01 Oct Business Finance Excel Question
Total: 50 points. Show all work for full credit (annotate relevant formulae in excel, substantial penalties otherwise). Make sure your presentation is clear and staple in the order of the questions. Excel table rules apply (show no more than 1 page of repeated rows, 5-point penalty otherwise).
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.
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