A convertible bond, which we did not cover in the lecture, is a type of bond issued by companies that can be converted into a pre-determined numbershares of the same company's stock when the investor wants to do so.

We will make the simplifying assumption that the company has a zero probability of a default so that the expected cash flows from the bond is determined by its face value and coupon rate.

Suppose the company's bond has a 2-year maturity as of today, face value $100, and coupon rate 30%. The rate of return on short-term government securities (risk-free rate) is 5%. Suppose also that the discount rate on thecompany's bondalways equals the risk-free rate plus 1%. Discount rate on thecompany's stock is given by the CAPM-implied expected return. After a year, investors have an option to convert the bond into one share of the stock, if they prefer to do so. This conversion happens after the coupon is paid.

(a)Suppose that investors expect next year's dividend to be $5. If you knowfor certain that the dividend growth rate will be 4%, that the stock will have a market beta of 0.5, that the risk-free rate will stay at 5%, and that the expected return on the market will be 11% next year, what will be the price of the stock next period (Hint: Use Gordon growth model)?

(b)If you know for certain that the risk-free rate will stay at 5%, what will be the price of the bond next year? (Hint: Recall that abond's maturitychanges every year. You may round up the number.) Will the investor convert the bond to a stock next year?