9. This question guides you through thinking about the role of collateral in lending. Suppose you are a mortgage lender. You have just lent to a homeowner and his house serves as the collateral. Suppose his houses current price is $100,000. Assume interest rate is zero and ignore time-value of money throughout this problem.

(a) Suppose you lent him $80,000. Thus, this mortgage has a loan-to-value ratio (LTV) of 80%. How negative does the housing price return have to be for it to be possible that you lose money on this investment?

(b) Suppose you lent him $90,000 (LTV = 90%). How negative does the housing price return have to be for it to be possible that you lose money on this investment?

(c) Suppose you lent him $90,000 (LTV = 90%). Now, you learned that it is very slow to foreclose the house upon default. More importantly, during the foreclosure process, the homeowner will stop maintaining the house or even vandalize it, so on average the houses value drops an additional 10% during the foreclosure process. Now, how negative does the housing price return have to be for it to be possible that you lose money on this investment?