Reading 67: Introduction to the Valuation of Fixed Income

答案和详解如下：

31．James Walters, CFA, has collected data on the three year term structure of interest rates, shown in the table below as bond equivalent yields.

Walters would like to compute the price of a Treasury note with a coupon rate of 5.375% paid semi-annually and 1.5 years left to maturity. The price of this note is closest to:

A)   99.76.

B)   99.64.

C)   98.65.

D)   100.00.

The correct answer was A)

The semiannual coupon payment as a percentage of par is 5.375 / 2 = 2.6875. The price is:

2.6875 / [1 + (0.055227 / 2)]
+ 2.6875 / [1 + (0.055537 / 2)]²
+ 102.6875 / [1 + (0.055444 / 2)]³

= 2.6153 + 2.5442 + 94.5999 = 99.7594

32．Assume an option free 5 percent coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option free bond is priced at 101.76. With the term structure flat at 6 percent what is the value of the embedded put option?

A)   -3.59.

B)   3.59.

C)   -1.76.

D)   1.76.

The correct answer was B)

The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option free bond.

The value of the option free bond is computed as follows: PMT=5, N=2, FV=100, I=6, CPT PV=-98.17(ignore sign).

The option value = 101.79 –- 98.17 = 3.59

33．Using the following spot rates for pricing the bond, what is the present value of a three-year security that pays a fixed annual coupon of 6%?

§ Year 1: 5.0%

§ Year 2: 5.5%

§ Year 3: 6.0%

A)   100.10.

B)   95.07.

C)   100.00.

D)   102.46.

The correct answer was A)

This value is computed as follows:

Present Value = 6/1.05 + 6/1.055² + 106/1.06³ = 100.10

The value 95.07 results if the coupon payment at maturity of the bond is neglected.

34．Assume that an option free 5 percent coupon bond with annual coupon payments has two years to maturity. A callable bond that is the same in every respect as the option free bond is priced at 91.76. With the term structure flat at 6 percent what is the value of the embedded call option?

A)   -8.24.

B)   4.58.

C)   6.41.

D)   10.10.

The correct answer was C)

The option value is the difference between the option-free bond price and the corresponding callable bond price.

The value of the option free bond is computed as follows: PMT=5, N=2, FV=100, I=6, CPT PV=-98.17(ignore sign).

The option value = 98.17 – 91.76 = 6.41

35．An investor has the following choices available:

§ She can buy a 10 percent semi annual coupon, 10-year bond for $1,000.

§ She can reinvest the coupons at 12 percent.

§ She can sell the bond in three years at an estimated price of $1,050.

Based on this information, the average annual rate of return over the three years is:

A)   11.5%.

B)   13.5%.

C)   9.5%.

D)   10.0%.

The correct answer was A)

Step 1. Find the FV of the coupons and interest on interest:

N = 3(2) = 6; I = 12/2 = 6; PMT = 50; compute FV = 348.77

Step 2. Determine the value of the bond at the end of 3 years:

$348.77 + 1,050.00 = $1,398.77

Step 3. Equate FV (1,398.77) with PV (1,000) over 3 years (n = 6):

compute I = 5.75(2) = 11.5%.