[20 pts] The average life of a bond is defined as

= (_(t=1)^TtPCFt)/(_(t=1)^T PCFt)

where PCF_t is the principal cash flow at time t, and T is the maturity of the bond.

a. [1 pt.] What is the average life of a zero-coupon bond? Show work

b. [1 pt.] What is the average life of an interest only bond? Show work

c. [2 pts] Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that

lim(c0) =T+1/2

where c is the mortgage contract rate.

d. [16 pts] Compute the realized average life of a 30 yr., 5/1 ARM with initial rate of 4%, and a margin of 2%. The underlying index is (date in yrs., index in %): (0,2), (1,3), (2,3), (3,2.5), (4,3), (5,5), (6,5), and (7-30,6). The loan is never prepaid, nor curtailed, nor defaults. There are no rate or payment caps. Annotate excel, or show all work.

[6 pts] A borrower is faced with choosing between two fully amortizing level-payment loans. Loan A is available for $75,000 at 10% MEY for 30 years, with 6 points included in the closing costs. Loan B would be made for the same amount, but at 11% MEY for 30 years, with 2 points included in the closing costs. Neither loan defaults/is curtailed.

[4] If the loan is to be repaid after 15 years, which is the better choice?

[2] If the loan is repaid after 5 years, which is the better choice?

Hint: Use the effective cost of borrowing to make the decision. Show work.

3. [14 pts]

[2] Describe the model of firm equity as a call option on assets of the firm. What does it mean for this option to be out-the-money?

[3] Why were many thrifts insolvent by the early 1980s?

[4] Using the equity model in A, and the concept of forbearance, describe and explain the behavior of thrifts, both insolvent and solvent, in the early 1980s.

[2] How does securitization help mitigate the problem described in B?

[3] Describe how securitization eventually played a role in the creation of the RE bubble of the early- to mid-2000s.

[10 pts] You have had a 30yr FA FRM at 9% for 6 years. The original principal was 1,000,000. You are considering a cash-out refi into a 15-year mortgage at 7.5%. The old mortgage has a prepay penalty of 3% if payoff occurs before year 8. The new mortgage has fees of 4%, and no prepay penalty. The additional cash is for a $60,000 car, and can be borrowed at 9% over 10 years, with upfront fees of 1%.

Assume that all fees will be financed, and that under either scenario you will be moving 10 years from now. Ignore taxes, the option to wait to refinance, and assume no loan is prepaid, curtailed, nor ever defaults.

What is the NPV of refinancing? Show work.