1) Pension funds pay lifetime annuities to recipients. If a firm remains 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 $10 million per year to beneficiaries. The yield to maturity on all bonds is 13%.
There are only two assets available for investment: four year zero coupon bonds and 20-year zero coupon bond.
a. How much of each of these bonds will you want to hold to both fully fund and immunize your obligation?
b. Suppose that 1 year has passed, and the yield to maturity on all bonds remains the same. You will need to reexamine the position. Is it still immunized? If not, what actions are required? How much of each of these bonds will you want to hold to both fully fund and immunize your obligation?
2) A 10 -year bond with a coupon rate of 6%, a yield to maturity of 7%, and a duration of 7.7 years, is priced at $929.76. If the bond's yield goes up by 50 basis points,
a) what is the percentage change in the bond's price
b) given the percentage change from part a, what is the bond price after the change?
c) Use your calculator to do the regular present-value calculations to find the bond's new price at its new yield to maturity.
3) A convertible bond has the following features:
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Coupon
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7.25%
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Maturity
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June 15, 2020
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Market price of bond
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$83.00
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Market price of underlying common stock
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$38.00
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Annual dividend
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$1.20
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Conversion ratio
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18.50 shares
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Calculate the conversion premium for this bond.
4) Find the duration of a 6% coupon bond making annual coupon payments if it has two years until maturity and a yield to maturity of 7%.