University of Texas at Dallas
Jindal School of Management
FIN4300
Problem Set #3
Fall 2014
Important note: Please submit paper copy of your solutions
Due Dates: Dec. 8 for Section 002 and Section 501; Dec. 9 for Section 001 (all in-class)
1. Suppose you are a portfolio manager at Paulson & Co. Inc. Today is the last day of
April 2013. Your portfolio did not do well in the most recent month. After learning about the post earnings announcement drift, you decide to give it a try. You gather most recent earnings information on 100 stocks as of April 30 2013. After examining the earnings surprises, you decide to buy an equally weighted portfolio of the top 10 stocks with the most positive earnings surprises. At the same time,
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(a) What is the annual coupon payment of a bond that trades at par and has the yield to maturity equal to the interest rate, 4%? The bond has a face value of $1,000 and pays annual coupons.
(b) What is the price of an annual coupon bond with a face value of $1,000, a coupon rate of 10%, and 30 years to maturity?
1
4. Suppose the term structure of interest rates are not flat. The one year spot rate, r1 , is
6.01%/year, the two-year and the three-year spot rates, r2 and r3 , are both 5%/year.
(a) What are the forward interest rates for the second and the third year?
(b) Consider a zero-coupon bond with the face value of $1,000 and three years to maturity. What should be the bond price today?
5. In your calculations, please round computed prices to the second decimal place (e.g.,
220.78 instead of 220.7765).
A risk-free annuity A pays two annual payments of $100 (the first payment is made in a year).
(a) If the term structure of interest rates is flat and the interest rate is 61.80%/year, what is the price of the annuity?
(b) What is the yield to maturity of the annuity?
(c) The term structure suddenly changes and now the spot interest rate for one year
(r1 ) is 80%/year and the spot interest rate for two years (r2 ) is 50%/year. As it turns out, the price of the annuity stays the same as in part (a). What is the yield to maturity of the annuity now?
(d) Suppose that there are two
(d) Calculate the actual dollar change in price of the bond for a 100 bps increase in yield.
17) The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to:
Calculate the price of this bond if the stated annual interest rate, compounded semiannually, is:
(2) Long-term bonds: Example: On January 1, 2006, Fumatsu Electric issues 10% stated rate bonds with a face value of $1 million. The bonds mature in 5 years. The market rate of interest for similar issues was 12%. Interest is paid semiannually beginning on June 30, 2006. What is the price of the bonds? (a) Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) (b) Calculate the Present Value of the Annuity Payments (Interest)
b. Suppose a Series F, with a $100 par value and a 9.75 percent cumulative dividend, has a
What would the present value of the account be if the discount rate is only 4%?
If I denotes the interest on a principal P (in dollars) at an interest rate of r per year for t years, then we have
(TCO F) Warren Corporation's stock sells for $42 per share. The company wants to sell some 20-year, annual interest, $1,000 par value bonds. Each bond would have 75 warrants attached to it, each exercisable into one share of stock at an exercise price of $47. The firm's straight bonds yield 10%. Each warrant is expected to have a market value of $2.00 given that the stock sells for $42. What coupon interest rate must the company set on the bonds in order to sell the bonds-with-warrants at par?
If the real rate of interest is currently 2.5%, find the nominal rate of interest on
A payment of $1,000 will occur ten years from now. Compute the present value of this cash flow.
1. Is it possible for the three year bond price to increase while the ten year bond price falls due ONLY to changes in the term structure?
A sum of $ 5000 is invested at a compound interest rate of 6.3 % per annum. (a) Write down an expression for the value of the investment after n full years.
b. Since the perpetuity will be worth $10 in year 7, and since that is roughly
When the policyholders retire, they can choose to buy an annuity from an insurance company using the previous lump sum. The annuity will offer 20 annual payments paid at the end of each year. The payment amounts depend on interest rate at retirement and can be formulated by solving: