Consider a simple scenario in which there are only two possible future (take the “future” to be one year from now) states of the world, the risk-free rate is zero, and the risk premium of every risky asset is zero (so the appropriate discount rate for all future cash flows is simply zero). The future states are sluggish growth, which occurs with probability 0.4, and robust growth, which occurs with probability 0.6. In the event of sluggish growth, the assets of firm Cumulonimbus are likely to be worth S$110 million, and the event of robust growth, they will be worth S$250 million. Cumulonimbus has debt, which requires a single payment of S$140 million in the future. The debt agreement has a covenant which stipulates that Cumulonimbus may not issue any debt with equal or higher priority to the existing debt. The remainder of Cumulonimbus’s capital structure is equity. (So, if they pay off the debt successfully, the entire remaining value of the firm will belong to the equityholders.) Assume a very efficient and streamlined (and therefore unrealistic) bankruptcy process—if Cumulonimbus fails to pay the debt, the debtholders immediately become the new equityholders in the firm (and can operate it as they see fit), and the current equityholders receive nothing. 

1(a). What is the current value of Cumulonimbus’s debt?

1(b). What is the current value of Cumulonimbus’s equity?

Now suppose Cumulonimbus has a new investment opportunity, codenamed Project Cirrus. This project re- quires an initial investment of S$20 million, which Cumulonimbus does not have; if it wants to do the project, it must go to financial markets to issue new securities. But if it does, the project will generate additional future value of S$30 million in the event of sluggish growth, and S$25 million in the event of robust growth.

Suppose Cumulonimbus issues new equity to raise the S$20 million necessary to do Project Cirrus.

1(c). What is the current value of Cumulonimbus’s debt now?

1(d). What is the current value of Cumulonimbus’s equity now?

1(e). Is Project Cirrus a positive NPV project?

1(f). Will the equity holders want to contribute the S$20 million necessary to do the project? Why or why not? Explain briefly. Does it matter whether the equityholders who contribute the S$20 million are the same people as the current equity holders, or different people?

Suppose the management of Cumulonimbus comes up with an unusual idea. They ask the debtholders to agree to reduce the face value of their debt to 131.5 million, even though they are under no obligation to do so. If the debtholders agree to this proposal, Cumulonimbus will attempt to raise an additional S$20 million in equity to do Project Cirrus.

 1(g). Suppose the debtholders agree to this proposal. Will equity holders be willing to contribute the necessary S$20 million to do Project Cirrus? Why or why not? Explain briefly.

1(h). Are the debtholders better off if they agree to management’s proposal, or if they refuse? Explain briefly.