# Fi801 Solution Mannual

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 = (100/97.546).5 – 1 = 1.25%; r3 = (100/94.510).33 -.1 = 1.90%; r4 = (100/90.524).25 – 1 = 2.52%.

b. Upward-sloping.

c. Lower (the yield on the bond is a complicated average of the separate spot rates).

10.a.Price today is 108.425; price after 1 year is 106.930.

b. Return = (106.930 1 8)/108.425 - 1 = .06, or 6%.

c. If a bond’s yield to maturity is unchanged, the return to the bondholder is

equal to the yield.

11.a.False. Duration depends on the coupon as well as the maturity.

b.False. Given the yield to maturity, volatility is proportional to duration.

c.True. A lower coupon rate means longer duration and therefore higher volatility.

d.False. A higher interest rate reduces the relative present value of (distant) principal repayments.

12.

13. 7.01% (the extra return that you earn for investing for two years rather than one is 1.062/1.05 – 1 = .0701).

14. a. Real rate = 1.10/1.05 – 1 = .0476, or 4.76%

b. The real rate does not change. The nominal rate increases to 1.0476 x 1.07 – 1 = .1209, or 12.9%.

15.With annual coupon payments:

€92.64

16.a.

b.

Interestrate| PV ofInterest| PV ofFace value| PV of Bond| 1.0%| $5,221.54 | $9,050.63| $14,272.17|

2.0%| 4,962.53 | 8,195.44| 13,157.97|

3.0%| 4,721.38 | 7,424.70| 12,146.08|

4.0%| 4,496.64 | 6,729.71| 11,226.36|

5.0%| 4,287.02 | 6,102.71| 10,389.73|

6.0%| 4,091.31 | 5,536.76| 9,628.06|

7.0%| 3,908.41 | 5,025.66| 8,934.07|

8.0%| 3,737.34 | 4,563.87| 8,301.21|

9.0%| 3,577.18 | 4,146.43| 7,723.61|

10.0%| 3,427.11 | 3,768.89| 7,196.00|

11.0%| 3,286.36 | 3,427.29| 6,713.64|

12.0%| 3,154.23 | 3,118.05| 6,272.28|...

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