Introduction to the valuation of debt securities (Reading 57)


Exercise Problems:


1. An investor is evaluating a set of bonds from which he will select two issues. The investor’s objective is to find bonds with cash flows that will precisely match a known stream of future obligations. Which of the following two issues will most likely to meet the investor’s objective?
A. A putable bond and a floatingrate bond. B. A mortgagebacked security and a convertible bond. C. A zerocoupon bond and a Treasury strip.


Ans: C;
C is correct because both the zero coupon and Treasury strip bonds have cash flows that can be estimated with certainty.
The following are three situations where there is difficulties in estimating future cash flows:


2. Assuming an annual discount rate of 5%, which of the following is closest to the value of a 10year, 6% coupon, $1000 par value bond with semiannual payments?
A. $1077.2. B. $1077.9. C. $1075.0.


Ans: A;
The calculator solution is N=10, PMT=60, 1/Y=5, FV=1000, CPT > PV=1077.2


3. Tapper, Inc. has two $1,000 par value bonds outstanding that both sell for 758.18. The first issue has 15 years to maturity and an annual coupon of 6%. The second issue has the same yield to maturity as the first one, pays annual interest as well, but has only 5 years remaining till maturity. The annual interest payment on the second issue is closest to:
A. $25.23. B. $27.83. C. $29.46.


Ans: B;
We can calculate the YTM from the first issue and use it in the second bond calculation.
Step1: calculate YTM from the first issue N=15, PMT=60, FV=1000, PV=758.18 CPT > 1/Y=9
Step2: since two bonds have the same YTM, we can calculate the annual interest payment for the second bond: N=5, 1/Y=9, FV =1000, PV=758.18 CPT > PMT = 27.83


4. Tiffany Zheng purchased a $1,000 par value, 0% coupon bond with 16 years to maturity one year ago. The YTM (semiannually compounding) was 6.0%. Now one year later, with market rates remaining the same, Zheng purchases an annuity with a semiannual payment of $30 for 15 years. Which of the following gives the closest combined value of the two investments based on the 6% semiannual yield?
A. $1,000. B. $27.83. C. $29.46.


Ans: A;
Zheng’s two investments combine to form a 15year, $1,000 face value, 6.0% semiannual coupon bond.
This combined investment would sell at par because the YTM (6%) equals the coupon rate (6%).
Thus the combined value is $1,000.


5. Consider a $100 par value bond. It has a 6% coupon paid annually and 10 years to maturity. The bond is valued at $102.08 today with a discount rate of 5.5%. One day later, the discount rate increases to 6.5%. Assuming the discount rate remains at 6.5% over the remaining life of the bond, the price of the bond between today and maturity will most likely:
A. Decline then remain unchanged. B. Decline then rise. C. Rise then decline.


Ans: B;
B is correct because if the discount rate rises to 6.5% from 5.5%, the price of a bond declines. At a discount rate of 6.5%, the bond sells at a discount to face value. As a discount bond approaches maturity, it will rise in price over time until it reaches par at maturity.


6. An 8% coupon, $100 par value bond matures in 2 years and is selling at $98.79 to yield 8 percent. One year ago this bond was sold at a price of $97.02 to yield 9 percent. The bond pays interest annually. The change in price attributable to the change in maturity is closest to:
A. 4.97. B. 3.21. C. 1.22.


Ans: C;
The price of the bond one year ago was $96.03 to yield 9%. If the yield stays at 9%, the price of the bond today is: 8/(1+9%)^{1}+108/(1+9%)^{2}= $98.24
The change in price attributable to moving to maturity = $98.24 – $97.02 = $1.22 

7. The U.S. Treasury spot rates are listed as follows. The arbitragefree value of a 2year Treasury, $100 par value bond with a 6% coupon rate is closet to:
A. $107.03. B. $105.25. C. $99.75.


Ans: B;
B is correct because the value of bond =_{}+_{}+_{}+_{} =$105.25


8. If the price of a U.S. Treasury security is higher than its arbitragefree value, an arbitrage profit can be generated by:
A. buying the U.S Treasury security, stripping it and selling the strips. B. shorting the U.S. Treasury security and calling it from the issuer. C. shorting the U.S. Treasury security and reconstructing it from strips.


Ans: C;
C is correct because strips can be purchased to create a synthetic U.S. Treasury security to cover the short at a price lower than the price at which the U.S Treasury security was shorted, generating an arbitrage profit.


9. Given the following information in the table, which of the following gives the closest value for a 0% coupon, 5year, $100 par value optionfree bond?
A. 78.12. B. 80.05. C. 79.94.


Ans: A;
The appropriate discount rate = 4.5%+0.5%=5.0%
The semiannual discount rate is therefore 2.5%.
The value of the corporate bond using semiannual discount rate = _{}=$78.12 

10. A 3year amortizing security with a par value of $4,000 and a 6% coupon rate has an expected cash flow of $1,365 per year. No principal prepayment is allowed. Assuming a discount rate of 5%, the security is most likely to have a present value of:
A. 4,109. B. 4,000. C. 3,717.


Ans: C;
C is correct because _{}+_{}+_{}=3,717 