Working capital and firm value relationship estimation model

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carrying the estimation in two steps increases efficiency. The weight matrix of a GMM1 is given by;

𝐴_1𝑁 = (1

𝑁∑ 𝑍_𝑖^∗′

𝑁

𝑖=1

𝐻𝑍_𝑖^∗) −¹… … … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 17

where H is a T – 2 square matrix with twos in the main diagonals, minus ones in the first sub diagonals, and zeros otherwise.

The weight matrix of a GMM2 if given by, 𝐴_𝑁 = (1

𝑁∑ 𝑍_𝑖^∗′

𝑁

𝑖

∆𝜀̂∆𝜀_𝑖 ̂_𝑖^′𝑍_𝑖^∗) −¹ … … … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 18

Where ∆𝜀̂_𝑖 = ∆𝜀̂_𝑖… , ∆𝜀̂_𝑖𝑇 are the residuals from a consistent GMM1 of ∆𝑦_𝑖.

5.3 WORKING CAPITAL AND FIRM VALUE RELATIONSHIP ESTIMATION MODEL

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things constant, the value of the firm is maximised and this is the optimal working capital investment level. Beyond this point, any additions to working capital investments reduce firm value because increases in carrying costs (financing and opportunity costs) outweigh the reduction in shortage costs. It is therefore hypothesised that the relationship between the working capital investment level and the value of the firm is concave as a result of benefits (at lower levels) and costs (at higher levels).

The hypothesised non-linear relationship between working capital investment and firm value was tested by regressing firm value was against working capital investment represented by CATA, CATA² and control variables. CATA and its square were included in the estimation model to help determine the breakpoint of the working capital investment-value relationship; that is, the benefits of working capital investment and the negative effects of investing excessively in working capital. In estimating the working capital investment-firm value relationship, the study followed the models used by Tong (2008) to study the relationship between optimal Chief Executive Officer (CEO) ownership and firm value, (Martínez-Sola et al., 2013b) to estimate the relationship between trade credit policy and firm value and (Martínez-Sola et al., 2013a) to estimate the cash holdings and firm value relationship. The estimation equation for the working capital investment-value relationship is given below;

𝑉𝐴𝐿𝑈𝐸_𝑖𝑡 = 𝛽₀+ 𝛽₁𝐶𝐴𝑇𝐴_𝑖𝑡 + 𝛽₂𝐶𝐴𝑇𝐴_𝑖𝑡²+𝛽₃𝑆𝐼𝑍𝐸_𝑖𝑡 + 𝛽₄𝐿𝐸𝑉𝐸𝑅𝐴𝐺𝐸_𝑖𝑡+ 𝛽₅𝑀𝑇𝐵_𝑖𝑡 + 𝜂_𝑖+ 𝜆_𝑡 + 𝜀_𝑖𝑡 … … … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 19

where 𝑉𝐴𝐿𝑈𝐸_𝑖𝑡 the dependent variable is the firm value as proxied by the Tobin’s Q. The Tobin’s Q was calculated as the market value of the enterprise’s equity plus the book value of interest-bearing debt to the replacement cost of its fixed assets. The main independent variables of interest are CATA it which represents current assets to total assets (working capital investments) holding by firm 𝑖 at time 𝑡 and CATA²_it(current assets to total assets squared).

CATA² was included in the regression model in order to test the quadratic relationship between the level of working capital investment and firm value. The level of working capital investment can also be measured with respect to the level of sales. Therefore, an alternative working

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capital investment measure, current assets to sales; CAS it and its square CAS²it were used in the alternative estimation regression model as a way of testing the robustness of the findings. The study also included control variables; SIZEit, LEVERAGEitand MTBit. Two proxies for firm size; the natural logarithm of market capitalization (LNMCAP) and and the natural logarithm of total assets (LNTA) were used in this study. MTBit, calculated as the ratio of market value of equity to book value of equity is used as a proxy for growth opportunities. LEVERAGEit measuring the level of debt employed by the firm and calculated as the proportion of total debt to total assets held by the firm. 𝜂_𝑖 and 𝜆_𝑡 capture unobservable heterogeneity and time effects respectively.

ε_it is the error term.

If an optimal level exists, this means that when a firm deviates from the optimal point it reduces its value. In order to test whether deviating from the target reduces firm value, the working capital investment model (Equation 8) from the previous section was re-estimated in a linear form. The resultant equation is given below.

𝐶𝐴𝑇𝐴_𝑖𝑡 = 𝛽₀+ 𝛽₁₂𝐶𝐿𝑇𝐴_𝑖𝑡 +𝛽₁₃𝑃_{𝐺𝑅𝑂𝑊𝑇𝐻𝑖𝑡} +𝛽₁₄𝑁_{𝐺𝑅𝑂𝑊𝑇𝐻𝑖𝑡}+ 𝛽₁₅𝑆𝐼𝑍𝐸_𝑖𝑡

+ 𝛽₁₆𝐼_𝑖𝑡+𝛽₁₇𝑂𝐶𝐹𝑇𝐴_𝑖𝑡 + 𝛽₁₈𝐿𝐸𝑉𝐸𝑅𝐴𝐺𝐸_𝑖𝑡 + 𝛽₁₉𝑅𝐺𝐷𝑃_𝑖𝑡+ 𝛽₂₀𝑀𝐾𝑇𝑃𝑂𝑊𝐸𝑅_𝑖𝑡 + 𝜂_𝑖 + 𝜆_𝑡+ 𝜀_𝑖𝑡… … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 20

All the variables in the equation remained as they were previously defined.

The residuals obtained from the linear working capital investment model were taken as deviations from the target level of working capital investment. The residuals were termed DFT and were the absolute values of the residuals obtained from the linear estimation model of the working capital investment model in Equation 20. Residuals obtained when LNMCAP was used as a proxy for size were be termed DFT1 and the residuals obtained when LNTA was used as a proxy for size were be termed DFT2. These residuals were included in the working capital investment-firm value model and replaced the variables CATA and CATA² and the alternative;

CAS and CAS². The resultant model is given below.

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𝑉𝐴𝐿𝑈𝐸_𝑖𝑡 = 𝛽₀ + 𝛽₁𝐷𝐹𝑇_𝑖𝑡 +𝛽₂𝑆𝐼𝑍𝐸_𝑖𝑡 + 𝛽₃𝐿𝐸𝑉𝐸𝑅𝐴𝐸𝐺𝐸_𝑖𝑡+ 𝛽₄𝑀𝑇𝐵_𝑖𝑡+ 𝜂_𝑖 + 𝜆_𝑡 + 𝜀_𝑖𝑡… … … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 21

where all the other variables; (SIZEit, LEVERAGEitand MTBit) are as they were previously defined and are the control variables in the equation. DFTit is the absolute value of residuals of estimation results of the working capital investment equation re-estimated in a linear form.

DFTit is the focus independent variable and is expected to be inversely related to the value of the firm, because when firms deviate from their optimum level of working capital investment they reduce their value.

In order to study how both positive (above optimal working capital investment level) and negative (below optimal working capital investment level) deviations affect the value of the firm a dummy variable; Dummy DFT was introduced. Dummy DFT was defined as above-optimal working capital investment level * DFT. Dummy DFT takes the form 1 (for positive residuals to represent above-optimal) and 0 otherwise. The resultant estimation model is shown below

𝑉𝐴𝐿𝑈𝐸_𝑖𝑡 = 𝛽₀+ 𝛽₁𝐷𝐹𝑇_𝑖𝑡 + 𝛽₂𝐷𝑢𝑚𝑚𝑦 𝐷𝐹𝑇_𝑖𝑡+𝛽₃𝑆𝐼𝑍𝐸_𝑖𝑡 + 𝛽₄𝐿𝐸𝑉𝐸𝑅𝐴𝐺𝐸_𝑖𝑡+ 𝛽₅𝑀𝑇𝐵_𝑖𝑡+ +𝜂_𝑖+ 𝜆_𝑡 + 𝜀_𝑖𝑡 … … … … 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 22