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. 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)