Laidler AG wishes to issue perpetual bonds with a face value of €1,000, these will have a 5% coupon rate. Coupons will be paid annually. Laidler will set a call premium at €100 over face value. For simplicity, assume these bonds can only be called at the end of the first year. Also assume there is an equal chance that by the end of the year interest rates will do one of the following: 1) Fall to 3.57%. If so, the bond price will increase to €1,400. 2) Increase to 8.33 %. If so, the bond price will fall to €600. a) Show that if the bond is not callable, its expected value to an investor today is worth €1,000. The appropriate discount rate is 5%.
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- Suppose you have an obligation to pay € 56 000 in 8 years time. To avoid interest risk you intend to hedge with two bonds. You can use one zero coupon bond that matures 10 years from now, and one bond that pays coupons once a year at the rate of 5% and matures in 3 years with a face value of 100. Assume a flat yield curve. (a) What amount do you have to invest in each of the two bonds during the first year to hedge your obligation if the yield is 5%? What is the payoff at maturity (face value) of your investment in the zero coupon bond? How many units of the coupon bond do you have to buy? (Assume that you can buy any fractional amount of the bonds.) (b) What is the value of your portfolio today if immediately after the investment the market rate falls to 4%? What will be the value in 8 years if interest rates will not change again?You will be paying $8,600 a year In tultion expenses at the end of the next two years. Bonds currently yleld 7%. Q. What is the present value and duration of your obligation? b. What maturity zero-coupon bond would Immunize your obligation? c. Suppose 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, that is, to the difference between the value of the bond and that of your tultion obligation? d. What if rates fall Immediately to 5% ? Complete this question by entering your answers in the tabs below. Required A Required B Required C Required D What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.) \table[[,,,],[Present value,,,,,],[Duration,,years,,,]]Suppose that yield rates on zero coupon bonds are currently 26 for a one-year maturity, 3% for a two-year maturity and 4.% for a three-year maturity (all effective annual rates). Suppose that someone is willing to borrow money from you starting one year from now to be repaid three years from now at an effective annual interest rate of 6.5146438635186%. Construct a transaction in which an arbitrage gain can be obtained. What is your positive net gain for net investment of 0? (net cashflow at t-3) 01345 One possible correct answer is: 0.030250290387703
- Consider a long forward contract to purchase a coupon-bearing bond whose current price is $910. We will suppose that the forward contract matures in 9 months. We will also suppose that a coupon payment of $45 is expected after 4 months. We assume that the 4-month and 9-month risk-free interest rates (continuously compounded) are, respectively, 3% and 4% per annum. Explain how an arbitrageur can make profits from this scenario.A company must make a payment of $2500 in 5 years. Four-year zero coupon bonds and seven-year zero coupon bonds are available for investment. These bonds could be purchased in any quantity and the yield rate is 3% effective. Let A and B be the face values of the 4-year and 7-year zero-coupon bonds, respectively, that are purchased to satisfy full immunization against any changes in interest rates. Find A. Possible Answers A 1262 1431 C 1618 D 1725 E 1962Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 6.5%, payable annually, and a par value of $1,000. The 1-year interest rate is 6.5%. Next year, there is a 35% probability that interest rates will increase to 8% and a 65% probability that they will fall to 5%. What will the market value of these bonds be if they are noncallable?
- An insurance company is thinking about purchasing bonds A and B with zero coupons to cover some of its future liabilities. The redemption periods for these zero-coupon bonds are seven and twenty years, respectively.£11 million is due in 11 years, and £14 million is due in 16 years, according to the list of its liabilities.Determine bond B's value at an effective 5% annual interest rate so that Redington's theory of immunization's first two requirements are met. (correct answer=6.419) (using formulas, no tables)The company SunInc wants to launch a new product and therefore needs to raise new financing. SunInc issues a bond with a face value of EUR 1000 and a maturity of 5 years. The coupon rate is EUR 45 and the payment annually. What is the yield to maturity? Please also explain how you calculated it.Taussig Corp.'s bonds currently sell for P1,150. They have a 6.75% annual coupon rate and a 15-year maturity, but they can be called in 6 years at P1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds, the YTC or the YTM?
- Suppose that you buy a TIPS (inflation-indexed) bond with a 1-year maturity and a coupon of 2% paid annually. Assume you buy the bond at its face value of $1,000, and the inflation rate is 10%. a. What will be your cash flow at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What will be your real return? c. What will be your nominal return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)For the following questions, assume the normal case that coupon payments are semi-annual. a. What is the yield to maturity on a 10-year, 5.3% coupon bond if the bond is currently selling for $1,000? b. For the bond above, suppose that immediately after purchase market rates change to 3.00%. If you hold the bond for 3 years and then sell it, what is your effective annual return on this investment? a. The YTM is % (enter response rounded to decimal places; i.e., x.xx%) b. Your effective annual return is % (enter response rounded to decimal places; i.e., x.xx%)The 3-year, 5-year, and 7-year zero rates are 1%, 2%, and 3%. The rates are given per annum with annual compounding. a) What are the zero-coupon bond prices with maturities of 3 years, 5 years, and 7 years? (Assume that you receive a face value of $100 for each of these bonds on their maturity dates). b) What is the forward rate for an investment initiated 3 years from today and maturing 5 years from today? (Give your answer per annum with continuous compounding)? c) What is the forward rate for an investment initiated 3 years from today and maturing 7 years from today? (Give your answer per annum with annual compounding)?