Hi I had a question regarding a finance problem on financing through debt vs equity:

A young start-up with several different potentials for growth is looking to raise financing for one of three projects. All projects require an investment today, and have a single (possibly random) cash flow one year from now.

Options: 1. Build mansions. Due to the recent housing crisis this is a risky proposition and will result in a payoff of zero with 85% probability. However, if the housing market recovers, which will happen with 15% probability, the project's payoff will be $19 million.

2. Open a lemonade stand. This is a safer proposition than building mansions. In particular, the projects's payoff will be $2 million or $5 million with equal probability.

3. Deposit the money in a bank. The bank promises an interest rate of 20%. However, there is a 10% chance that the bank will become insolvent, in which case depositors will simply get their money back but earn no interest.

In total the start-up is looking for $2.5 million in financing, which will be enough to finance either of the three projects. Once the financing is raised, the CEO is free to choose any project she wishes. It is not possible to write a contract at the time of financing to restrict project choice ex-post.

Assume risk neutrality & a 10% discount rate.

a) Compute the NPV of each project

b) Suppose the company raises all of the financing it needs from outside equity. What share of the firm's equity must be promised to investors? Which project will be chosen? What is the payoff to the start-up's original owners?

c) Suppose the company raises all the financing through debt. As per standard legal practice, creditors have no say in which project the firm chooses. What is the face value of the debt and the payoff to the start-up's original owners?

d) Suppose that despite standard legal practice, creditors ar able to influence the firm's decisions. Which project will creditors prefer? What will be the payoff to the start-up's original owners if the terms of financing are as in part b and if the creditors are able to exert their influence? If ex-ante everyone anticipates that the creditors are able to exert their influence the terms of financing will be different from part b. In this case, what will be the face value of the debt and the payoff to the start-up's original owners?

e) in light of the above numerical example, discuss the financing preferences of young firms. Suppose that at the time of the debt issue, a contract can be written specifying the choice of a project. Which of the three projects would be preferred in the contract?

f) explain why in the real world creditors may be able to exert influence despite equity having the right to make all decisions as long as the firm is solvent.