Problem: Due to the market meltdown a technology company was unable to raise new equity. Their investment bank advised them they could issue a five-year zero coupon $100 bond with two conversion options. The terms would be conversion rights for each bond into 50 of the underlying shares after 5 years, otherwise repayment at par. The bond also allows conversion into 100 shares in 3years if share price then is below $1.0. If the shares trade now at $1.0, the volatility of the underlying security is 0.45, the risk free rate is 7.00%, the underlying shares have no dividend and assuming there is no default risk:
Q1. What is the first option embedded in the convertibles worth, and how many underlying shares does it represent?
Q2. What is the second option embedded in the convertibles worth, and how many underlying shares does it represent?
Q3. Assuming the risk free rate is constant over time what should be the price of the convertible?