Chapter 3: 10-5B (page 329)
A zero-coupon bond with face value \(1,000 and maturity of five years sells for \)746.22. What is its yield to maturity? What will happen to its yield to maturity if its price falls immediately to $730?
6.029% and 6.4965%
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A coupon bond paying semi-annual interest is reported as having an ask price of 117% of its $1,000 par value. If the last interest payment was made one month ago and the coupon rate is 6%, what is the invoice price of the bond?
Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble perpetuity. Suppose, therefore, that you are managing a pension fund with responsibilities 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 time 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 entire fund and immunize your obligation?
b. What will be the par value of your holdings in the 20-year coupon bond?
Rank the following bonds in order of descending duration.
Bond | Coupon | Time to Maturity | Yield to maturity |
A | 15% | 20 | 10% |
B | 15 | 15 | `10 |
C | 0 | 20 | 10 |
D | 8 | 20 | 10 |
E | 15 | 15 | 15 |
Which security has a higher effective annual interest rate?
a. A three-month T-bill with face value of \(100,000 currently selling at \)97,645.
b. A coupon bond selling at par and paying a 10% coupon semi-annually.
You buy an eight-year bond that has a 6% current yield and a 6% coupon (paid annually). In one year, promised yields to maturity have risen to 7%. What is your holding-period return?
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