Merton model’s prediction and empirical evidence on bond and equity prices reaction to new bond issues

ABSTRACT

I use the Merton model as a theoretical framework to assess 1) the expected impact of a new bond offering on existing bond and stock prices, and 2) how the bond and stock price reactions are conditioned on characteristics of the new and existing bonds and the planned use of the new funds. Consistent with the Merton model prediction, I find negative and significant average abnormal returns of issuers’ existing bonds over a three-day event window surrounding the announcement of new bond issues. In contrast, average abnormal stock returns of the issuing firms are positive but insignificant. Bond market announcement returns estimated using daily corporate bond data from TRACE are more negative for longer-term outstanding bonds and less negative when the new bonds are junior to existing bonds. I also find that the bond price reaction (stock price reaction) is more negative (less positive) when funds are to be used for expansion than when they are to be used to repurchase stock.

KEYWORDS:

• Merton model
• new bond issues
• corporate bonds
• event study

JEL CLASSIFICATION:

• G10
• G14
• G35

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ If the stock repurchase is considered as negative equity issuance, the net equity issuance is negative in most years during the same period.

² Includes all non-convertible debt, Medium-Term Notes (MTNs) and Yankee bonds, but excludes CDs and federal agency debt.

³ http://online.wsj.com/news/articles/SB10001424052702304026804579410711208114586?mg=reno64-wsj

⁴ This is a model that began with Merton (1974) and Galai and Masulis (1976) and is a general model used in the extant literature. I refer to the model as the Merton model in the present paper.

⁵ Kolodny and Suhler (1988) find that the equity market returns surrounding new debt offering announcements are zero while Akhigbe, Easterwood, and Pettit (1997) document negative equity market reactions to new debt offering announcements.

⁶ Akhigbe, Easterwood, and Pettit (1997) obtain Friday bond transaction price information from the Commercial and Financial Chronicle, and from Dow-Jones News Retrieval. This bond price information is for bonds traded on the NYSE.

⁷ Kolodny and Suhler (1988) estimate monthly bond returns for 66 debt offerings during 1973-1981 and Akhigbe, Easterwood, and Pettit (1997) calculate weekly bond returns for 399 debt offerings during 1980-1992.

⁸ Other needed assumptions can be found in Merton (1974).

⁹ It can also be expressed as the payoff of a bond is equivalent to the payoff of the assets of the firm plus a short position in a call option on the assets of the firm.

¹⁰ Put-call parity: s(t)-c(t)= ke^−rT-p(t). s(t) is the spot price of the underlying asset at time t; c(t) is the value of the call at time t. p(t) is the value of the put at time t; and ke^−rT is the present value of a zero-coupon bond with a face value of k maturing at time T.

¹¹ This may not be the case when a firm intends to use the newly raised funds for stock repurchases where a firm’s debts increase but assets do not, or refinancing current debt where neither assets nor debts rise.

¹² These predictions are based on the assumption that the intended use of newly borrowed funds is expansions. In my following analysis, I show that the wealth transfer hypothesis also predicts that an intended use of newly raised funds for stock repurchases is associated with negative bond returns and positive stock returns. In contrast, negligible bond and stock market reactions to new debt offering announcements are expected when the newly raised funds are used to refinance existing debt. On average, new debt offering announcements will be associated with negative abnormal bond returns and positive abnormal stock returns for different intended uses of newly raised funds.

¹³ When the intended use of newly borrowed funds is stock repurchases, a firm’s asset value will not change. Accordingly, the value of Equation (13)(13) $\frac{\mathrm{\partial }{P}_{bs0}}{\mathrm{\partial }{A}_0}\frac{\mathrm{\partial }{A}_0}{\mathrm{\partial }{D}_s}=\frac{1000\times N(-d_1)}{D_s}>0$(13) will be zero and Equation (14)(14) $\begin{array}{rl}& \frac{\mathrm{\partial }{P}_{bj0}}{\mathrm{\partial }{D}_s}+\frac{\mathrm{\partial }{P}_{bj0}}{\mathrm{\partial }{A}_0}\frac{\mathrm{\partial }{A}_0}{\mathrm{\partial }{D}_s}=\frac{\mathrm{\partial }{P}_{bj0}}{\mathrm{\partial }{D}_s}+\frac{\mathrm{\partial }{P}_{bj0}}{\mathrm{\partial }{A}_0}\\ & =\left[\frac{N(d_1)-e^{-rT}N(d_1-\sigma \sqrt{T})}{D_j}\right.\\ & \left.-\frac{N({d_1}^{\mathrm{\prime }})-e^{-rT}N({d_1}^{\mathrm{\prime }}-\sigma \sqrt{T})}{D_j}\right]\times 1000\end{array}$(14) will become: $\frac{\mathrm{\partial }{P}_{bj0}}{\mathrm{\partial }{D}_s}=-\left[\frac{e^{-rT}N(d_1-\sigma \sqrt{T})+e^{-rT}N(d_1^{\mathrm{\prime }}-\sigma \sqrt{T})}{D_j}\right]\times 1000<0$

¹⁴ Smith and Warner (1979) predict that the issuance of debt with higher priority will expropriate wealth from current bondholders.

¹⁵ A larger debt issue imposes a greater loss potential on existing bondholders since it increases the firm’s burden of interest and principal payments. Thus, the firm will have stronger incentives to invest in risky investment projects. The larger debt issue also results in a larger decrease in the value of a firm’s collateral. Accordingly, I expect to observe a negative relationship between bond excess returns surrounding the new debt offerings and the ratio of the new debt offering value relative to the firm’s total asset.

¹⁶ When the intended use of newly raised funds is stock repurchase, the derivative of stock and bond prices with regard to time to maturity, T, is:

$\begin{array}{rl}& Stocks:\frac{\mathrm{\partial }{F}_0}{\mathrm{\partial }T}=\{(p{A}_{0}N({d_1}^{\mathrm{\prime }})-(pD+C)e^{-rT}{N}^{\mathrm{\prime }}(d_2))\left(\frac{(r+\frac{1}{2}{\sigma }^2)T-ln(A_0/D)}{2\sigma T\sqrt{T}}\right)\\ & +\frac{1}{2}(pD+C)e^{-rT}{N}^{\mathrm{\prime }}(d_2)\sigma T^{-0.5}+(pD+C)r{e}^{-rT}N(d_2)\}/C>0\\ & Bonds:\frac{\mathrm{\partial }{L}_0}{\mathrm{\partial }T}=-N^{\mathrm{\prime }}(-d_1)\frac{A_0}{D^2}\frac{\left[ln(A_0/D)-(r+{\sigma }^2/2)T\right]}{2\sigma T^{1.5}}\times 1000<0\end{array}$

The proofs are upon request

¹⁷ The assumption of ln (A₀/D)>(r+σ²/2)T holds in my sample. I use my empirical data to check the validity. D (A0) is measured as a firm’s total long-term debt outstanding (asset) at the preceding fiscal year of the announcement. I use 3-month Treasury bill interest rate at the announcement month to proxy for the risk-free interest rate r. Asset risk, σ², is the standard deviation of unlevered stock returns (std. dev.), which is estimated using daily stock returns over the window −240 to −40 prior to the event date. Unlevered returns are computed by multiplying the stock returns by (1 − Leverage), where Leverage is the ratio of the book value of total debt to the sum of the book value of total debt and market value of equity at the end of the corresponding fiscal year. A firm’s debt maturity, T, is defined as the weighted average of the existing bonds’ maturities, using the principal of each existing bond relative to the total debt outstanding as weights. Then I calculate the difference between the value of ln (A₀/D) and (r+σ²/2)T. In my sample, only 8 out of 859 debt offerings have negative differences.

¹⁸ In unreported results, I split the sample into credit crisis period (from December 2007 to July 2010) and non-crisis period (our sample period outside of December 2007 to July 2010), and high and low interest rate periods. The results across each of these two periods are qualitatively similar to results reported in the paper. Following Graham and Harvey (2001), and Barry et al. (2008), a month is defined as low interest rate month if the interest rate falls within one of bottom three deciles and as ‘high’ if the interest rate is in one of the top three deciles of average monthly rates in prior 10 years.

¹⁹ More requirements on bond transactions data can be seen in Ederington, Guan, and Yang (2015).

²⁰ For example, on 20 March 2006, Home Depot Inc. issued $4 billion of debt to finance its acquisition of Hughes Supply Inc., a distributor of construction, repair and maintenance products. Another example is, on 24 October 2007, the wireless phone company America Movil sold $1 billion of long-term bonds to use the proceeds to upgrade their networks to third-generation technology, expanding its network in Brazil, and switching its Puerto Rico network to GSM from CDMA technology.

²¹ Ederington, Guan, and Yang (2015) constructed daily bond price using three weighting schemes: 1) by trade size, (2) by the square root of trade size, and (3) equally, and found that the square root weighting gave slightly more powerful tests than the other two.

²² For each new debt offering, I compare the seniority of the new bond to the seniorities of all existing bonds. As an example, suppose a firm issues a senior unsecured bond. Further suppose that this company had five bonds outstanding prior to the issuance, two are senior secured bonds and the remaining three are junior bonds. The abnormal bond standardized returns of the former two bonds would be reported in the ‘New < Existing’ category and the latter three in the ‘New > Existing’ category. Within each category, the firm’s abnormal returns to existing bonds are computed on an equal-weighted basis.

²³ Spiess and Affleck-Graves (1999) use the median number of issues per year as a benchmark since their interest is in long-term post announcement stock performances.