Answer Happy

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