa Moraes and Nagano ( 2014 ), which usually implies a Gaussian distribution. The selection of any cash flow process implies the assumption of either a continuous time framework (Constantinides and Richard 1978 ; Baccarin 2009 ) or a discrete time framework (Stone 1972 ; Penttinen 1991 ; Gormley and Meade 2007 ). Data sets are hardly used with the exception of Salas-Molina et al. ( 2018 ).

Cost functions. The linear cost assumption is also a common pattern with the exception of Baccarin ( 2002 , 2009 ), that considered more general cost functions. However, there also exist differences in the linear approach. While Baumol ( 1952 ) and Miller and Orr ( 1966 ) considered only fixed costs, Tobin ( 1956 ) and the subsequent works included fixed and variable costs in their models.

Objectives. It is also important to note that all models focus on a single objective, namely, cost, neglecting risk analysis. However, the works by Stone ( 1972 ), Hinderer and Waldmann ( 2001 ), Gormley and Meade ( 2007 ) are remarkable initial attempts to include uncertainty in the analysis of the best policies. The use of forecasts seems to be a sound strategy to reduce uncertainty in the CMP as shown in Salas-Molina et al. ( 2017 ). To handle the inherent uncertainty of cash flows, Salas-Molina et al. ( 2018 ) introduce the concept of risk analysis in a multi-objective approach to the CMP. Finally, Salas-Molina et al. ( 2020 ) extended the multi-objective approach to three different goals: cost, risk, and stability.

Solvers. There are also differences in the techniques used for solving the CMP. However, three solving techniques stand out: analytic solutions as in Baumol ( 1952 ), Tobin ( 1956 ), Miller and Orr ( 1966 ), Constantinides and Richard ( 1978 ), Hinderer and Waldmann ( 2001 ), Schroeder and Kacem ( 2020 ); dynamic programming as in Eppen and Fama ( 1969 ), Daellenbach ( 1971 ), Penttinen ( 1991 ), Chen and Simchi-Levi ( 2009 ); and approximate techniques as in Archer ( 1966 ), Stone ( 1972 ), Gormley and Meade ( 2007 ), da Costa Moraes and Nagano ( 2014 ).

Bank accounts. Although cash management systems with multiple bank accounts are the rule rather than the exception in practice, almost all previous models derive policies for a single bank account and provide no method to extend their results to multiple bank accounts. Only Baccarin ( 2009 ) approached the CMP from a multidimensional perspective to deal with multiple bank accounts. More recently, Salas-Molina et al. ( 2020 ) considered multiple bank accounts in the CMP and Salas-Molina et al. ( 2021 ) proposed a formal analysis of cash management models with multiple bank accounts based on graph theory.

Open research questions in cash management

From the previous review, it can be concluded that all relevant issues regarding cash management have been covered by the aforementioned cash management models. However, our taxonomy allows for the identification of open research questions in cash management, as we discuss next. From Table 1 , we can infer that bound-based models seem to be a common pattern in cash management. However, recent proposals have questioned the use of bounds (Baccarin 2009 ; Herrera-Cáceres and Ibeas 2016 ) and probability distribution assumptions to derive optimal policies (Schroeder and Kacem 2019 , 2020 ). Indeed, the ultimate goal of cash managers is not to find the best set of bounds but the best policy disregarding the required steps to achieve it. The utility of forecasts in cash management have been demonstrated in Gormley and Meade ( 2007 ) and Salas-Molina et al. ( 2017 ). These results must encourage cash managers to rely on time-series forecasting or machine learning techniques to reduce uncertainty in the near future.

In addition to its critical importance for real-world institutions, empirical cash flows are not common in cash management literature, with the exception of Emery ( 1981 ), Gormley and Meade ( 2007 ) and Salas-Molina et al. ( 2017 ), Salas-Molina et al. ( 2018 ). Common assumptions imply Gaussian, independent, and stationary cash flows in the form of a random walk or a diffusion process (Miller and Orr 1966 ; Constantinides and Richard 1978 ; Baccarin 2009 ). However, real-world cash flows may not accommodate such strong assumptions. As a result, the particular statistical properties of cash flows and their ability to predict them are research questions worth addressing.

The assumption of linear cost functions is not as restrictive in cash management as it may appear at first glance. However, considering piece-wise linear cost functions as in Katehakis et al. ( 2016 ) or even non-linear cost functions as in Baccarin ( 2002 , 2009 ) may allow a better representation of real-world cash management problems. A closely related topic is the selection of risk measures when considering not only cost but also the risk of alternative policies as an additional objective in cash management, as suggested by Salas-Molina et al. ( 2018 ). The authors used the standard deviation of daily costs as a measure of risk; however, alternative measures of risk can also be explored (Artzner et al. 1999 ; Szegö 2002 ; Rockafellar and Uryasev 2002 ). Indeed, a comprehensive risk analysis of cash management represents an appealing research area in cash management.

Obtaining a policy that optimizes some objective functions is not straightforward. Beyond the discussion about the required assumptions to apply one technique or another, a rather unexplored issue is the optimality of the solutions provided by each method. While dynamic or linear programming ensure optimality, evolutionary algorithms, or particle swarm optimization they return only approximate solutions. However, there is a lack of supporting technology in the form of software applications for cash management that deserves the attention of the research community. The computing times, robustness of the solutions provided, and deployment costs of alternative methods are also worth exploring. From Table 2 , we observe that only Baccarin ( 2009 ) and Salas-Molina et al. ( 2020 ) approached the cash management problem considering multiple bank accounts. Since the presence of several accounts is very common in practice, cash management models that can handle multiple bank accounts and transactions between them constitute an interesting topic.

It is important to highlight that open research questions do not arise by exploring only one dimension at a time. On the contrary, chances are that new research opportunities derive from a combination of values that received little attention of the research community. As an example, consider an unconstrained model using forecasts obtained from empirical cash flows that aim to minimize a multi-objective cost-risk function with piecewise linear cost functions through linear programming within a cash management system with multiple bank accounts.

The existence of multiple dimensions in CMP implies that the selection of cash management models, cost functions, solvers, and many other factors is a complex task. It seems clear that no cash management model is best for any decision-making context. As a result, the design of methodologies to select the appropriate models to solve CMP is an additional open research question. The set of all relevant operating conditions that are important in the decision-making context can be expressed as a set of parameters (Hernández-Orallo et al. 2013 ) that can ultimately be used to select models according to the preferences of practitioners. Multiple criteria decision-making techniques can help deal with multidimensional problems in finance. An example of the application of these techniques to the context of evaluating clustering algorithms in financial risk analysis can be found in Kou et al. ( 2014 ). More recently, Kou et al. ( 2021a ) proposed the use of a hybrid multicriteria decision-making process in which different models were used to rank available alternatives.

Except for Salas-Molina et al. ( 2017 ) and Salas-Molina et al. ( 2018 ), the use of datasets and the application of forecasting models in cash management are scarce. We argue that time-series prediction models and other machine learning techniques may enhance decision-making in finance. We refer interested readers to recent reference books by Dixon et al. ( 2020 ) and Consoli et al. ( 2021 ), reviews by West and Bhattacharya ( 2016 ) and Henrique et al. ( 2019 ), and applications by Moubariki et al. ( 2019 ), Li et al. ( 2021 ), Kou et al. ( 2021b ) and Manthoulis et al. ( 2021 ).

Finally, we must also point out that the integration of external factors, such as the impact of a financial crisis, in cash management models is also an interesting future line of research. In Section 2, we review the related literature on CMP from economic and financial perspectives. In Section 4, we review the most relevant contributions to CMP from the decision-making perspective. By combining these two approaches, we expect that cash management decision-making models can be enhanced with additional relevant factors. We consider this integration to remain an important open research question in cash management.

Concluding remarks

In this study, we review the research literature relevant to the cash management problem since the first contribution by Baumol ( 1952 ) to the most recent contributions. We use this review to identify several research opportunities in cash management. We propose a new taxonomy based on the main dimensions of the cash management problem: (i)the model deployed, (ii)the type of cash flow process considered, (iii)the particular cost functions used, (iv)the objectives pursued by cash managers, (v)the method used to set the model and solve the problem, and (vi)the number of accounts considered. We use these six important dimensions as a framework to classify the most relevant contributions in cash management. Linking the dimensions with the reviews, we performed a multidimensional analysis of these contributions, which ultimately allowed us to highlight several open research questions in cash management. As a result, topics such as risk analysis in cash management, the utility of forecasts, and the possibility of handling multiple accounts have been identified as new research opportunities. Researchers may extend the number of dimensions, suggest new instances for each dimension, or even link unexplored instances to enrich the analysis of the cash management problem.

Availability of data and materials

not applicable.

Abbreviations

Cash management problem

Automated teller machine

Bound based model

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Acknowledgements

We wish to express our thanks to Universitat Politècnica de València, the Spanish Ministry of Science, CSIC and ICREA Academia for their support.

Research supported by projects:

\(\bullet\) Crowd4SDG (H2020-872944);

\(\bullet\) CI-SUSTAIN (PID 2019-104156GB-I00);

\(\bullet\) TAILOR (H2020-952215);

\(\bullet\) TED2021-131295B-C31;

\(\bullet\) TED2021-130187B-I00;

\(\bullet\) PID2019-105986GB-C21 (funded by MCIN/AEI /10.13039/501100011033 and by the “European Union NextGeneration EU/PRTR”);

\(\bullet\) VALAWAI (funded by the European Commission under Grant 101070930);

\(\bullet\) 2021 SGR 00299;

\(\bullet\) 2021 SGR 00754.

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Salas-Molina, F., Rodríguez-Aguilar, J.A. & Guillen, M. A multidimensional review of the cash management problem. Financ Innov 9 , 67 (2023). https://doi.org/10.1186/s40854-023-00473-7

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ARTICLE REVIEW OF “FINANCIAL MANAGEMENT AND ACCOUNTING IN STATE ISLAMIC RELIGIOUS COUNCILS IN MALAYSIA: A GROUNDED THEORY” BY ABDUL RAHIM ABDUL RAHMAN AND ANDREW GODDARD

Financial management and accounting are pivotal in any organization since the success or failure of the organization depends on how the assets are managed within the organization (Accounting Schools Online, 2012) regardless of its nature whether it is a business or religious entity. However, as argued by the researchers in this sociology research, the study on cultural and social background is needed in order to understand the organization’s management. This is in line with what has been found by Hofstede (1998) that organizations have cultures, even parts of organizations may possibly have different subcultures.

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How restaurants can use data to maximize financial management, performance

A panel at the Fast Casual Executive Summit examined how restaurants can use coaching, technology and other tools to maximize coaching, location collaboration, compliance and more.

Nov. 6, 2024 | by Bradley Cooper — Editor, ATM Marketplace & Food Truck Operator

There are many factors that determine a restaurant's success, especially financial management and location performance. However, measuring these data points and improving upon them can be a major challenge. A panel at the Fast Casual Executive Summit held from Oct. 13 to 15 in Denver, Colorado examined how restaurants can use coaching, technology and other tools to maximize coaching, location collaboration, compliance and more.

Brad Adams, president, CEO and chairman of Qvinci Software, moderated the discussion with panelists John Geyerman, chief strategy officer, WOWorks, Johnny Tellez, COO, Blaze Pizza and Kathleen Wood, founder and CEO of Kathleen Wood Partners LLC.

One primary issue that makes gathering data difficult is manual processes that are slow to implement and take up much of a manager's time.

"Excel and Google Sheets are only going to hold you for so long," Wood said. Instead, she recommended finding a technology program that "will grow with you," so you can reallocate manager's time elsewhere.

However, in order to utilize this data effectively, restaurants need to have it centralized in one place.

Tellerz said once you have that data in one centralized location, you can start drawing lines, and "tell a story from that data."

This can be a challenge for franchisees, since Geyerman said they all have disparate ways of collecting data and some are leery to share financial data due to concerns of the franchisors out to get them.

Instead, franchisors have to find a way to break old patterns and get everyone on board with the same system, even when they are different brands involved.

"Every franchise system we have acquired has had a legacy system way of doing things and we have to break that pattern," Geyerman said.

Scalability is also an issue here, as it can be difficult to find a solution that scales with a restaurant as it grows.

Tellerz reiterated that a truly scalable location is centralized so "one person is handling it," and not 20.

Wood said that many restaurants build systems separately and when they try to bring them together, they realize they don't work together. Instead, restaurants should develop a wider strategic map.

"What is your strategic map for scaling and how does that map with financial and people plans?" Wood said.

When looking at coaching franchisees to meet key performance indicators, the panelists said its very important to ensure you're measuring the right things and giving the right data to franchisees.

For example, Wood said that many managers have to perform 250 tasks during a shift so adding too much data on all those tasks and you have just added more complexity.

Tellerz said the key is to deliver "the right sets of data at the right time together."

As an example, Wood said rather than giving franchisees a list of every KPI, instead focus on the ones that do move the lever financially.

Tellerz agreed, stating that, "You have to tie it down financially. My way to convince franchisee is show them how it helps or hurts their bank account."

Another problem with performance is that many franchisees don't trust franchisors, or they view performance reviews negatively.

Geyerman pointed out franchisees usually always discount what franchisors have to say. He said a better way to approach getting franchisees on board with standards to boost key performance indicators is to show them data comparing them to their peers.

"That tends to give credibility because they can see where they sit in relation to their peers."

Tellerz said Blaze Pizza has ditched the traditional performance review in favor of a virtual coach who can help them implement best practices. This creates a more collaborative feel to the relationship.

"It feels like you are talking to a peer and mentor instead of the police," he said.

This plays directly into an issue of making sure franchisees stay in compliance with goals and standards.

Geyerman said it's going to come down to whether your franchisees trust you or not. If they trust you, they're going to go along with your standards because they believe it's in their best interests.

"You have to circle it back to what it does for me," Tellerz said. He added you shouldn't just measure for measuring's sake.

Wood also argued to the importance of developing good leadership so that brands can "coach people into how to pull those (KPI) levers."

In conclusion, all panelists agreed that the three most important elements to financial success with data is to:

• Centralize data in one place.
• Tell a story.
• Tie it back to how it directly benefits the franchisee.

Bradley Cooper

Bradley Cooper is the editor of ATM Marketplace and Food Truck Operator. He was previously the editor of Digital Signage Today. His background is in information technology, advertising, and writing.

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