Fair market value of assets as replacement costs of capital in Tobin’s Q

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Fair Market Value of Assets as Replacement Costs of Capital in Tobin’s Q

Wouter Lakeman

July 2017

Amsterdam Business School University of Amsterdam

Thesis MSc. Finance

Study track Corporate Finance Supervisor: Dr Tomislav Ladika

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Abstract: This paper proposes a new approach to clearing measurement error from Tobin’s Q.

Since the original theoretical composition of this ratio by Tobin in 1968, there has been a discussion on how to accurately measure Tobin’s Q in practice. This paper contributes to this discussion by proposing to include the fair market value of a firm’s property, plant and equipment, instead of the frequently used book value, as replacement cost of capital. This paper proposes and tests the idea that this will lead to a more appropriate measure of a firm’s Tobin’s Q. Using a sample from 131 U.S. oil and gas exploring and producing firms for a period from 2005 to 2016, this paper empirically tests if the new Q-measure provides a better explanation of the deviation in investment. This is done by assessing the investment-Q relation and is tested by a linear regression analysis with corporate investment as dependent variable and comparable measures for Q as independent variables. There was no evidence found that the fair market value provides a better estimator than the book value as replacement cost of capital in Tobin’s Q measure throughout.

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Statement of originality

This document is written by Wouter Lakeman who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Acknowledgements

First and foremost, I would like to thank Dr Tomislav Ladika for his interesting courses in the MSc. program and supervising my Master’s Thesis. Your general information and comments were very useful in gaining insights into the theoretical models, but also in obtaining practical skills. Furthermore, I would like to thank my family for supporting me throughout my studies and for their feedback on early versions of this thesis.

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1. Introduction

Tobin’s Q (henceforth, Q) plays an important role in both the economic and finance literature for an extensive amount of time. According to Erickson & Whited (2012) it has actually become unarguably the most used variable in the corporate finance literature. However, the question remains how researchers and analysts could precisely estimate the ratio, which is defined as the market valuation of a firm divided by the replacement costs of its assets. The precise measurement has been a topic of discussion ever since the theoretically proposed variable was tried to estimate in practice. This paper proposes to add to this discussion and provides an updated measure Q by using unique regulatory disclosures from the oil & gas exploration and production industry.

A number of theories have been proposed as to why the current measurement of the ratio is not satisfactory in identifying investment opportunities. Information on potential corporate investment is useful to determine the allocation of individual and institutional funds, but is also useful for setting up monetary and fiscal policies by governmental institutions (Tobin, 1969). There is an extensive amount of literature on this subject and the main agreement of these papers is that all corporate investment should be attributable to Tobin’s Q measure, at least theoretically (Hayashi, 1982). However, in recent literature a proper measurement of Tobin’s Q has been identified as one of the key problems (Peters and Taylor, 2016). This paper will use a unique way of identifying one of the major components of this measure and investigate if this leads to a more reliable way of estimating Q.

After the introduction in its macro-economic concept, Q was gradually adopted in corporate finance literature. Empirical evidence from Erickson and Withed (2000, 2006) points out that the explanatory power of the variable for corporate investment remains at R2_-levels around 0.5, although theoretically Q has to explain all of the deviations in corporate investment. Attempts by Erickson and Withed (2000) to more precisely describe the components of the ratio,

among others the market value of debt, resulted in reasonable improvement in R2_{-values. Peters}

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6 capital, which has improved the measure, but is still not completely satisfactory as it only provides an R2 _{value of around 0.5, leaving room for further precision.}

This research paper proposes a new way to more accurately measure Q. This will take the form of quantifying the fair market value of company’s property, plant and equipment (PP&E). There lies a unique opportunity to measure these in practice in a specific sector, namely the oil and gas industry. Due to the large investment of this industry, regulations require production and exploration firms in this sector to disclose an estimation of their proved oil and gas reserves. In addition, the companies are required to provide a standardized measure of the free cash flow that could be generated from these reserves. These statements, which form one of the sector-specific components of the companies 10-k filings, provides additional information and therefore potentially a more precise measure for Q can be validated. This is the main goal of this paper. To come to a more appropriate measure for Q, this paper will examine a means to further specify the nominator and denominator in the original equation. The nominator should be equal to the total market value of the firm, both of the equity component as well as of the debt component.

The first discussion in Q theory of the regulatory disclosures of US companies in the oil and gas industry was by Jin and Jorion (2006), which is the starting point for this paper. This research provide a possible new way to quantify the replacement cost of assets. This paper will focus on a new way for this component and combine it with different proxies from related literature.

This paper contributes to the existing literature in the following ways: First, it aims to provide a new, sector-specific way of estimating Tobin’s Q. These could be used in following research papers in this sector. Second, it proposes a method to value the oil and gas reserves with a unique dataset for the oil and gas industry, and assessing the quality of regulatory disclosures related to these reserves. Finally, it provides additional explanatory variables for corporate investment in the oil and gas industry.

First step was to value the reserves of oil and gas companies. Then, this value was used to make two new measurements for Q, which are hypothesized to be closer to the actual value of Q. The power of these measures was tested by assessing its predictive power for investment. The

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7 competing measures were proxies for Q proposed by Lindenberg & Ross (1981) and Peters & Taylor (2016). Simple linear regressions model produced lower R2_{values than the original} measures. When additional company-specific as well as industry-specific control variables were added to the regression, no change in outcome was provided. Subsamples in which the circumstances may be favored for the new measure also did not produce any new results, measured by R2_{-value. Therefore, this research can be continued by re-assessing the valuation} that was used to compose the measure or a different sample in another industry can be selected to find if Q can be improved by including the fair market value of assets as the replacement costs of capital.

This paper is organized as follows. A background on Q and the current theory and models from related literature is discussed in section 2. In this section, the various proxies for Q that are currently used are discussed and the hypotheses for this paper are formed. Section 3 will describe this paper’s methodology for quantifying investment opportunities and proposes two new measures for Q in the oil and gas industry. In section 4, a valuation model for oil and gas reserves will be explained, which is the building block for the new proxy. Section 5 will discuss the data sources that are used in this paper and provides summary statistics. In section 6 the empirical results are presented from both the valuation of reserves and the results from empirical tests assess the quality of the new Q proxies. Section 7 will provide a discussion of the results. Section 8 concludes.

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2. Literature review

2.1 A background on Tobin’s Q

A common topic in economic theory is the behavior of corporate investment (Eckbo, 2008). Over the last half century, the corporate finance literature has been expanding to a great extent on investment theory. One of the key theories in this literature is that investment is explained by the Q-ratio, which is defined by Tobin (1969) as the market valuation of the firm divided by its replacement costs of capital. The replacement cost of capital is the cost that the company would pay if it were to replace its assets and buy new assets on the market. The central theory is that if Q is larger than 1, the firm would create value by investing. This is because the company would then be adding value to the purchase price, as the market values these assets more when they are acquired by the company (Tobin, 1969). On the contrary, if the ratio would be lower than 1, the company would be better off divesting some of its assets. The intuition behind this is that if the company has a Q ratio of over 1, the company adds value to its shareholders, which would provide an incentive to invest (Tobin, 1969).

Q was first introduced in economic literature as a method for estimating the investment curve in the Mundell-Fleming model, but later it has become a widely researched topic in the finance literature as well (Erickson and Whited, 2000). Its adoption ranges from being a benchmark of investment opportunities to a widely used explanatory variable for diverse corporate phenomena. This paper will go deeper into the fundamental characteristics of Q. The first acknowledgement of investment proxies in related literature was by Tobin in his paper on an equilibrium approach to monetary theory (Tobin, 1968). In his study on monetary economics, he provides a general framework to analyze monetary policy. In this approach, aggregate demand can be affected by changing the market valuation of firm’s assets, relative to its replacement cost. In this way, the firm’s assets are valued higher after new investments, which create an increasing effect for corporate investment. This generates a possibility for monetary policies to increase aggregate demand, as monetary instrument could influence the interest rate, thereby the company’s cost of capital and the market valuation of the firm’s assets.

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9 As described earlier, Q is also one of the most used variables in empirical corporate finance literature, as it is often used to describe various corporate phenomena, representing a firm’s incentive to invest (Erickson and Withed, 2006). Therefore, there lies an extensive amount of literature in empirical corporate finance about Q. The first mention of the theoretical propositions behind Q is in a paper by Brainard and Tobin (1968), in which the authors propose a model to demonstrate the econometric issues in financial model building. Brainard and Tobin (1968) provide a financial model to estimate the curves in the IS-LM model and in this paper, the authors propose the theory that the ratio of market value of equities relative to the replacement costs of physical assets is the major determinant of corporate investment. The rationale behind this theory, is that markets value the investment more than its replacement costs, if this ratio is larger than 1. The author further argue that a reduction of the required rate of return will increase the market valuation and therefore allow for more investment opportunities. Originally, the theory is used to describe monetary policy in the IS-LM model and provides a theoretical framework of how a drop in interest rates could trigger aggregate investment. One year later, Tobin elaborated this model in another paper on monetary theory (Tobin, 1969), from which the measure got his name.

2.2 The use of Tobin’s Q

The intuition behind Tobin’s paper has been transferred from the field of economics, proposed by Tobin, into the finance literature, of which Erickson and Whited have made various additions. The ratio of the market valuation of the firm divided by its replacement costs of assets can be used to explain a series of corporate phenomena as well. The intuition behind the ratio itself could be explained by a mathematical derivation of the ratio.

The idea behind the investment-Q relation is that if a company has a high q-value, i.e. more than 1, the company can create positive net value from investing, as the market value of its assets are higher than the replacement cost of capital. This means the company adds value to investment and therefore it would make sense to increase investment. Regressing investment on Q would have to show a positive, significant relation.

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10 However, the theoretical proposition that investment would only rise if Q > 1 and that all corporate investment should be explainable by the Q measure has not been empirically verified. There are a number of ways proposed in related literature that have addressed this problem and provide possible solutions to the misalignment of variation in corporate investment and Q.

In corporate finance theory, Q is used as an explanatory variable for various corporate phenomena. Often, the ratio is used to proxy a firm’s valuation, such as in Bebchuk, Cohen and Ferrell (2004). In their paper on corporate governance, they investigate which corporate governance provisions, such as staggered boards or takeover defenses, are contributing to the market valuation of the firm. A proxy for the market valuation is then given by Q, as this provides an indication of how the market values the company’s ability to create value for shareholders.. An example of the use of Q in paper of accounting principles is found in Daske et al. (2008), who analyze the effect of mandatory reporting in IFRS affects the firm’s potential to create investment opportunities, as measured by Q. The use of Q has even entered the law discipline, as for example Coffee (2007) investigates the impact of law enforcement on Q, to evaluate the comparison between civil law origins and common law origins.

The widely spread use of Q in a range of academic literature has put a lot of importance to the subject of precise measurement. However, as is noted in Chung and Pruitt (1994), the measure may require an extensive knowledge of statistical models and therefore its use has not transferred to real-world analysis by financial managers. Instead, financial managers often rely upon readily available valuation metrics, such as relative valuation tools. Therefore, there lies an incentive to provide an easy-to-calculate, but precise measure for Q. The following chapter will elaborate on the different proxies that are currently used in academics and the advancement in clearing the proxies of Q from measurement error.

2.3 Measurement and measurement error of Tobin’s Q

As stated in the previous section, the measurement of Q has been a topic of discussion ever since the measure was theoretically proposed by Tobin in 1969. An econometric background on the intuition of Q theory is described by Hayashi(1982). This summarizes the neoclassical investment theory, which suggest that the investment opportunities of firm are perfectly

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11 described by Tobin’s Q ratio. However, Hayashi already acknowledges the difference between marginal Q and average Q. The difference between these variables is that the marginal Q is actually what the measure is supposed to inform, namely the ability of the company to add value to new capital investment. To estimate this, one has to obtain a forward looking perspective on how the company potentially would increase value of assets. As this is relative difficult to obtain, as no publicly information is perfectly capable of informing us on this matter. Therefore, it is mostly only possible to investigate the company’s current capability of adding value to assets, with the average Q. This measures how the company has been able to improve the value of investment in the past, as accounting values are almost always based on historical values.

However, average Q has already provided statistical power, such as Peters and Taylors (2016) found when comparing their Q-measures to deviations in actual investments. To put the measure in practice, both the nominator and the denominator require advanced measuring techniques, as the information necessary is not easily available or accessible. Perfect and Wiles (1994) test five estimators for Q.

There lies an extensive amount of literature, which objective is to provide a more appropriate measure for Q by clearing it from measurement error. A currently influential work on this subject is provided by Erickson and Withed. In their 2000 paper, they use sophisticated econometrical models to estimate, among others, the market value of debt. This includes high-order moment GMM approach, which provides improved estimators in statistical use. This measure is widely adopted in estimating Q and has led to an increased explanatory power of Q. In addition, Erickson and Whited (2006) provide a survey on the historical achievement on finding proxies for Q.

One of the early contributions to the discussion is from Lindenberg and Ross (1981), who propose a method to estimate the market value of debt more accurately. However, it is relative difficult to use as their component for replacement costs of capital are not required to be disclosed by small firms and also limited for large firms. Also, their estimation for debt is relatively difficult to estimate for a large sample of firms, as it requires a company-specific methodology.

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12 Perfect and Wiles (1994) construct a total of 5 different measure for Q, looking mostly at the market valuation of the firm, which is used to compose the nominator of the ratio. Their estimators range from simple-to-construct to more complex estimators. In addition they test the method described by Lindenberg and Ross (1981) and Hall (1990). They find that the most robust is the ratio provided by Lindenberg and Ross (1981), which uses a technique to value the total bonds in the nominator.

Adam and Goyal (2008) evaluates the most frequently used proxy for Q, the market-to-book assets (MBA) ratio and benchmark this ratio to other proxies for investment opportunities, the market-to-book equity ratio and an earnings-price ratio. They test these measure by using a real options approach to calculating the actual investment opportunities in the mining sector. This sector requires an extensive disclosure of the quality and content of their mines. As real investment options often are unobservable to outsider, quantifying the resources of mining firms provides them insight in the information content of commonly used proxies (Adam and Goyal, 2008). Their results show a relative high information content for the MBA ratio, which suggest that this measure for Q provides adequate information content on investment opportunities.

However their R2_{-values show, with the highest being 0.32, indicate that other factors are more}

influential to investment opportunities and provides room for improvement.

A new approach is provided by Peters and Taylor (2016), which is one of the most recent additions to the Q literature. The authors suggest that as the U.S. economy has shifted from a traditional production industry into an economy driven by technology. Therefore, they suggest to capitalize research and development expense into the balance sheet, as expenditure on these item has become increasingly important for firms to remain competitive (Peters and Taylor, 2016). Their solution to include intangible assets into the Q-ratio has resulted in a stronger relation between actual investment and Q.

2.4 Fair Market Value as replacement costs

An interesting point of view regarding the replacement cost of capital is provided by Jin and Jorion in their 2008 paper on firm hedging activities. In their research, they study the hedging activities of oil and gas producers to evaluate their effect on the valuation of the firms.

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13 Their valuation is, among others, measured by Q, in which they define the replacement cost of the firm’s assets by the book value of current assets and market value of the oil and gas reserves. This leads to a different interpretation of Q and creates the insight that it is used to determine the firm’s unique way of converting investments into market value.

This provides a new way of measuring and interpreting Q, which will be called QDCF Historical trends may provide an opening to make a new interpretation and computation for Q. For example, after 2014 the oil price dramatically dropped. This has led to a standstill in the oil and gas industry with respect to investments. However, the market valuation of the firms has not dramatically changed so much, so this could create the suggestion that investment-Q relation did not hold in this part. An explanation could be provided by assessing the denominator part in Q, which made sure that the Q ratio remains stable over the period of oil price decline. Figure 1, located at the end of this paper, provides an overview of the investment rate, measured as capital expenditure over property, plant and equipment for all US oil and gas exploration and production firms from 2005 to 2015. From this figure we could derive that investment have not lowered in 2008, although the financial crisis had dropped market capitalization of these firms significantly. The figure could provide the suggestion that investment is delayed. However, also the rise in stock prices of 2016 has not created an increase in investments.

2.5 Hypotheses

This paper follows up on the recent advancements in the literature on solving the measurement problem of Q. The recent deviation in the oil and gas sector from the investment-Q relations could provide an opportunity to test new measures. The hypotheses for this paper are described in this section. This study builds forth on the Q measure that was first used in the Jin and Jorian (2006), which used the Standardized Measure of Discount Cash Flows to compose Tobin’s Q. As the measure will try to approximate the replacement cost of capital more closely, this should lead to an improved predictive power of the measure for actual investment. This paper will test this hypothesis by providing a possible solution for the measurement error in this industry. The main hypothesis is therefore as following:

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14 ▪ Main Hypothesis: The predictive power of Q for investment is higher if Q is measured by

including the market value of PP&E as replacement cost of capital.

Additionally, this paper will investigate if including intangible assets in the replacement costs of capital will lead to a more precise measure of Q. This was proposed by Peters & Taylor (2016). These findings will be tested to find if the Q proxies based on market valuation of replacement costs of capital will be improved when intangible assets are added to the equation.

▪ Sub Hypothesis: Q provides a better explanation for corporate investment if intangible expenses are also included in the dependent variable, beside capital expenditure.

As pointed out by, among others, Fazzari, Hubbard and Peterson (1988), other factors may be also influencing corporate investment. In section 2.2, examples are provided in which Q has been used as an explanatory variable in various research papers. It could be interesting to find if the newly proposed Q measures remain their positive significant coefficient with investment when other regressors are added to the analysis. The additional regressors will be further specified in section 3.3. The final sub hypothesis is therefore as follows:

▪ Sub Hypothesis: The newly proposed Q variables hold a statistically significant relationship in the investment-Q regression when additional variables are added to the equation.

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3 Methodology for estimating and assessing Q

3.1 A new measurement for Q using Fair Market Value

Building forth on the issues mentioned in the introduction and literature review, this section describes the methodology used to compose and test the new Q-ratios, which shall be referred to as QDCF-TOT_{and Q}DCF-PHY_{. In this research a new way to measure Q is found, namely by} assessing the market value (MV) of the oil & gas reserves and dividing it by the book value (BV) costs of these. This will find a unique way of interpreting investment opportunities. Then, the investment ratios of these companies will be regressed on the new Q measure to find if it has superior explanation power over other measures of investment opportunities. For comparison, other proxies for Q will be tested to find which measure provides the most explanatory power. The remainder of this chapter is organized as follows. This section describes the necessary components of the proposed proxy for Q. Section 3.2 describes how this measure differs from various other proxies that are used to approximate Q. Section 3.3 states the methods to find additional explanatory variables, besides Q, which help to explain corporate investment. Finally, section 3.4 describes the tests to which the new Q measures is benchmarked with the current measures.

As introduced in the beginning of this paper the original measure of Q is defined as follows:

𝑄 = 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑖𝑟𝑚

𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡𝑠 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙

The replacement costs should match the price the firm has to pay on the market to replace their current assets with new capital goods. These replacement costs are typically measured by the ending balance of the property, plant and equipment (PP&E) of a firm’s balance sheet. As indicated before, Peters & Taylor (2016) add the intangible assets to the replacement cost of capital, for which they capitalize the research and development expenses from the income statement.

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16 The new measure will include the fair market value as the replacement costs of capital for the firm. This would reflect the actual price the company has to pay on the market to replace their current producing assets. These will be calculated by making a discounted cash flow analysis of the firm’s producing assets. The non-producing assets will be measured by its book value. Therefore, the book value of the companies’ reserves will be subtracted from PP&E, to keep the value from assets after then reserves. Then, the market value of the reserves will be added. This will create a value for replacement costs that is closer to its market value. The new measure, which will be called QDCF-PHY_{will take the form of the following:}

𝑄𝐷𝐶𝐹−𝑃𝐻𝑌₌𝑀𝑉 𝑐𝑜𝑚𝑚𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑜𝑓 𝑑𝑒𝑏𝑡 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠

𝐵𝑉 𝑜𝑓 𝑃𝑃&𝐸 − 𝐵𝑉 𝑃𝑟𝑜𝑣𝑒𝑑 𝑅𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝑀𝑉 𝑃𝑟𝑜𝑣𝑒𝑑 𝑅𝑒𝑠𝑒𝑟𝑣𝑒𝑠

Other components of this measure include the market capitalization of the firm, which will be calculated by multiplying the number of outstanding shares by the year-end market price for the stock plus the book value of preferred equity. Book value of preferred equity and book value of total debt is collected from company’s 10-k filings. The complete construction of the market value of proved reserves is described in section 4. Current assets and book value of PP&E will also be derived from company’s financial statements.

As Peters & Taylor (2016) find, intangible assets are also important when composing a proxy for Q. Therefore, an additional measure will be composed, which includes the intangible assets that are not listed on the balance sheet:

𝑄𝐷𝐶𝐹−𝑇𝑂𝑇₌ 𝑀𝑉 𝑜𝑓 𝐶𝑜𝑚𝑚𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑜𝑓 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑜𝑓 𝑑𝑒𝑏𝑡 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠

𝐵𝑉 𝑜𝑓 𝑃𝑃&𝐸 − 𝐵𝑉 𝑃𝑟𝑜𝑣𝑒𝑑 𝑅𝑒𝑠𝑒𝑟𝑣𝑒𝑠 − 𝑀𝑉 𝑃𝑟𝑜𝑣𝑒𝑑 𝑅𝑒𝑠𝑒𝑟𝑣𝑒𝑠 + 𝐵𝑉 𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒 𝐴𝑠𝑠𝑒𝑡𝑠

The book value of intangible assets will come from an estimate portion of intangible capital that does not appear on the company’s balance sheet. A special database from Compustat provides these values. More information on the origination of other data is found in section 5.

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3.2 Benchmarking variables of Q

The new proposed measure is then benchmarked with other proxies for Q that are currently used in other academic papers. The first proxy is the most commonly used proxy, namely including the book value of liabilities in the numerator and the book value of PP&E in the denominator. This measure is proposed by Lindenberg and Ross (1981), as they provide an intuitive measure, which can be approximated by easy-to-find variables from company filings. A similar measure is used in Fazzari, Hubbard and Petersen (1988) and Erickson & Whited (2012). The formula is as follows:

𝑄𝐿𝑅₌𝑀𝑉 𝑜𝑓 𝐶𝑜𝑚𝑚𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑜𝑓 𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝑜𝑓 𝑑𝑒𝑏𝑡 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠

𝐵𝑉 𝑜𝑓 𝑃𝑃&𝐸

. This simply-to-construct measure is further improved by adding an estimation of the firms intangible assets, provided by Compustat and calculated by the methodology of Peters and Taylor (2016). The key change to the QLR_{measure is the addition of the stock of intangible assets.} Rationale behind this new measure is that firms investment in research and development is not recognized as capital expenditure, but should be treated as capital expenditure, as knowledge has become an increasingly important asset for companies (Peters & Taylor, 2016). Their measure is therefore composed as follows:

𝑄𝑃𝑇 ₌𝑀𝑉 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐵𝑉 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠

𝐵𝑉 𝑃𝑃&𝐸 + 𝐵𝑉 𝐼𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒 𝑎𝑠𝑠𝑒𝑡𝑠

The regression analysis is further discussed in section 3.3. If these regression analyses are completed, the final step is to find out which other factors are used to provide explanatory power on investment opportunities in the oil and gas sector, which is described in section 3.4.

3.3 Regressions analyses with investment variables

The first test for estimating the predictive power of QDCF_{in comparison to Q}PT_{and Q}LR_is a simple regression analysis with the four Q proxies as independent variables, in separate regressions, and corporate investment as dependent variable. Actual investment of companies is reported in their 10-k filings. These records provide year-end values of capital expenditure, which

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18 is most often defined as the purchase of fixed assets (Stolowy & Ding, 2015). According to Peters and Taylor (2016), research and development expense are not included in the standardized computation of capital expenditure. Therefore, these costs will be capitalized by their year-end sum of expenses. In addition, Compustat offers a sample of pre-calculated intangible capital expenditure, which are also used to include in the investment composition. These variables are valued with the method from Peters and Taylor (2016). As investments vary among small and large firms, the actual investment is then divided by the net year-end value of property, plant and equipment, which provides an investment ratio.

The regression analysis will be performed for all four estimated proxies. The first

regression formula will be as follows:

REGRESSION 1: Q proxies on physical investment 𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖𝑡 = 𝛼𝑖𝑡+ 𝛽1∗ 𝑄𝑖𝑡

The total investment ratio that is used in this regression is measured as follows:

𝑃ℎ𝑦𝑖𝑐𝑎𝑙 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝐵𝑉 𝑜𝑓 𝑃𝑃&𝐸

Peter and Taylor (2016) differentiate between physical investment on total investment, with a distinction on investments in research and development. These costs are included as intangible investments and are summed up with physical investment to form total investment. Corrado, Hulten and Sichel (2009) find that investment in intangible capital can be proxied by taking 20% of the selling, general and administrative expenses (SG&A). Therefore, this is used in the investment ratio for total investment, together with research and development expenses (R&D).

REGRESSION 2: Q proxies on total investment 𝑇𝑜𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑖𝑡= 𝛼𝑖𝑡+ 𝛽1∗ 𝑄𝑖𝑡

The total investment ratio that is used in this paper is measured as follows:

𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 + 𝑅&𝐷 + 0.20 ∗ 𝑆𝐺&𝐴

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19 As is showed in the previously discussed literature, empirically tests prove that not all variation in corporate investment is explainable by Tobin’s q. An additional regressor is therefore the occurrence of financial constraints, which could proxy corporate investment, as pointed out by Fazarri, Hubarts and Peters (1988). Therefore, this paper also test which other measure could be explanatory variables for corporate investment and, especially, if the new measures for Q remain a significant relationship with investment in a multiple regression analysis.

Farre-Mensa and Ljungqvist (2013) survey the current literature on measures of financial constraints and identifies and test five possible proxies of financial constraints. The first measures are easy to interpret, namely paying dividends and having a credit rating. These would indicate financially capability to expenditure. The findings of Farre-Mensa and Ljunqvit point out that neither of these measure identify firms that behave as a financially constraint firm. However, Farre-Mensa and Ljungqvist provide suggestive evidence that these measures for financial construct do not satisfactory measure the actual financial constraints. The final part of this paper is therefore devoted to testing additional variables that measure financial constraints. The final regression formula with additional measure will use four widely-used measures, as described by Farre-Mensa and Ljungqvist (2013) and based on the measures from Kaplan and Zingales (1997).

The measures by Kaplan and Zingalas (1997) were further specified in Lamont, Polk and Saa-Requejo (2001), which are used in this study. These variables are the total debt, cash, cash flow and dividends, each divided by total assets. The fifth variable from Lamont, Polk and Saa-Requijo (2001), market value over assets, is not included in this research for its resemblance to the Q measures as this could cause multicollinearity effects between the regressors. The dependent variable, Investment Ratio, is either physical or total investment, as described in section 3.3, based on which measure has the highest R2_{-value after regression 1 and 2 are performed.}

The equation including the additional variables is:

REGRESSION 3: Additional firm-specific variables

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20 The final regression has the three different Q measure as first independent variable and

a measure for price index as second independent variable. This price index measure is calculated by multiplying the share of the three most sold products – crude oil, natural gas and natural gas liquids (NGL) – on total revenue, by the index price of these products. The rationale behind this additional variable is that, by intuition, the selling price may have a large impact on the investment ratio as well. For example, the oil price has dropped from $ 115 per barrel in June

2014 to under $ 35 at the end of February 20161_{. As Figure 1 shows, corporate investment in the}

oil and gas industry has decreased in the same period. Therefore, this relation is also included in this paper with the following regression analysis:

REGRESSION 4: Additional price variables 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑖𝑜𝑖𝑡 = 𝛼𝑖𝑡+ 𝛽1∗ 𝑄𝑖𝑡+ 𝛽2∗ 𝑃𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥𝑡

3.4 Test statistics

If all ratio are computed, they are tested for the equality of the means, the medians and the variances to determine if the ratio are significantly different from each other. Both test for these differences is the standard t-test with a pooled standard deviation and is performed as follows:

𝑡 =

𝑄1 − 𝑄2

𝑆

𝑝

∗ √

2 _𝑛

In addition, a Pearson correlation coefficient will be estimated with regarding to the comparability of the ratios. and the Pearson correlation coefficient is computed as:

𝜌

𝑄1,𝑄2

=

𝑐𝑜𝑣(𝑄1, 𝑄2)

𝜎

𝑄1

𝜎

𝑄2

As discussed in section 3.3, after the difference in Q ratios is determined, the ratios are regressed in a simple and multiple linear regression on investment rates. To find the effect of a

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21 change in the investment ratio, as explained by the proxies for Q, the regression will be based on an OLS panel regression with fixed time effects and fixed company effects. The performance of the four measures for Q in explaining variation in investment will be tested on two measures.

The main hypothesis states that the newly proposed Q measures provide a better explanation for corporate investment than the formerly used Q measures. The comparison between the Q measures is the coefficient of determination, provided by the R2_{-value and the} adjusted R2_{-value. The R}2_{-value measures the fraction of the investment ratio that is explained by} Q, in regression 1 and 2, and the fraction that is explained by Q and the other regressors, in regression 3 and 4. To adjust for the additional regressors in regression 3 and 4, and possibly the additional observations that are used in all regression, the adjusted R2_{is also computed as this} provides the explanatory fraction, or the better fit of the model, but does not necessarily increase when additional regressors are used in the regression (Stock and Watson, 2012). To remove the effect of additional observations on additional R2_{, all comparing regressions with the different Q} measures have the exact same firm year observations. The first sub hypothesis is also measured by deviation in R2_{. For the second hypothesis the coefficients of the Q proxies will be assessed.}

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22

4. Methodology for valuation of oil and gas reserves

The most important component of the new measure for Q is a market valuation of the firm’s replacement costs of capital. This section outlines the methodology applied for valuing oil and gas proved reserves.

As discussed in chapter 3, this paper aims to use the market value of the proved reserves of oil and gas companies as the replacement costs of capital. This market value will be measured by assessing the standardized measure of discounted cash flows relating to proven oil and gas reserves. In every 10-k of oil and gas companies this measure can be found, as required by the

Financial Accounting Standards Board by ASC 932.2

Information on the various components is retrieved from description in company’s 10-k, as well as the text provided in regulation ASC 932. The regulatory disclosure of a standardized measure of discounted cash flows for oil and gas companies was effective from 1982. The FASB decided to require this information disclosure on the sector to better inform investors on the current state of the company and thereby reducing information asymmetry (Clinch and Magliolo, 1992). As the oil and gas exploration and production sectors requires large investment upfront and cash flows are expected to come over a long period, investors could be reluctant to invest in these companies if less information would be provided. The standardized measure of discounted cash flows is composed of seven obligatory statements which include the following:

a. Future cash inflows from the direct production and sale of all the firm’s proved reserves

b. Future development costs c. Future production costs d. Future income tax expense e. Future net cash flows

f. Discount from applying a cost of capital of 10% g. Discounted future cash flows

2_{The full text of the obligatory disclosure on discounted cash flows can be found in Appendix A. Patoukas,} Sloan and Giedt (2016) further discuss the usability of this measure with respect to oil and gas royalty trusts.

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23 The information provided is unaudited and therefore not formally checked on its precise content. Therefore, using the data for the proposed purpose of this study requires a number of amendments and modification, which will be explained in the following subsections. It should be noted that the content of this disclosure provides interesting information, which could be used as input in a fair market valuation.

4.1 Estimation of cash flows

The first component of the standardized measure provides a good starting point for the valuation of its reserves and especially for its expected cash flows. These are the future cash inflows of the proved reserves. This amount is estimated by multiplying the total expected barrels of oil, or cubic feet of natural gas, with the respective year-end market price. As the proved reserves are estimated with over 90% probability and are the only reserves that are found on the company’s balance sheet, this quantity is kept as reported. However, the measure is then multiplied by the current year-end market prices of oil and gas. As the company expects multiple years to actually develop, produce and sell the reserves, as is reported in the discounted value, this may not be an accurate display of the expected selling price. Therefore, a synthetic future prices is used, as provided by Pilbeam (2013) and multiplied by the quantities sold each year by the appropriate future price. The synthetic future price for both the oil and gas price by the following basic future pricing rule:

𝐹𝑜𝑟𝑤𝑎𝑟𝑑𝑡= 𝑆𝑝𝑜𝑡0∗ (1 + 𝑟𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒0)𝑡

where Forwardt is the selling price at which the quantity of oil will be multiplied, Spott is the year-end price of the reported year and the risk free rate is the 10-year, 20-year or 30-year US Treasury bond rate. Effectively, this will mean that the expected annual cash flow for each of the estimate years will be multiplied by a synthetic rate, which would proxy a forward rate.

The second and third component of the SMOG are the development and production costs. These expected costs are estimated by the engineers and financial experts of the company (Clinch and Magliolo, 1992). These are costs that are essential in making a proved oil or gas reserve field exploitable. There is a clear distinction between production and development costs and this

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24 difference is mostly concerned with the timing of the costs. Development costs are cost incurred after a resource is proved to be economically feasible and when the site is getting extract resources from territories. It involves the construction of equipment to retrieve the resources from the ground, including building pumps and wells company (Clinch and Magliolo, 1992). After the first resources are produced from the well, the costs are referred to as production costs. This involves all the variable costs related to employment, logistics and maintenance. This could provide an option to estimate the timing more precisely.

As these projections are provided by experts, there would be little incentive to adjust these costs for better estimates. However, the development costs could provide insights in the current state of the reserve. If expected development costs are high, we can expect the cash flows to be postponed. This will be further discussed in additional regressions on a subsample.

Fourth item on the SMOG is the future income tax expense related to the net result from extracting the oil or gas. The expected costs provide insight into the marginal tax rate that the company faces. However in some cases, no tax expense is provided and these may be firm-specific. If no income tax expense is disclosed, these will be estimated these by applying the practice from Graham (1996), which provides measurements for the corporate marginal tax rate. The author provides empirical evidence that the tax variable as suggested by Shevlin (1990) provides a good proxy for the marginal tax rate. However, these are difficult to calculate as they require extensive knowledge of the company’s financial performance. Due to the relative large sample size, an alternative option will be used as described by Graham (1996). This measure is a dichotomous variable and consists of either the statutory tax rate, or is zero if there is a net operating loss (NOL) in the prior years, which allow for a NOL carryforward. According to Graham (1996) these are reasonable alternatives and provide better expected tax values than most commonly used variables for income tax. Therefore, the previous year is assessed and an income tax rate of 35.0% is applied, the statutory tax rate in the United States, or a discount by the maximum the amount that is allowed to carryback forward.

The fifth item on the SMOG is the discount component relating to the timing of future cash flows. These will be improved by discarding the standard 10% discount rate and applying a

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firm-25 specific discount rate. In the original requirements, for every company the same discount rate is used, namely 10%. This may not be very accurate and will not be comparable to use as an appropriate measure of the market value of reserves. Therefore, a new discount rate is estimated for every firm-year that is in the dataset. This will be done by the valuation methods described in Damodaran (1997) and is set forth in section 4.2.

As is shown in Appendix B, the company is not required to disclose the exact timing of the production of oil and gas reserves and the timing in which the resources are extracted and the well is depleted. This requires to make assumptions on the annual expected production. The information that is disclosed is only the sum of all future cash flows, the effect of discounting for the entire forecasted period and the final sum of discounted cash flows. Following a lack of information, an assumption is made in this paper that the oil is produced on a straight-line basis and every year the exact same amount is depleted from the well. Also, the years of production are exact integers, so every production of oil and gas reserves has to be in an exact amount of years. This simplification in the calculation of the rate of depletion of the oil reserves was adopted considering the large sample size of the dataset and the limited available information. The timing of the future cash flows shall be derived on trial-and-error basis in which a range of possible timings is applied, ranging from 1 to 30 years, and find what is the best fitting timing in years. This opportunity is provided by the final component of the SMOG, which is the discounted future cash flows.

4.2 Estimation of discount rates

After estimating the provided timing of cash flows. a firm- and year-specific discount rate will be applied to the respective annual cash flow. The commonly-used weighted average cost of capital function is described in Berk and DeMarzo (2014). The return on debt and the return on equity are composed by using market data. The return on equity is estimated as following:

𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 = rf+ β ∗ 𝑈. 𝑆. 𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑖𝑠𝑘 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 + 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑅𝑖𝑠𝑘 𝑃𝑟𝑒𝑚𝑖𝑢𝑚

The risk free rate should benchmark investment horizon and is therefore different for the timing of cash flows (Damodaran, 2016). This will be either the 10 year or 30 year interest rate

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26 from zero-coupon US treasury bonds. As the expected timing of future cash flows is ranging between 1 and 30 years, the risk-free rate will be picked depending on the expected timing of depletion of the reserve.

Beta’s will be calculated by regressing the monthly stock returns on the S&P Composite Index for a maximum period of five years, or 60 monthly periods. If this data is unavailable, the minimum estimation period is 2 years, or 24 monthly periods. The Data section of this paper provides a detailed overview of the input used for this measure. Equity risk premium is composed of the premium that company stocks have listed over their risk-free rate. These are determined by the geometric average difference between US stocks from the Dow Jones Industrial Average and Treasury bonds, as these go back to 1886.

The geographical location of the proved oil and gas reserves is not limited to the United States. The company’s 10-k provides a description which fraction of the reserves is located in foreign territory. However, these disclosures are not comparable as companies differ in stating either the exact country or the region in which their operations take place. Therefore, these locations are sorted into geographical categories, based on different country risk premiums to account for the different risk component of operating in foreign countries. The country risk premium would then be determined by the average of all countries that are categorized into the region. The listed countries will be divided into the following categories: 1) North America & Europe, 2) Russia, Asia & Latin America and 3) Africa and Middle-East. Table 3 provides an overview of the percentage of properties located in each regional segment. This table also reports the estimated rating and is provided a spread as based on Damodaran’s estimates of country risk premiums (Damodaran, 2017)

The cost of debt for each year t and each firm i is determined as follows: 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡𝑖𝑡= rf+ spread𝑖𝑡

As most of the companies in the sample have no publicly traded debt, there is no ready-to-use return on debt available. Therefore, a synthetic debt rating will be composed by calculating the interest coverage ratio for each firm. This measure shows the capability of each company to

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27 pay off its debtholder by the amount of their earnings (Koller et al., 2010). As these companies have relative high deprecation expenses from the depreciation of reserves, the earnings before interest, taxes, depreciation and amortization (EBITDA) will be used for this ratio, which is formed as follows:

𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜𝑖𝑡 =

𝐸𝐵𝐼𝑇𝐷𝐴𝑖𝑡

𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑖𝑡

Damodaran (2017) provides an overview for average expected spread per interest coverage ratio category. These ratios can be found in Table 4.

Finally, to match the investment horizon of the sale of the remaining oil and gas reserves, this paper uses a company specific time interval for risk-free bonds, which is either the 10-year zero-coupon interest rate from the Unites States or the 30-year Treasury bond as the risk-free rate.

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5. Data

This section describes the data that is used in this study. As discussed in the previous section, the oil and gas industry provides a unique opportunity to estimate the fair market value of its property, plant and equipment. Therefore, all the items from the standardized measure of discounted cash flows are collected for all available years for all available companies. The regulations that require extensive documentation of proved reserves for oil and gas companies date back from 1982, when the Financial Accounting Standards Board proposed a standardized measure of reserves valuation. This data is included in Standard&Poor’s CapitalIQ database, which provides the measure for a period from 2005. As this database will provide the most accurate information and to make sure new accounting policies are included, this data will be used for the period from 2005 to 2016.

The other components of the QDCF_{measures, as well as the components of the various} other measures, are collected from the Compustat database or the database from the Center of Research in Stock Prices (CRSP). A special note has to be made on finding the book value of intangible assets, which are a part of the QDCF-TOT_{and Q}PT_{proxies. These values are derived from} a special database in Compustat which provides the portion of intangible assets that does not appear on the company’s balance sheet.

To focus on companies that are primarily engaged in the exploration and production of oil and gas, the data collection will be filtered on the SIC sector 1311, the code for US companies primarily engaged in operating oil and gas properties. This sector code is then used in the database of the CRSP to screen all potential firms. These companies may be identified in the Compustat under different names, as companies may have changed their name, e.g. following a merger. Appendix B provides a full overview of all the companies that were used in this research. The largest firms in the sample, based on total assets, include ConocoPhilips, Occidental Petroleum Corporation and Anadarko Petroleum Corporation. Large so-called supermajors, such as Royal Dutch Shell and British Petroleum, which also have a listing in the United States, have a significant portion of their business related to midstream and downstream activities. As a result, the portion of their property that is directly related to oil and gas reserves is relative

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29 small. Therefore, these companies are not included in this study as it would be hard to estimate the fair market value of its midstream and downstream business. Other requirements for the data is the availability of continuous monthly stock return in the period from 2005 to 2016.

Table 1 provides a summary of statistics of all the companies that were included in this paper. These statistics gain insights in the size of the companies active in this industry and the financial ratios. Also the components of the standardized measure of discounted cash flows are included in this table, which show the relative large deviation in oil and gas reserves throughout the sample.

Monthly stock returns are downloaded from CRSP of all companies with SIC code 1311 from 1977-2016 to obtain all the betas with 5 years of data. Stock returns are regressed at the S&P Composite Index returns, also available in the CRSP database, at a rolling basis. For each month from 5 year prior to 2005 until 2016, unique betas for each company/month combination are obtained.

Data from additional variables that are used in Regression 1 as discusses in section 3.4 are from Compustat. These are composed by data items from balance sheets and income statements. The cash flows variable is the total operating results before extraordinary items plus depreciation and amortization, both divided by total assets. The cash variable is the total of cash and short term investments over total assets. Dividend yield is the sum of common dividend and preferred dividends over total assets. Data from the index prices on crude oil, natural gas and natural gas liquids that are used in Regression 4 are from Datastream.

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6. Empirical results

This section describes the results from the empirical analyses performed in this paper. In subsection 6.1, an elaboration on the findings from the valuation of oil and gas reserves can be found. In subsection 6.2 the results from the empirical test of the new Q-measure are reported, in comparison to other frequently-used proxies for Q. In subsection 6.3 the results of the test with additional regression coefficients can be found, including financial constraints. Subsection 6.4 provides results for subsample analyses.

6.1 Results from oil and gas reserves valuation

The valuation of the oil and gas reserves is performed as described in section 4 and results are displayed in Table 4. The first step was to estimate the annual cash flows from the sale of all oil and gas reserves. The only disclosure of the timing of cash flows was the total discount that was subtracted from the future cash flows. Therefore, assumptions had to be made on the depletion of the oil and gas reserves. By programming a backwards reasoning program in statistical software, the estimated timing of cash flows is calculated. This was done on trial-and-error basis, where for each firm-year observation all possible years of discounting from 1 year to 30 years were used as timing of cash flows. After obtaining all possible values after discounting, the value closest to the reported discounted value was used and the amount of years that was used for this, was stored as the estimated timing. This resulted in mean of 14.4 years and a median of 14.5 years, with a total range from 1 year to 30 years. This could indicate that for some reserves it would take either a very long time to make the extraction producible, or it is very difficult to get the oil out of the ground, e.g. if the oil is found deep under the sea. This firm-specific and year-firm-specific amount of years is then used to divide the total amount of cash inflows by the amount of year to retrieve the estimated yearly cash flow. To illustrate the process of estimating the amount of discounting years, an example for one observation is discussed below.

In 2012, Abraxas Petroleum Corp. reported estimated future after-tax cash flows from the sale of reserves of $ 664.0 million. After discounting, the standardized measure of future cash flows reported was $ 278.1 million, providing an estimated effect of discounting of $ 385.9 million. Backwards reasoning provides a best-fitting estimate of 21 discounting years with a standard

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31 10% discount rate, with the assumptions of straight-line depletion and the same amount of oil and gas sold each years. The control for this results is performed by dividing the total cash inflows by 20 or 22 years and discounting with a 10% discount rate for these years. This resulted in a discounted value that is not closer to the reported value than when 21 years are used, therefore this is the amount of years that is used. Finally, applying a synthetic forward rate, with the 20-year US Treasury bond rate to the annual cash flows, and discounting by the estimated weighted average cost of capital of 11.4% for the same 21 years, the new valuation of the reserves was $ 240.0 million.

Second item to consider in the estimation of cash flows was the future price of oil and gas sales. To provide a better estimate of the future prices of oil and gas, a synthetic future loan is composed which increased the selling price of oil and gas. Then the simplified forward rate was applied with respect to the amount of forecasted years. This resulted in higher annual cash flows, which would more accurately reflect the expected market selling prices in the future.

Table 4 further provides an overview of the key variables that were used in the valuation of the reserves. Table 3 reports the country risk premium that was added to the required return on equity. After calculating return on debt and return on equity, an estimate for the weighted average cost of capital was determined. The median value of the weighted average cost of capital is around 11.6%, which is higher than the ordinary 10% that is used in the standardized measure. We would therefore expect that the revalued discounted cash flows is a lower estimate, especially since the mean value is even higher, at 12.5%. These estimates for cost of capital are similar to the mean values provided by Damodaran (2017). Finally, the weighted average costs was used to discount the future cash flows, with the appropriate timing.

After applying the same principles with firm-specific years of discounting and discount rates in the standardized measure for all firm-year observations, the median valuation of oil and gas reserves decreased from $ 821.5 million to $ 769.0 million. The mean value of the reserves increased from $ 3,498.6 million to $ 3,549.7 million. This shows that the relative larger reserves are valued higher after applying a firm-specific cost of capital than the standard 10% cost of capital.

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32

6.2 Results from evaluating the performance of Q

DCF

The results from valuating the oil and gas reserves from the companies in the sample were used as a component in the new Q measures, QDCF-PHY_{and Q}DCF-TOT_{. The formula for this} measure is provided in the Methodology section. This measure is subsequently tested for its predictive power of corporate investment against the other proxies, QLR_{and Q}PT_{. Summary} statistics for the four measures can be found in Table 5 Panel A. The mean value of QDCF-PHY_is 1.519, which is higher than QLR_{, with a mean of 1.441. The mean value of Q}DCF-TOT_{is 1.399 and is} also slightly above QPT_{, which has a mean of 1.350. Median values of the before mentioned Q} proxies are 1.20, 1.17, 1.15 and 1.11, respectively. As these last two proxies have additional items in the denominator of the Q proxy, this result is in line with expectations.

The remainder of Table 5 provides an overview of the three tests that are performed to evaluate the significant difference between the Q proxies. All ratios have been estimated by using a simplified version of the methods described in each paper. As some of the components are equal for each ratio, it would be insightful to find the correlation coefficients between each ratio. Table 5 Panel B shows that there seem to be a correlation between each ratio. The correlation coefficient between QPT_{and Q}LR_{is relative high.}

In addition, the ratios are tested to be significantly different from each by comparing the means and variances. Panel C of Table 5 provides an overview of the t-tests which were used to test for the means. The results show that the means of all variables are significantly different from each other at the 1% level.

The main goal of this research is to test if the newly proposed measures, QDCF-PHY_and QDCF-TOT_{better explain corporate investment than their counterparts, Q}LR_{and Q}PT_{respectively.} To test the additional explanatorily benefits of the new Q-measure, a panel data regression with fixed firm and year effects has been run to find to what extend the variation of the investment ratio is attributable to deviations in Q. The results from Regression 1 and Regression 2 can be found in Table 6. This table shows the results for the OLS panel regression of the four composed measures on actual investment. A difference is made between physical investment, of which results are displayed in Panel A, and total investment, of which results are displayed in Panel B.

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33 Physical investment is estimated by the ratio of capital expenditure by the total assets for each company and for each year. Total investment includes R&D expenses plus 20% of SG&A expenses as capital expenditure as well. However, as very few companies reported actual R&D expenses, effectively this included additionally in almost all cases only the 20% SG&A expenses.

The composition of these independent variables are described in the Methodology section of this paper. Panel A describes the results for using physical investment, measured as capital expenditure divided by total assets. This panel shows that all four measures have a statistically significant positive relationship with physical investment at the 0.1% level when regressed as sole independent variable. The coefficient of the Q measure range from 0.0393, for QDCF-PHY_{, to 0.0495,} QDCF-TOT_{. The highest R}2_{value comes from the regression with Q}DCF-TOT_{, namely 0.078, which also} has the highest adjusted R2_{-value, namely 0.063. The lowest R}2_{and adjusted R}2_{are from the} regression with QDCF-PHY_{. Overall results from this table find that Q}DCF-PHY_{is not better explaining} corporate investment than QLR_{, but Q}DCF-TOT_{is a better explanatory variable than Q}PT_.

The newly found measure for Q are subsequently regressed to their closest counterpart. For QDCF-PHY_{this is Q}LR_{and for Q}DCF-TOT_{this is Q}PT_{. The regression results for these analyses are} displayed in columns (5) and (6) of Panel A. The coefficients of QDCF-PHY_{and Q}LR_{in column (5) lost} their significance when they are combined in a regression with each other. The same results come from a regression of QDCF-TOT_{combined with Q}PT_{. R}2_{-values are little affected by combining two} Q-measures in one regression.

Panel B from Table 6 contains the similar regression analysis as Panel A, with the only difference that the dependent variable is total investment, instead of physical investment. These definitions are proposed by Peters & Taylor (2016), of which a simplified modification is used, whereby total investment also includes 20% of the total selling, general and administrative expenses (SG&A). The effect of regressing the Q measures on this more complete measure for investment is that both the regression coefficients and R2_{-values increased in regression (1) to (6).} All regression coefficients in regression (1) to (4) increased in significance, although these were already significant at the 0.1% level in panel A. The best performing measure in this regression is QPT_{, with an R}2_{-value of 0.206. When Q}DCF-PHY_{and Q}LR_{were combined in a multiple regression in}

Fair market value of assets as replacement costs of capital in Tobin’s Q