A firm wants to raise $30m to invest in a project. After the $30m invest- ment, the firm will have a total asset value of $100m. The risk-free rate is 10%, and the volatility of the return on assets is 20%.
(a) If the firm wants to issue 10-year debt (zero-coupon), what face value do they need to set?
(b) Now imagine that the bond has been issued (with a face value that you found in the previous part), but that the stockholders can choose an action that changes the nature of the cash flows. Namely, the shareholders can: (1) do nothing, (2) take an action that will immediately reduce the value of the assets from $100m to $99m and at the same time raise the volatility to 30%. Will the shareholders take this action?
(c) If the bondholders anticipated this possibility when they were of- fered to invest in the company, what do you expect they would have demanded as a face value?
(d) Would the shareholders have an incentive to include a covenant pro- hibiting the action in part (b) above?