Context

Suppose we have an imaginary economy with a lot of entrepreneurs. Each entrepreneur needs

extemal funding of IDR $100$ million for a project. There are two risk categories for the project:

high$-$risk and low$-$risk. The cash flow returs of a high$-$risk project equals IDR $$500$ million

$($probability $=0\mathrm{.}25)$ and IDR $0($poobubility$=1-0\mathrm{.}25=0\mathrm{.}75).$ On the other hand, the low$-$risk project

generates cash flows IDR $125$ million, always $($probability$=1).$ By assuming risk$-$neutrality

$($universal$)$ and the risk$-$free rate is zero $($no discounting$),$ cach project creates IDR $125$ million on

average. The eatrepreneurs have positive NPV$,$ since $125-100>0.$

However, the bank does not kow the probability to generate the cash flow for each peoject,

but the entrepreneur know. Sappose the bank can't find a way to know the riskisness of a project

by serecaing the project. The bank only knows the estimated probability for low$-$risk projects,

which equals to $20\%$ of all case. The entrepreneur takes his project only if he las 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 competitices is the credit market.

Questions

$1.$ Suppose that the bank has following statemeat: "With probability $0\mathrm{.}8$ the project is a high$-$risk,

the project fils to generate cash flow with probability $0\mathrm{.}75,$ and with probabliny $0\mathrm{.}2$ 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: $0\mathrm{.}80\mathrm{.}25100(1+r)+0\mathrm{.}2100(1+n)=100."$ 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 be back 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 bolds some share $(a>0)$ of the firm, which implies the

bank will receive share of $$ from the firm"s casl 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.