When we derived the put-call parity relationship (for non-dividend paying stocks), we showed that the put was equivalent to a combination of the call, the stock and riskless borrowing/lending. Obviously, we could use the put-call parity relation to solve for the value of any of these four components (not just the put price) with respect to the other three.
Let's consider one particular application of this. Think about a firm that is made up entirely of (zero-coupon) debt and equity, that is, Vf = B + E, where B is the market value of the (risky) bond and E is the market value of the equity of the firm. Consider the equity of the firm as a call option on the value of the firm, where the strike price is the maturity payment due the debtholders (call it D).
a) Using the put-call parity relation, solve for the value of the equity "call option" in terms of the three other components.
b) Using your answer to part a), what are the components of the value of equity in this firm? How will the equity-holders think about risk?
c) Using the put-call parity relation, solve for the market value of the bond (B) with respect to the other components. (Remember that since Vf = B+E, that B=Vf - E.) What are the components of the value of the bond? How will the bond-holders think about risk?
d) Let's say that Firm A (the debt+equity firm above) merges with another firm in a different industry (call it Firm B). Firm B has no debt, and no new debt is issued at the merger, nor is any feature of the debt of Firm A re-negotiated. Given your answer to part c), how do you think the bondholders of Firm A will feel about the merger? What about the stockholders of Firm A?