兹维博迪金融学第二版试题库08TB

48. The ________ of a bond price measures the sensitivity of the bond price to a change in the yield to

maturity.

(a) callability (b) convertibility (c) immutability (d) elasticity

Answer: (d)

49. Suppose you buy a 25-year pure discount bond with a face value of $1,000 and a yield of 6% per year.

A day later market interest rates drop to 5% and so does the yield on your bond. What is the proportional change in the price of your bond?

(a) a decrease of 26.74% (b) a decrease of 21.10% (c) an increase of 26.74 (d) an increase of 21.20

Answer: (c)

50. Suppose you buy a 25-year pure discount bond with a face value of $1,000 and a yield of 6% per year.

A day later market interest rates rise to 5% and so does the yield on your bond. What is the elasticity of the bond price to the change in the yield?

(a) –0.62% (b) –1.27% (c) –1.60% (d) –2.67%

Answer: (c)

8-13

Short Problems

1. Consider a five-year fixed-income security which promises $120 per year. Calculate the value of the

security if the market interest rate rises from 5% to 6% per year. Answer: n i PV PMT Result 5 5 ? $120 PV = $519.54 n i PV PMT Result 5 6 ? $120 PV = $505.48 The price drops by $14.06.

2. Consider a four-year fixed-income security which promises $120 per year. Calculate the value of the

security if the market interest rate falls from 7% to 6% per year. Answer: n i PV PMT Result 4 7 ? $120 PV = $406.47 n i PV PMT Result 4 6 ? $120 PV = $415.81 The price increases by $9.34.

3. Discuss the general principles about the relation between prices and yields of coupon bonds. Answer: Principle #1: Par Bonds. If a bond's price equals its face value, then its yield equals its coupon rate. Principle #2: Premium Bonds. If a coupon bond has a price higher than its face value, its yield to maturity is less than

its current yield, which is in turn less than its coupon rate.

Principle #3: Discount Bonds. If a coupon bond has a price lower than its face value, its yield to maturity is greater

than its current yield, which is in turn greater than its coupon rate.

8-14

4. List some reasons why differences in the prices of fixed-income securities of a given maturity may

arise. Answer: Differences in the prices of fixed-income securities of a given maturity may arise due to

differences in coupon rates, default risk, tax treatment, callability and convertibility.

5. Explain why it is important to have a method for valuation of fixed-income contracts. Answer: (1) The parties to the contracts need to have an agreed-upon valuation procedure in

setting the terms of the contracts at the outset.

(2) Since market factors determining the value of fixed-income contracts change over

time, both buyers and sellers have to reevaluate them each time they are traded.

6. Consider a five-year pure discount bond with a face value of $1,000. If its current price is $775,

compute its annualized yield. Answer: n i PV FV Result 5 ? –$775 $1,000 i = 5.23%

7. A four-year bond has a coupon rate of 6% per year, a price of $950, and a face value of $1,000.

Calculate its current yield and yield to maturity. Answer: Current yield = coupon/price = 60/950 = 6.32% To calculate yield to maturity: n i = YTM PV FV PMT Result 4 ? –$950 $1,000 $60 YTM = 7.49%

8-15

8. What is the current price of a bond that has a coupon rate of 7%, a return rate of 8%, and a face value

of $1,000? Assume that this bond will mature in five years. Compare the current price of the bond against its face value. Answer: n i = YTM PV FV PMT Result 5 8 ? $1,000 $70 PV = $960.07 Because the price of the bond is below its face value, it is a discount bond.

9. A five-year coupon bond has a coupon rate of 5%, a return rate of 6%, and a face value of $1,000.

What is its current price and how does it compare to its face value? Answer: n i = YTM PV FV PMT Result 5 6 ? $1,000 $50 PV = $957.88 Because the price of the bond is below its face value, it is a discount bond.

10. What is the yield to maturity of a five-year coupon bond with a current price of $850, a face value of

$1,000, and coupon rate of 7%? Answer: n i = YTM PV FV PMT Result 5 ? –$850 $1,000 $70 YTM = 11.07%

11. Five years ago, English and Co. issued 30 year coupon bonds with a par value of $1,000. At the time

of issuance, the yield to maturity was 6 percent per year and the bonds sold at par. The bonds are currently selling at 85 percent of their par value. Assuming that the coupon is paid annually, what is the current yield to maturity?

Answer: Five years ago, the bonds were issued at par, which means at the time yield to maturity equaled coupon rate. So the annual coupon is 0.06 x $1,000 = $60.

For the current yield to maturity:

n i = YTM PV FV PMT Result 25 ? –850 1,000 60 YTM = 7.33%

8-16