GloboCorp Industries has hired you to help price a so called reverse convertible bond that they are
Question:
GloboCorp Industries has hired you to help price a so called "reverse convertible bond" that they are considering issuing as part of a recapitalization. GloboCorp is currently all-equity financed, with 50m shares outstanding, and the current share price is $80 per share. The firm does not pay dividends, the annualized volatility of their equity, implied from listed equity options, is 35%, and the behavior of the firm's asset value is consistent with the assumptions of the Black-Scholes model.
The type of security that GloboCorp is considering issuing is a reverse convertible bond. Like a typical convertible bond, the security can be considered as a combination of a particular type of standard bond and a particular option to convert the bond into common stock (equity). However, the key distinguishing feature of a reverse convertible bond is that the conversion decision is at the discretion of the issuer. That is, the conversion decision is made by the firm's managers (who seek to maximize value for existing equity holders) not by the holders of the bond!
The proposed issue involves 1 million bonds, which have a face value of $1,000 per bond, pay no coupons, and mature in 3 years. The bonds feature a conversion ratio of 25. That is, if the issuer exercises the conversion option, each bond will be converted into 25 shares of equity. Finally, suppose that the conversion option has a "European" exercise style and can only be exercised at the bond's maturity date.
The entire proceeds from issuing the reverse convertible will be used to pay a special dividend to equity holders. Hence, the proposed transaction is a pure recapitalization. Suppose further that the issuance of these bonds is unanticipated by the market and that the firm is not expected to make any other changes to their capital structure or raise any additional capital over the next 3 years. (So, no share repurchases, no debt issues, no equity issues, etc.)
The risk-free rate is 5% (EAR) at all maturities. Suppose there are no corporate taxes, no financial distress costs, and all securities are correctly priced.
A. Supposing the firm does not exercise the reverse conversion feature, what is the promised total payoff (in $) to the reverse convertible bondholders on the bond's maturity date. (i.e., what is the aggregate promised payoff on the entire bond issue if the bonds are not converted)?
B. Supposing that the firm exercises the option to convert, how many new shares will be issued? What fraction of the entire shares outstanding (and therefore of the firm's total asset value) will the bondholders own? At what aggregate firm asset value will the issuer be just indifferent to exercising the conversion option? Will the issuer find it optimal to convert the bond for asset values above or below this indifference point?
C. Based on your answers to Parts A and B, the reverse convertible bond issue (i.e., a long position in the entire aggregate bond issue) can be considered as a position in a risk-free zero-coupon bond, combined with a particular option contract. What are the details of these two implicit positions?
D. How much will GloboCorp raise by issuing the reverse convertible bond? What is the yield to maturity (expressed as an EAR) of the bond at issuance?