Chapter 6 CFIN6
Chapter 6 Solutions
6-1
$1,000
Minimum $40
stock price 25
==
$1,000
Minimum $25
stock price 40
==
6-2 a. Each bond can be converted into 40 shares of common stock.
6-3 Selling the bond would generate $980. Converting the bond and selling the common stock would
6-4 Calculator solution:
N = interest payments remaining until maturity = 10 x 2 = 20
I/Y = 6.0/2 = 3.0
PMT = Interest payment = (0.045 x 1,000)/2 = $22.50
6-5 Calculator solution:
N = interest payments remaining until maturity = 4 x 2 = 8
I/Y = 7.0/2 = 3.5
PMT = Interest payment = (0.05 x 1,000)/2 = 25
FV = 1,000
PV = ? = -931.26
Chapter 6 CFIN6
Equation solution:
8
8
1
1
1(1.035)
Value $1,000 $25 0.035
(1.035)
−
=+
6-6 Calculator solution:
N = interest payments remaining until maturity = 8 x 2 = 16
I/Y = 4.0/2 = 2.0
PMT = Interest payment = (0.09 x 1,000)/2 = 45
FV = 1,000
PV = ? = -1,339.44
6-7 Calculator solution:
N = interest payments remaining until maturity = 4 x 2 = 8
I/Y = 5.0/2 = 2.5
PMT = Interest payment = (0.06 x 1,000)/2 = 30
FV = 1,000
PV = ? = -1,035.85
6-8 Calculator solution:
N = interest payments remaining until maturity = 6 x 2 = 12
I/Y = 12.0/2 = 6.0
PMT = Interest payment = (0.08 x 1,000)/2 = 40
FV = 1,000
PV = ? = -832.32
6-9 a. Market rate = 5%
Calculator solution for Bond S:
N = interest payment remaining until maturity = 1
I/Y = 5
PMT = Interest payment = 100
FV = 1,000
PV = ? = -1,047.62
Calculator solution for Bond L:
N = interest payments remaining until maturity = 15
I/Y = 5
PMT = Interest payment = 100
FV = 1,000
PV = ? = -1,518.98
b. Market rate = 7%
Calculator solution for Bond S:
N = interest payment remaining until maturity = 1
I/Y = 7
PMT = Interest payment = 100
FV = 1,000
Chapter 6 CFIN6
PV = ? = -1,028.04
Calculator solution for Bond L:
N = interest payments remaining until maturity = 15
I/Y = 7
PMT = Interest payment = 100
FV = 1,000
PV = ? = –1,273.24
6-10 Equation solution (set up):
5
5
1
11
(1 YTM)
$621 $0 $1,000
YTM (1 YTM)
−
+
=+
+
Calculator solution for YTM:
N = 5
PV = -621
Chapter 6 CFIN6
b. Equation solution (set up):
( )
( ) ( )
18
YTM
12
8
1
1
$1,105 $45 $1,000
YTM YTM
1
22
+
−
=+
+
Calculator solution for YTM:
N = 4 x 2 = 8
PV = -1,105
6-12 Interest payments = [0.055($1,000)]/2 = $27.50
Number of interest payments remaining until maturity = 5 x 2 = 10
Equation solution (set up):
PMT = 27.50
FV = 1,000
I/Y = ? = 2.5, which is the six-month yield
YTM = 2.5 x 2 = 5.0%
Chapter 6 CFIN6
6-13 a. Interest payments = [0.04($1,000)]/2 = $20
Number of interest payments remaining until maturity = 16 x 2 = 32
Equation solution (set up):
b. Number of interest payments remaining until call date = 3 x 2 = 6
Call price = $1,040
Equation solution (set up):
( )
( ) ( )
16
YTC
12
6
1
1
$714 $20 $1,016
YTC YTC
1
22
+
−
=+
+
6-14 a. Interest payments = [0.085($1,000)]/2 = $42.50
Number of interest payments remaining until maturity = 17 x 2 = 34
Equation solution (set up):
Chapter 6 CFIN6
b. Number of interest payment remaining until call date = 4 x 2 = 8
Call price = $1,085
Equation solution (set up):
( )
( ) ( )
18
YTC
12
8
1
1
$1,046 $42.50 $1,089
YTC YTC
1
22
+
−
=+
+
6-15 a. Current yield = (0.07 x 1,000)/996 = 0.070 = 7.0%
Capital gains yield = (1,006 – 996)/996 = 0.01 = 1.0%
Total yield = [(0.07 x 1,000) + (1,006 – 996)]/996 = 80/996 = 0.080 = 8.0% = 7.0% + 1.0%
Chapter 6 CFIN6
6-16 (1) Market value of the bond two (2) years after issue:
Calculator solution:
N = interest payments remaining until maturity = 8 x 2 = 16
I/Y = 6/2 = 3
PMT = Interest payment = (0.10 x 1,000)/2 = 50
FV = 1,000
PV = ? = -1,251.22
1(1.03)
(2) Market value of the bond three (3) years after issue:
Calculator solution:
N = interest payments remaining until maturity = 7 x 2 = 14
I/Y = 6/2 = 3
PMT = Interest payment = (0.10 x 1,000)/2 = 50
FV = 1,000
PV = ? = -1,225.92
6-17 (1) Market value of the bond today:
Calculator solution:
N = interest payments remaining until maturity = 11 x 2 = 22
I/Y = 10/2 = 5
PMT = Interest payment = (0.07 x 1,000)/2 = 35
Chapter 6 CFIN6
FV = 1,000
PV = ? = -802.55
(2) Market value of the bond in one year:
Calculator solution:
N = interest payments remaining until maturity = 10 x 2 = 20
I/Y = 10/2 = 5
PMT = Interest payment = (0.07 x 1,000)/2 = 35
FV = 1,000
PV = ? = -813.07
6-18 a. Current yield = (0.04 x 1,000)/1,000 = 0.04 = 4.0%
Capital gains yield = (929 – 1,000)/1,000 = -0.071 = -7.1%
Total yield = 4.0% – 7.1% = –3.1% = ($40 – $71)/$1,000
b. Equation solution (set up):
Chapter 6 CFIN6
Calculator solution for YTM:
N = 9
PV = -929
6-19 a. Calculator solution:
N = interest payments remaining until maturity = 7
I/Y = 6.0
PMT = Interest payment = (0.06 x 1,000) = $60
FV = $1,000
PV = ? = -1,000.00
b. & c. Because the bond is currently selling at par—that is, its current value is $1,000—its value will
remain at $1,000 for the remainder of its life as long as market interest rates do not change. As
a result, the current yield and capital gains yield each year will be:
6-20 a. Calculator solution:
N = interest payments remaining until maturity = 3
I/Y = 11.0
Chapter 6 CFIN6
Equation solution:
b. & c. The current yield and capital gains yield during the next three years will be:
(1) Year 1: Current price = $731.19 (three years remain until maturity)
Input N = 2, I/Y = 11, PMT = 0, and FV = 1,000; compute PV = -811.62, which will be the
value of the bond when two years remain until maturity.
(2) Year 2: Current price = $811.62 (two years remain until maturity)
Input N = 1, I/Y = 11, PMT = 0, and FV = 1,000; compute PV = -900.90, which was the
value of the bond when one year remains until maturity.
(3) Year 3: Current price = $900.90 (two years remain until maturity)
Input N = 0, I/Y = 11, PMT = 0, and FV = 1,000; compute PV = -1,000, which was the value
of the bond at maturity.