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Context Suppose we have an imaginary economy with a lot of entrepreneurs. Each entrepreneur needs external funding of IDR 1 0 0 million for a

Context
Suppose we have an imaginary economy with a lot of entrepreneurs. Each entrepreneur needs
external funding of IDR 100 million for a project. There are two risk categories for the project:
high-risk and low-risk. The cash flow returns of a high-risk project equals IDR 500 million
(probability =0.25) and IDR 0(probability=1-0.25=0.75). On the other hand, the low-risk project
generates cash flows IDR 125 million, always (probability=1). By assuming riskneutrality
(universal) and the riskfree rate is zero (no discounting), each project creates IDR 125 million on
average. The entrepreneurs have positive NPV, since 125-100>0.
However, the bank does not know the probability to generate the cash flow for each project,
but the entrepreneur knows. Suppose the bank cant find a way to know the riskiness of a project
by screening the project. The bank only knows the estimated probability for low-risk projects,
which equals to 20% of all cases. The entrepreneur takes his project only if he has a strictly positive
expected payoff, by taking into account what he has to pay back to the bank. We may assume that
the economy has perfect competition in the credit market.
Ques%ons
1. Suppose that the bank has following statement: With probability 0.8 the project is a high-risk,
the project fails to generate cash flow with probability 0.75, and with probability 0.2 the project is
a low-risk project. So, to create a break even condition, the bank needs to charge an interest rate r
by using: 0.8\times 0.25\times 100(1+r)+0.2\times 100(1+ r)=100. Is there any creditworthy entrepreneur who
would accept the interest rate? What is wrong with this statement?
2. By assuming debt financing, what interest rate the bank will charge in the equilibrium condition?
and what kind of projects are financed by the bank? Who is credit rationed?
3. By using equity financing, the bank holds some share a (a >0) of the firm, which implies the
bank will receive share of a from the firms cash flows. Proof that the bank would finance both
high and low risk projects. In addition, both high and low risk project holders pay the fair capital
cost. Explain.

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