Principles of Corporate Finance: Valuing Bonds
CHAPTER 3
Valuing Bonds
Answers to Problem Sets
1. a. Does not change
b. Price falls
c. Yield rises.
2. a. If the coupon rate is higher than the yield, then investors must be expecting a decline in the capital value of the bond over its remaining life. Thus, the bond’s price must be greater than its face value.
b. Conversely, if the yield is greater than the coupon, the price will be below face value and it will rise over the remaining life of the bond.
3. The yield over 6 months is 3.965/2 = 1.79825%. Therefore, PV = 3/1.0179825 + 3/1.01798252 +…. + 103/1.017982534 = 130.37
4. Yields to maturity are about 4.3% for the 2% coupon, 4.2% for the 4% coupon, and 3.9% for the 8% coupon. The 8% bond had the shortest duration (7.65 years), the 2% bond the longest (9.07 years).
5. a. Fall (e.g., 1-year 10% bond is worth 110/1.1 5 100 if r 5 10% and is worth 110/1.15 = 95.65 if r = 15%).
b. Less (e.g., See 5a).
c. Less (e.g., with r = 5%, 1-year 10% bond is worth 110/1.05 = 104.76).
d. Higher (e.g., if r = 10%, 1-year 10% bond is worth 110/1.1 = 100, while 1- year 8% bond is worth 108/1.1 = 98.18).
e. No, low-coupon bonds have longer durations (unless there is only one period to maturity) and are therefore more volatile (e.g., if r falls from 10% to 5%, the value of a 2-year 10% bond rises from 100 to 109.3 (a rise of 9.3%). The value of a 2-year 5% bond rises from 91.3 to 100 (a rise of
9.5%).
6. a. Spot interest rates. Yield to maturity is a complicated average of the separate spot rates of interest.
b. Bond prices. The bond price is determined by the bond’s cash flows and the spot rates of interest. Once you know the bond price and the bond’s cash flows, it is possible to calculate the yield to maturity.
7. a. 4%
b. PV = $1,075.44
8. a. PV
b. PV
c. Less (it is between the 1-year and 2-year spot rates).
9. a. r1 = 100/99.423 – 1 = .58%; r2
Valuing Bonds
Answers to Problem Sets
1. a. Does not change
b. Price falls
c. Yield rises.
2. a. If the coupon rate is higher than the yield, then investors must be expecting a decline in the capital value of the bond over its remaining life. Thus, the bond’s price must be greater than its face value.
b. Conversely, if the yield is greater than the coupon, the price will be below face value and it will rise over the remaining life of the bond.
3. The yield over 6 months is 3.965/2 = 1.79825%. Therefore, PV = 3/1.0179825 + 3/1.01798252 +…. + 103/1.017982534 = 130.37
4. Yields to maturity are about 4.3% for the 2% coupon, 4.2% for the 4% coupon, and 3.9% for the 8% coupon. The 8% bond had the shortest duration (7.65 years), the 2% bond the longest (9.07 years).
5. a. Fall (e.g., 1-year 10% bond is worth 110/1.1 5 100 if r 5 10% and is worth 110/1.15 = 95.65 if r = 15%).
b. Less (e.g., See 5a).
c. Less (e.g., with r = 5%, 1-year 10% bond is worth 110/1.05 = 104.76).
d. Higher (e.g., if r = 10%, 1-year 10% bond is worth 110/1.1 = 100, while 1- year 8% bond is worth 108/1.1 = 98.18).
e. No, low-coupon bonds have longer durations (unless there is only one period to maturity) and are therefore more volatile (e.g., if r falls from 10% to 5%, the value of a 2-year 10% bond rises from 100 to 109.3 (a rise of 9.3%). The value of a 2-year 5% bond rises from 91.3 to 100 (a rise of
9.5%).
6. a. Spot interest rates. Yield to maturity is a complicated average of the separate spot rates of interest.
b. Bond prices. The bond price is determined by the bond’s cash flows and the spot rates of interest. Once you know the bond price and the bond’s cash flows, it is possible to calculate the yield to maturity.
7. a. 4%
b. PV = $1,075.44
8. a. PV
b. PV
c. Less (it is between the 1-year and 2-year spot rates).
9. a. r1 = 100/99.423 – 1 = .58%; r2