Question I: The Diamond Model $(35$ points$)$

Vandelay Industries would like to fund a new project in importing and

exporting goods. To do this, they will need funding to cover various

startup costs. Assume the following:

The probability that the project is successful is $75\%,$ and the

probability of failure is $25\%.$

The company needs to raise $$100,000$ to start its operation, and in

a successful state, the project will be worth $$150,000,$ while it

will be worth its initial $$100,000$ if it fails.

H$.$E$.$ Pennypacker, a "wealthy American industrialist" also wants to fund

a new project in clothing retail. He also decides to pursue funding for

various startup costs. Assume the following:

The probability that the project is successful is $75\%,$ and the

probability of failure is thus $25\%.$

The company needs to raise $$100,000$ to start its operation, and in

a successful state, the project will be worth $$150,000,$ while it

will be worth its initial $$100,000$ if it fails.

Assumptions for both projects:

Bankruptcy costs are $50\%.$

Potential lenders require a rate of return of $5\%.$

Monitoring Costs are $$100$ per each $$25,000$ that the bank funds

The projects are independent of one another

Assume Vandelay Industries pursues direct financing. To what

should a potential lender set the face value of a loan to Vandelay

Industries? Now assume that the bankruptcy costs increase to $75\%.$

What should the face value of the loan be$?(7$ points$)$

Return to the original assumption that bankruptcy costs are $50\%.$

Vandelay Industries receives news that the project is successful.

What return does the firm receive? What return does the lender

receive? $(7$ points$)$

Vandelay Industries offers to pay back the $($direct financing$)$

lender less than the face value you calculated above, claiming that

a series of unfortunate events made the project a failure. What

should the lender do$?(3$ points$)$

Calculate the following probabilities: $(3$ points$)$

a$.$ Vandelay Industries and Pennypacker's projects both succeed

b$.$ One of the two projects fails

c$.$ Both Vandelay Industries and Pennypacker's projects fail

If a bank were only to finance Pennypacker's project, what would

its probability of default be$?$ What is the bank's probability of

default be if it funds both projects? $(3$ points$)$

What rate should the bank promise to repay its depositors if it

decides to fund both projects? $(4$ points$)$

For what face value is monitoring feasible for the bank? $(3$ points$)$

What are the expected profits for the bank? $(5$ points$)$