Question: PART A: Consider a binomial tree for interest rates. The interest rate the first period is 4% and rates move up or down by 1% per year; all interest rates are compounded annually. The probaility of a move up is 60%. Answers which are interest rate or a yield should be expressed with two decimal places showing basis points. Dollar amounts should include two decimals showing cents.
1) Use the tree to determine the value of a 3-yr zero coupon bond with face value of $100 incorporating the interest rate uncertainty.
2) Repeat the calcuation for a 2-year zero and for a 1-year zero.
3) Use the valuations from the prior questions to determine the spot rate for each year. (valuations from questions 1 & 2)
4) The expected value of the interest rate in the third year is 4.40% (0.36x6% + 0.48x5% + .16x4%). Explain why the 3-year spot rate is so much lower than this expected value.
5) Use the interest rate factors(value today of $1 delivered in the future) implied by question 1 to value a coupon bond making payments of $500, $500, and $10,500.
6) Use the interst rate factors to value a mortgage making payments of $10,000 in each of the 3 years
7) Modify the tree of question 1 for the 3-year zero coupon bond to incorporate a default risk of 1% per year. What is the value of this bond based on these calcuations and what is the spot yield?
PART B: When offered a choice of three contracts, which would be the best one. Which has more value at different interest rates? What is the interest is negative? Should you compute future value, present value, or something in between?
-The first contract makes 3 payments of $150,000 at the end of each next 3 years
-The second contract makes a single payment of $465,000 at the end of the third year
-The third contract makes an immediate payment of $440,000 and no other paymnts.
-the contracts are otherwise equivalent(ceteris paribus) Perform an analysis of these contracts based on the current interest rate environment as summarized in the H15 realease.
Write an explanation indiciating what action is the best to take and why. include tables and graphs to support conclusion. Comment on the different between using Present value versus future value for decision of this form. also discuss how the need to pay current living expenses affects the decision, and how the possibility of an increase in interest rates due to inflation might affect the decision