Determinants of corporate call policy for convertible bonds

CORFIN-00626; No of Pages 23 Journal of Corporate Finance xxx (2012) xxx–xxx

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Determinants of corporate call policy for convertible bonds Tao-Hsien Dolly King a,⁎, David C. Mauer b, 1 a b

Belk College of Business, University of North Carolina at Charlotte, Charlotte, NC 28223, United States Mays Business School, Texas A&M University, College Station, TX 77843, United States

a r t i c l e

i n f o

Article history: Received 19 April 2011 Received in revised form 21 June 2012 Accepted 26 June 2012 Available online xxxx JEL classification: G13 G30 G32

a b s t r a c t For a sample of convertible bonds issued during the period 1980 through 2002, we empirically investigate the determinants of call policy. We find that the risk of a failed call over the call notice period helps explain why firms call only after conversion value exceeds call price by a substantial safety premium. We find strong evidence that cash flow considerations and a desire to mitigate agency conflicts influence call policy. We also find evidence that the decision to issue and subsequently call a convertible bond is influenced by a desire to obtain backdoor equity financing and to finance growth options. There is no evidence, however, that firms with favorable inside information are more likely to delay calls. Finally, we find that a significant portion of calls are associated with restructuring and merger activity, and with bond rating upgrades and downgrades. In these cases, there is little if any call delay. © 2012 Elsevier B.V. All rights reserved.

Keywords: Convertible bond Call policy Call delay Call notice period Soft call provision

1. Introduction A considerable amount of research focuses on why firms issue convertible bonds. 2 Once a convertible bond is issued, however, the firm must decide when to call the bond. In a perfect capital market and in the absence of a call notice period, it is well known that it is optimal to call a convertible bond as soon as its conversion value exceeds the effective call price. 3 This policy minimizes the value of the bondholders' conversion option and thereby maximizes the market value of equity. Starting with Ingersoll (1977b), however, researchers document that the average firm substantially deviates from this policy by waiting until the conversion value of the bond exceeds the effective call price by a wide margin. A variety of explanations have been offered for this puzzle including transaction costs associated with a call notice period (Emery and Finnerty, 1989; Ingersoll, 1977b; Jaffee and Shleifer, 1990), signaling (Harris and Raviv, 1985), substitutability of voluntary and forced conversion (Constantinides and Grundy, 1987), and cash flow advantage to not calling and forcing conversion (Asquith and Mullins, 1991). More recently, Asquith (1995) finds that the call delay of the average firm is much smaller than it may appear, once call protection, cash flow advantage, and a safety cushion to avoid a failed call are taken into account.

⁎ Corresponding author. Tel.: +1 704 687 7652. E-mail addresses: [email protected] (T.-H.D. King), [email protected] (D.C. Mauer). 1 Tel.: +1 979 862 1283. 2 For example, see Green (1984), Brennan and Kraus (1987), Stein (1992), and Mayers (1998). 3 The optimal call policy for callable convertible bonds in a perfect capital market was first established by Brennan and Schwartz (1977, 1980) and Ingersoll (1977a). Conversion value is the market value of the shares into which the bond can be converted and the effective call price is the call price from the bond's call price schedule, plus accrued interest from the last coupon payment date. 0929-1199/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jcorpfin.2012.06.011

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Although a large literature has evolved to explain why the average firm deviates from the perfect capital market optimal call policy, there is little literature that empirically examines the joint determinants of corporate call policy for convertible bonds. 4 This is surprising, given the significant variation of observed call policies. In this paper, we fill this gap in the literature by examining the joint determinants of corporate call policy for convertible bonds. We use a large sample of convertible bond issues to investigate the following questions. Do firms delay calls of convertible bonds beyond the amount which can be explained by factors argued to explain call delay? What factors explain variation in call policy for convertible bonds? Do existing theories of optimal call policy, and in particular theories about why firms deviate from the perfect capital market norm, help explain variation in probability of call, call delay, and premium at call announcement? We start our analysis by collecting all publicly traded convertible bond issues by nonfinancial firms during the period from 1980 to 2002. We then use various data sources to identify whether a bond is subsequently called, matures, or continues to be outstanding up through December 31, 2010. Starting with the point in time when a bond is first callable, we compute conversion value and effective call price on a daily basis up through the final disposition of the bond (i.e., call, maturity, or still outstanding). Over this time period, we count the number of trading days that conversion value exceeds the effective call price by various amounts to compute measures of call delay. We find that a nontrivial proportion of our sample is called during the initial call protection period using a soft call provision, which allows the firm to call the bond and force conversion if certain conditions are met. For other bonds, we find that when there is a cash flow advantage to calling (i.e., the dividend on the converted shares is less than the after-tax coupon on the bond) and when the conversion value has reached a sufficient premium above the effective call price, the firm is quick to call the bond. For example, when there is a cash flow advantage, the mean (median) number of trading days that conversion value exceeds 120% of the call price is only 33 (2). Nevertheless, even for this subsample of called bonds there is a considerable variation in call policy, as reflected in a standard deviation of 88 trading days. Call delay statistics for bonds that do not get called tend to be much longer. Surprisingly, this is true even when there is a cash flow advantage to calling. In particular, not called bonds with a cash flow advantage to calling have a mean number of trading days that conversion value exceeds 120% of the effective call price of 419. This suggests that safety premium and cash flow advantage explanations by themselves cannot explain why firms delay calls of convertible bonds. To get a better understanding of why some firms call promptly while others do not, we first focus on a set of theories which argue that the decision to issue convertible bonds is not separable from the call decision. In particular, Stein (1992) argues that a growing firm may find convertible debt financing cheaper than either an equity issue or a straight debt issue when it faces high information asymmetry costs and has high leverage. He argues that calling to force conversion to equity reduces leverage while allowing the firm to get equity into its capital structure through the backdoor. Mayers (1998) extends this idea by arguing that convertible debt financing may help the firm to finance a sequence of current and future investments. Thus, the firm can use convertible debt financing to fund current investment and subsequently use the call option to force conversion to equity when its growth options are in-the-money. We find strong evidence to support both theories in that the convertible bond issuers in our sample have high growth, few internal sources of funds, and face costly external equity and debt financing. We also find that the decision to call coincides with an increase in investment and financing activity. Related to the decision to issue convertibles, Lewis et al. (1999, 2003) and Loncarski et al. (2009) suggest that convertibles are designed to be either “equity-like” or “debt-like” at issue, and that firms are likely to follow a call policy that is linked to the initial purpose of issuing the convertibles. We find that convertibles designed to be more “equity-like” are more likely to be called eventually. We then use our sample of called and not called bonds to examine the determinants of the three key attributes of call policy: (i) probability of call, (ii) call delay, and (iii) premium of conversion value to effective call price at call announcement. We find strong evidence that call policy is influenced by a desire to build a safety premium of conversion value to effective call price, presumably to avoid the risk of a failed conversion-forcing call at the end of the call notice period. In particular, the probability that a firm calls a bond is decreasing in the volatility of its stock price when conversion value does not exceed the effective call price by at least a 20 percent safety premium; a rule of thumb recommended by investment bankers. 5 We find, however, that more liquid firms tend to delay calls and there is some weak evidence that more liquid firms tend to wait for higher premiums of conversion value to effective call price before calling their bonds. These findings are consistent with the notion that more financially constrained firms tend to build larger precautionary cash balances (see, e.g., Kim et al., 1998) and thereby also tend to be more cautious when using a call provision to force conversion. We also find that call policy is influenced by agency conflicts in that firms which are more likely to have agency problems are less likely to call their bonds and significantly delay calls. In contrast, consistent with the Stein (1992) and Mayers (1998) theories, we find that firms experiencing recent growth are more likely to call their bonds and that firms facing costly external equity and debt financing are less likely to delay calls. Consistent with our descriptive analysis, call delays are significantly decreasing in the cash flow advantage of calling. We find no evidence, however, that firms delay calling their convertible bonds to signal favorable information to the market. Indeed, opposite the prediction that firms signal managers' favorable inside information by delaying calls, we find that the probability of calling is increasing and call delay is decreasing the more favorable is managers' inside information. Finally, we find that the probability of calling is increasing and call delay is decreasing when the

4 This is not true of nonconvertible bonds, where Vu (1986) and more recently King and Mauer (2000) provide thorough analyses of the joint determinants of corporate call policy. We discuss the literature that examines specific aspects of the determinants of corporate call policy for convertible bonds below. 5 See footnote 7.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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convertible bond receives a rating upgrade or downgrade, and when the firm is undergoing significant asset and/or financial restructuring, financial distress, or mergers and acquisitions. As noted above, there is little research attempting to explain variation in corporate call policy for convertible bonds. For a sample of convertibles with conversion value greater than the call price in any January or July between July 1971 and July 1981, Constantinides and Grundy (1987) find that the probability a firm calls the bond over the next six months is increasing in the bondholders' yield advantage, which is the difference between the coupon on the bond and the dividend on the converted shares. They find little evidence that any other factor influences the probability of call. For similarly in-the-money convertibles, Ederington et al. (1997) test the influence of a variety of factors on the probability of call for a sample of convertible bonds that were issued between January 1970 and December 1981. They find that the probability of call is decreasing in the firm's cash flow advantage, which following Asquith and Mullins (1991), they define as the difference between the dividend on converted shares and the after-corporate tax coupon on the bond. They too, however, find no evidence that any other factors reliably influence corporate call policy. A handful of studies examine various cross-sectional determinants of the premium of conversion value to call price at call announcement. In a sample of 80 calls between 1977 and 1993, Krishnan and Rao (1996) find evidence that the premium is positively related to firm risk characteristics (e.g., equity beta) and negatively related to the difference between the after-tax coupon on the bond and the dividend on converted shares. Sarkar (2003) examines the determinants of in- or out-of-the-money calls (i.e., positive or negative premium calls) for a sample of called bonds during the period January 1993 to December 1997. His results are consistent with the cash flow advantage hypothesis in that a call is more likely at a premium when the coupon on the bond is low, the dividend on the converted shares is high, and the corporate tax rate is high. Finally, in a sample of 229 calls during the period 1986 to 2000, Altintig and Butler (2005) find little evidence that any factors influence premiums at call announcement after adjusting observed call premiums for the theoretical premium justified by the call notice period. Our paper contributes to the literature in three important ways. First, by focusing on the call policy of firms after convertible bonds are issued, we are able to study the joint determinants of call policy for all convertibles regardless of whether they are actually called. This avoids the bias associated with examining variation in call policy for only called bonds. 6 Second, we provide the first comprehensive analysis of the determinants of the three key attributes of call policy, i.e., probability of call, call delay, and premium at call announcement. Indeed, as far as we know, we are the first to examine the determinants of call delay. Finally, and most importantly, our joint analysis of call policy determinants yields a number of new results. First, the risk of a failed call over the call notice period helps explain why firms delay calls of convertibles. Second, agency conflicts influence call policy in that firms which are more likely to face substantial conflicts have lower call probabilities, longer call delays, and larger premiums at call announcement. Third, growth and costly external finance jointly influence the decision to issue a convertible bond and to subsequently call and force conversion. Fourth, we find no evidence that information signaling encourages firms to delay calls. Fifth, a significant proportion of calls are associated with and influenced by asset/debt restructurings, mergers, and bond rating upgrades and downgrades. Lastly, we confirm that cash flow considerations influence certain attributes of call policy. The remainder of the paper is organized as follows. We develop our hypotheses in Section 2 and describe our sample in Section 3. We examine the growth and financial characteristics of firms issuing convertible bonds and the subsequent investment and financing activity for those that call in Section 4. In Section 5, we test hypotheses about variation in corporate call policy for convertibles. We present conclusions in Section 6. 2. Factors hypothesized to influence convertible bond call policy In a perfect capital market and in the absence of a call notice period the firm should call a convertible bond as soon its conversion value exceeds the call price. In this section, we discuss factors argued in the literature to induce firms to deviate from this perfect capital market call policy. We also derive predictions for how these factors will influence the probability of call, call delay, and premium at call announcement. 2.1. Call notice period When a call is announced, the firm typically gives bondholders a minimum of 30 days to decide whether to convert their bonds into shares or redeem the bonds for the call price. Ingersoll (1977b) is the first to note that the flexibility to choose the maximum of the conversion value or the call price gives bondholders a valuable put option with a maturity equal to the length of the call notice period. Assuming bondholders wait to exercise the option at the end of the notice period, they will choose to redeem the bonds for the call price if conversion value falls below the call price. Because this put option has value, it presumably raises the cost of calling the bond and thereby encourages the firm to delay calling until the conversion value is some nontrivial amount above the call price. As shown by Ingersoll (1977b), however, this logic fails unless it is costly to the firm to have the put option finish in the money. With the addition of realistic underwriting fees associated with financing the cost of a failed call (i.e., the put option finishing in-the-money and the firm having to redeem the bonds for their call price), Ingersoll (1977b) shows that the firm will delay 6 Asquith (1995) is the first to employ this sampling strategy, but his analysis does not focus on the joint determinants of call policy. Ederington et al. (1997) follow a similar sampling strategy, but they focus only on the probability of call for a subset of bonds that are trading at a premium of conversion value to call price.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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calling the bond until the conversion value is above the call price. 7 Consistent with intuition, he also finds that the magnitude of the premium of conversion value to call price is an increasing function of the volatility of the conversion value. In effect, as stock price volatility increases and the bondholders' put option increases in value, the firm will wait for a higher conversion value before calling the bond to minimize the risk of a costly failed call. Subsequent authors, most notably Emery and Finnerty (1989) and Jaffee and Shleifer (1990) expand on this idea by observing that the size of the cash redemption payment resulting from a failed call could cause severe liquidity problems or even financial distress. They argue that riskier firms and firms that would have difficulty raising cash on short notice to redeem bonds would delay calling to force conversion until the probability of a failed call is negligible. We therefore predict that firms with high stock price volatility and/or low liquidity will have longer call delays and will wait for higher premiums of conversion value relative to call price before calling their convertibles. We also predict that the probability of a call is decreasing in volatility and increasing in liquidity. There are, however, two important caveats. First, the relation between probability of call (or premium at call announcement) and stock price volatility is likely to be sensitive to the magnitude of the premium of conversion value to call price. Specifically, we might expect that the strength of the effect of volatility on probability of call (and premium at call announcement) dissipates once a “sufficient” safety premium is reached. 8 Our empirical tests take this possibility into consideration. Second, the predicted effects of volatility on call policy might be reversed if the objective of minimizing the value of the conversion option in the bond dominates concern about the risk of a failed call. Since the value of the conversion option is increasing in volatility, a desire to minimize the value of the option could encourage the firm to call the bond sooner (e.g., at a lower premium) as volatility increases.

2.2. Cash flow advantage Asquith and Mullins (1991) define the cash flow advantage of a convertible bond as the difference between the dividend on the converted shares and the after-tax coupon payment on the bond. All else equal, if the cash flow advantage is positive, the firm should not call to force conversion; and if the cash flow advantage is negative, the firm should call the bond as long as the conversion value exceeds the call price. We therefore predict that the probability of call is decreasing in the cash flow advantage, call delay is increasing in the cash flow advantage, and the premium of conversion value to call price is increasing in the cash flow advantage. Constantinides and Grundy (1987) argue that bondholders will voluntarily convert if the yield advantage of the bond is negative, where the yield advantage is the difference between the coupon on the bond and the dividend on the converted shares. To see how the bondholders' yield advantage interacts with the firm's cash flow advantage, let C denote the annual dollar coupon of the bond, D denote the annual dividend on the converted shares, and τ denote the marginal corporate tax rate. 9 There are three regions: I. II. III.

C(1 − τ) b C b D C(1 − τ) b D b C D b C(1 − τ) b C

Positive cash flow advantage Positive cash flow advantage Negative cash flow advantage

Negative yield advantage Positive yield advantage Positive yield advantage

Note that there is not a region where the firm would call to force conversion (negative cash flow advantage) and bondholders would voluntarily convert (negative yield advantage). This suggests that by focusing our empirical tests on the firm's cash flow advantage we face little risk of falsely predicting that the firm should call to force conversion when in reality the firm would choose not to call because bondholders would voluntarily convert.

2.3. Information signaling Harris and Raviv (1985) propose an information signaling explanation for why firms delay calling convertible bonds. They imagine a situation where the manager has favorable private information about her firm. They argue that by delaying the call, the manager can credibly convey this information to the market and hence raise the value of the firm. Following Barclay and Smith (1995), we use the future change in earnings as a proxy for the manager's inside information and predict a negative relation between the change in earnings and the probability of call, a positive relation between the change in earnings and call delay, and a positive relation between the change in earnings and premium at call announcement. It is possible, however, that managers with favorable inside information may desire to call convertible bonds more promptly, thereby reversing the information signaling predictions. The reason is that a manager with favorable information may call and force conversion now rather than allow bondholders to voluntarily convert later at a much higher conversion value when the 7 Mauer (1993) shows that refunding transaction costs will cause the firm to delay calling a nonconvertible bond when its market value first reaches the call price. He shows that this effect causes the price path of a callable bond to be a concave function of interest rates, reaching a maximum price above the call price. 8 For example, Asquith (1995) argues that a 20 percent safety premium is standard in practice. He notes: “Twenty percent is the minimum percentage usually recommended by investment bankers, and it is the percentage cited by Brigham (1966) in his survey of managers.” 9 Note that we assume bondholders' tax rates on interest income and dividends are the same, and so we ignore personal income taxes. See Asquith and Mullins (1991) for an analysis of some special cases where the tax rates may not be equal.

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inside information becomes public. This alternative view predicts a positive relation between the change in earnings and the probability of call, and negative relations between the change in earnings and call delay and premium at call announcement. 2.4. Agency conflicts Starting with Jensen and Meckling (1976) and Green (1984), the literature argues that convertible debt helps mitigate agency conflicts. Since high growth firms are expected to have more agency problems, researchers argue that these types of firms will use more convertible debt in their capital structures. 10 Using a firm's market-to-book ratio as a proxy for growth opportunities, we would expect that a high market-to-book firm is less likely to call for redemption outstanding convertible debt, since the benefit of having convertible debt in its capital structure will be eliminated. 11 We therefore predict a negative relation between the market-to-book ratio and the probability of call, and positive relations between the market-to-book ratio and call delay and premium at call announcement. A firm with a high market-to-book ratio may also have high external financing costs. This suggests that high market-to-book firms will be more likely to delay a call because it is costly to raise the cash necessary to redeem non-converted bonds. Thus, similar to the agency cost prediction, we would expect high market-to-book firms to be more likely to delay a call and wait for higher premiums of conversion value over call price. 2.5. Backdoor equity financing and financing future growth Stein (1992) argues that a growing firm with a lack of internal funds may find convertible debt financing cheaper than either an equity issue or a straight debt issue. In particular, he argues that convertible debt financing helps to overcome the adverse selection cost associated with external equity financing and the high cost of external straight debt financing because the firm is assumed to be faced with considerable financial distress risk (i.e., it has a high current leverage ratio). The call feature plays an important role in Stein's model in that it allows the firm to force conversion to reduce leverage, and thereby get equity into the firm's capital structure through the backdoor. Mayers (1998) extends Stein's model to consider how convertible debt financing may be used to help finance a sequence of current and future investments. In particular, the firm can use convertible debt financing to fund current investment and then call and force conversion to equity when it chooses to exercise its growth options. Although a forced conversion does not in itself fund future growth options, it frees up internal funds that would otherwise be used to service the convertible debt, and provides additional equity to support new straight and/or convertible debt financing. The Stein (1992) and Mayers (1998) theories imply that the decision to issue convertible bonds is not separable from the decision to call and force conversion. The Stein theory predicts that firms issuing convertibles should have high growth, few internal sources of funds, and face costly external equity and debt financing. In such a setting, he predicts that the firm will be quick to call and force conversion to equity as long as the firm's circumstances do not change (e.g., an unanticipated increase in internal sources of funds) and the firm's stock price rises above the conversion price so that a call will force conversion. Additionally, as originally suggested by Lewis et al. (1999, 2003), we would expect that the convertible issue is “designed” to be more “equity-like” than “debt-like”, having a relatively high probability of eventual conversion when it is issued. In contrast, note that the agency theory explanation for convertibles would predict the opposite; high-growth firms are likely to delay a call and the convertible debt issue will be designed to be more “debt-like” when it is issued. Although not inconsistent with these predictions, Mayers' sequential financing theory provides additional predictions around the time of calls. In particular, Mayers' theory predicts that the decision to call a convertible should coincide with an increase in investment and financing activity. 12 We test the implications of Stein's (1992) backdoor equity hypothesis by comparing the characteristics of firms issuing convertible bonds to matched control samples of firms not issuing convertible bonds, and by comparing the characteristics of convertible bond issuers who call to those who do not call. We test the additional implications of Mayers' (1998) sequential financing hypothesis by examining investment and financing activity around convertible bond calls. Finally, we test the joint implications of Stein's and Mayers' hypotheses for call policy by examining whether firms with high growth and a need for external financing call promptly (i.e., higher probability of call, less call delay, and smaller premium of conversion value to call price). 2.6. Event driven calls and bond rating changes Convertible bonds may be called for a variety of reasons not related to the factors discussed above. In our sample, we find a significant fraction of calls occur around debt and/or asset restructurings, mergers, bankruptcies, and other events. To the extent that these events motivate the decision to call the bond, it is difficult to make predictions about the timing of event driven calls. Calls may also be motivated by bond rating upgrades and downgrades. If the convertible bond is upgraded, the firm may desire to call the bond and issue another with a lower coupon. We therefore predict a positive relation between upgrade and probability 10

See, for example, Kahan and Yermack (1998) and Billett et al. (2007). This assumes that the firm does not replace the called debt with another issue of convertible debt or use some other financial contracting device to mitigate agency conflicts. 12 Emery et al. (1994) and Mayers (1998) find evidence of significant growth in assets, capital expenditures, and financing activity around convertible bond calls. 11

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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of call, and negative relations between upgrade and call delay and premium at call announcement. Of course, holding the bond rating constant, we would have similar predictions if the interest rate falls below the coupon rate on the bond. It is more difficult to predict the influence of a bond rating downgrade on call policy. Since the bond's coupon is now too low given the new higher credit risk, one could argue that the firm would not call the bond to reap the benefits of the low-cost financing. Alternatively, the firm may want to decrease leverage to reduce the probability of financial distress, and would therefore desire to call the bond as soon as possible. The cheap financing argument suggests that a downgrade reduces the probability of call and increases call delay and premium. The increased financial distress alternative suggests the opposite predictions. Ultimately, it is an empirical question how a downgrade influences call policy. 2.7. Other factors Since larger firms may be more sophisticated and have lower costs of external financing, we might expect them to call convertible bonds closer to the perfect capital market policy. Additionally, the original maturity elapsed and the current amount of the bond issue outstanding (relative to the original principal amount) might also influence call policy. For example, if a large proportion of the issue's original maturity is elapsed and/or a small amount of the original principal amount remains (because of sinking fund retirement and/or voluntary conversion), then we expect the firms to be less motivated to go through the cost of calling the bond for redemption. 3. Convertible bond sample, call policy statistics, and variables used in the empirical tests We first describe the construction of the convertible bond sample. We then examine call delay statistics and premiums of conversion value to effective call price at call announcement and over the life of the bonds. Finally, we define the variables used in the empirical tests. 3.1. Convertible bond sample Since we are interested in the factors that motivate firms to call convertible bonds, we start with all convertible bonds that were issued during the period from 1980 to 2002 and track them over their lives until they are called, mature, voluntarily converted, or continue to be outstanding through December 31, 2010. Using the SDC Global New Issues Database, we extract all U.S. publicly-traded convertible securities that were issued during the period 1980 to 2002. Excluding convertible preferred stock issues and issues by financial firms gives an initial sample of 1275 issues, of which 235 (or about 18%) are not callable. We then use SDC, Mergent Fixed Income Securities Database (FISD), and Moody's Manuals to collect information on bond characteristics (e.g., coupon, issue date, and maturity date), conversion information (e.g., conversion ratio at issue and conversion price at issue), and the call price schedule. 13 A requirement that the bond has a valid call price schedule (i.e., a complete set of prices and dates), and excluding bonds with special features (e.g., LYONS, exchangeable, variable rate, and convertible into something other than the issuing firm's common equity) reduces the sample to 1000 issues. For this sample, we collect from Moody's Bond Record (1980–1989), Moody's Annual Bond Record (1990–1999), Mergent Annual Bond Record (2000–2010), FISD, and Bloomberg information on whether a bond was called, including the redemption date and price. For the 532 bonds that are called, we then search for the call announcement date in the Wall Street Journal Index and LexisNexis. We are able to find announcement dates for 438 called bonds. We then collect stock price data from CRSP to compute daily conversion value for each bond from the first call date to the redemption date (if called), maturity date (if not called), or December 31, 2010. 14 After eliminating bonds with insufficient CRSP data, we are left with a final sample of 829 convertible bonds of which 427 are called. Table 1 reports the distribution of the final sample by year issued and year called. Table 2 reports the distribution of convertible bond issues by various categories. Of the 427 called bonds, 32 or 7.5% are called while still in the call protection period using a soft call provision. Additionally, 61 bonds are called within one month after call protection expires and a further 33 bonds are called within the next five months. Both the soft calls and early calls are potentially important, because they are likely to be made when the conversion value is substantially above the call price. These can skew average premiums in the sample, and may partly account for the large premiums at call announcement observed by earlier researchers. A significant number of calls appear to be associated with influential “events”. For every call in the sample, we searched the Wall Street Journal Index and LexisNexis for significant events in the year of the call announcement. We also note whether any firms in the sample were delisted from the CRSP tapes because of merger or bankruptcy in the year of the call announcement. We find that 133 out of 427 calls (or 31% of calls in the sample) have influential events in the year of the announcement, including mergers, debt and/or asset restructuring, financial distress, and bankruptcy. Since these calls may be motivated for reasons not related to the factors discussed in Section 2, we are careful to analyze them separately, or dummy them out in multivariate tests. Observe in Table 2 that 21% of the sample has no call protection (i.e., they are callable immediately after issue), 48% of the sample has hard call protection, and 31% of the sample has soft call protection. For the 259 bonds with soft call protection, the 13

We also gather information on call protection and whether the bond has a soft call feature from SDC, FISD, and Moody's Manuals. The first call date is the issue date for bonds without hard call protection, or when a bond has a soft call provision. As discussed above, a soft call provision allows the firm to call the bond only if certain conditions are met. We discuss the various combinations of hard, soft, and no call protection below. 14

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 1 Distribution of convertible bond sample by year issued and year called. The sample includes all convertible bond issues of nonfinancial companies during the period 1980 to 2002 that are convertible into the common stock of the issuing company and for which data is available to compute daily conversion value from issue date to call date, maturity date, or December 31, 2010. The initial sample of convertible bond issues is from the SDC Global New Issues Database. Year

Issued

Called

1980–1981 1982–1983 1984–1985 1986–1987 1988–1989 1990–1991 1992–1993 1994–1995 1996–1997 1998–1999 2000–2001 2002–2003 2004–2005 2006–2007 2008–2010 Total

102 104 104 164 46 50 87 32 57 23 53 7

10 30 21 63 29 31 68 46 60 29 12 7 12 8 1 427

829

typical soft call provision specifies that the firm cannot call the bond unless the closing price of the common stock exceeds 130% of the conversion price (i.e., the par value of the bond divided by the number of shares received at conversion) for at least 20 out of 30 consecutive trading days. Note that soft call premiums as high as 50% are not unusual. Additionally, as noted above, 7.5% of the calls in the sample are executed during soft call protection using a soft call provision. For the entire sample of 829 convertible bonds, the mean (median) minimum call notice period is 28 (30) days, with a range from 10 to 60 days. This “minimum call notice period” is reported in the bond issue prospectus and specifies the minimum number of days the firm must notify bondholders in advance of redemption. When the bond is called, the actual call notice period tends to be longer. Thus, for the 427 called bonds, the mean (median) actual call notice period is 31 (32) days, with a range from 12 to 92 days. Lastly, Table 2 reports the incidence of bond rating upgrades and downgrades in the sample for called bonds and not called bonds, respectively. For called bonds, we compare the Moody's and/or Standard and Poor's bond rating at issue to the rating immediately before call announcement to classify the bond as receiving an upgrade, downgrade, or no change; and for not called bonds, we compare the Moody's and/or Standard and Poor's bond rating at issue to the rating immediately before the maximum premium of conversion value to call price over the life of the bond to classify the bond. 15 As seen in the table, nontrivial proportions of the called bond sample receive an upgrade (17%) or a downgrade (23%) immediately prior to being called. In comparison, we see a smaller proportion of not called bonds receiving upgrades (7%), and a smaller but still nontrivial proportion of not called bonds receiving downgrades (14%). Overall, the distributions of rating changes for called and not called bonds are significantly different from each other at the 1% level according to a chi-square test.

3.2. Call delays and premiums For each bond in the sample, we compute the number of trading days that conversion value exceeds the effective call price by various amounts from the day that call protection expires through the call announcement day for called bonds and the earlier of the bond maturity or December 31, 2010 for not called bonds. For bonds with a soft call provision, the days delayed count starts as soon as the soft call condition is satisfied and the firm does not call the bond. The daily conversion value is the conversion ratio (i.e., number of shares received per bond upon conversion) times the daily closing price per share. The conversion ratio is adjusted for stock splits and stock dividends. The effective call price is the call price from the call price schedule, plus accrued interest from the last coupon payment date. Table 3 reports the cumulative number of trading days that the bond is not called while conversion value exceeds the effective call price (Panel A) or exceeds 120% of the effective call price (Panel B), for bonds that are called and for bonds that are not called. The table also reports days delayed when the firm has a cash flow advantage to call (i.e., dividend on converted shares is less than after-tax coupon on the bond) and when the firm does not. The dividend on converted shares is the largest annual dividend per share on the common stock times the conversion ratio. The largest annual dividend per share is from the period starting with the year call protection (or soft call) ends through the earlier of call year, bond maturity year, or 2010. The after-tax coupon is the

15 In all cases where we are able to collect information on both Moody's and Standard and Poor's bond ratings, the upgrade, downgrade, and no change classifications are in agreement. Bond ratings at issue are collected from SDC and FISD. Bond ratings immediately before call announcement or maximum premium are collected from FISD, Moody's Bond Record, and Standard and Poor's Bond Guide. For not called bonds, we also collect bond ratings immediately before the date where conversion value exceeds the call price by at least 10%, 20%, 30%, and 40% for 25 or more consecutive trading days. Our results are robust whether we use these ratings or the rating immediately before the maximum premium to classify not called bonds.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 2 Convertible bond sample by categories. Category

No. of bonds

Called Called during call protection perioda Called within one month after protection Called within six months after protection Not called Influential events around call No influential events around call Types of influential events Delisted — merger or bankruptcy Merger and acquisition activity Debt and/or asset restructuring Significant operating losses Financial distress Hard call protection only Range = 1–5 years Mean = 2.15 years Median = 2 years Soft call protection Range = 1–15 years Mean = 2.57 years Median = 2 years No hard or soft call protection Types of soft call provisions — x out of y days by z%b x y z 20 30 30% to 75% 20 20 40% or 50% 30 30 40% or 50% All other c Minimum call notice period Range = 10–60 days Mean = 28.18 days Median = 30 days Actual call notice periodd Range = 12–92 days Mean = 30.69 days Median = 32 days Bond rating changee Called bonds Upgrade Downgrade No change Not call bonds Upgrade Downgrade No change Total no. of issues

427 32 61 94 402 133 294 33 59 21 17 3 396

% of category 7.49 14.29 22.01 31.15 68.85 24.81 44.36 15.79 12.78 2.26

% of total no. 51.51 3.86 7.36 11.34 48.49 16.04 35.46 7.73 13.82 4.92 3.98 0.70 47.77

259

31.24

174

20.99

215 24 14 6 829

83.01 9.27 5.41 2.32

427

25.93 2.90 1.69 0.72 100.00

51.51

72 100 255

16.86 23.42 59.72

8.69 12.06 30.76

29 55 318 829

7.21 13.68 79.10

3.50 6.63 38.36 100.00

a

Called during the call protection period using a soft call provision. Call allowed if stock price exceeds the conversion price by at least z% for x out of y consecutive trading days. As reported in the bond issue prospectus. d From call announcement date to redemption date. e For called (not called) bonds, we compare the Moody's and/or Standard and Poor's bond rating at issue to the rating immediately before call announcement (maximum premium of conversion value to call price over the life of the bond) to classify the bond as receiving an upgrade, downgrade or no change. b c

annual coupon payment multiplied by one minus the contemporaneous (with the maximum dividend) marginal corporate tax rate from the Graham simulated tax rate database. As seen in Panel A, the average delay for bonds that are called is 118 trading days while the average delay for not called bonds is 582 trading days. The median days delayed are much shorter, with that for not called bonds shorter than that for called bonds (i.e., 17 versus 39 trading days). The reason is that a large proportion of not called bonds are close to maturity, which tends to shorten the median call delay for not called bonds. Observe that call delays tend to be shorter when the firm has a cash flow advantage to calling. For example, average (median) call delay for called bonds is 78 (41) trading days when the firm has a cash flow advantage to calling versus 461 (316) trading days when it does not. Notice in Panel B, however, that call delays are dramatically shorter when a safety premium of 20% must be crossed before a call is classified as delayed. In particular, with a 20% safety premium and when the firm has a cash flow advantage to calling, the average (median) call delay is only 33 (2) trading days. Thus we see that firms that do call do so very quickly when they have a comfortable safety premium and when there is a cash flow advantage to calling. An interesting question is what happens to the bonds that are not called? On the one hand, we see that when there is a cash flow advantage to calling, approximately one-half of Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 3 Descriptive statistics of the number of trading days that convertible bond calls are delayed. Call delay is the number of trading days after call protection expires that conversion value exceeds the effective call price (Panel A) or exceeds 120% of the effective call price (Panel B) and the bond is not called. The conversion value is the conversion ratio (i.e., number of shares received per bond upon conversion) times the daily closing price per share. The conversion ratio is adjusted for stock splits and stock dividends. The effective call price is the call price per bond from the call price schedule, plus accrued interest from the last coupon payment date. The days delayed count starts the day after call protection expires and continues through the call announcement day for called bonds and the earlier of the bond maturity or December 31, 2010 for bonds that are not called. For bonds with a soft call provision, the day count starts as soon as the soft call condition is satisfied and the firm does not call the bond. The day counts reflect the cumulative number of days, not the consecutive number of days. There is a cash flow advantage (disadvantage) to the firm from calling the bond if the dividend on the shares received upon conversion is less (greater) than the after-tax coupon payment on the bond. The dividend is the largest annual dividend per share on the common stock times the conversion ratio. The largest annual dividend per share is from the period starting with the year call protection (or soft call) ends and ending the earlier of call year, bond maturity year, or 2010. The after-tax coupon payment is the annual coupon multiplied by one minus the contemporaneous marginal corporate tax rate from the Graham simulated tax rate database. Event calls include cases where (1) the firm has significant operating losses in the year of the call announcement (17 calls), (2) the firm has significant merger and acquisition activity in the year of the call announcement (59 calls), (3) the firm was delisted from the CRSP database within a year of the call announcement because of merger or bankruptcy (33 calls), (4) the firm has significant debt and/or asset restructuring in the year of the call announcement (21 calls), or (5) the firm was in financial distress (e.g., debt downgrades) in the year of the call announcement (3 calls). Group

All bonds

Cash flow advantage to call

Cash flow disadvantage to call

Dividend b after-tax coupon Mean

Median

SD

N

Mean

Dividend > after-tax coupon

Median

SD

N

Mean

Median

SD

N

41 1 51 15

125 144 112 993

382 122 260 295

461 241 532 784

316 112 371 422

849 510 924 1281

45 11 34 107

Panel B. Number of trading days delayed: conversion value ≥ (1.20)(Effective call price) Called 65 1 260 427 33 2 Event calls 35 0 157 133 22 0 Called − event calls 78 7 294 294 38 8 Not called 487 1 987 402 419 1

83 94 78 901

382 122 260 295

336 176 388 677

131 47 183 599

715 442 781 1175

45 11 34 107

Panel A. Number of trading days delayed: conversion value >effective call price Called 118 39 319 427 78 Event calls 67 1 204 133 51 Called − event calls 141 53 357 294 90 Not called 582 17 1082 402 508

not called bonds never reach the 20% safety premium on a single trading day (i.e., the median call delay is only 1 trading day). On the other hand, when there is a cash flow disadvantage to calling, firms clearly refuse to call regardless of the number of trading days that conversion value exceeds 120% of the effective call price. Indeed, for this sample of bonds, the median number of trading days that conversion value exceeds 120% of the effective call price is 599 days or about 29 months based on 21 trading days in a month. In unreported results, we compute call delay for the subsamples of convertible bonds issued from 1980 to 1989 (520 bonds) and from 1990 to 2002 (309 bonds) to see if call delay varies over time. Interestingly, we find that delays are much shorter during the more recent time period. For example, for called bonds the average (median) delay is 147 (50) trading days for bonds issued in 1980–1989, while the average (median) delay is 41 (3) trading days for bonds issued in 1990–2002. However, when the firm has a cash flow advantage to calling and when the delay criterion is that conversion value must exceed the effective call price by at least 20%, the comparison is much closer. Thus, average (median) delay is 36 (3) trading days for bonds issued in 1980–1989, while the average (median) delay is 22 (0) trading days for bonds issued in 1990–2002. We also compute call delay statistics for the subsample of bonds that mature before the end of the sample period (i.e., December 31, 2010) versus those that maturity after the end of the sample period, and for subsamples of bonds grouped by original maturity less than 10 years and original maturity greater than 10 years. Call delay statistics are virtually identical for calls grouped by bonds that mature before the end of the sample period (655 bonds) versus those that mature after the end of the sample period (174 bonds). For example, for bonds with a cash flow advantage to calling and with premiums that exceed the effective call price by at least 20%, the average call delays for both subsamples are 33 days and the median call delays differ by 1 day (i.e., 3 days versus 2 days, respectively). Call delay statistics also tend to be similar for bonds grouped by original maturity. In particular, for bonds with a cash flow advantage to calling and for which the conversion value exceeds the call price by at least 20%, the average (median) call delay for bonds with a maturity less than 10 years is 27 (0) days while it is 34 (1) days for bonds with a maturity greater than 10 years. Thus, there are no systematic differences in call delay statistics for bonds maturing before and after our sample period ends or for bonds grouped by original maturity. These results are available upon request. Overall, our evidence on call delays is consistent with the findings of Asquith (1995), in that bonds that have a cash flow advantage to calling and that have their conversion value exceed a reasonable safety premium are called with relatively little delay. This is the experience of the average/median firm, however. A quick perusal of the variation in call delay in any category of called or not called bonds in Table 3 reveals that there is a considerable amount of variation in call delay in the sample. It is important to investigate whether factors not captured by safety premium and cash flow advantage can help explain this variation. Panel A in Table 4 reports the premium of conversion value to effective call price at call announcement for called bonds and various subsamples of called bonds. Note that the premium is computed one trade day prior to the call announcement day to mitigate the influence of the announcement on the conversion value. Similar to previous researchers, we find that calls are announced when the conversion value is above the call price. For the full sample of 427 called bonds, the average (median) Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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T.-H.D. King, D.C. Mauer / Journal of Corporate Finance xxx (2012) xxx–xxx

Table 4 Descriptive statistics of the premium of conversion value to effective call price. The premium of conversion value (CV) to effective call price (CP) is computed as (CV/CP − 1) × 100. The conversion value is the conversion ratio (i.e., number of shares received per bond upon conversion) times the daily closing price per share. The conversion ratio is adjusted for stock splits and stock dividends. The effective call price is the call price per bond from the call price schedule, plus accrued interest from the last coupon payment date. In Panel A, the premium at call announcement is computed one trade day prior to the call announcement day to mitigate the influence of the call announcement on the conversion value. In Panel B, the maximum premium is over the period from the first call date (or soft call protection end date) to the call announcement date for called bonds, or the minimum of the maturity date or December 31, 2010 for not called bonds. There is a cash flow advantage (disadvantage) to the firm from calling the bond if the dividend on the shares received upon conversion is less (greater) than the after-tax coupon payment on the bond. The dividend is the largest annual dividend per share on the converted bond times the conversion ratio. The largest annual dividend per share is from the period starting with the year call protection (or soft call) ends and ending the earlier of call year, bond maturity year, or 2010. The after-tax coupon payment is the annual coupon multiplied by one minus the contemporaneous marginal corporate tax rate from the Graham simulated tax rate database. Event calls are as described in Table 3. Soft and early calls include cases where the firm called during the deferred call period using a soft call provision (32 calls) or called within one month after the end of call protection (61 calls). Note that 25 event calls were called early, so that the number of calls in the fourth row of Panel A is 427 − 133 − 32 − 61 + 25 = 226. Group

All bonds

Mean

Median

SD

N

Panel A. Premium of conversion value to effective call price (%) at call announcement Called 29.57 18.57 82.78 427 Event calls 12.89 −3.95 80.12 133 Called − event calls 37.12 22.99 82.99 294 Called − event calls − soft and early calls 33.89 19.61 90.09 226

Cash flow advantage to call

Cash flow disadvantage to call

Dividend b after-tax coupon

Dividend > after-tax coupon

Mean

Median

SD

N

Mean

Median

SD

N

28.38 13.44 35.39 29.84

19.40 −3.66 23.36 20.43

77.42 81.25 74.69 80.26

382 122 260 199

36.69 6.82 50.32 63.75

23.22 −5.03 13.60 14.16

119.66 69.29 131.00 141.89

45 22 34 27

Panel B. Maximum premium of conversion value to effective call price (%) during life of bond Called 53.25 31.45 93.40 427 51.13 Event calls 41.68 15.92 98.09 133 42.00 Called − event calls 58.49 36.55 90.89 294 55.41 Not called 150.78 24.86 582.44 402 155.63

31.66 16.40 36.42 19.19

88.32 100.35 81.94 663.30

382 122 260 295

71.29 13.44 82.00 137.42

27.20 −3.66 43.32 43.44

128.60 71.77 141.44 250.61

45 22 34 107

premium is 30% (19%). In unreported results, we find that the premiums at call announcement are roughly similar in the 1980s and 1990s. In particular, the average (median) premiums for the 1980–1989 and 1990–2002 subsamples are 28% (19%) and 33% (16%), respectively. A similar equivalence is observed for bonds that mature before and after our sample period end of December 31, 2010 and for bonds grouped by original maturity. For example, the median call premiums for bonds maturing before and after the end of the sample period are both 19%, while the median call premiums for bonds with a maturity less than and greater than 10 years are 17% and 19%, respectively. As with the call delay statistics, these results are available upon request. To estimate the economic cost to the firm from allowing conversion value to exceed the effective call price by such a wide margin, for the median firm in the sample we compute the value of the convertible bond at issue and at the optimal call point assuming the firm follows the perfect capital market optimal call policy or the suboptimal policy of calling when conversion value is 19% above the effective call price (i.e., a “perfect foresight policy” where the call price equals the actual stock price on the call announcement date). As shown in the Appendix A, given the median sample firm's conversion value to effective call price at the call announcement of 18.57% and the $50 million principal value of the convertible bond, the economic loss at issue is $4.3 million and the economic loss at the optimal call point is about $3.7 million. Thus it appears as if the premiums observed in the sample are economically significant. Perhaps not surprising, the average (median) premium is smaller when there is a cash flow advantage to calling the bond than when there is not; the comparison is 28% (19%) versus 37% (23%). Also note that the full sample statistics conceal significantly smaller premiums for the 133 “event calls”, where the average (median) premium is only 13% (− 4%). Panel B in Table 4 reports statistics for the maximum premium over the period from the first call date (or soft call protection end date) to the call announcement date for called bonds, or the minimum of the maturity date or December 31, 2010 for not called bonds. Not surprisingly, maximum observed premiums for called bonds tend to be significantly higher than premiums at call announcement. More interesting, however, are the maximum premiums for not call bonds. Focusing on the sample where the firm has a cash flow advantage to calling, note that although the average maximum premium is quite large at 156%, the median maximum premium is only 19%. Apparently, the median firm does not view 19% as a large enough safety premium to allow it to call the bond despite there being a cash flow advantage from doing so. To sum up, consistent with the findings of call delay above, there is significant variation in the premium of conversion value to effective call price at call announcement (for called bonds) and at maximum premium (for called and not called bonds). We subsequently explore the factors that help explain the variation in call delay and premium. 3.3. Variables used in the empirical tests We match the issuers of the 829 convertible bonds in the sample with firms in the Compustat database to draw various comparisons. We find a Compustat match (criteria discussed below) with complete data to compute all of the variables discussed below for the issuers of 765 convertible bonds. In this sample, 400 bonds are called and 365 bonds are not called. Depending on the analysis, the variables discussed below are typically computed at different points in time (e.g., immediately prior to issue date Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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and call announcement date for called bonds). We discuss the timing of variables as we present our empirical tests. All variables discussed below are winsorized at the 1% and 99% levels for the particular variable in the full sample, except fraction of original maturity elapsed and dummy variables. Lastly, all dollar variables are inflation-adjusted to December 2009 using the CPI. 3.3.1. Call notice period We test for the influence of call notice period on call policy using stock price volatility and liquidity. We use a minimum of 100 and a maximum of 250 continuously compounded daily stock returns prior to the relevant day (e.g., call announcement day for called bonds) to compute the monthly standard deviation of the stock price. We compute liquidity as the ratio of cash plus marketable securities to the aggregate call price, where the aggregate call price is computed as the total number of bond outstanding times the effective call price per bond. We expect a negative (positive) relation between probability of call and volatility (liquidity), and positive (negative) relations between call delay and premium at call announcement and volatility (liquidity). 3.3.2. Cash flow advantage We use the ratio of the dividend on converted shares to the after-tax coupon on the bond to measure the cash flow advantage of calling. As discussed above, the dividend is the largest annual dividend per share over the life of the bond times the contemporaneous conversion ratio, and the after-tax coupon is the annual coupon payment times one minus the marginal corporate tax rate from the Graham database. We expect a negative relation between the probability of call and the ratio of dividend to after-tax coupon, and positive relations between call delay and premium at call announcement and the ratio of dividend to after-tax coupon. 3.3.3. Information signaling Insiders' anticipated change in firm quality is proxied by the future change in earnings. We compute the future change in earnings as the difference between EBIT in year t + 2 and EBIT in year t divided by the absolute value of EBIT in year t, where for example, year t + 2 is the fiscal year end two years after the call announcement date and year t is the fiscal year end immediately prior to the call announcement date. The information signaling hypothesis predicts a negative relation between the probability of call and the change in earnings, and positive relations between call delay and premium at call announcement and the change in earnings. As noted above, however, it is possible that these predictions are reversed if the firm's objective is to minimize the value of the bondholders' conversion option. 3.3.4. Agency conflicts The potential for agency conflicts is proxied by the market-to-book asset ratio, where the market value of assets is computed as the book value of assets plus the difference between the market and book values of equity. We expect a negative relation between the probability of call and the market-to-book ratio, and positive relations between call delay and premium at call announcement and the market-to-book ratio. 3.3.5. Backdoor equity and sequential financing Growth and the need for external funding are predicted to motivate the use of convertible bond financing and the desire to call the bonds and force conversion to equity. At issue and at several points in time during the life of a convertible bond, we use several measures of growth. These include asset growth, CAPEX growth, and the market-to-book ratio (as defined above), where asset (CAPEX) growth is defined as the change in the book value of total assets (CAPEX) from year − 1 to 0 divided by the book value of total assets (CAPEX) in year − 1, with year 0 being the reference year (e.g., year of issue). 16 We use the firm's financing deficit to measure the demand for external financing, which following Frank and Goyal (2003) and John and Litov (2010), is computed as the sum of cash dividends, investments, and change in working capital minus internal cash flows, with all components scaled by the book value of total assets. We use several other variables to measure debt-related financing costs (leverage ratio), equity-related financing costs (offer size, stock price run up, and change in earnings), and liquidity/profitability (cash and return on assets). 17 Finally, following Lewis et al. (1999, 2003) and Loncarski et al. (2009), we measure the equity component of a convertible bond at issue (i.e., the probability that the bond will be converted into equity at maturity) with option 16 Note that we also use the market-to-book ratio to proxy for the potential for agency conflicts, with the prediction that high market-to-book value firms will desire to keep their convertible bonds outstanding as a financial contracting devise to mitigate agency conflicts. Both the agency and the Mayers' (1998) theories predict that firms issuing callable bonds will have high market-to-book values at issue. During the life of the bond, however, the agency theory perspective predicts that firms have little incentive to call convertible bonds promptly, while the backdoor equity financing theory of Stein (1992) and the sequential financing theory of Mayers (1998) predict that the firm will be much more likely to call the bonds promptly when a call will force conversion. 17 Stein's (1992) theory for why firms issue convertibles assumes that firms face considerable debt and equity-related financing costs. He assumes that debt costs result from financial distress risk attributable to high current leverage and that equity costs result from adverse selection caused by asymmetric information. We measure leverage as the ratio of long-term debt or long-term debt plus debt in current liabilities (i.e., total debt) to the book value of assets. We assume that convertible debt issuers face high equity-related financing costs when the offer size is large, the issue follows a substantial increase in the firm's stock price, and the change in earnings is large. The offer size is computed as the log of offer size in constant dollars, the stock price run-up is computed as the cumulative raw return of the stock over the 60 days prior to the issue, and the change in earnings is computed as described above under information signaling. Finally, cash is the ratio of cash plus marketable securities to the book value of assets and return on assets is the ratio of earnings before interest, taxes, depreciation, and amortization (EBITDA) to the book value of total assets. We examine these variables at points in time during the life of the convertible bond issue, since a change in liquidity/profitability may influence the need to call the bonds.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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delta. The computation is Δ ≡ exp(− δT)N(d1), where δ is the issuing firm's continuously compounded dividend yield for the fiscal year-end immediately preceding pthe ffiffiffi issue date, T is the number of years until maturity for the convertible bond, 
  d1 ¼ lnðS=X Þ þ r−δ þ σ 2 =2 T =σ T , S is the stock price at the issue date, X is the conversion price, r is the continuously compounded risk-free rate estimated from a 10-year U.S. Treasury bond on the issue date, σ is the annualized standard deviation of the continuously compounded common stock returns using a minimum of 100 and a maximum of 250 daily stock returns immediately prior to the issue date, and N(⋅) is the cumulative probability under a standard normal distribution function. We anticipate that relative to industry-matching firms and non-calling convertible bond issuers, firms that call their convertibles will have greater growth and demand for external funds, and will design their convertible debt to be more equity-like (i.e., larger delta) at issue. Additionally, we expect that the probability of call is increasing in growth and the financing deficit, and call delay and the premium at call announcement are decreasing in growth and the financing deficit. 3.3.6. Event driven calls and bond rating changes We either estimate regressions with and without event driven calls or use an event call dummy variable. Similarly, we use dummy variables for bond rating upgrades and downgrades. Although it is uncertain how call policy is affected by influential events and bond rating downgrades, we expect a positive relation between upgrade and probability of call, and negative relations between upgrade and call delay and premium at call announcement. 3.3.7. Other factors We use a few other control variables in our regressions. Firm size is the natural logarithm of total assets in constant dollars. We also control for the bond's remaining maturity and amount outstanding. We transform remaining maturity into fraction of original maturity elapsed, which is computed as the number of months from the time the bond is issued to the reference month (e.g., call announcement month), converted into years, divided by the maturity year minus the offer year. Additionally, we scale the amount outstanding by the original issue amount. 4. Convertible bond issuance and the decision to call Table 5 reports mean and median growth and financial characteristics of convertible bond issuers immediately prior to the issue date (Panel A), the first call date (Panel B), and the maximum premium date (Panel C). The sample is grouped by whether the bond is called or not called, and for each group we report characteristics for an industry-matching sample. The industry matching samples are constructed using the firm with the median characteristic (e.g., asset growth, CAPEX growth, etc.) in the sample firm's 4-digit SIC code. Consistent with Stein's (1992) theory, Panel A reveals that firms issuing convertible bonds have high growth, strong demand for external funds, and face costly external equity and debt financing. In particular, observe that mean and median asset growth, CAPEX growth, and financing deficit are significantly larger for convertible bond issuers than their industry matches. Additionally, we see in Panel A that convertible bond issuers tend to have significantly higher leverage ratios, higher stock price run up, and larger changes in earnings than their industry matches, which suggests that convertible bond issuers tend to face higher costs of debt and equity financing. 18 Interestingly, observe that the called bond sample has significantly larger mean and median delta (i.e., the probability that the bond will be converted to equity) than the not called bond sample. This suggests that called bonds are “designed” to be called when they are issued, which is also consistent with Stein's backdoor equity financing argument. Finally, note that consistent with agency theory, not called bonds have significantly larger mean and median market-to-book ratios than called bonds. Panels B and C examine characteristics at the first call date and the maximum premium date, respectively. The first call date is the end of hard or soft call protection; or in the case where a bond has no hard or soft call protection, the first call date coincides with the issue date. The maximum premium date is the day over the period from the first call date to the call announcement date for called bonds or the minimum of the maturity date or December 31, 2010 for not called bonds where the premium of conversion value to effective call price reaches a maximum. As seen in the Panels, convertible bond issuers continue to have significantly higher growth rates and leverage ratios than their industry comparison firms around the first call date (Panel B) and maximum premium date (Panel C). Table 6 reports investment and financing activity in the years around convertible bond calls (i.e., forced conversion). According to Mayers' (1998) sequential financing theory, calls of convertible bonds which force conversion should coincide with heavy investment and financing activity. Thus we examine capital expenditures, issuance of long-term debt, issuance of common and preferred stock, and total sources of funds for calling firms and their industry matching firms for years − 5 through + 4 relative to the year of the convertible bond call (year 0). 19 The activity levels are scaled by total assets and the industry matching sample is constructed using the median firm in the sample firm's 4-digit SIC code. Finally, since Compustat includes conversion proceeds in common equity, we subtract conversion proceeds from common and preferred stock in year 0. 18 Consistent with our interpretation of convertible issuer characteristics, Brown et al. (2011) find that the forecasted issue cost of a seasoned equity issue for a sample of convertible bond issuers during 2000–2008 is higher than the actual cost of issuing convertible bonds, where issue cost is measured as the sum of the offering discount and gross spread. 19 We also examined R&D expenditures in the years around convertible bond calls but found no significant differences between calling firms and industry matching firms.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 5 Investment and financing characteristics of firms calling and not calling convertible bonds at the issue date, first call date, and maximum premium date. Variable

Called bonds (N = 400)a

Industry match (N = 400)b

Not called bonds (N = 365)

Industry match (N = 365)b

Mean

Median

Mean

Median

Mean

Median

Mean

Median

Panel A. Issue date Asset growth CAPEX growth Market-to-book ratio Financing deficit Leverage ratio (long-term debt) Leverage ratio (total debt) Log of offer size Stock price run up Change in earnings Delta Cash plus mkt. sec. ÷ total assets Return on assets

0.436*** 0.034*** 1.679** 0.094*** 0.241 0.308** 5.458*** 0.129 0.937** 0.715*** 0.113** 0.133*

0.291*** 0.015* 1.370** 0.052*** 0.205** 0.298** 4.972*** 0.129 0.552*** 0.777*** 0.067* 0.145**

0.196*** 0.015*** 1.608 0.036*** 0.158*** 0.280*** NA 0.054*** 0.445* NA 0.109 0.090***

0.073*** 0.003*** 1.490*** 0.021*** 0.182*** 0.280*** NA 0.001*** 0.275*** NA 0.103*** 0.107***

0.635 0.056 1.834 0.136 0.224 0.340 6.016 0.142 0.191 0.619 0.139 0.120

0.428 0.024 1.540 0.099 0.179 0.321 5.628 0.123 0.331 0.744 0.070 0.127

0.157*** 0.012*** 1.617*** 0.037*** 0.119*** 0.270*** NA 0.060*** 0.243 NA 0.117** 0.088***

0.099*** 0.003*** 1.501 0.021*** 0.109*** 0.282*** NA 0.015*** 0.232 NA 0.093 0.104***

Panel B. First call date Asset growth CAPEX growth Market-to-book ratio Financing deficit Leverage ratio (long-term debt) Leverage ratio (total debt) Cash plus mkt. sec. ÷ total assets Return on assets

0.209* 0.010 1.617 0.035 0.323* 0.339** 0.108* 0.131***

0.121 0.006 1.332 0.023 0.303 0.323 0.065 0.134***

0.105*** 0.006 1.585 0.028 0.165*** 0.283*** 0.110 0.092***

0.074*** 0.003 1.526*** 0.018 0.197*** 0.292*** 0.104*** 0.096***

0.263 0.016 1.578 0.048 0.299 0.369 0.125 0.110

0.137 0.005 1.442 0.023 0.298 0.355 0.076 0.108

0.105*** 0.007* 1.599 0.032* 0.126*** 0.279*** 0.120 0.076***

0.077*** 0.002 1.495** 0.018 0.117*** 0.293*** 0.100** 0.095***

Panel C. Maximum premium date Asset growth CAPEX growth Market-to-book ratio Financing deficit Leverage ratio (long-term debt) Leverage ratio (total debt) Cash plus mkt. sec. ÷ total assets Return on assets

0.242*** 0.018 1.666*** 0.042* 0.299 0.352 0.105*** 0.134***

0.149* 0.084 1.379*** 0.017 0.296 0.325 0.059* 0.136**

0.207* 0.016 1.636 0.024*** 0.161*** 0.282*** 0.114 0.081***

0.171** 0.012* 1.589*** 0.016 0.185*** 0.289*** 0.107*** 0.088***

0.424 0.024 2.365 0.064 0.281 0.340 0.138 0.118

0.173 0.010 1.600 0.016 0.271 0.317 0.076 0.125

0.201*** 0.014 1.684*** 0.038** 0.123*** 0.271*** 0.125 0.067***

0.169 0.010 1.572 0.021 0.120*** 0.290*** 0.100*** 0.085***

Notes: all variables are measured at the fiscal year end immediately prior to the issue date (Panel A), first call date (Panel B), or maximum premium date (Panel C). The first call date is the end of hard or soft call protection; or in the case where a bond has no hard or soft call protection, the first call date coincides with the issue date. The maximum premium date is the day over the period from the first call date to the call announcement date for called bonds or the minimum of the maturity date or December 31, 2010 for not called bonds where the premium of conversion value to effective call price reaches a maximum. The called and not called bond industry matching samples are constructed using the median firm in the sample firm's 4-digit SIC code. Asset growth is the change in the book value of total assets from year −1 to 0 divided by the book value of total assets in year −1, where year 0 is the reference year (e.g., year of issue in Panel A). CAPEX growth is the change in capital expenditures from year −1 to 0 divided by the book value of total assets in year −1. The market-to-book ratio is computed as the sum of the book value of total assets plus the market value of common stock minus the book value of common stock all divided by the book value of total assets. The financing deficit measures the demand for external financing and is computed as the sum of cash dividends, investments, and change in working capital minus internal cash flows. All of the components of the financing deficit are scaled by the book value of total assets. See Frank and Goyal (2003) and John and Litov (2010) for details of the financing deficit calculation. The leverage ratio based on long-term debt is computed as the ratio of long-term debt to the book value of total assets and the leverage ratio based on total debt is computed as the ratio of long-term debt plus debt in current liabilities to the book value of total assets. The log of offer size is the natural logarithm of the dollar amount (in millions) of the convertible bond issue. The stock price run up is the cumulative raw return of the stock over 60 days prior to the issue date. Delta measures the equity component of a convertible bond at issue (i.e., the probability that the bond will be converted into equity at maturity) and is computed as Δ ≡ exp(−δT)N(d1), where δ is the issuing firm's continuously compounded dividend yield for the fiscal 
  pffiffiffi year-end immediately preceding the issue date, T is the number of years until maturity for the convertible bond, d1 ¼ lnðS=X Þ þ r−δ þ σ 2 =2 T =σ T , S is the stock price at the issue date, X is the conversion price, r is the continuously compounded risk-free rate estimated from a 10-year U.S. Treasury bond on the issue date, σ is the annualized standard deviation of the continuously compounded common stock returns using a minimum of 100 and a maximum of 250 daily stock returns immediately prior to the issue date, and N(⋅) is the cumulative probability under a standard normal distribution function. The change in earnings is the difference between EBIT in year t + 2 and EBIT in year t divided by the absolute value of EBIT in year t, where t + 2 is the fiscal year end two years after the date (e.g., issue date) and year t is the fiscal year end immediate prior to the date (e.g., issue date). Cash is the ratio of cash plus marketable securities to the book value of total assets. Return on assets is the ratio of earnings before interest, taxes, depreciation, and amortization (EBITDA) to the book value of total assets. a In the called bonds' mean and median columns, we report the results of difference in mean and median tests for called bond and not called bond variables. We use ***, ** and * to denote significance at the 1%, 5%, and 10% levels, respectively. Difference in means' significance levels is based on a t-test that assumes unequal variance when an F-test for equal variance is rejected at less than or equal to the 10% level. Difference in medians' significance levels is based on the Wilcoxon rank-sums test. b In the industry match mean and median columns, we report the results of difference in mean and median tests for called and not called bond variables and the variables for the respective industry matching sample. We use ***, **, and * to denote significance at the 1%, 5%, and 10% levels, respectively. Difference in means' significance levels is based on a t-test that assumes unequal variance when an F-test for equal variance is rejected at less than or equal to the 10% level. Difference in medians' significance levels is based on the Wilcoxon rank-sums test.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

14

T.-H.D. King, D.C. Mauer / Journal of Corporate Finance xxx (2012) xxx–xxx

Table 6 Investment and financing activity around convertible bond calls. Year

Activity level/Total assets (%)

Change in activity level/total assets (%)

Called bonds (N = 400)

Industry match (N = 400)

Called bonds (N = 400)a

Mean

Median

Mean

Panel A. Capital expenditures −5 5.42 3.65 −4 5.91 4.14 −3 6.41 4.83 −2 7.35 5.71 −1 7.93 5.96 0 8.77 6.32 1 9.98 6.51 2 10.94 6.43 3 10.67 5.58 4 10.77 5.21

2.83 3.32 4.15 5.05 6.22 6.37 6.70 6.06 5.94 5.40

1.95 2.94 3.63 4.29 4.90 5.00 4.83 4.49 4.02 3.53

0.48 0.50 0.94 0.59 0.84 1.21 0.95 −0.27* 0.10

0.13 0.22 0.40 0.21 0.20 0.29 0.00 0.00** 0.00***

0.30 0.50 0.65 0.86* 0.41 0.57 −0.39** 0.31 −0.21**

Panel B. Issuances of long-term debt −5 4.59 1.53 −4 5.77 2.11 −3 6.48 1.97 −2 7.39 2.70 −1 9.77 3.18 0 12.97 1.64 1 15.67 1.89 2 14.68 1.00 3 17.44 1.40 4 14.70 0.38

1.42 1.48 2.07 2.23 3.30 2.87 3.22 3.68 3.53 2.63

0.00 0.10 0.48 0.85 1.41 0.93 0.56 0.20 0.13 0.00

1.18 0.71 0.91 2.38 3.20 2.70 −0.99 2.76 −2.74**

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.02 0.07 0.16 0.17 0.09 0.07 0.03 0.01

0.85 −0.15** −0.30*** 0.51* 1.38 −0.97*** 0.78 −1.10** 0.99

0.00 0.00*** 0.00* 0.00 0.01 −0.00*** 0.00*** 0.00*** 0.00**

3.76 6.90 9.76 12.54 18.21 3.96 12.08 10.24 5.49 5.05

1.75*** 1.92** 0.91*** 3.24* 7.22 −0.28*** 1.22 1.06* −2.40***

0.00 0.00 0.00 0.00 0.00 0.00*** 0.00* 0.00* 0.00***

Mean

Median

Panel C. Issuance of common and preferred stock −5 1.64 0.06 0.40 −4 2.49 0.11 0.42 −3 2.33 0.14 0.40 −2 2.04 0.22 0.59 −1 2.55 0.29 1.30 0 3.93 0.46 2.14 1 2.96 0.24 0.89 2 3.74 0.17 1.02 3 2.63 0.09 0.88 4 3.63 0.07 0.89 Panel D. Total sources of funds −5 7.51 1.44 −4 9.27 3.03 −3 11.19 4.51 −2 12.10 5.64 −1 15.34 6.14 0 22.57 5.85 1 22.29 2.46 2 23.51 1.97 3 24.57 2.10 4 22.17 0.74

8.83 8.64 12.47 14.08 17.08 11.47 18.64 12.61 9.99 15.34

Industry match (N = 400)a Median

Mean

Two-sample test p-valuesb t-test

Wilcoxon

0.00 0.00 0.18** 0.38*** 0.09 0.00*** 0.00*** 0.00*** 0.00***

0.46 0.99 0.36 0.39 0.32 0.17 0.02 0.33 0.00

0.26 0.88 0.57 0.03 0.30 0.00 0.01 0.48 0.45

-0.02 0.43 0.07 0.64 −0.14 0.57 0.54 −0.03 −0.69

0.00*** 0.00*** 0.00*** 0.00*** 0.00 0.00*** 0.00*** 0.00*** 0.00***

0.02 0.66 0.26 0.06 0.06 0.24 0.65 0.20 0.32

0.27 0.96 0.12 0.65 0.49 0.50 0.34 0.51 0.07

0.02 −0.04 0.15 0.59 0.69 −0.83* 0.15 -0.12 0.04

0.00 0.00 0.00 0.00*** 0.00 0.00*** 0.00*** 0.00*** 0.00

0.05 0.79 0.32 0.88 0.30 0.88 0.53 0.27 0.28

0.12 0.54 0.97 0.54 0.07 0.03 0.15 0.81 0.32

0.00*** 0.25*** 0.00*** 0.00*** −0.25 0.00*** 0.00 0.00 0.00***

0.00 0.10 0.83 0.23 0.00 0.00 0.11 0.22 0.00

0.00 0.00 0.21 0.10 0.00 0.00 0.00 0.00 0.00

−0.72*** 3.29*** 1.12*** 1.81*** −4.67 8.42*** −5.42 −2.69 7.00***

Median

Notes: the table reports investment and financing activity and changes in investment and financing activity for years −5 through +4 relative to the year of the convertible bond call (year 0). Levels and changes in levels of variables are scaled by the book value of total assets in year −1. The change in investment and financing activity in year t is computed as the difference in activity in years t and t − 1. The industry matching sample is constructed using the median firm in the sample firm's 4-digit SIC code. Panel A reports capital expenditures (Compustat DATA128) scaled by total assets, Panel B reports issuances of long-term debt (Compustat DATA111) scaled by total assets, Panel C reports issuance of common and preferred stock (Compustat DATA108) scaled by total assets, and Panel D reports total financing sources (Compustat DATA112) scaled by total assets. Note that we subtract conversion proceeds from common and preferred stock in year 0. a In the mean and median columns, we report the results of paired tests comparing changes in year 0 with the changes in other years. We use ***, **, and * to denote significance at the 1%, 5%, and 10% levels, respectively. b The p-values reported in the t-test and Wilcoxon columns are from two-sample tests comparing the called bond sample changes and the industry matched sample changes for each year.

Consistent with the sequential financing theory notice that the levels of capital expenditures, long-term debt, equity, and total financing are much larger for calling firms than for their industry matching firms over the entire time span from − 5 to + 4. Observing the changes in activity levels, note that for calling firms there is typically an increase in both investment and financing activity in the year of the call and also often in the next couple of years following the call. Furthermore, these increases are Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

T.-H.D. King, D.C. Mauer / Journal of Corporate Finance xxx (2012) xxx–xxx

15

typically significantly larger than any changes observed for industry matching firms. In particular, observe that the median changes in capital expenditures for calling firms are significantly larger than those of the industry matching sample in years + 1 and + 2, and observe that the mean and median changes in total sources of funds are typically significantly larger than those of the industry matching sample in years 0, + 1, and + 2. To provide additional evidence on the financing activity of calling firms around the year of the call, Table 7 reports the total number and dollar amount of convertible bond issues, straight bond issues, and common and preferred stock issues of calling firms in years − 2 to + 2 relative to the year of the convertible bond call (year 0). 20 As shown in the table, there are generally large increases in the dollar amount of all sources of external finance in the year of call. Thus, note that the percentage increase in the dollar amount of convertible bond issues, straight bond issues, and common and preferred stock issues from year − 1 to year 0 are 86%, 9%, and 57%, respectively. 21 Overall, this is strong evidence consistent with Mayers' (1998) sequential financing theory that as firm's growth options move in the money it will call outstanding convertible bonds and use the equity infusion thereby obtained to raise external financing. 5. Determinants of call policy We examine the determinants of call policy for the sample of convertible bonds. We first report descriptive statistics for the variables used in the empirical tests. We then examine the determinants of the probability of call, call delay, and the premium at call announcement. 5.1. Descriptive statistics Table 8 reports descriptive statistics for the variables. For called bonds, all variables are computed immediately prior to the call announcement date; and for not called bonds, all variables are computed immediately prior to the maximum premium date. Notice that the mean monthly stock price standard deviation for the full sample and the called and not called subsamples is roughly one-half the investment banker-recommended safety premium of 20%. Thus, over a notice period of 30 days, the average firm in the sample waits until the premium of conversion value to effective call price is at least twice the monthly standard deviation of the stock price. 22 Also note that firms in the sample appear to be quite liquid, with mean and median ratios of cash plus marketable securities to total assets of 0.12 and 0.07, respectively. The ratio of cash plus marketable securities to the aggregate call price tells a more constrained story, in that although the mean is well above 1.0 the median is well below 1.0. In particular, the median ratios of cash plus marketable securities to the aggregate call price for the called and not called groups of firms are 0.64 and 0.59, respectively. It appears as if the median firm in the sample would be unable to easily pay the redemption price if the call failed to force conversion. Also observe that the change in earnings is dramatically larger in the called bond sample than in the not called bond sample. For example, the median comparison is 0.31 versus − 0.06. This economically and statistically significant difference is inconsistent with the information signaling explanation for call delays, which argues that firms delay calls because future good performance will lead to voluntary conversion. Finally, note that relative to firms that do not call their bonds, calling firms have significantly larger proportions of rating upgrades (17% versus 8%) and downgrades (23% versus 12%). 5.2. Probability of call Table 9 reports estimates of the determinants of call probability using unconditional and conditional probit models. The unconditional probits estimate effects on the probability of call without regard for the premium of conversion value relative to effective call price. The conditional probits estimate effects on the probability of call separately for bonds that meet a 20% threshold of conversion value relative to effective call price and those that do not meet the specified threshold. In particular, a called bond meets the 20% threshold if conversion value equals or exceeds the effective call price by 20% the day before the call announcement. A bond that is not called meets the 20% threshold if conversion value is greater than or equal to effective call price by 20% for at least 25 consecutive days. Probit results using 10%, 30%, and 40% thresholds are similar to those reported in Table 9 and are available on request. To facilitate interpretation of results, we report the marginal effects on the probability of call for a one standard deviation change in explanatory variables. The marginal effects for bond rating upgrade and downgrade dummy variables are for a discrete change of dummy variable from 0 to 1. We report z-values which test whether the underlying probit coefficient estimates are equal to zero in parentheses below the marginal effects. Finally, note that for the conditional probits we report marginal effects when the threshold is met and when it is not met. We footnote marginal effects in the met threshold column with a, b and c to denote whether the underlying probit coefficient estimates are significantly different from each other at the 1%, 5%, and 10% levels, respectively. The probits provide strong evidence that the risk of a failed call over the notice period influences the probability of call. Consistent with the call notice period hypothesis, observe that the probability of call is decreasing in stock price volatility. 23 Note 20

The data on security issues is from the SDC database. Note that the percentage increase in the dollar amount of straight bond issues from year −2 to year −1 is 70%. It appears as if calling firms are issuing the majority of straight debt in the year prior to the call. 22 Asquith (1995) finds a similar result in his sample of convertible bonds issued in 1980 through 1982. 23 Although the probability of call is generally also increasing in the ratio of cash plus marketable securities to the aggregate call price, the underlying probit coefficient estimates are not statistically significant. 21

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

16

T.-H.D. King, D.C. Mauer / Journal of Corporate Finance xxx (2012) xxx–xxx

Table 7 Number and dollar amount of security issues around convertible bond calls. Year

Number

Panel A. Convertible bond issues −2 73 −1 48 0 44 1 23 2 14 Panel B. Straight bond issues −2 −1 0 1 2

45 52 70 47 71

Panel C. Common and preferred stock issues −2 47 −1 47 0 60 1 30 2 28

$ Amount ($M)

% Change

% Change

Number

$ Amount ($M)

5187.7 4305.8 8010.7 3777.0 1836.2

−34.25 −8.33 −47.73 −39.13

−17.00 86.04 −52.85 −51.38

6280.4 10,665.0 11,629.7 8693.3 10,915.1

15.56 34.62 −32.86 51.06

69.65 9.15 −25.25 25.56

3982.7 3795.0 5940.7 3646.9 3797.5

0.00 27.66 −50.00 −6.67

−4.71 56.54 −38.61 4.13

Notes: the table is constructed using security issue data from the SDC database. The table reports the total number and dollar amount of security issues and changes in the total number and dollar amount of security issues for calling firms over years −2 through +2 relative to the year of the convertible bond call (year 0). The percentage change in number of issues (dollar amount) in year t is computed as the difference in number of issues (dollar amount) in years t and t − 1 divided by the number of issues (dollar amount) in year t − 1. Panel A reports convertible bond issues, Panel B reports straight bond issues, and Panel C reports common and preferred stock issues.

that the relation between probability of call and stock price volatility is nonlinear, since the coefficient on squared volatility tends to be significantly positive. This suggests that the negative effect of volatility on the probability of call dissipates at large volatility. Interestingly, the negative marginal effect of volatility in the unconditional probits is driven by bonds that never reach a 20% threshold. To see this, note in the conditional probits that the marginal effect of volatility on the probability of call is only significant when the threshold is not met. This is consistent with the notion that once a sufficient safety premium is achieved, stock price volatility over the call notice period is no longer an important consideration for call policy. However, note that the effect of volatility on call probability is economically significant if the bond does not reach the threshold. Based on the predicted probabilities for the regressions, a one-standard deviation increase in stock price volatility decreases the probability of call by 88% (0.586/0.665) and 180% (0.638/0.355) in samples with and without event calls, respectively. The cash flow advantage hypothesis predicts that the larger is the ratio of the dividend on converted shares to the after-tax coupon on the bond the lower the likelihood of call. As seen in Table 9, we find support for the cash flow advantage hypothesis. Interestingly, the dividend to after-tax coupon ratio is significantly negative only when the threshold is met, which indicates that concern about cash flow considerations is conditional on having reached a safety premium. However, observe that the change in earnings has a uniformly positive effect on the probability of call in every probit model in Table 9. Assuming that the change in earnings captures managers' inside information about the firm's future prospects, the significantly positive marginal effect is inconsistent with the Harris and Raviv (1985) signaling model which predicts that managers with favorable private information are more likely to delay calling convertible bonds. The positive marginal effect of the change in earning on the probability of call is consistent, however, with the argument that managers with favorable inside information call promptly to expropriate from bondholders the likely much higher future value of the conversion option. Consistent with the agency theory explanation for why firms use convertible bond financing, the probits indicate that higher market-to-book firms are less likely to call their convertibles. As one might expect, this negative relation is significant only for bonds that meet the threshold and are therefore candidates to be called. Using the without event call sample and the marginal effect for the “Met Threshold” estimation, a one standard deviation increase in the market-to-book ratio decreases the probability of call by 30% (0.107/0.355), based on the predicted probability for the regression. Notice in Table 9 that we also find evidence supporting Mayers (1998) sequential financing motive for calling convertible bonds, since the probability of call is increasing in CAPEX growth. 24 In particular, using the without event call sample and the marginal effect for the “Met Threshold” estimation, a one standard deviation increase in CAPEX growth increases the probability of call by 26% (0.091/0.355). In contrast, however, we find no evidence that the demand for external financing, measured by financing deficit, increases the probability of call. Notice that rating upgrades and rating downgrades have a positive effect on the probability of call, and like the effect of the market-to-book ratio on call probability, this positive rating effect is only significant if the threshold is met. Thus, as long as the

24

Although we do not report it in the table, the probability of call is also increasing in asset growth.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

T.-H.D. King, D.C. Mauer / Journal of Corporate Finance xxx (2012) xxx–xxx

17

Table 8 Descriptive statistics of the determinants of convertible bond calls by whether a bond is called or not called. Variable

Monthly stock price std. dev. Cash plus mkt. sec. ÷ total assets Cash plus mkt. sec. ÷ call price Dividend ÷ after-tax coupon Change in earnings Market-to-book ratio Asset growth CAPEX growth Financing deficit Leverage ratio Log of offer size Stock price run up Rating upgrade (%) Rating downgrade (%) Log of firm size Fraction orig. maturity elapsed Amount out. ÷ original issue amt.

Called bondsa

All bonds

Not called bonds

Mean

Median

Std. dev.

N

Mean

Median

Std. dev.

N

Mean

Median

Std. dev.

N

0.130 0.121 2.559 0.926 0.066 1.974 0.301 0.016 0.038 0.344 5.724 0.267 12.549 17.647 8.256 0.289 0.930

0.117 0.066 0.626 0.158 0.231 1.476 0.151 0.007 0.004 0.214 5.095 0.191

0.059 0.140 9.167 1.672 2.477 1.731 0.558 0.098 0.169 0.159 2.005 0.315

0.049 0.116 9.652 1.227 1.849 0.857 0.336 0.072 0.126 0.155 1.824 0.263

2.124 0.205 0.247

0.146 0.138 2.446 1.204 −0.268 2.317 0.424 0.024 0.064 0.340 6.016 0.331 7.671 12.329 7.765 0.279 0.971

0.064 0.161 2.616 2.018 2.986 2.294 0.708 0.119 0.205 0.203 2.150 0.353

8.405*** 0.280*** 1.000

400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400

0.129 0.076 0.587 0.000 −0.055 1.610 0.173 0.010 0.016 0.317 5.628 0.231

2.236 0.248 0.204

0.115*** 0.106*** 2.662 0.672*** 0.370*** 1.662*** 0.189*** 0.009** 0.015 0.348 5.458*** 0.212*** 17.000*** 22.500** 8.703*** 0.297 0.892***

0.105*** 0.064** 0.638 0.215 0.313*** 1.390*** 0.128*** 0.005* −0.002*** 0.325 4.972*** 0.144***

8.046 0.200 1.000

765 765 765 765 765 765 765 765 765 765 765 765 765 765 765 765 765

7.553 0.160 1.000

2.256 0.288 0.131

365 365 365 365 365 365 365 365 365 365 365 365 365 365 365 365 365

Notes: the sample includes convertible bonds that are issued between January 1, 1980 and December 31, 2002. For called bonds, the variables are computed at the nearest time immediately prior to the call announcement day. For not called bonds, the variables are computed at the nearest time immediately prior to the day that the bond reaches the largest premium of conversion value relative to effective call price. All variables are winsorized at the 1% and 99% levels of the full sample of “All bonds” except fraction of original maturity elapsed, amount outstanding divided by original issue amount, and rating upgrade and downgrade. All dollar values are inflation-adjusted to December 2009 using the CPI. The monthly standard deviation of the stock price is computed using a minimum of 100 and a maximum of 250 continuously compounded daily stock returns prior to the call announcement day or maximum premium day. The ratio of cash plus marketable securities to call price uses the aggregate call price computed as the total number of bonds outstanding times the effective call price per bond, which is the call price from the call price schedule, plus accrued interest from the last coupon payment date. The dividend to after-tax coupon ratio is computed as the largest annual dollar dividend per share times the contemporaneous conversion ratio divided by the after-tax annual dollar coupon payment of the bond. The largest annual dividend per share is from the period starting with the year call protection (or soft call) ends and ending the earlier of the call year, bond maturity year, or 2007. The marginal corporate tax rate is from the Graham database. Change in earnings is the difference between EBIT in year t + 2 and EBIT in year t divided by the absolute value of EBIT in year t, where year t + 2 is the fiscal year end two years after the call announcement (maximum premium) and year t is the fiscal year end immediately prior to the call announcement (maximum premium). Market-to-book ratio is the market value of assets divided by the book value of assets, where the market value of assets is the book value of assets plus the difference between the market and book values of equity. Asset growth is the change in the book value of total assets from year −1 to 0 divided by the book value of total assets in year −1, where year 0 is the call announcement year (called bonds) or the maximum premium year (not called bonds). CAPEX growth is the change in capital expenditures from year −1 to 0 divided by the book value of total assets in year −1. The financing deficit measures the demand for external financing and is computed as the sum of cash dividends, investments, and change in working capital minus internal cash flows. All of the components of the financing deficit are scaled by the book value of total assets. See Frank and Goyal (2003) and John and Litov (2010) for details of the financing deficit calculation. The leverage ratio is the ratio of long-term debt plus debt in current liabilities to total assets. The log of offer size is the natural logarithm of the dollar amount (in millions) of the convertible bond issue. The stock price run up is computed as the cumulative raw return of the stock over the 60 days prior to the call announcement day or maximum premium day. Rating upgrade (downgrade) is a dummy variable equal to one when the convertible bond's S&P's (or Moody's) bond rating improves (deteriorates) over the period from the issue date to the month prior to the call announcement (maximum premium) month. The log of firm size is the natural logarithm of total assets in constant dollars using the producer price index. The fraction of original maturity elapsed is computed as the number of months from the time the bond is issued to the call announcement (maximum premium) month, converted into years, divided by the maturity year minus the offer year. The amount outstanding divided by the original issue amount is computed using the amount outstanding the month prior to the call announcement month for called bonds or the amount outstanding the month prior to the maximum premium month for not called bonds. a In the called bonds' mean and median columns, we report the results of difference in mean and median tests for called bond and not called bond variables. We use *** and ** to denote significance at the 1% level and 5% level, respectively. Difference in means' significance levels is based on a t-test that assumes unequal variance when an F-test for equal variance is rejected at less than or equal to the 10% level. Difference in medians' significance levels is based on the Wilcoxon rank-sums test.

bond's conversion value exceeds the call price by a comfortable safety margin, the firm is significantly more likely to call and force conversion if the bond experiences an upgrade or a downgrade. Recall our earlier discussion that calling after an upgrade is consistent with a refinancing motive, while calling after a downgrade is consistent with a de-leveraging motive. Finally, observe in Table 9 that firm size and fraction of original maturity elapsed also have significant effects on call probability. 25 Interestingly, firm size has a positive marginal effect on the probability of call when the threshold is not met, which suggests that larger firms might be marginally less concerned about building a safety premium before calling to force conversion. A similar pattern is observed for the variable fraction of original maturity elapsed; as the bond approaches maturity the firm is more likely to call if the bond did not meet the threshold. In sharp contrast, however, as the bond approaches maturity the firm is less likely to call if it did meet the threshold.

25 Note that we do not include the variable amount outstanding divided by the original issue amount in the probits, since the variable has zero variability for not called bonds (i.e., all not called bonds have a ratio of 1.0 at the point in time where the ratio is measured).

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 9 Determinants of call probability for convertible bonds. Variables

Unconditional probit

Conditional probit: 20 percent threshold With event calls

With event calls Stock price standard deviation Squared stock price standard deviation Cash plus marketable securities ÷ call price Dividend ÷ after-tax coupon Change in earnings Market-to-book ratio CAPEX growth Financing deficit Leverage ratio Log of offer size Stock price run up Rating upgrade dummy Rating downgrade dummy Log of firm size Fraction of original maturity elapsed Model chi-square Pseudo R2 Observed prob. of call Predicted prob. of call No. of observations

−0.281 (−3.50)*** 0.227 (2.93)*** 0.001 (0.04) −0.088 (−4.20)*** 0.067 (2.74)*** −0.097 (−3.14)*** 0.017 (0.81) −0.052 (−2.26)** 0.001 (0.01) −0.061 (−2.84)*** −0.070 (−2.52)** 0.086 (4.22)*** 0.084 (3.97)*** 0.045 (2.00)** 0.007 (0.33) 151.67*** 0.16 0.523 0.512 765

Without event calls −0.334 (−3.65)*** 0.235 (2.59)*** 0.008 (0.35) −0.096 (−3.77)*** 0.094 (3.47)*** −0.098 (−2.81)*** 0.045 (2.00)** −0.052 (−2.04)** −0.018 (−0.69) −0.073 (−3.23)*** −0.042 (−1.42) 0.080 (3.75)*** 0.058 (2.67)*** 0.036 (1.54) −0.022 (−0.89) 134.34*** 0.18 0.431 0.397 641

Met threshold a

−0.100 (−0.70) 0.121c (0.71) 0.032b (1.33) −0.219a (−5.42) *** 0.091 (2.36)** −0.068 (−1.76)* 0.071 (1.95)* −0.093a (−2.55)** 0.008 (0.20) −0.073 (−2.21)** −0.097 (−2.34)** 0.108b (3.89)*** 0.101b (2.74)*** −0.001a (−0.01) −0.199a (−6.15)*** 155.52*** 0.34 0.608 0.665 765

Without event calls Not met threshold −0.586 (−4.34)*** 0.479 (3.82)*** 0.130 (3.02)*** −0.039 (−0.90) 0.082 (2.04)** −0.126 (−1.17) −0.004 (−0.14) −0.024 (−0.60) −0.052 (−1.26) −0.062 (−1.66)* −0.038 (−0.87) 0.022 (0.45) 0.002 (0.06) 0.157 (3.90)*** 0.367 (5.46)*** 155.52*** 0.34 0.608 0.665 765

Met threshold b

−0.037 (−0.18) −0.040c (−0.14) 0.043 (1.83)* −0.197a (−4.94)*** 0.127 (3.18)*** −0.107c (−2.05)** 0.091 (2.23)** −0.085 (−2.24)** −0.038 (−0.91) −0.126c (−3.65)*** −0.075 (−1.71)* 0.105b (3.74)*** 0.083a (2.36)** −0.008a (−0.23) −0.215a (−6.05)*** 225.47*** 0.35 0.431 0.355 641

Not met threshold −0.638 (−4.44)*** 0.496 (3.64)*** −0.197 (−0.94) −0.063 (−1.30) 0.124 (3.11)*** −0.030 (−0.42) 0.031 (0.95) −0.069 (−1.41) −0.030 (−0.74) −0.040 (−1.03) −0.004 (−0.07) 0.014 (0.27) −0.027 (−0.77) 0.148 (3.25)*** 0.328 (5.17)*** 225.47*** 0.35 0.431 0.355 641

Notes: the table reports the marginal effects on the probability of call for a one standard deviation change in explanatory variables. The marginal effects for rating upgrade and downgrade dummy variables are for a discrete change of dummy variable from 0 to 1. The marginal effects are computed from probit regressions which estimate the determinants of the call decision for a sample of convertible bonds that are issued between January 1, 1980 and December 31, 2002. Probits are estimated with and without event calls, which are calls where the firm had significant operating losses, merger and acquisition activity, debt and/or asset restructuring, or financial distress in the year of the call announcement. The unconditional probits estimate effects on the probability of call without regard for the premium of conversion value relative to the effective call price. The conditional probits estimate effects on the probability of call separately by whether a bond met or did not meet a 20% premium of conversion value relative to effective call price. A bond meets the 20% threshold if it is called when its conversion value is greater than or equal to 120% of its effective call price, or if a bond is not called, it has at least 25 consecutive days where its conversion value is greater than or equal to 120% of its effective call price. For called bonds, the explanatory variables are computed at the nearest time immediately prior to the call announcement day. For not called bonds, the explanatory variables are computed at the nearest time immediately prior to meeting the 25 consecutive day threshold requirement, or the nearest time immediately prior to the day that the bond reached the largest premium of conversion value relative to effective call price. All variables are defined in earlier tables. We report z-values which test whether the underlying probit coefficient estimates are equal to zero in parentheses below the marginal effects. The z-values are computed using robust standard errors. ***, **and * denote whether the underlying probit coefficient estimate is significantly different from zero at the 1% level, 5% level, and 10% level, respectively. a, b, and c denote whether the met and not met probit coefficient estimates are significantly different from each other at the 1% level, 5% level, and 10% level, respectively.

5.3. Call delay Table 10 reports regressions examining the determinants of call delay. The dependent variable is the number of trading days that conversion value exceeds the effective call price (columns 1 and 2) or 120% of the effective call price (columns 3 and 4) and the firm does not call the bond. Days delayed are measured from the first day call protection expires to the call announcement date for called bonds or the minimum of the bond maturity date or December 31, 2010 for not called bonds. For bonds with a soft call provision, the day count starts as soon as the soft call condition is satisfied and the firm does not call the bond. All exogenous variables are measured immediately prior to the first time that conversion value exceeds the effective call price or 120% of the effective call price. In cases where the conversion value of the bond never exceeds the effective call price (i.e., zero call delay), the variables are measured immediately prior to the maximum premium of conversion value to effective call price. The table reports OLS and duration regressions. The coefficients in the OLS regressions are multiplied by 1/21 and are therefore in units of trade months delayed. Since the dependent variable, days delayed, measures the duration of call delay we also estimate Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 10 Determinants of call delay for convertible bonds. Variables

Constant Monthly stock price standard deviation Squared monthly stock price standard deviation Cash plus marketable securities ÷ call price Dividend ÷ after-tax coupon Change in earnings Market-to-book ratio CAPEX growth Financing deficit Leverage ratio Log of offer size Stock price run up Event call dummy Rating upgrade dummy Rating downgrade dummy Log of firm size Fraction of original maturity elapsed Amt. out. b original issue amt. dummy Adjusted R2 Model chi-square No. of observations

Dependent variable: no. of trading days

Dependent variable: no. of trading days

Conversion value > effective call price

Conversion value ≥ (1.20) (Effective call price)

OLS regression

Duration regression

OLS regression

Duration regression

−18.899 (−1.94)* 112.507 (1.51) −377.637 (−2.07)** 0.797 (3.52)*** 2.533 (3.47)** −0.303 (−0.59) 3.189 (3.23)*** 14.856 (1.60) 5.010 (0.81) −30.145 (−4.00)*** −3.698 (−5.90)*** 2.534 (0.68) −14.768 (−7.13)*** −6.863 (−1.81)* −14.967 (−6.35)*** 3.895 (6.43)*** 70.335 (10.14)*** −8.011 (−3.25)*** 0.40

2.860 (4.00)*** 9.170 (1.60) −20.661 (−1.50) 0.020 (2.90)*** 0.396 (4.42)*** −0.223 (−4.75)*** 0.278 (1.98)** −2.027 (−1.94)* 1.614 (2.65)*** −1.604 (−2.28)** −0.007 (−0.14) 0.602 (1.25) −1.577 (−7.65)*** −0.316 (−1.31) −0.669 (−3.59)*** 0.167 (3.35)*** 3.786 (8.44)*** −0.631 (−3.63)***

−24.006 (−2.81)*** 147.552 (2.21)** −450.551 (−2.72)*** 0.813 (3.76)*** 2.325 (3.55)*** −0.154 (−0.33) 3.235 (3.40)*** 13.997 (1.62) 3.820 (0.68) −25.599 (−3.63)*** −3.011 (−5.34)*** 2.251 (0.65) −11.869 (−6.58)*** −6.586 (−1.92)* −13.948 (−6.77)*** 3.356 (6.14)*** 61.243 (9.73)*** −7.747 (−3.58)*** 0.40

2.065 (1.96)* 12.473 (1.16) −35.899 (−0.95) 0.016 (2.23)** 0.436 (4.20)*** −0.241 (−4.16)*** 0.215 (1.56) −2.250 (−1.66)* 2.077 (2.85)*** −2.395 (−2.57)** 0.090 (1.23) 0.587 (1.07) −1.207 (−3.48)*** −0.649 (−2.04)** −1.056 (−3.97)*** 0.163 (2.39)** 4.624 (7.96)*** −0.780 (−3.28)***

765

313.584*** 765

765

251.142*** 765

Notes: the regressions estimate the determinants of call delay for a sample of convertible bonds that are issued between January 1, 1980 and December 31, 2002. The dependent variable, call delay, is the number of trading days that conversion value exceeds the effective call price (or 120% of the effective call price) and the firm does not call the bond, as measured from the first day that call protection expires to the call announcement day for called bonds or the minimum of the bond maturity date or December 31, 2010 for not called bonds. For bonds with a soft call provision, the day count starts as soon as the soft call condition is satisfied and the firm does not call the bond. The coefficients in the OLS regressions are multiplied by 1/21, which rescales the regression function to trade months delayed. Except where noted below, all variables are measured immediately prior to the first time that conversion value exceeds the effective call price (or 120% of the effective call price) and are defined in earlier tables. In cases where the conversion value of the bond never exceeds the effective call price (i.e., zero call delay), the variables are measured immediately prior to the maximum premium of conversion value to effective call price. In the duration regression, we use the exponential regression model (one of the parametric survival time models) and estimate the coefficients using maximum likelihood estimation with a Newton–Raphson algorithm. The parameter estimates are expressed in the form of accelerated failure time coefficients. The z-statistics in parentheses below the duration regression coefficient estimates are computed using robust standard errors; and the t-statistics in parentheses below the OLS coefficient estimates are computed using robust standard errors. We use ***, **, and * to denote significance at the 1% level, 5% level, and 10% level, respectively.

duration regressions. In these regressions, we use the exponential regression model – the parametric survival time model appropriate for regressors that do not vary with time – and estimate the coefficients by maximum likelihood estimation using a Newton–Raphson algorithm. The parameter estimates are expressed in the form of accelerated failure time coefficients (see, e.g., Hosmer and Lemeshow (1999, pp. 273–289)). The z-statistics in parentheses below the duration regression coefficient estimates are computed using robust standard errors; and the t-statistics in parentheses below the OLS coefficients estimates are computed using robust standard errors. As seen in the table, there is little evidence that stock price volatility or squared volatility influences call delay. Interestingly, the liquidity variable (i.e., cash plus marketable securities to the aggregate call price) does influence call delay, but the directional influence is opposite the prediction. Based on the notion that more liquid firms should be less likely to delay call since they have cash on hand to cover the redemption price should the call fail to force conversion, call delay should be decreasing in corporate Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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liquidity. We find, however, that call delay is increasing in corporate liquidity, and significantly so in the OLS and duration regressions. This positive relation could simply reflect the fact that firms that build excess cash balances tend to be more cautious and therefore also tend to delay calling to force conversion. Similarly, firms that build large cash balances presumable do so to hedge future funding needs because they face financing constraints (see, Kim et al., 1998). These firms would be unlikely to view cash balances as funds that could be used to pay the call price on a failed conversion-forcing call. Along these lines, a positive relation between call delay and liquidity would be consistent with Mayers' (1998) sequential financing theory in that firms with plenty of internal cash flow do not need to force conversion to equity to support additional debt or convertible financing. For these reasons, perhaps it is not surprising that call delay is positively related to corporate liquidity. Consistent with the cash flow advantage hypothesis, we find that call delay is positively related to the ratio of dividend to after-tax coupon. For example, in the duration regression in column 2, a one standard deviation increase in the ratio of dividend to after-tax coupon increases call delay by 94% (100[e (0.396)(1.672) − 1]). Using the corresponding OLS regression coefficient, a one standard deviation increase in the ratio of dividend to after-tax coupon increases call delay by more than 4 months (2.533 × 1.672). Thus, there is strong evidence that cash flow considerations are a key determinant of convertible bond call decisions. Similar to the probit analysis of the probability of call, there is no evidence in support of the information signaling hypothesis. Specifically, rather that the predicted positive relation between call delay and change in earnings, we find a negative relation in all of the delay regressions. In contrast, we find strong support for agency conflicts influencing call policy, since all of the coefficients on the market-to-book ratio are positive. Using the OLS and duration model estimates in the first two columns, a one standard deviation increase in the market-to-book ratio increases expected call delay by 62% (100[e (0.278)(1.731) − 1]); which according to the OLS estimate translates into an increase of about 6 months (3.189 × 1.731). Thus, firms with greater potential for agency conflicts (i.e., high market-to-book firms) are much less likely to call their bonds promptly. We find mixed support for the Stein (1992) backdoor equity and Mayers (1998) sequential financing theories. On the one hand, growth as measured by CAPEX growth and demand for financing as measured by the financing deficit tend not to be significant and often have the wrong sign. Indeed, rather than the predicted negative relations, the coefficient estimates on CAPEX growth in the OLS regressions are positive, and all of the coefficient estimates on financing deficit in the OLS and duration regressions are positive and significantly so in the duration regressions. One the other hand, we find evidence that higher debt related financing costs and equity-related financing costs encourage firms to call and force conversion to equity more quickly. In particular, we find negative coefficient estimates on leverage ratio (as a proxy for financial distress costs) and log of offer size (as a proxy for adverse selection costs associated with information asymmetry) in all of the delay regressions in Table 10. Event calls and calls associated with rating upgrades and downgrades are all less likely to be delayed. For example, in the duration models in column 2, a rating upgrade and a rating downgrade decrease call delay by 27% (100[e −0.316 − 1]) and 49% (100[e −0.669 − 1]), respectively. Interestingly, call delay is significantly increasing in firm size. This is hard to explain; especially if one assumes that larger firms tend to be more sophisticated than smaller firms. Finally, note that firms are reluctant to call older convertibles (i.e., positive coefficients on fraction of original maturity elapsed) and tend not to delay calling bonds with periodic sinking fund payments or where bondholders are starting to voluntarily convert (i.e., negative coefficients on dummy variable for amount outstanding less than original issue amount). 26

5.4. Premium at call announcement Table 11 reports regressions of premium of conversion value to effective call price at call announcement for all called bonds (column 1), all called bonds except those called during call protection using a soft call provision and bonds called within one month after the end of call protection (column 2), and bonds called when conversion value is at least 120% of the effective call price (column 3). Note that the premium is computed one day prior to the call announcement day and that all variables are computed at the nearest time immediately prior to the call announcement date. Finally, t-statistics computed using robust standard errors are in parentheses below parameter estimates. Consistent with the call notice hypothesis, all three regressions reveal a positive relation between premium and stock price volatility. Interestingly, this relation is nonlinear, since the coefficients on squared volatility are significantly negative, which suggests that the positive relation between premium and volatility dissipates at high levels of volatility. The effect of volatility is highly economically significant. Using the regression in column 1, a one standard deviation increase in monthly stock price volatility increases the mean premium by 0.25 (from a mean of 29% to 54%). Similar to the call delay regressions, we find that the premium is increasing in corporate liquidity. As we noted earlier, the explanation could simply be that firms build liquidity because they are more conservative and that this explains why they choose to delay calling until the premium is sufficiently high. Although the coefficients on the ratio of dividend to after-tax coupon are positive as predicted, they are not significantly different from zero. The coefficients on the market-to-book ratio, however, are significantly positive, consistent with the strong 26 One might be tempted to conclude that a firm would be more reluctant to call a convertible to force conversion if bondholders are already starting to voluntarily convert. There are, however, at least two possible explanations for why a firm is actually more eager to call. First, the firm may have favorable inside information that when revealed will increase the value of the bondholders' conversion option. As we have argued above, it should be the firm's objective to minimize the value of this conversion option. The fact that bondholders are starting to voluntarily convert (i.e., amount outstanding less than original issue amount) is evidence in favor of this explanation, since as favorable inside information becomes public we would expect more bondholders to voluntarily convert. Second, it is possible that voluntary conversion – for example, because conversion value is high – encourages the firm to call and force all bondholders to convert.

Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Table 11 Determinants of premium of conversion value to effective call price. Variables

All called bonds

All called except soft and early calls

Bonds called when CV ≥ 1.2 CP

Constant

−0.836 (−2.55)** 5.052 (2.22)** −18.790 (−2.82)*** 0.020 (1.93)* 0.015 (0.49) 0.010 (0.48) 0.270 (3.82)*** 0.342 (0.82) 0.063 (0.18) −0.498 (−1.43) 0.028 (1.31) 0.310 (1.97)** −0.070 (−0.85) 0.119 (1.10) −0.052 (−0.40) 0.040 (1.28) −0.388 (−1.68)* 0.093 (1.24) 0.21 400

−0.558 (−1.55) 2.477 (1.19) −11.135 (−1.82)* 0.019 (1.82)* 0.047 (1.45) −0.001 (−0.02) 0.178 (2.31)** −0.340 (−0.64) 0.579 (2.18)** −0.646 (−1.78)* −0.025 (−1.26) 0.302 (1.79)* −0.319 (−4.08)*** 0.076 (0.69) 0.046 (0.33) 0.074 (1.86)* −0.162 (−0.66) 0.043 (0.62) 0.24 310

−1.534 (−2.11)** 15.744 (1.73)* −59.587 (−1.71)* 0.022 (1.82)* 0.098 (1.05) 0.049 (1.00) 0.171 (1.68)* 0.877 (1.28) −0.063 (−0.11) −1.163 (−1.25) 0.022 (0.57) 0.098 (0.36) 0.494 (2.55)** −0.004 (−0.03) 0.056 (0.17) 0.085 (1.09) 0.434 (0.98) 0.090 (0.61) 0.19 189

Monthly stock price standard deviation Squared monthly stock price standard deviation Cash plus marketable securities ÷ call price Dividend ÷ after-tax coupon Change in earnings Market-to-book ratio CAPEX growth Financing deficit Leverage ratio Log of offer size Stock price run up Event call dummy Rating upgrade dummy Rating downgrade dummy Log of firm size Faction of original maturity elapsed Amt. out b original issue amt. dummy Adjusted R2 No. of observations

Notes: the regressions estimate the determinants of the premium of conversion value to effective call price for a sample of convertible bonds that are issued between January 1, 1980 and December 31, 2002. The dependent variable is the premium the day before the call announcement day. The explanatory variables are computed at the nearest time immediately prior to the call announcement day. All variables are defined in earlier tables. The first regression estimates the determinants of the premium at call announcement for all called bonds. The second regression excludes bonds that are called during the deferred call period using a soft call provision (32 bonds) or are called within one month of the end of the deferred call period (58 bonds). The third regression includes only called bonds where the conversion value (CV) one day before the call announcement is at least 120% of the effective call price (CP). We report t-statistics computed using robust standard errors in parentheses below coefficient estimates. We use a ***, **, and * to denote significance at the 1% level, 5% level, and 10% level, respectively.

support for the agency conflict hypothesis in the probability of call and call delay regressions in Tables 9 and 10, respectively. Similar to the previous analyses, we find no support for the information signaling hypothesis, since the coefficients on the change in earnings are not significantly different from zero. We find weak and inconsistent support for the backdoor equity and sequential financing theories, since the coefficients on CAPEX growth and financing deficit are not significantly negative; and little support for the debt- and equity-related financing costs motive for firms to call, since there is little evidence that the coefficients on leverage and log of offer size are significantly negative. Finally, consistent with the univariate analysis in Table 4, the regressions in Table 11 show that calls associated with restructurings and other major corporate events tend to be called at lower premiums. There is no reliable evidence, however, that any of the other variables in the regressions influence call premiums. 6. Conclusions We examine the determinants of corporate call policy for convertible bonds in a sample of 829 bonds issued during the period from 1980 to 2002. Tracking the bonds forward in time until eventual call or maturity, we find that the perfect capital market policy of calling when conversion value first exceeds the call price is soundly rejected. We find evidence, however, that call policy for the average firm can at least partly be explained by a desire to call only after a safety premium of conversion value above call price is achieved to avoid the risk of a failed call, and by calling only when there is a cash flow advantage to doing so (i.e., dividend on converted shares less than after-tax coupon on the bond). When these conditions are met, the average call delay is 33 days and the median call delay is only 2 days. Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Although the average/median firm does not appear to delay calling their convertible bonds when conditions are right, there is a large amount of unexplained variability in corporate call policy. The key contribution of this paper is that we seek to explain this variability with an extensive analysis of the joint determinants of call policy, including the probability of call, call delay, and premium at call announcement. Our analysis sheds new light on a number of extant theories of corporate call policy. First, we find evidence that the risk of a failed call over the call notice period helps explain why firms are reluctant to call convertibles, and do so only after conversion value exceeds call price by a wide margin. Second, we find strong evidence that agency conflicts influence call policy in that firms which are more likely to face substantial conflicts are more reluctant to call, have significantly longer call delays, and tend to call only when the premium of conversion value relative to call price is large. Third, we find that cash flow considerations (i.e., dividend on converted shares versus after-tax coupon) influence the probability of call, call delay, and premium at call announcement in that firms are reluctant to call bonds when the dividends on the converted shares exceed the after-tax coupon on the convertible bond. Fourth, we find some evidence consistent with the argument that a desire to obtain backdoor equity financing and to finance the exercise of future growth options influences the joint decision to issue and subsequently call a convertible bond. Fifth, we find no evidence to support the information signaling hypothesis for call delays. On the contrary, we find that firms which have more favorable inside information are less likely to delay calls. Finally, we find that a significant portion of call decisions are associated with restructuring and merger activity, and with bond rating upgrades and downgrades. Both “event calls” and calls associated with rating changes are more likely and to occur with little delay. Acknowledgments We thank Alex Butler, Jay Li, the editor (Jeff Netter), and an anonymous referee for many helpful comments and suggestions. We also thank Jun Chen, Chia-Wen Ho and Xinde Zhang for excellent research assistance. Appendix A. Estimating the economic loss from suboptimal call policy We measure the economic loss from suboptimal convertible bond call policy using an arbitrage-free binomial option pricing framework that allows for optimal voluntary conversion and optimal call to force conversion. Modeling the dynamics of the stock price – the underlying state variable – as a multiplicative binomial random walk, at each node in the binomial tree the value of the convertible bond, CB, is equal to Max[Min(B, CP), CV], where B is the value of the convertible bond over the next time step assuming no call or voluntary conversion, CP is the call price, and CV is the value received by bondholders if they voluntarily convert (i.e., conversion ratio times share price at the node). Note that the bondholders' conversion option and the firm's call option are American options, and that the model assumes that should bondholders choose to voluntarily convert they will do so as a block. We compute two measures of the economic loss from suboptimal call policy. The first measure computes the loss at issue (i.e., ex ante) as the difference between the value of the convertible bond at issue assuming the firm follows the perfect capital market optimal call policy (i.e., calling as soon as conversion value rises above the call price) and the value of the convertible bond at issue assuming the firm follows a perfect foresight call policy. The perfect foresight call policy assumes that the call price equals the conversion value computed using the actual stock price on the call date, where the actual stock price is determined by the specific example from our sample of convertible calls (e.g., the stock price at the call announcement date for the median firm in the sample). The second measure computes the loss at the optimal call point (i.e., at a future node in the binomial tree) as the difference between the convertible bond value assuming an optimal call policy and the aforementioned perfect foresight policy. For illustrative purposes, we compute these two measures of economic loss for the firm in our sample with the median premium of conversion value to call price at the call announcement. The inputs for the median firm are as follows: Issuer: Kroger Co. Principal amount: $50 million Issue date: 4/1/1981 Maturity date: 6/15/2006 Par value: $1000 Conversion ratio: 34.1997 Conversion price: $29.24 = (par value) / (conversion ratio) Call price (initial): 110.25% of par value Call protection: no initial call protection (i.e., callable immediately) Share price at issue: $25.50 (Note: the conversion option and the call option are out-of-the-money) Stock price volatility (sigma): 32.09% p.a. Dividend yield: 6.42% continuous p.a. Coupon rate: 10.25% Coupon frequency: every six months (i.e., 3% every 6 months) Yield-to-maturity at issue: 10.25% Risk-free rate: 13.14% (10-year Treasury note rate) Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011

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Length of binomial time step: 0.083 or every month Premium of conversion value to call price at call: 18.57% Call date: 9/15/1982 Using the premium of conversion value to call price at call, the perfect foresight call policy sets the call price equal to the conversion value at the call date: 

CV −1 110:25

 ¼ 0:1857⇒CP ¼ CV ¼ ð1:1857Þð110:25Þ ¼ 130:72:

At the optimal call policy, the price of the convertible bond at issue is 104.05% of par value. In contrast, under the perfect foresight call policy, the price of the convertible bond at issue is 112.65% of par value. Based on the median firm's $50 million convertible bond issue, the economic loss at issue is (1.1265 − 1.0405)($50 m) = $4,300,000. The economic loss at the optimal call point is a little more complicated because there are many nodes in the binomial tree at which the firm would optimally call the convertible bond and force conversion. As such, the economic loss at the optimal call point depends on the time-step and stock price at which it is computed. For example, choosing time step 15 and a stock price of $32.90 we may determine that the firm will optimally call the bond and force conversion because the conversion value, 112.52%, exceeds the call price, 110.25%. The convertible bond value at this node is therefore 112.52% of par value. 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Please cite this article as: King, T.-H.D., Mauer, D.C., Determinants of corporate call policy for convertible bonds, J. Corp. Finance (2012), doi:10.1016/j.jcorpfin.2012.06.011