Fabozzi Ch 03 HW Answers

Chapter 3 – Measuring Yield

2. What is the effective annual yield (EAY) if the semiannual periodic interest rate is 4.3%?
Periodic rate = r = 4.30% m = 2
EAY = (1 + r)m – 1 = (1.0430)2 – 1 = 8.7849%

3. What is the yield to maturity of a bond?
The YTM is the discount rate that equates the cash flows to the price. It is the “promised yield” from holding the bond IF the bond is held to maturity and the coupons are reinvested at the YTM.

4. What is the yield to maturity calculated on a bond-equivalent basis?
Bond equivalent basis or Bond Equivalent Yield (BEY) is the common way to quote YTM. It is double the period rate. Therefore BEY is a semi-annual APR.

5. Each bond shown in the table below has a par value of $1,000 and pays interest semiannually.

Bond
Coupon Rate (%)
Number of Years to Maturity
Price
W
7
5
$884.20
X
8
7
$948.90
Y
9
4
$967.70
Z
0
10
$456.39

Show the cash flows and calculate the YTM for each bond.

Period
Cash Flow for Bond W
Cash Flow for Bond X
Cash Flow for Bond Y
Cash Flow for Bond Z
1
$35
$40
$45
$0
2
$35
$40
$45
$0
3
$35
$40
$45
$0
4
$35
$40
$45
$0
5
$35
$40
$45
$0
6
$35
$40
$45
$0
7
$35
$40
$45
$0
8
$35
$40
$1,045
$0
9
$35
$40

$0
10
$1,035
$40

$0
11

$40

$0
12

$40

$0
13

$40

$0
14

$1,040

$0
15

$0
16

$0
17

$0
18

$0
19

$0
20

$1,000

YTM W = 9.9993%
YTM X = 8.9997%
YTM Y = 9.9995%.
YTM Z = 7.9999%.

7. Consider the following $1,000 par value bond with an 11% Coupon rate and 18 years to maturity. The market price is $1,169.00.
The bond is callable at par in exactly 13 years and each year after.
The bond is putable at par value in exactly five years. This is the only put date.

(a) Calculate the yield to maturity.
(b) Calculate the yield to first par call.
(c) Calculate the yield to put.
(d) Suppose that in addition to the par call schedule, the bond can also be called at 105.5% of par in eight years. Calculate the yield to worst for this bond. Hint: You must calculate the yield for each call date.