There is a $100M property (Property A) that will be worth either $120M or $90M in one year with an equal probability (50%/50%).

Year	0	1	Probability
		120	0.5
	100
		90	0.5

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

Debt

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.

Equity

8. What is the payoff to the levered equity position in Property A for each state of nature at t=1? The equity investor (borrower) uses Loan B to finance the property investment.

$ M if the property value is 120

$ M if the property value is 90

9. What is the present value of the equity?

Hint: There are two methods to calculate the equity value. Method 1: Recall the balance sheet: Property value = Debt + Equity. Method 2: The equity DCF based on the expected rate of return to the equity that is calculated in Q10.

10. What is the expected rate of return to equity?

Hint: If you already calculated the equity value in Q9, you can simply calculate the expected rate of return. Alternatively, if you want to first calculate the expected rate of return to equity, you can use the WACC formula.

11. Compare the present value of equity with the present value of the following asset portfolio: a long property, a short riskless debt, and a long default option. Should they be equal or different?

The PV of equity is $ M (copied from Q9).

The PV Portfolio: Property value ($100M)

Riskless debt ($ M copied from Q2)

+ Default Option ($3.1M copied from Q4 and Q5)

= $ M

These two values should be {equal / different}.