Variable definitions

Like most papers attempting to explain the diversification discount, we use the excess value which is the standard methodology developed by Berger and Ofek (1995).⁷

More precisely, excess value EV and imputed value I(V) are defined as

The excess value of a company is the natural logarithm of the ratio of a firm’s actual value to its imputed value. A firm’s imputed value is the sum of the imputed values of its segments, with each segment’s imputed value being equal to the segment’s sales (or assets) multiplied by its industry median ratio of total capital (market value of equity plus book value of debt or market value estimate of debt) to sales (or assets).

V = firm total capital (market value of equity at the end of the calendar year t

plus book value of debt at the end of the calendar year t)

AI = accounting item (sales or assets at the end of the firm fiscal year t) Indi (V/AI)mf = ratio of total capital to an accounting item for the median focused firm in the same industry as segment i

7 Though Mansi and Reeb (2002) contend that diversification leads to lower firm risk, and find that book values of debt are a more downward biased proxy of the market value of debt for diversified firms, relative to undiversified firms. This finding suggests that measures of firm values based on book values of debt systematically undervalue diversified firms (e.g., Glaser and Muller, 2010). However, recent literatures still use excess value for diversification valuation (e.g., Lelyveld and Knot, 2009;

Hund et al., 2010; Chou and Cheng, 2012; Hoechle et al., 2012).

n = number of segments in segment i’s firm at the end of the firm fiscal year t The industry median ratios are based on the narrowest SIC grouping (two-, three-, or four-digit) that includes at least five single-line businesses and sufficient data for computing the ratios. In our regressions, we use excess value as the dependent variable. Following Hoechle et al. (2012), we apply a third alternative excess value measure that is based on both sales and assets. The underlying presumption behind this hybrid measure is that in some industries asset multiples are more meaningful, while in other industries sales multiples could be more meaningful. A lower standard deviation of the multipliers of focused firms in an industry is assumed to imply a higher precision in measurement. Thus it implies a more meaningful imputed segment value. We use this approach to define hybrid excess value by calculating imputed values for each firm segment based on both sales and asset multiples, and choosing the one for which the industry standard deviation is lowest.⁸

We further follow Hund et al. (2010) in using the annual change in excess value (defined as EV_t – EV_t-1) to be the dependent variable in other regressions as well.

Thus, we not only examine whether corporate liquidity eliminate the discount effect of diversification, but further focus on the change of status in each variable over time.

Also, since the methodology of excess value uses book value of debt as a proxy for market value of debt, it captures changes in the market value of equity relative to the book value of the firm, but not changes in the market value of debt relative to the book value of the firm. Therefore, the excess value measure is really a measure of excess shareholder value.

For the measures of corporate liquidity, besides traditionally used cash holdings, we

8 We use asset multiples and hybrid measure and disregard sales multiples. Since focusing on sales multiple can lull ones into assigning tremendous amounts of value to firms that are generating high revenue growth while actually losing significant amounts of money. In addition, revenue is an incomplete measure of performance given its lack of focus on profitability and cash flow.

apply net cash-to-assets ratio as a more representative proxy. It measures the unconditional liquidity which purely results from operating activities other than raising debts. We also use a dummy variable Dummy_HL equals 1 for net cash-to-assets ratio being positive, and 0 otherwise. This dummy proxy provides us with definition of high-liquidity firms and low-liquidity firms. We include other secondary variables consistent with the literature (e.g., Berger and Ofek, 1995), and further include the interaction terms between diversification and corporate liquidity to examine the crossing effect of diversification strategy and corporate liquidity. We provide more details on the definition of the variables in Tab le 1.

Table 1 Definitions of variables

This table displays the definition of variables. The full sample period is from 2005 to 2010.

The sample consists of all firms with data reported on both the Compustat Industrial Annual and Compustat Segments data files.

Variables Proxy for Definition Supporting literature

EV Excess value The log of the ratio of total market value to imputed value using median industry multipliers.

Hund et al (2010), Berger and Ofek (1995)

Hybrid EV Hybrid excess value

The calculating imputed values for each firm segment based on both sales and asset multiples, and choosing the one for which the industry standard deviation is lowest.

Hoechle et al. (2012)

Entropy Entropy The sum of the proportion of sales from segments of firm multiplied by the natural log of reciprocal of proportion of sales from segments of firm.

Hund et al (2010)

Cash Cash-to-assets ratios

Cash and marketable securities divided by total assets.

Cash holdings (including cash equivalents) and short-term investment minus total long-term debt (that is, interest-bearing debt) scaled by total assets.

Passov (2003), Flannery and Lockhart (2009), Islam (2012) Dummy_HL High liquidity A dummy variable that equals 1 for net

cash-to-assets ratio being positive and 0 otherwise.

Profit Profitability The ratio of EBIT to sales. Hund et al (2010), Berger and Ofek (1995)

Capex Growth opportunities

The ratio of capital expenditures to sales. Hoechle et al (2012), Berger and Ofek (1995)