Please use Excel to complete the problem below.
Immunization
Your company has just built and patented a laser defense system and is planning on installing the equipment in various locations around the country. To finance the installations, you, the CFO, have borrowed $1 billion, which your company will need to repay in five years. The market interest rate is 8%, so the present value of this obligation is $680,583,197. You decide to fund the obligation using three-year zero-coupon bonds and perpetuities that make annual coupon payments.
1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that consists of the zero-coupon bonds and the perpetuities.)
2. Now suppose that one year has passed and that the market rate is still 8%. You need to ensure that the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If not, what do you need to do to fully fund and immunized the obligation?
Duration
1. What is the duration of a 10-year, 6% bond if the market rate on bonds of similar quality is 5.8%?
2. Now suppose that the yield to maturity has changed to 5.81%. Using Macaulay duration, what is the approximate percent change in the price of the bond? (You do not need to recalculate Macaulay duration using 5.81%. Use the duration value that you found in Problem 1.)
3. Using convexity, what is the approximate percent change in the price of the bond?
Please use Excel to complete the problem below.
Immunization
Your company has just built and patented a laser defense system and is planning on installing the equipment in various locations around the country. To finance the installations, you, the CFO, have borrowed $1 billion, which your company will need to repay in five years. The market interest rate is 8%, so the present value of this obligation is $680,583,197. You decide to fund the obligation using three-year zero-coupon bonds and perpetuities that make annual coupon payments.
1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that consists of the zero-coupon bonds and the perpetuities.)
2. Now suppose that one year has passed and that the market rate is still 8%. You need to ensure that the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If not, what do you need to do to fully fund and immunized the obligation?
Duration
1. What is the duration of a 10-year, 6% bond if the market rate on bonds of similar quality is 5.8%?
2. Now suppose that the yield to maturity has changed to 5.81%. Using Macaulay duration, what is the approximate percent change in the price of the bond? (You do not need to recalculate Macaulay duration using 5.81%. Use the duration value that you found in Problem 1.)
3. Using convexity, what is the approximate percent change in the price of the bond?
Related questions
| 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 $3.5 million per year to beneficiaries. The yield to maturity on all bonds is 17.5%. |
| a. | If the duration of 5-year maturity bonds with coupon rates of 14.8% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 8% (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?
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