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- Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?b. What will be the par value of your holdings in the 20-year coupon bond?pension funds pay lifetime annuities to recipients. if a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. the yield to maturity on all bonds is 15%. a. if the duration of 5-year maturity bonds with coupon rates of 11% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 7% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?A pension fund faces a promised outflow of $5 million in 6 years. Its managers plan to dedicate a portfolio comprised of the following two bonds to meet this obligation. a. What must be the proportions ((W7, W6) or (Weight(A), Weight(B)) of the two bonds in this 2-security portfolio to immunize it against changes in interest rates? b. What is the yield to maturity for the immunized portfolio? c. How much needs to be invested in each bond to build an immunized portfolio with an expected value of $5 million in 6 years? d. Suppose that it is now 3 years later and that there has been a parallel increase in interest rates of 2%. Explain how immunization at least partially protects this portfolio. That is, what are the sources of losses and gains associated with each of the bonds caused by the increase in interest rates? How do they offset each other?
- You are managing a pension plan that is due to pay $11 million a year for 15 years with the first payment one year from today and $8 million a year for 10 years with the first payment 5 years from today. You can use a zero coupon bond with 4 years to maturity and a 20 year coupon bond with a duration of 12.31 years to immunize your portfolio. The interest rate is 7 percent for all maturities. How many zero coupon bonds will you have to purchase? Assume annual cash flows and compounding in your calculations.Suppose that a pension fund manager anticipates the purchase of a 20-year 8 percent coupon T-bond at the end of two years. Interest rates are assumed to change only once every year at year end. At that time, it is equally probable that interest rates will increase or decrease 1 percent. When purchased in two years, the T-bond will pay interest semiannually. Currently, it is selling at par a. What is the pension fund manager’s interest rate risk exposure? b. How can the pension fund manager use options to hedge that interest rate risk exposure?Your friend recommends that you invest in a three-year bond issued by Toyota, Inc., that will pay annual coupons of 10 percent. Similar investments today will yield 6 percent. How much should you pay for the bond?
- As corporate treasurer, you have to pay $21 million in one year and again in two years. Bonds of all maturities currently yield 7%. If you buy zero-coupon bonds with a maturity equal to the duration calculated in the previous part, what should be their combined face value (in $)?A mutual fund plans to purchase $500,000 of 30-year Treasury bonds in four months. These bonds have a duration of 12 years and are priced at 96-08 (32nds). The mutual fund is concerned about interest rates changing over the next four months and is considering a hedge with T-bond futures contracts that mature in six months. The T-bond futures contracts are selling for 98-24 (32nds) and have a duration of 8.5 years. If interest rate changes in the spot market exactly match those in the futures market, what type of futures position should the mutual fund create? How many contracts should be used? If the implied rate on the deliverable bond in the futures market moves 12 percent more than the change in the discounted spot rate, how many futures contracts should be used to hedge the portfolio? What causes futures contracts to have a different price sensitivity than the assets in the spot markets?The Bissette LLC Fund is looking to buy bonds with a $1,000 face value, an 8% coupon, payable semiannually, and a maturity of 5 years. Currently, the bond sells at $880.00. What is the yield to maturity?
- You are given the following information concerning a noncallable, sinking fund debenture: Principal: $1,000 Coupon rate of interest: 7 percent Term to maturity: 12 years Sinking fund: 3 percent of outstanding bonds retired annually; the balance at maturity If you buy the bond today at its face amount and interest rates rise to 12 percent after five years have passed, what is your capital gain or loss? Assume that the bond pays interest annually. Use Appendix B and Appendix D to answer the question. Use a minus sign to enter the loss amount, if any, as a negative value. Round your answer to the nearest dollar. $ If you hold the bond 12 years, what do you receive at maturity? -Principal or All coupon payments? What is the bond's current yield as of right now? Round your answer to the nearest whole number. % Given your price in a, what is the yield at maturity? Round your answer to the nearest whole number. % What proportion of the total debt issue is retired by the…As a bond fund manager, you are considering 10-year corporate bonds issued by Mellon Bank (MB). Each MB bond has a $1,000 par value with 8% annual coupon rate. The coupons are paid semi-annually. The estimated rate of return on MB bond is 10%. One year later, the yield increases to 11%. What is your holding period return of the bond? A. 8.20% B. 4.11% C. -6.79% D. -3.35%A portfolio for a pension fund that you manage has payments resembling a perpetuity. You want to immunize the pension fund liability by purchasing 2 bonds: a zero coupon bond maturing in 6 years & a 10% coupon bond with a duration of 25 years. Assume the yield on both bonds & the pension fund is 7%. What percent of your portfolio should you invest in the zero-coupon bonds?
