Bond value (5) 2,000 1.500 1,000 500 $1,768.62) $1,04762 30-year bond 1-year bond $916.67 Interest Rate $502.11 Interest 19 15 20 rate (%) Value of a Bond with a 10 Percent Coupon Rate for Different interest Pites and Maturities Time to Maturity 1 Year $1,047.62 30 Years $1.768.62
Bond value (5) 2,000 1.500 1,000 500 $1,768.62) $1,04762 30-year bond 1-year bond $916.67 Interest Rate $502.11 Interest 19 15 20 rate (%) Value of a Bond with a 10 Percent Coupon Rate for Different interest Pites and Maturities Time to Maturity 1 Year $1,047.62 30 Years $1.768.62
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
I am not able to replicate the chart for a 30 year bond using the example from the previous page.
![INTEREST RATE RISK
Pg 169
the amount of risk a bond has is dependant on
0 remaining time to maturity.
2 coupon rate
GENERAL RULE
4
the longer the maturity the greater the interest rate risk
the lower the coupon rate, the the risk
(1)
Q
WHY?
Figure 6.2
par = 1,000
coupon rate=
t
10 compounded sem. annually.
current rate=05 = a × 62s
yield 1,000,10 = 100/2 = $50
step 1 PU of 1,000 in 30 years at
FU
1,000
PV = (H)
step 2= PV of a "so annuity
Annuity PV =
(17.025) 60
Co •
1- (1+r) +
-
- [ ]
>. [+- (lota]
·025
Current value of bond =
50
=
+05/2
[227.28
= 14545.43
1772/71
book answer
11768.62
9
EXAMPLE
6.1 Semiannual Coupons
in practice, bonds issued in the United States usually make coupon payments twice a year. So, if an
ordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but
this $140 will come in two payments of $70 each. Suppose we are examining such a bond. The
yield to maturity is quoted at 16 percent.
Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period mult
plied by the number of periods. In this case, with a 16 percent quoted yield and semiannual pay
ments, the true yield is 8 percent per six months. The bond matures in seven years What is the
bond's price? What is the effective annual yield on this bond?
Based on our discussion, we know that the bond will sell at a discount because it has a cou
pon rate of 7 percent every six months when the market requires 8 percent every six months. So, if
our answer is equal to or exceeds $1,000, we know that we have made a mistake.
To get the exact price, we first calculate the present value of the bond's face value of $1,000
paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent per
period, the value is:
Present value $1,000/1.08 $1,000/2.9372 = $340.46
The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate,
the present value of such an annuity is
Annuity present value = $70 x (1-1/1.08.08
=$70 x (1-3405.08
-$70 x 8.2442
-$57710
The total present value gives us what the bond should sell for:
170
Total present value-$340.46 +57710-$917.56
To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to
Effective annual rate= (1+08-1-16.64%
The effective yield, therefore, is 16.64 percent
FIGURE 6.2
Interest rate risk and
time to maturity
slope of
line is,
much steeper
PART 4
CHAPTER 6
Bond
value (5)
2,000
Valuing Stocks and Bonds
1.500
1,000
500
$1,768.62)
Interest Rates and Bond Valuation
$1,047.62
30-year bond
1
1-year bond
Interest Rate
5%
$916.67
$502.11
Interest
rate (%)
15
20
Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and Maturities
Time to Maturity
30 Years
$1.768.62
1 Year
$1,047.62](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c503aa7-3d61-4a6a-abae-cb420e8ecd0d%2Fc6a3259d-0fb7-462c-8af9-8896d4c9cf35%2F1hyns5_processed.png&w=3840&q=75)
Transcribed Image Text:INTEREST RATE RISK
Pg 169
the amount of risk a bond has is dependant on
0 remaining time to maturity.
2 coupon rate
GENERAL RULE
4
the longer the maturity the greater the interest rate risk
the lower the coupon rate, the the risk
(1)
Q
WHY?
Figure 6.2
par = 1,000
coupon rate=
t
10 compounded sem. annually.
current rate=05 = a × 62s
yield 1,000,10 = 100/2 = $50
step 1 PU of 1,000 in 30 years at
FU
1,000
PV = (H)
step 2= PV of a "so annuity
Annuity PV =
(17.025) 60
Co •
1- (1+r) +
-
- [ ]
>. [+- (lota]
·025
Current value of bond =
50
=
+05/2
[227.28
= 14545.43
1772/71
book answer
11768.62
9
EXAMPLE
6.1 Semiannual Coupons
in practice, bonds issued in the United States usually make coupon payments twice a year. So, if an
ordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but
this $140 will come in two payments of $70 each. Suppose we are examining such a bond. The
yield to maturity is quoted at 16 percent.
Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period mult
plied by the number of periods. In this case, with a 16 percent quoted yield and semiannual pay
ments, the true yield is 8 percent per six months. The bond matures in seven years What is the
bond's price? What is the effective annual yield on this bond?
Based on our discussion, we know that the bond will sell at a discount because it has a cou
pon rate of 7 percent every six months when the market requires 8 percent every six months. So, if
our answer is equal to or exceeds $1,000, we know that we have made a mistake.
To get the exact price, we first calculate the present value of the bond's face value of $1,000
paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent per
period, the value is:
Present value $1,000/1.08 $1,000/2.9372 = $340.46
The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate,
the present value of such an annuity is
Annuity present value = $70 x (1-1/1.08.08
=$70 x (1-3405.08
-$70 x 8.2442
-$57710
The total present value gives us what the bond should sell for:
170
Total present value-$340.46 +57710-$917.56
To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to
Effective annual rate= (1+08-1-16.64%
The effective yield, therefore, is 16.64 percent
FIGURE 6.2
Interest rate risk and
time to maturity
slope of
line is,
much steeper
PART 4
CHAPTER 6
Bond
value (5)
2,000
Valuing Stocks and Bonds
1.500
1,000
500
$1,768.62)
Interest Rates and Bond Valuation
$1,047.62
30-year bond
1
1-year bond
Interest Rate
5%
$916.67
$502.11
Interest
rate (%)
15
20
Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and Maturities
Time to Maturity
30 Years
$1.768.62
1 Year
$1,047.62
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