Suppose you are in charge of a bank, which is considering making a short-term loan to a private equity fund so that it can buy a company. This loan would involve you giving the private equity fund L dollars today. The fund would then need to repay (1 + r) x L dollars next year. If they choose not to deliver this payment, then you get the value of the company.

The company is currently worth $92.5m. Next year, the company will be worth either $100m (up state) or $80m (down state). The prevailing riskless rate is 2%.

a) What is the current price of an asset that pays $1 in the up state and $0 in the down state next year, S_Up?

b) What is the current price of an asset that pays $0 in the up state and $1 in the down state next year, S_Dn?

c) What is the size of the of largest possible riskless loan that you'd be willing to give the private equity fund? (Answer in millions of dollars)

d) Suppose the private equity fund asks for a $82.5m loan. What is the fair interest rate on this loan? (Answer in percent)

e) Suppose the private equity fund asks for a $82.5m loan. What is the total payment that the private equity fund needs to make to you next year (interest + principle) in order to avoid default? (Answer in millions of dollars)

f) Suppose the private equity fund asks for a $82.5m loan. How much money does the private equity fund save by defaulting on this loan in the down state next year? (Answer in millions of dollars)

g) Suppose the private equity fund asks for a $82.5m loan. What is the present value of the default option associated with this loan? (Answer in millions of dollars)