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One Coin Crypto (OCC), currently has assets with a market value of $100. Next year the market value of OCC's assets is going to increase by 50% or decrease by 40% depending on the state of the economy. The annual risk-free rate of interest is 0%. OCC has one share of common stock issued and outstanding as well as one corporate bond outstanding with a face value of $100 and a coupon rate of 5% maturing next year at t=1. The corporate bond has no callable features.
(a) Find today's value of OCC's corporate bond and common stock. What is the promised yield to maturity of the corporate bond equal to?
(b) Now suppose that in addition to the 5% coupon we also make the corporate bond convertible (at the discretion of the bondholder) into 2 shares of common stock. In other words, the bondholder has the right but not the obligation to exchange their bond into 2 shares of common stock when the bond matures. What is today's value of OCC's convertible corporate bond and common stock? What is the promised yield to maturity (YTM)? How about the promised yield to conversion (YTC)?
(c) Finally, how would your answers to part (b) change if the corporate bond were instead convertible into 9 shares of common stock?
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