Optimal Level of Cash Holdings

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Optimal Level of Cash Holdings

Abstract

This research proposes a framework to estimate the optimum level of cash for a typical firm. This is done by determining the marginal value of cash holdings of a set of portfolios of firms and multiplying this with the relative cash holdings within that portfolio, thus creating a proxy for the Market Value of Cash holdings. The marginal value of the Cash holdings is determined with the model used by Pinkowitz and Williamson (2003), which allocates the market valuation of a company towards different balance sheet items, including Cash. The use of rolling portfolios gives continuous information on the Marginal Value of Cash holdings which should indicate the optimal level of Cash Holdings. We are however unable to find such a point, either due to flaws in our assumptions or dataset or due to unknown factors.

By: F.J.H. Oosterhoff

Thesis Coordinator: H. Gonenc

Institution: Rijksuniversiteit Groningen

Faculty of Economics and Business

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1) Introduction

The academic world of finance has seen an increase of attention for the cash flows and cash balances of companies in the last two decades, closely followed by media attention. The availability of cash and other liquid assets, such as marketable securities, are more and more seen by stakeholders as both an opportunity and as a threat to the future value of a company. Companies however differ largely in the level of cash they keep on hand. Some companies hold large balances, as for example Microsoft who held $49 billion in 2003, Ford $38 billion and General Motors a total of $32 billion, according to Foley, Hartzell, Titman and Twite (2007). But as we have seen in the media and as many scholars have shown, too much cash can provide room for laziness or even induce adverse actions by managers. Lang, Stulz and Walkling (1991) for example find that companies with large cash balances but low growth opportunities invest more than their cash-strapped competitors and they invest in negative NPV projects.

Certainly companies have a need to hold cash for future payments and investments. And since raising cash by going to liquidity suppliers such as banks and stock markets entails transactions costs, a certain level of cash is preferred. But how much? Isn’t it likely too much cash breeds laziness since managers do not feel the need to raise cash by making profits? Or that due to the abundance of cash a company may become careless in picking their projects since they have enough cash to start these projects anyway? Or it may be even worse, that managers are able to start up projects which mostly enhance the status of the manager, not necessarily the value of the company. We therefore ask ourselves: is it possible to determine at what point a company has too much cash and that this abundance of cash will eventually hurt their future value?

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finance. In order to determine the marginal value of a dollar on the balance sheet we will use the valuation tool developed in Fama and French (1998) and used and adapted by many other scholars, such as Pinkowitz and Williamson (2003) and Faulkender and Wang (2006). This model allocates the market assessment of the valuation of a company into its most important balance sheet components. One component is Cash and the value this model places on this variable is seen as the marginal value. As we will later see, most studies found that $1 extra cash results in more or less than $1 extra Market Value, depending on different criteria.

This study will take an approach which builds upon this string of literature. This paper has a criticism on those papers, namely that most research in this field is focused on either the marginal value of the entire sample or on a limited amount of subsets. Most scholars divided their dataset into a few subparts, based on characteristics such as whether the company is likely to face bankruptcy problems. For example Denis and Sibilkov (2004, WP) use this technique and use 6 different determinants of whether a firm is financially constrained, but this still effectively splits their dataset in half on each criteria. Dittmar and Marth-Smith (2007) do this as well, but in this research the dividing criteria is the governance structure of a company. Even though in practice it is safe to assume those subparts can be compared and inferences can be drawn from them, theoretically it isn’t sound to compare these parts, since their differences may stem from quite different sources. In order to determine an optimal relative cash level, continuous information on the market value of a dollar throughout the dataset is required. This paper therefore will take a slightly different approach and compare all companies simultaneously with a build-in step to detect a pattern in the differences between the various companies.

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for a point where the marginal value of a dollar is equal to its cost, which would be the optimum amount, we will look at the total market value of cash holdings. From this an optimum point can also be established.

Before we can look at the total market value of cash holdings it is important to understand what costs and benefits cash balances may have for a company. This influences our assumptions and we therefore need a thorough understanding of what impact different relative cash level may have. Adding a dollar to the balance sheet has costs, such as transaction costs. It can also have benefits, by providing the positive opportunity to quickly act upon new opportunities. In our opinion, one cost is especially important; the Agency Cost of Free Cash Flow. This theory argues companies and their managers may make value-decreasing decisions when they have access to too much cash. When cash is abundantly available, the incentive to raise cash by making profits in order to keep the company running is lowered. So at large relative levels of cash this factor is expected to have a big impact. It is mainly this cost which we expect will eventually diminish the added value of a new dollar to a point where it is no longer beneficial to accumulate more cash. This point where the costs of adding more cash to current balances outweighs the benefits is what this research will try to find.

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Based upon related literature we find it logical an optimum exists and therefore this research will look at the following hypothesis:

H1: An optimum cash balance exists

As far as we can see, current research has not attempted to establish whether an optimum cash level exists. Most research which investigated the marginal value of a dollar divided their dataset into two parts and found significant differences between these subsets. No attempts have been made to determine an optimal cash level or even examine more than 3 subparts of their dataset. We believe this will be a valuable contribution to this field, since the outcomes may give companies and its investors an indication of the impact of accumulating more cash based on current cash levels of a particular company. And investors may be able to place a discount on the value of a particular firm depending on its cash level, given the fact that that cash level will have an influence on future value.

This paper is divided into 7 sections. In the next section, section 2, existing literature will be discussed in order to establish the boundaries of this paper and what related research teaches us. In section 3.1 the model which will be used to determine the marginal value of cash and marketable securities will be explained, in 3.2 the rolling portfolio approach will be discussed and in 3.3 the model to determine the optimum relative cash balance will be established. In section 4 the chosen industry and the dataset will be discussed and section 5 will contain the results of our findings. After a discussion of potential problems in section 6, this paper arrives at its conclusions in section 7.

2) Related Literature

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with the second approach, which takes cash levels as an influence on the future profitability of companies. We will discuss several implications of holding cash and how this may influence the (future) value of a company. A third important factor we will look at is the model used to determine the marginal value of a dollar. The marginal value of a dollar says something about how much an extra dollar on the balance sheet would add to the market valuation of that company. Simply said, if the marginal value of a dollar is below its cost, a company should not accumulate cash, since it has a negative impact on its future value. The model to determine this value is an important base for this study and the literature which established this model will be discussed in Section 2.3.

2.1 Cash levels are a result of day-to-day business

Early academic work focused on the internal workings of a company as a rationale for cash levels. Keynes (1936) described a transaction motive to be able to make payments without experiencing transactions costs. If a company has no cash at all, it will need to raise money for every payment and thus incur transactions costs. It will also be forced to delay payments in some instances and avoiding these costs are good business sense according to this paper. In this study a precautionary motive to be able to fund investments is also described. This can be viewed as a predecessor to the Information Asymmetry Problem, which will be discussed in Section 2.2.3. Academics also looked at inventories and estimated what levels of cash is needed in order to sustain regular business operations. Well known examples in this field are the paper Optimal Cash Balance Levels by Girgis (1968) and work from Baumol, such as The Transaction Demand For Cash: An Inventory Theoretic Approach (Baumol (1952)). Both papers constructed models to determine how much cash on hand was needed to withstand inventory level changes. The renewed interest in the field of cash holding, combined with new insights, has sparked recent research as well. Kim, Mauer and Sherman (1998) find that the cost of external financing is an influence on corporate liquidity holdings. Ozkan and Ozkan (2004) find evidence which indicates a “firms' growth opportunities, cash flows, liquid assets, leverage and bank debt are important in determining cash holdings.”

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2.2 Holding Cash as an influence on (future) profitability

As mentioned in the Introduction, holding cash entails costs and benefits and these are affected by the current cash levels of a company. These costs and benefits, both direct and indirect, can have a major impact on operations and future value. The academic literature on this (opportunity) cost of cash is large and abundant. Discussing all factors in depth is not the focus of this study and would encompass to much for this paper. We will therefore address in our opinion the most influential determinants of the impact of holding cash; transaction costs, proxy effects, information asymmetry costs and agency costs. Among other scholars, the importance of these determinants were mentioned by e.g. Fama and French (1998) and Kim, Mauer and Sherman (1998).

We expect the costs of newly raised cash to behave as depicted in Figure 1. Their characteristics will be discussed in Section 2.2.1 through 2.2.4.

Figure 1 Cost of Cash at Different Cash Levels

2.2.1 Transaction Costs

Transaction Cost is the most straightforward one of the before mentioned costs. Most transaction costs are direct, constant and independent of how much liquidity you request. Examples are interest, dividends or brokerage fees. Transactions costs can however vary with size and both economies and diseconomies of scale exist. One well known economy of scale is the fact that large companies often have credit ratings, something

0% 2% 4% 6% 8% 10%12% 14%16%18%20%

(O

p

por

tunit

y)

Cos

t of

C

ash

Relative Cash Level

Transaction costs Proxy effects

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most smaller companies do not have. Credit ratings eases raising cash through debt and lowers its cost. This and other economies of scale in raising cash is described in Lee, Lochhead, Ritter, and Zhao (1996).

Some transaction costs show diseconomies of scale. A well known example is the under pricing effect in IPOs. For large companies the stock market is the only place to raise cash in large amounts, but initial public offerings often have substantial transaction costs. In an IPO it is difficult for the issuing company and its underwriters to foresee market demand and they therefore set a low price in order to place the full IPO. An example is the IPO of Netscape in 1995. Shares were offered by the underwriter for $28, but demand was very high and prices rose to $75 that day and closed at $58. If Netscape and its advisors had been able to forecast this, they would have been able to raise $30 dollars more per share. Although $30 is an extreme example, under pricing of shares is very common. An overview of literature is provided by Loughran, Ritter and Rydqvist (1994).

These and other forms of transactions costs which entail more than just its initial brokerage fees exist. Avoiding these costs by maintaining a certain cash balance is something a company does in practice, as is for example shown by Opler et al (1999) and Bates, Kahle and Stulz (2006). Although a company can’t avoid transaction costs, time pressure adds significantly to the cost of new liquidities and therefore a certain cash balance is preferred in order to at least avoid high costs due to time pressure.

Closely related to these transaction costs, which is the cost of raising new capital, is the cost of holding cash. For example, if a part of the cash holdings of a company is held in a foreign currency and a change in the exchange rate for that foreign cash holding occurs, it experiences costs or benefits. Many companies hedge against this risk, which will prevent large negative shocks, but this obviously entails costs as well. Evidence consistent with this view is presented by Foley, Hartzell, Titman and Twite (2007) who find that firms which face high repatriation costs of foreign currency hold more cash abroad. In this instance the transaction cost of converting foreign cash has an influence on (foreign) cash holdings and firms with higher repatriation costs will relatively have higher cash holdings.

On average transaction costs are expected to be constant for every dollar raised. This is depicted in Figure 1 as a constant line. Economies and diseconomies of scale may influence this cost, but on average we expect it to be constant.

2.2.2 Proxy effects

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phenomenon that investors (mis)take current conditions for future expectations. As described in e.g. Miller and Modigliani (1961) a change in dividends is assumed by the market to say something about (proxy for) the future profitability of a company, even though this may very well not be the case. A company may therefore feel obliged to maintain previous dividend levels, even though it may be in the best interest of that company to divert those funds towards other uses. A certain level of cash to be able to maintain current payout levels in order not to upset the market and raise its future external financing costs is therefore preferred.

At low relative cash levels these proxy effects are most likely to occur and thus the costs are relatively high. The more cash a company has however, the less likely these proxy effects are likely to occur and thus its expected cost drop. The effect is shown in Figure 1 as an exponentially downward sloping area.

2.2.3 Information Asymmetry Costs

The Information Asymmetry Theory, for which the paper of Myers and Mayluf (1984) is a highly influential one, argues that a company and its liquidity suppliers experience asymmetries in their information levels on companies, projects, acquisitions, etc. At a time when a company may have all the necessary information about a project; its risks, costs and future cash flows, banks and other liquidity suppliers may not have this superior information and are therefore reluctant to supply debt. Equity holders also fear that companies will issue equity at a time when the stock is overpriced and investors will be hesitant to buy this new equity.

This occurs because liquidity suppliers do not know whether they have full information about the risks and future cash flows. They will therefore need to take more pessimistic views on the profitability in order to incorporate the likelihood that the real risks and cash flows are worse than their predictions. These pessimistic expectations translate into higher transaction costs, such as higher interest rates on debt or lower prices for share issuances, then if all information was known to all parties. Newly raised cash will come at a cost and sometimes at such a high cost due to information asymmetry, the cost is so high that the company can’t afford it and has to forgo a positive NPV project (Opler, Pinkowitz, Stulz and Williamson (1999)).

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2.2.4 Agency Costs

There is also a downside to having (too much) cash available. Scholars argue that too much cash on hand is detrimental to a company’s future value in a way which is known as the Agency Cost of Free Cash Flow. A company may use its excess cash to start up negative NPV projects (see e.g. Jensen (1986)) or use it to make value decreasing acquisitions. Harford (1998) for example finds that “cash rich firms are more likely to make acquisitions, that these acquisitions are more likely to be diversifying acquisitions, and that they are more likely to decrease shareholder wealth.” Many studies have been done in the field of agency costs such as Dittmar and Mahrt-Smith (2007), Harford, Mansi and Maxwell (2006) and Pinkowitz, Stulz and Williamson (2006) who all find evidence which is consistent with the Agency Cost Theory: too much cash leads to actions which have an adverse effect on a company’s value. This may either be due to the fact that managers of a firm use that cash to excessively fund projects or because they perceive the discount costs of cash flows to be lower since they don’t need outside financing for their projects. This means the more cash available, the higher the likelihood negative NPV actions will be undertaken. Simply said; the more cash a company has, the higher its Agency Costs.

It is this effect we expect to lower the marginal value of (large) cash holdings. And not only do large cash holdings increase the chance of misbehavior, it increases this chance exponentially. At low levels, hardly any negative NPV actions can be undertaken by managers. The more easy access to capital however, the larger the misbehavior by managers. Some scholars argue against this theory, such as Mikkelson and Partch (2003) who find no evidence firms with low cash holdings perform any better than cash-rich firms. We however follow the literature which does find evidence for Agency Costs and we expect this cost to have a large influence at large relative cash holdings. This is depicted in Figure 1 by an exponentially upward sloping line.

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The literature supporting this model to estimate the marginal value of cash balances is discussed in the next section.

2.3 Determining the marginal value of a dollar

The last decade much research has been done into the valuation of cash balances. Most notably Faulkender, Wang (2006) and Pinkowitz, Williamson (2003) have constructed models to determine the value of a dollar in Cash and Marketable Securities on the balance sheet of a company. They base their models on a framework suggested by Fama and French (1998) who created a model to estimate the value impact of dividends and interest payments. The working of this model is very important for this study and therefore its working are extensively discussed in Section 3.1. In this section we will focus on the different results the scholars find by using this model.

The model to determine the marginal value of a dollar originates from the paper called Taxes, Financing Decisions, and Firm Value by Fama and French (1998). Their model allocates the Market Value of a company into several components, namely Earnings, Assets, Research & Development and Debt. They build this model in order to test the hypothesis that dividends have a negative effect on market value and that debt has a positive influence. This model allows them to estimate the effect on market value if one of those components changes. In contrast with their predictions they find dividends have a positive effect and debt a negative effect on market value. They infer that changes in these components have a substantial informational value which is large enough to reverse the hypothesized effects. In a way, this is related to the previous mentioned cost in Section 2.2.2 of Proxy Effects, stating that changes in balances and cash flows is conveyed by investors to have informational value on the future profitability of a company.

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A slightly different approach is taken by Faulkender, Wang (2006) who modify their version to compensate for time-varying risk factors by using the return of the stock as the basis. By scaling this to a benchmark stock return, instead of Assets as the two previously mentioned articles do, they believe their model is an improvement. All the used components are the same and therefore their results can be interpreted in the same way. They come to similar conclusions as Pinkowitz and Williamson (2003) and find that “larger cash holdings, higher leverage, better access to capital markets” and the choice of dividends over stock repurchases have a negative influence on the marginal value of a dollar on the balance sheet. They find marginal values ranging from $0.39 to $1.19.

Most scholars however use the model proposed by Pinkowitz and Williamson (2003), as for example by Dittmar and Marth-Smith (2007) and Denis and Sibilkov (2004). The first use it to determine the value of a dollar on the balance sheet under different corporate governance regimes and find poorly governed firms have their cash balances valued at $0.42 to $0.88 per dollar, half of well governed firms. Denis and Sibilkov (2004) use the model to determine the impact of financial distress such as the possibility of bankruptcy on the size and value of cash holdings and find that “cash holdings are more valuable for financially constrained firms than for unconstrained firms.”

Tests on the validity of the model itself are done as well, as for example by Pinkowitz, Stulz and Williamson (2006) who test the relationship between the market value of a company and its cash holdings, depending on the investor protection of the country the company resides in. They expect a lower market valuation of cash holdings since Agency Costs of Free Cash Flow are more likely in countries with less investor protection. They however find a less significant relationship between firm market value and cash holdings, which indicates the results from this model are influenced by many factors.

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policy have their highest impact and where they are reversed or outweighed by other factors. This research will propose a framework which may be used in the future to investigate these effects. In this research we will focus on incorporating all factors, but future studies may be able to use this framework and build upon it by testing the influence of these factors. How this is done will be explained in the following Methodology Section.

3) Empirical Methodology

The main aim of this research is to determine whether investors show a preference for a certain cash level and if a specific point exists where all cost en benefits have their most positive influence. This will be done by determining the marginal values of cash holdings of 247 companies placed in rolling portfolios of 50 companies each. This marginal value will be offset against their relative level of cash and marketable securities which results in a proxy for the Market Value of a particular cash holding. How this all works is explained in the following sections. In 3.1 we will explain the model which is used to determine the marginal value, in 3.2 the rolling portfolio approach will be discussed and lastly in section 3.3 the model to determine the optimum relative cash balance will be presented.

3.1 Empirical model

The marginal value of the cash balances will be determined with the valuation tool used by Pinkowitz and Williamson (2003). As mentioned in the Introduction and Related Literature, this model allocates the market assessment of the valuation of a company into its most important balance sheet components and their respective changes, namely Earnings, Net Assets, Research & Development, Interest payments, Dividends and Cash & Marketable Securities. Net Assets are Total Assets minus Cash and Marketable securities, effectively splitting Assets into two components. This is done in order to examine Cash separately from the other assets. These six items are examined in three ways; the base is the expectation of future value, which is the base of any valuation, according to the perfect market view. The model however also incorporates deviations from expectations by including current levels and the growth trends of the firm by incorporating deviations from last period to current. These three approaches are discussed in detail in the following sections.

3.1.1 Base of Model: Future Value Expectations

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way to measure investors’ expectations, the reported levels of the companies of 2 years into the future are used in this model. According to the evidence presented by Fama (1990) the market can predict up to two years ahead and therefore this timeframe will be used. The future balances will proxy for expectations of the future value and works in the following way: the model gives the investor the possibility of perfect foresight, as if the investor can see perfectly into the future. This is assumed in a perfect market, but since in practice investors usually aren’t that well in predicting the future, the model gives the investors the possibility to decide how much of this perfect foresight is used. In a perfect market the current market value of a company would be entirely explained by future reported items, but as we know and will see this is not the case in practice. But expectations of future levels are very important and are incorporated into the model in this way.

3.1.2 Deviations from Expectations of Reported Levels

As said, we do not live in a perfect world with a perfect market and perfect foresight and this means in practice investors usually don’t have all the necessary information concerning a company. Upon the release of information about the company, in this case the reporting of cash flows and balance sheet items, the investors usually change their valuation of a company, since very often the reported balances and earnings deviate from their expectations. We therefore also need to include the current balances, since in practice the market valuation is based upon the differences from the expected balances. Or said differently, the publication of current levels will have an influence on the valuation and this needs to be included into the model.

3.1.3 Trend Expectations

The change in the levels of the balance sheet compared to the previous period is included as well, since in practice investors expect a company to behave according to a trend. Investors usually expect a company to continue to perform as they did in the previous periods. A certain continuity in the cash flows and balances of a company is expected, but often this is not the case. So the deviation from a previous period is included in the model, since investors expect a trend and if this trend is broken, this affects the valuation of a company.

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i,t

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Description Variable DataStream

Code DataStream Description Market Valuation V i,t - A i,t WC08001 + WC18199 - WC02999

Market Capitalization + Net Debt - Assets

Earnings E i,t WC01551

Net Income Before extraordinary items and preferred dividends

Future ΔE i,t-2 Past ΔE i,t+2

Net Assets ΔNA i,t-2 WC02999 - WC02001

Assets - Cash & Marketable Securities

Future ΔNA i,t+2

R & D RD i,t WC01201

Future ΔRDi,t-2 Research & Development

Past ΔRD i,t+2

Interest I i,t WC01251

Interest

Future ΔI i,t-2

Past ΔI i,t+2

Dividends D i,t WC18192

Dividends

Future ΔD i,t-2

Past ΔD i,t+2

Future MV ΔV i,t+2 (WC08001 + WC18199 - WC02999)t+1 - (WC08001 + WC18199 - WC02999)

Future Market Value - Current Market Value

Cash C i,t WC02001

Cash & Marketable Securities

Future ΔC i,t+2

Table 1 Variables of the Marginal Values Allocation Model and its DataStream codes

For more information on this model, see among others Fama, French (1998), Pinkowitz and Williamson (2003), Faulkender and Wang (2006).

3.2 Rolling portfolios

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sections. This research takes this a step further and investigates whether a relationship exists between the relative level of cash balances and its valuation. Ideally the marginal value for each company should be calculated. Because this will most likely give too much weight to individual characteristics, portfolios are preferred. In this research so-called rolling portfolios will be constructed. These rolling portfolios were first used by Jaffe (1974) and Mandelker (1974) and since then used extensively.

Of the 247 companies used portfolios of 50 companies are constructed. The portfolios are based on the relative level of Cash and Marketable Securities to the Assets of the companies, starting with the companies with the lowest levels. The first portfolio contains company 1 through 50 with the smallest relative cash levels, the second portfolio company 2 - 51, the third 3 – 52 and so on and so on, until portfolio 198, which will contain company 198 through 247. This last portfolio contains the 50 companies with the largest relative cash balances.

Using this method has several theoretical advantages. First of all, it solves any statistical issues that may come up with the comparability of the portfolios. Even though we can safely assume that the two portfolios used in other researches can be compared if the entire sample is split in two, theoretically there is no way to proof this. It’s highly unlikely, but significant differences may exist between the companies in the lower and upper half, which would refute any inferences made based on the examination of their differences.

Second, it also gives less weight to outliers and will thus smooth any misguiding information they provide. Even though outliers normally should be included, we are interested in the optimum level of the entire market and outliers often have a large but non-informational impact. With the use of rolling portfolios this problem is solved, since outliers are used less frequently in the determination of the marginal values. While companies with an average level of cash will be used in 50 different portfolios, companies which have a very distinct ratio will only be used in a few portfolios, depending on how far they are from the edge of the dataset. For example the company which is ranked 20th will only be used in 20 portfolios, this in contrast with a typical company in the middle of the dataset, which will be used in 50 different portfolios.

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change, which would be the case if the portfolios were based on a non-chancing characteristic such as an alphabetical order or the year of foundation of a company. The fact that the basis of the portfolio is a variable means observations of only 1 year can be included, since other years are not applicable for that particular portfolio. This was for example proven by Mitchell and Stafford (2000) who find their results change significantly when they investigate their constructed portfolios on different base years. For our research this would mean that if more years are to be included, the portfolios would have to be based on the cash level for that year. This in turn would mean that observations in several years from one company would wind up in different portfolios. Effectively that would be the same as adding more companies to the dataset and we feel our number of observations is large enough to have confidence in our results.

Fama and French (1998) find another statistical problem with rolling portfolios which however is not applicable to this research. The problem they mention is that the number of firms changes through different time periods, which is partly a survivorship bias problem. This however is not applicable for this research, because as mentioned just above, this research focuses on one year, a natural outcome of using the rolling portfolio approach. The number of firms thus doesn’t change throughout our portfolios and this problem doesn’t play a role here.

The formula developed in 3.1 will be applied to all 198 portfolios. Every portfolio of 50 companies will have its own marginal value of a dollar of cash balances and this will be used for further investigation, explained in the following section.

3.3 Hyperbolic Regression

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marginal value, Figure 3 shows an increasing negative relationship between relative Cash Levels and Marginal Value. The levels of Market Value displayed in Figure 2 and 3 have no real economic meaning, since the level of Cash is scaled to Assets. If this hadn’t been the case, we would find real Market Value of Cash Holdings. In our approach the term ‘Market Value of Cash’ actually proxies for Market Value, it isn’t an indication of real value, only an indication of the slope of real Market Value.

Figure 2 Expectation of Market Value of Cash – Diminishing effects of benefits

Figure 3 Expectation of Market Value of Cash – Increasing effects of costs

A different representation of the expected levels and values is displayed in Appendix 3. For the formula to represent the proxy for Market Value of Cash expect:

0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 10 Ma rgina l Valu e of C ash

Ma

rk

et

V

alue of C

ash

Portfolio number

Level of liquid assets Marginal value Market Value of Cash

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 10 Ma rgina l Valu e of C ash M arket Valu e of C ash Portfolio number

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Y = c

1

+ ( x – c

2

)

β

The variables are explained in Table 2.

Y Regression Line

c1 Constant 1

x Relative Cash level

c2 Constant 2

β

Exponential coefficient

Table 2 Variables of the Hyperbolic Regression Estimate

We are interested in finding the optimum point and thus optimum relative Cash Level. At point ( c1 , c2 ) the

theoretical optimum is found. c2 represents the value where the optimum cash level is attained, c1 represents

the theoretical height of the total marginal value. How this line is formula is established is displayed in Appendix 5.

In order to statistically investigate this formula, it is transformed into its logarithmic counterpart

log (Y) = a + β log ( x – b )

which can be estimated with most statistical packages.

3.4 Robustness Test

Determining the optimal relative Cash Level in this way is new and its results may be refuted by approaching the dataset differently. We will test the strength of our results by applying the same methods to a different set of portfolios, in this instance containing 150 companies each. This gives us 98 data points, a number substantially lower than the 198 points used in the 50 Company Portfolio approach. We however have our doubts about the statistical validity of using 50 companies per portfolio and want to see whether using 150 companies supplies different results.

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4) Data and Summary Statistics

For this research industrial American companies listed on the NYSE are used, the data comes from DataStream. 2003 is taken as a base year, data from 2001 is used as trend information and data reported for 2005 proxies for future expectations. For each firm 8 items were used, its DataStream codes and descriptions can be found in section 3.1; Table 1. This industry is chosen since it contains a large number of firms, namely 321, and all information is publicly available. We choose one industry, so we can expect companies will experience similar future prospects. A large part of the valuation of a company is based on future prospects and each industry has its own outlook, so containing more industries would influence our results in a way we can’t control for. We assume all companies within one industry face similar prospects so that the market valuation of the different companies isn’t influenced by very different future growth prospects. Even though it is most likely not the actual case, in this way we implicitly assume all companies have the same growth perspectives and any differences in Market Valuation can be attributed to differences in the reported items. Another reason to pick companies from only one industry is given by the research of Damodaran (1997) which shows that industries have substantial differences in the level of cash and marketable securities from each other, in his opinion due to different demands in investment and free cash needs each industry faces. Chudson (1945) also already reported systematic differences in cash balances between industries, even though he finds evidence profitability also has a significant influence on differences in cash levels. Including several industry groupings would thus contaminate our data with extra uncontrollable factors and therefore we investigate companies from only one industry grouping.

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Companies: 321

Too few years 49

V

i,t

- A

i,t 0,307 0,087 5,034 -1,015 0,829 247

Earnings

i,t+2

i,t , which

tells us what the Marginal Value of a dollar on the balance sheet is. In our total sample the Marginal Value of 1 dollar is estimated at $0.96 with one standard deviation of $0.42. This is in line with other studies, which as mentioned in the Introduction and Related Literature have values of around $1, with varying values based upon the way they look at companies and its balances.

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Description Variable Coefficient Std. Error Probability Significant

Constant C 0,155 0,172 0,367

Earnings

i,t+2

-9,275 4,208 0,029 **

Dividends

D

i,t

6,851 2,097 0,001 *** Future

ΔD

i,t-2

-1,462 2,591 0,573 Past

ΔD

i,t+2

4,249 1,754 0,016 ** Future MV

ΔV

i,t+2

-0,275 0,066 0,000 *** Cash

C

i,t

0,959 0,420 0,024 ** Future

ΔC

i,t+2

-0,685 0,487 0,161 R2 0,582 F-statistic 18,749

Adjusted R2 0,551 Prob. (F-statistic) 0,000 Table 5 Regression Estimate of Market Value Model

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Figure 5 Relative Cash Levels of Portfolios – 50 Company Portfolios

In Figure 6 the Marginal Value of each portfolio is displayed. The first 50 portfolios show a pattern which at first sight looks more than irregular and out of line with the rest of the sample. We reexamined our dataset to see whether any anomalies could be found which explains this pattern, but we didn’t find any. We therefore assume the outcomes are correct.

Figure 6 Marginal Value of 50 Company Portfolios

The values shown in Figure 6 appear to be in contradiction with our results displayed in Table 6, where it states that the Marginal Value of Cash is around $0.96. Figure 4 shows Marginal Values of as high as $25 and as low as

0,000 0,050 0,100 0,150 0,200 0,250 0,300 1 9 ₁₇ ₂₅ ₃₃ ₄₁ ₄₉ ₅₇ ₆₅ ₇₃ ₈₁ ₈₉ ₉₇ 10 5 11 3 12 1 12 9 13 7 14 5 15 3 16 1 16 9 17 7 18 5 19 3

Cash Level - 50 Company Portfolios

-30,000 -20,000 -10,000 0,000 10,000 20,000 30,000 1 ₁₁ ₂₁ ₃₁ ₄₁ ₅₁ ₆₁ ₇₁ ₈₁ ₉₁ 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 Ma rgina l Valu e of C ash H old ing Portfolio Number

Marginal Value of 50 Company Portfolios

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-$25 for the Market Value of one dollar. This is highly unlikely and we therefore need to question the statistical validity of using 50 companies in a portfolio. We assume these outcomes are due to the fact that 50 companies in each portfolio is not enough to give accurate answers. As mentioned in the Methodology section we will also test our model on a new set of portfolios, in this instance containing 150 companies. The extremes shown by the first 50 portfolios of 50 companies disappear when portfolios of 150 companies are used. This is displayed in Figure 7. As is apparent in the 50 companies-portfolio case the marginal value of cash seems to be upward sloping, another indication our assumptions are incorrect or not present in this dataset.

Figure 7 Marginal Value of 150 Company Portfolios

5.2 Hyperbolic Regression Model

5.2.1 Optimum cash level for Portfolios consisting of 50 companies

Now that we have gathered all the relevant information, we can turn our attention to the Hyperbolic Regression Model. This will tell us whether in the eyes of the market an optimal relative level of Cash & Marketable securities exists. In Table 6 the outcomes of the regression estimates for the hyperbolic model is displayed. The low (Adjusted) R2 draws immediate attention. Only 3% of the data points is explained with this model and thus the regression line is a very poor fit. No conclusions with statistical significance can be based upon these outcomes. Figure 6 and 7 already hinted at the possibility and this regression output shows for this dataset the optimal relative Cash balances and its total Market Value can’t be estimated.

-1,500 -1,000 -0,500 0,000 0,500 1,000 1,500 2,000 2,500 1 6 ₁₁ ₁₆ ₂₁ ₂₆ ₃₁ ₃₆ ₄₁ ₄₆ ₅₁ ₅₆ ₆₁ ₆₆ ₇₁ ₇₆ ₈₁ ₈₆ ₉₁ ₉₆ Ma rgina l Valu e of C ash Ho lding Portfolio Number

Marginal Value of 150 Company Portfolios

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Variable Coefficient Std. Error Prob. Significant Constant -2,784 0,586 0,000 ***

Log(PF50+0)

0,260 0,130 0,049 **

R2 0,037

Adjusted R2 0,028

Table 6 Hyperbolic Regression Model Output: 50 Company Portfolios

Plotting the Market Value of the cash balances gives the same indication. The Market Value is displayed in Figure 7 and this plot confirms our previous result no significant pattern can be detected. As hypothesized, a downward sloping Market Value line was expected and this does not seem to be the case.

Figure 8 Proxy for Market Value of Cash Holdings

Since the outcomes are not what we expected, we look at the 198 separate regression estimates to try and detect whether the problem may originate from there. Since we see unexpected and irregular outcomes in the previous part, we check the statistical validity of our 198 regression lines. Of all the portfolios we list its Adjusted R2 to try and detect any anomalies. The results are displayed in Table 7. The Mean and Median are comparable to the R2 of the regression estimate, but large extremes are present.

Mean Median Maximum Minimum Observations Adjusted R2 0,551 0,574 0,891 0,226 198 Table 7 Descriptive Statistics of Adjusted R2

-1,500 -1,000 -0,500 0,000 0,500 1,000 1,500 1 ₁₀ ₁₉ ₂₈ ₃₇ ₄₆ ₅₅ ₆₄ ₇₃ ₈₂ ₉₁ 10 0 10 9 11 8 12 7 13 6 14 5 15 4 16 3 17 2 18 1 19 0 Proxy for Ma rket Valu e of C ash Portfolio Number

Market Value of Cash

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We also plot all the Adjusted R2 to see if any pattern is apparent. This is displayed in Figure 9. A pattern is clearly visible; the portfolios 50 through 105 show a substantially lower R2. This corresponds to companies with relative cash levels of 2.7% up to 6.5%. The plot of R2 should not show a pattern, it should show a normal dispersion around its mean of 55.1% which clearly isn’t the case. This is most likely due to unknown external factors, such as for example differing regulation or transaction costs for companies who have more than 6.5%. As mentioned, it may also be an anomaly in our dataset, but since we couldn’t find one, we suspects other influences. Finding this influence however falls outside of the scope of this research and may be investigated by future studies.

Figure 9 Development of Adjusted R2 of 198 Regression Estimates

5.2.2 Optimum cash level for Portfolios consisting of 150 companies

The statistical validity of using 50 companies per portfolio is questionable. We therefore also use the approach of portfolios consisting of 150 companies. This seems to solve some of the irregularities experienced with the 50 Company approach and we will repeat our approach for this dataset. In Table 8 the regression estimate for the 150 company portfolio is displayed. R2 is substantially higher which indicates a better fit.

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Variable Coefficient Std. Error Prob. Significant

Constant -2,878 0,497 0,000 ***

Log(PF150-0.8463203533) -0,640 0,145 0,000 ***

R2 0,283

Adjusted R2 0,269

Table 8 Hyperbolic Regression Model Output: 150 Company Portfolios

Figure 8 however shows no declining Market Value of Cash Balances can be detected, as was hypothesized. If anything, Figure 8 and Figure 9 suggests that the Marginal and Market Value of Cash holdings increase if a company holds relatively more Cash. This is in contradiction with existing theory, especially the Agency Cost Theory, which says that after a certain point, more cash will have a negative impact on the market value of a company. Adding more cash should decrease the expected future market value since $1 on the balance sheet will not result in more than $1 in Market Value. All other Figures and Tables concerning the 150 Company Portfolio approach is placed in Appendix 3.

Figure 10 Proxy for Market Value of Cash Holdings – 150 Companies

6) Discussion

The outcomes shown in Section Results are substantially different from our expectations. Our assumptions may be flawed and/or it may be caused by several unknown or unincorporated effects. Since our assumptions were based on relevant theory, we have a short look at several differing factors which may influence our results. Relevant theory has indicated many factors may have an influence on the Market Value of Cash Holdings.

-0,100 -0,050 0,000 0,050 0,100 0,150 0,200 0,250 1 6 ₁₁ ₁₆ ₂₁ ₂₆ ₃₁ ₃6 ₄₁ ₄₆ ₅₁ ₅₆ ₆₁ ₆₆ ₇₁ ₇₆ ₈₁ ₈₆ ₉₁ ₉₆ Proxy for Ma rket Valu e of C ash Portfolio Number

Market Value of Cash - 150 Co

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Denis and Sibilkov (2007) find that whether a firm is financially constrained or not has a significant influence on the marginal value of cash balances. This is caused by the fact that financially constrained firms face higher transactions costs. Financially constrained means a firm has a high likelihood of defaulting on its payments since it is in or near bankruptcy. The possibility of bankruptcy will raise the price of new liquidities since the liquidity suppliers will require compensation of this bankruptcy cost. In line with this Kim, Mauer, and Sherman (1998) and Harford (1999) find that financially constrained firms hold more cash and that these holdings have a higher marginal value. The fact that firms have relatively high cash holdings and that these holdings have a high marginal value is caused by their financial outlook. It may be the case that if the used sample is corrected for whether a firm is constrained or not, the marginal value of large cash holdings is lower than the results show.

Pinkowitz and Williamson (2003) find other factors which may explain the high marginal value of large relative cash holdings. Besides the fact whether firms are in financial distress (financially constrained), they find the firms’ growth options, the volatility of their investment opportunities and to a lesser extent the occurrence of stockholder-bondholder conflicts have a significant impact on the marginal value of cash holdings. Even though our dataset consists of companies within one industry and one year, every company will be differing on these characteristics and compensating for this may improve our results.

Many other influences may exist, such as research by Harford, Mansi and Maxwell (2006) who find evidence firms “with high antitakeover provisions (weak shareholder rights) have smaller cash reserves” or evidence from Harford, Mikkelson and Partch (2003) who find evidence firms with large cash balances are better off during a downturn, since they are able to invest more and that this improves performance. The years 2001 – 2005 can be viewed as a period experiencing downturn and investors have taken into account this positive effects for firms who have large cash balances. Many more factors may exist, but as said in the introduction, the intention of this paper is to establish a framework to estimate optimal cash holdings. It may be up to other scholars to use this framework and investigate whether these effects have a significant influence.

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means the company’s market value will rise due to continued profitability and that at the same time their cash holdings increase due to large positive cash flows. This contradicts our assumption firms with large cash holdings are relatively valued lower than firms with small cash holdings, since in this theory large cash holdings correlate with profitability and thus positive market valuation.

7) Conclusion

This research proposes a framework to estimate the optimum level of cash for a typical firm. This is done by determining the marginal value of cash holdings of a set of portfolios of firms with a typical relative cash balance. The marginal value of the cash holdings is determined with the model used by e.g. Fama and French (1998) and Pinkowitz and Williamson (2003) which allocates the market valuation of a company towards different balance sheet items, including Cash. Out of a dataset of 247 companies rolling portfolios consisting of 50 companies each are constructed. Portfolio 1 contains company 1-50, Portfolio 2 the companies 2-51 and so on, thus constructing a rolling portfolio model.

Based upon existing literature is it hypothesized that after a certain relative cash level the total Market Value of Cash holdings drop. Holding cash entails benefits such as preventing transaction costs and the occurrence of Asymmetry of Information regarding profitability between a company and its liquidity suppliers. At a certain point however the benefits of holding more cash to prevent these costs is outweighed by the negative effects of increasing costs. Such an increasing cost is most notably the Agency Cost of Free Cash Flow which says too much cash gives leeway for the managers to use that cash for negative NPV projects such as value-decreasing acquisitions. More cash thus gives managers the room for actions which are detrimental to the future value of a company and thus accumulating more cash is something investors do not want.

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Appendices

Appendix 1 List of Tables and Figures

Name In section Description Page

Table 1 3.1.3 Variables of the Marginal Values Allocation Model and its DataStream codes Table 2 3.3 Variables of the Hyperbolic Regression Estimate

Table 3 4 Total Companies Used

Table 4 4 Descriptive Statistics of Dataset

Table 5 5.1 Regression Estimate of Market Value Model

Table 6 5.2.1 Hyperbolic Regression Model Output: 50 Company Portfolios Table 7 5.2.1 Descriptive Statistics of Adjusted R2

Table 8 5.2.2 Hyperbolic Regression Model Output: 150 Company Portfolios Table 9 App.2 Correlation Matrix of Variables

Table 10 App.4 Descriptive Statistics of Adjusted R2 : 150 Company Portfolio Figure 1 2.2 Influences of Costs of Cash at various Cash Levels

Figure 2 3.3 Expectation of Market Value of Cash – Diminishing effects of benefits Figure 3 3.3 Expectation of Market Value of Cash – Increasing effects of costs Figure 4 4 Distribution of companies used

Figure 5 5.1 Relative Cash Levels of Portfolios – 50 Company Portfolios Figure 6 5.1 Marginal Value of Portfolios: 150 Companies

Figure 7 5.1 Marginal Value of 150 Company Portfolios Figure 8 5.2.1 Proxy for Market Value of Cash Holdings

Figure 9 5.2.1 Development of Adjusted R2 of 198 Regression Estimates Figure 10 5.2.2 Proxy for Market Value of Cash Holdings – 150 Companies

Figure 11 App.3 Alternative view of Expectation of Market Value of Cash – Diminishing effects of benefits Figure 12 App.3 Alternative view of Expectation of Market Value of Cash – Increasing effects of costs Figure 13 App.4 Relative Cash Levels of Portfolios: 150 Companies

Figure 14 App.4 Marginal Value: 150 Company Portfolio

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Appendix 2 Correlation Matrix of Variables

V

i,t

i t+2

ΔV

i t+2

C

i t

Earnings E i,t 0,333

Future ΔE i,t-2 0,123 0,219

Past ΔE i,t+2 0,175 -0,210 0,041

Net Assets ΔNA i,t-2 0,148 0,327 0,155 -0,230

Future ΔNA i,t+2 0,241 0,167 0,084 0,205 0,175

R & D RD i,t 0,175 0,162 0,001 0,043 0,036 -0,087

Future ΔRDi,t-2 0,000 -0,013 -0,062 -0,083 0,148 0,002 0,021

Past ΔRD i,t+2 0,072 0,025 -0,027 0,061 0,054 0,196 0,053 -0,065

Interest I i,t -0,076 0,709 0,018 0,009 -0,016 -0,030 0,182 -0,091 0,000

Future ΔI i,t-2 -0,053 0,740 0,004 -0,006 0,053 -0,032 0,201 -0,086 -0,002 0,992

Past ΔI i,t+2 0,077 0,602 -0,097 -0,069 0,302 0,523 0,100 -0,036 0,161 0,535 0,568

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Appendix 3 Alternative Representation of Expected Hyperbolic Line

Figure 11 Alternative view of Expectation of Market Value of Cash – Diminishing effects of benefits

Figure 12 Alternative view of Expectation of Market Value of Cash – Increasing effects of costs 0 2 4 6 8 10 12 14 16 18 20 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1 2 3 4 5 6 7 8 9 10

Cash

level

in

per

catage

s

Ma

rg

inal

V

alue of cash

Portfolio number

Marginal value Level of liquid assets Market Value of Cash

0 2 4 6 8 10 12 14 16 18 20 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 0 2 4 6 8 10 12 14 16 18 Ma rgina l Valu e of C ash Ma rket Valu e of C ash Portfolio number

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Appendix 4 Figures and Tables for Portfolios consisting of 150 companies

Figure 13 Relative Cash Levels of Portfolios: 150 Companies

Figure 14 Marginal Value: 150 Company Portfolios

Mean Median Maximum Minimum Observations Adjusted R2 0,451 0,485 0,533 0,356 98 Table 10 Descriptive Statistics of Adjusted R2 : 150 Company Portfolio

0,000 0,020 0,040 0,060 0,080 0,100 0,120 0,140 0,160 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

Cash Level: 150 Company Portfolio

-1,500 -1,000 -0,500 0,000 0,500 1,000 1,500 2,000 2,500 1 6 ₁₁ ₁₆ ₂₁ ₂₆ ₃₁ ₃₆ ₄₁ ₄₆ ₅₁ ₅₆ ₆₁ ₆₆ ₇₁ ₇₆ ₈₁ ₈₆ ₉₁ ₉₆ Ma rg inal Valu e of C ash Ho lding Portfolio Number

Marginal Value of 150 Company Portfolios

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Figure 15 Development of Adjusted R2 – 150 Company Portfolios 0,000 0,100 0,200 0,300 0,400 0,500 0,600 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 R 2 Portfolio Number

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Optimal Level of Cash Holdings