Homework 4 Due Oct 29
1homework 4 Due Oct 29
1 Homework #4. (Due: Oct 29) Name: (ID: )
1. You have been hired by a small pension fund to help them design a bond portfolio to fund a $10 million obligation that will come due in 4 years. The managers of the fund would like to use 2 year zero coupon bond along with their existing bond portfolio A that includes following three zero coupon bonds with the corresponding portfolio weight: Security 5 year zeros 7 year zeros 10 year zeros Portfolio weight 25% 25% 50% Suppose that the yield to maturity on all bonds is 5% (in other words, the yield curve is flat at 5%).
a) How much money do you have to invest today in the bond market to entirely fund your obligation?
b) What is the durations of current existing bond portfolio A and the obligation (due in 4 years)?
c) How would you structure your holdings of the 2 year zero coupon bond and their existing portfolio A so that you are protected against the risk of interest rate fluctuations? Please indicate the dollar amount you would invest in each security.
2. You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.
a) What is the present value and duration of your obligation?
b) What maturity zero coupon bond would immunize your obligation?
c) Suppose that you buy a zero coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position (difference between the value of bond and that of your tuition obligation)? What if rates fall to 7%?
3. A 20-year maturity bond pays interest of $90 once per year and has a face value of $1,000. Its yield to maturity is 10%. You expect that interest rates will decline over the upcoming year and that the yield to maturity on this bond will be only 8% a year from now. What is the return you expect to earn by holding this bond over the upcoming year?
4. In the bond market, we find the following Treasury bonds and their prices: Bond price $980, $98, $96. Maturity 2 years, 1 year, 2 years. Face value $1,000, $100, $100. Coupon rate 10%, 0%, 0%. a) Compute the YTMs for the above three bonds. b) Using the two zero coupon bonds, compute the forward rate from the end of Year 1 to the end of Year 2. c) If you need the above coupon bond for your cash requirements but cannot buy it directly, how many 1-year and 2-year zero coupon bonds are needed to replicate its cash flows? What is the cost? d) Is there an arbitrage opportunity? If yes, how can you profit, and what are the arbitrage profits?
5. You are managing bond trading and forward loans at a large investment bank. Given YTMs for five zero-coupon bonds with various maturities and rates: 0.06, 0.065, 0.07, 0.065, 0.08. a) Is the intern correct when stating that a 3-year Treasury with a coupon of $100 and face $1,000 is trading at $1,000? Why or why not? b) How to structure bonds to match a future loan cash flow, and what is the quoted forward interest rate? c) If you buy the bond in (a), what is your return after one year given new YTM rates?
6. Florida Enterprise bonds: 8-year maturity, selling at $948, yield 5.9%. Find the coupon rate. Bond X (premium, semiannual, 8.5%, 7%, 13 years). Bond Y (discount, semiannual, 7%, 8.5%, 13 years). Calculate current prices and expected future prices at intervals, including graphing bond prices versus time to maturity.
7. Winter Time Adventures pays a dividend of $2.60 next year; previous dividend was $2.50. With a constant growth rate, what is the stock price in 11 years if the discount rate is 8%?
8. Panther Corp. stock: current price $68, return requirement 11%, constant dividend growth 3.75%. What was the most recent dividend paid? International Corp.: EPS $4.04, PE ratio 21, growth rate 5.5%. a) Estimate current stock price. b) Forecast stock price in one year. c) If no dividends paid, what is implied return? What does PE valuation suggest?
9. Scenario: AIM Inc., a profitable tech company, faces social and motivational issues. Your team must recommend solutions to pay inequity affecting 125 employees earning $35,000, and executives earning $500,000 or more. Describe problems, goals, tasks, propose a solution, support with scholarly references, apply teamwork concepts, and detail individual contributions. Prepare a presentation, 10 slides minimum with citations, formatted for clarity and readability.