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Question: consider a firm who needs 10m to initiate a project...

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Consider a firm who needs $10m to initiate a project. The payout of this project is $15m with probability 90% and $10m with probability 10% at the end of two years. Suppose that there are 1000 small investors each with $10,000 to lend. If the project is initiated, only the firm (borrower) knows the result of the project whiles the lenders can not see the results. Hence the lenders would need to monitor the borrower; otherwise the borrower would always report minimum result and just pay back $10,000 to each investor regardless of the outcome of the project. However, as long as one of the lenders pay $1,200 monitor fee to get the information on the results of the project, the information will be known to everyone and the firm will pay $15,000 to each investor if the project succeeds and $10,000 if the project fails. Assume all the investor have an extra $1,200.

a) Suppose the project is the only investment opportunity for the small investors. Will the small investor lend directly to the firm? Will the small investor pay the monitor fee? Why or Why not? (Assume each investor knows that there are many other small investors with $10,000 to lend, but each investor lives in an isolated island and cannot coordinate with other investors, he or she can only communicate with the firm) 

b) Will the project be funded if 1000 small investors can form a credit union? If yes, what is rate of return on the investment? 

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