Ch.7 Problem Solutions - CHAPTER 7 7-1 BOND VALUATION...

CHAPTER 7
7-1
BOND VALUATION
Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid
annually, the bonds have a $1,000 par value, and the coupon interest rate is 8
percent. The bonds have a yield to maturity of 9 percent.
WHAT IS THE CURRENT MARKET PRICE OF THESE BONDS?
0 1 2 3 10
9% . . .
80 80 80 80
PV = ? FV = 1,000
       
N
d
N
d d d
B
k
M
k
INT
k
INT
k
INT
V value s Bond



 



 
1 1
...
1 1
'
2 1
   






N
t
N
d
t
d
k
M
k
INT
1
1 1
       
10 10 2 1
09 . 1
1000
09 . 1
80
...
09 . 1
80
09 . 1
80
'



 



 
B
V value s Bond
   





 
10
1
10
09 . 1
1000
09 . 1
80
'
t
t
B
V value s Bond
With your financial calculator, enter the following:
N = 10
I = YTM = 9%
PMT = 0.08 x 1,000 = 80
FV = 1000
PV = V
B
= ?
PV = $935.82.
1

2

3

7-2
YIELD TO
MATURITY AND
CALL
Thatcher Corporation’s bonds will mature in 10 years . The bonds have a face
value of $1,000 and an 8 percent coupon rate, paid semiannually. The price of the
bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050 . What
is the yield to maturity? What is the yield to call?
_______________________________________________
(a)
0 1 2 3 20
i=? . . .
40 40 40 40
PV= 1,100 FV = 1,000
         
20 20 3 2 1
1
1000
1
40
...
1
40
1
40
1
40
'
d d d d d
B
k k k k k
V value s Bond



 





 
   





 
20
1
20
1
1000
1
40
'
t
d
t
d
B
k k
V value s Bond
With your financial calculator, enter the following to find YTM:
N = 10 x 2 = 20
PV = -1100
PMT = 0.08/2 x 1,000 = 40
FV = 1,000
I = YTM = ?
YTM = 3.31% x 2 = 6.62%
4

(b)
0 1 2 3 10
i=? . . .
40 40 40 40
PV= 1,100 FV = 1,050
   





 
N
t
N
d
t
d
B
k
ice Call
k
INT
V value s Bond
1
1
Pr
1
'
   





 
10
1
10
1
1050
1
40
'
t
d
t
d
B
k k
V value s Bond
With your financial calculator, enter the following to find YTC:
N = 5 x 2 = 10
PV = -1100
PMT = 0.08/2 x 1,000 = 40
FV = 1050
I = YTC = ?
YTC = 3.24% x 2 = 6.49%
5

7-3
BOND VALUATION
Nungesser Corporation has issued bonds that have a 9 percent coupon rate,
payable semiannually. The bonds mature in 8 years, have a face value of $1,000,
and a yield to maturity of 8.5 percent. What is the price of the bonds?
_______________________________________________
0 1 2 3 16
i=4.25 . . .
40 40 40 40
PV= ? FV = 1,000
       
16 16 2 1
0425 . 1
1000
0425 . 1
45
0425 . 1
45
0425 . 1
45
'







 
B
V value s Bond
   





 
16
1
16
0425 . 1
1000
0425 . 1
45
'
t
t
B
V value s Bond
The problem asks you to find the price of a bond, given the following facts:
N = 16
I = 8.5/2 = 4.25
PMT = 45
FV = 1,000
With a financial calculator, solve for PV = $1,028.60
6

7-4
CURRENT YIELD
AND YIELD TO
MATURITY
A bond that matures in 10 years sells for $985. The bond has a face value of
$1,000 and a 7 percent annual coupon.
a. What is the bond’s current yield?
b. What is the bond’s yield to maturity (YTM)?
c. Assume that the yield to maturity remains constant for the next 3 years.