A small engineering firm is commencing trials for a new battery technology. These trials will take one year to complete. The firms shares are currently trading at $12 per share. The firm does not pay dividends and is not expected to do so in the next two years. If the trials are unsuccessfull, the firm will be closed, and its patent sold for $5 per share. If the trials are successful, itss share price will increase to $27.35 and the firm will need to apply for regulatory approval, which will require further trials that will take one year to complete. If the firm is successful in obtaining regulatory approval, the firm will be sold to a major technology company for $55 per share. If approval is not gained, the firm will be closed and its patents sold for $15 per share. At each stage, the probability of success is the same. The firm has zero systematic risk. The risk-free rate is 3% per year and the market risk premium is 6%.

(a) According to the CAPM, what should be the expected return on the firms shares?

(b) An investor has an agreement with the firm giving her the right, but not the obligation, to acquire the firms shares in two years at the current market price of $12. What is the market value of the investors right?

(c) Suppose instead that the right in (b) was American. A trader offers to purchase the right from the investor at the price calculated in (b). Should the investor accept it (I.e. is the offered price fair)? Explain.

(d) what is the value of a security that pays $1 if the firm secures regulatory approval in the next two years, and otherwise pay zero? Explain.