There is a $100M property (Property A) that will be worth either $120M or $90M in one year with an equal probability (50%/50%). In this exercise, you will analyze the return to a non-recourse collateralized loan and the levered equity.

1.What is the expected rate of return to Property A? Hint: The amount of investment is $100M.

2. What is the present value (for the lender) of a $95M, one-year, zero-coupon, riskless loan? The riskless rate of return is 1%. Hint: The borrower promises to pay $95M at t =1 and no other payment.

3. What is the lenders payoff in each state of nature at t=1 for a $95M, one-year, zero-coupon, risky, non-recourse loan (Loan B) that is collateralized by Property A? Hint: The borrower promises to pay $95M dollars at t=1, but may strategically default on the loan.

$ M if the property value is 120

$ M if the property value is 90

4. What is the amount that Loan Bs lender will forgive (i.e., the payoff to the borrowers default option) in each state of nature at t=1? Hint: The lender has to forgive the difference between the promised payment and the collateral value.

$ M if the property value is 120

$ M if the property value is 90

5. The present value (i.e., premium) of the borrowers default option is $3.1M. What is the present value of Loan B for the lender?

6. What is the credit spread for Loan B? Hint: The credit spread is the difference in YTM between a credit-risky loan and a riskless loan. The YTM is the IRR on the basis of the promised payment.

7. What is the expected rate of return and the risk premium to Loan B? The expected rate of return is ________% and the risk premium is_______%. Hint: The expected rate of return is based on the expected payoff in the future. The risk premium is the difference in the expected return between a credit-risky loan and a riskless loan.