# Business Finance

1. [15 pts] The average life *τ* of a bond is defined as

where *PCFt* 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

where *c* is the mortgage contract rate.

d. [11 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 any excel and show all work.

2. [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.

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

b. [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]

A. [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?”

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

C. [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 1980’s.

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

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