Finance Assignment 2
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1
Chapter Six
(6-9)
Anthony has a choice of one or two bonds to purchase: a 5-year, $1,000 face value bond with 6% coupons, paid semi-annually, or a 5-year, $1,000 face value zero coupon. Both have a yield to maturity of 5.5%
a.
How much will each bond cost?
6% Bond
Zero Bond
N: (5*2) =10
N: 10
I/Y: (5.5%/2) =2.75%
I/Y: 2.75%
FV: $1000
(+/-)
FV: $1000 (+/-)
PMT: (6%/2)(1000)=30 (+/-)
PMT: $0
[COMP] PV: $1021.60
[COMP] PV: $762.40
b.
How much would Anthony pay for similar bonds, assuming a flat yield curve, if they were
available in maturity dates of 10 years? 15 years?
10 years
6% Bond
Zero Bond
N: (10*2) =20
N: 20
I/Y: (5.5%/2) =2.75%
I/Y: 2.75%
FV: $1000 (+/-)
FV: $1000 (+/-)
PMT: (6%/2)(1000)=30 (+/-)
PMT: $0
[COMP] PV: $1038.07
[COMP] PV: $581.25
15 years
6% Bond
Zero Bond
N: (15*2) =30
N: 30
I/Y: (5.5%/2) =2.75%
I/Y: 2.75%
FV: $1000 (+/-)
FV: $1000 (+/-)
PMT: (6%/2)(1000)=30 (+/-)
PMT: $0
[COMP] PV: $1050.62
[COMP] PV: $443.14
c.
Explain why the zero-coupon bond prices change more than the regular bonds.
When comparing bonds with coupons and those without, the change is significantly more in bonds with a zero-coupon. This is because payments (coupon rate) are made at specific intervals leading up to the bonds maturity date. So, money is received
2
throughout the bonds life plus the face value of the bond is returned at maturity. Zero-
coupon bonds don’t collect any payments, so they typically come at a discounted rate.
(6-12)
A 10-year, 12% semi-annual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,060. The bond sells for $1100. (Assume that the bond has just been issued.)
a.
What is the bond’s yield to maturity?
N: (10*2) =20
PV: 1100
FV: $1000
(+/-)
PMT: (12%/2)(1000)=60 (+/-)
[COMP] I/Y: 5.1849
YTM: (5.1849)(2)=
10.3698
b.
What is the bond’s current yield?
AnnualPmt
PV
60
∗
2
1100
=0.1091
10.91%
c.
What is the bond’s capital gain or loss yield?
YTM
−
Current yield
10.3698
−
10.91
= -0.5402
d.
What is the bond’s yield to call?
FV:1060
(+/-)
PMT:60
(+/-)
PV:1100
N:(4*2)= 8
[COMP] I/Y=5.0748
YTC: (5.0748)(2)= 10.1495
3
(6-16)
A bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediately after she purchased the bonds, interest rates fell to 7%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table: (assume semi-
annual compounding).
8% Price
7% Price
Percent Change
10-yr, 10% coupon
$1135.90
$1213.19
-6.80%
10-yr, zero
$456.39
$502.57
-10.12%
20-yr, zero
$208.29
$252.57
-21.26%
FV: $1000
(+/-)
FV: $1000
(+/-)
PMT: (10/2)(1000)=$50
(+/-)
PMT:$50
(+/-)
N: (10*2)=20
N:20
I/Y: (8/2)=4
I/Y: (7/2)=3.5
PV:
1135.90
PV: 1213.19
1135.90
−
1213.19
1135.90
∗
100
FV: $1000
(+/-)
FV: $1000
(+/-)
PMT: 0
PMT: 0
N: (10*2) =20
N: 20
I/Y: (8/2) =4
I/Y: (7/2) =3.5
PV:
456.39
PV: 502.57
456.39
−
502.57
456.39
∗
100
FV: $1000
(+/-)
FV: $1000
(+/-)
PMT: 0
PMT: 0
N: (20*2) =40
N: (20*2) =40
I/Y: (8/2) =4
I/Y: (7/2) =3.5
PV:
208.29
PV: 252.57
208.29
−
252.57
208.29
∗
100
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4
(6-18)
The real risk-free rate is 2%. Inflation is expected to be 3% this years, 4% next year, and 3.5% thereafter. The maturity risk premium is estimated to be 0.0005 x (t-1), where t=number of years to maturity. What is the nominal interest rate on a 7-yr government security? (Hint: Average the expected inflation rates to determine the inflation premium, IP).
r
d
= r*+ IP+ DRP+ LRP+ MRP
MRP=0.0005(7-1) =0.003
Average IP: 0.03
+
0.04
+
(
0.035
∗
5
)
7
=0.035%
r
d=
0.02
+
0.035
+
0.003
=
0.058
(6-20)
Pearl Jewellery Co. issued at par value a 15-year, 8% semi-annual coupon bond, face value $1000. At the end of 2 years the market yield fell to 6%. One year later, the market yield was 7.5%. If you purchased the bond at the end of year 2 and sold it one year later, how much was your capital gain or loss?
Purchase Price
Sold Price
FV:1000
(+/-)
FV:1000
(+/-)
PMT:
(1000)(0.08/2)=40
(+/-)
I/Y: (+/-)
N: ((15*2)-4)=26
N: (26-2)=24
I/Y: (6%/2)=3%
I/Y: (7.5%/2)= 3.75
[COMP] PV: $1178.77
[COMP] PV: $1039.11
Capital Loss
1039.11-1178.77= -$139.66
5
Chapter Seven
(7-6)
Suppose r
RF
=5%, r
M
=10%, and r
A
=12%
(a)
Calculate Stocks A’s beta
r
A
=r
RF
+β
A
(r
M
-r
RF
)
0.12=0.05+ β
A
(0.10-0.05)
0.12-0.05= β
A
(0.10-0.05)
0.07= β
A
(0.05)
β
A=
1.4
(b)
If Stocks A’s beta were 2.0, what would be A’s new required rate of return?
r
A
=0.05+2.0(0.10-0.05)
r
A
=0.05+2.0(0.05)
r
A
=0.05+0.1
r
A
=0.15
r
A
=
15%
(7-7)
The following table shows the annual returns over time for two stocks.
Probability
A
B
0.1
-3%
-10%
0.2
2
1
0.4
7
8
0.2
12
16
0.1
17
24
Calculate each stocks expected return, standard deviation, and coefficient of variation.
Stocks Expected Return
A
E(r
A
)=(0.1*-0.03)+(0.2*0.02)+(0.4*0.07)+(0.2*.12)+(0.1*0.17)
E(r
A
)=
0.07
B
E(r
A
)=(0.1*-0.10)+(0.2*0.01)+(0.4*0.08)+(0.2*.16)+(0.1*0.24)
E(r
A
)=
0.08
6
Standard Deviation
√
∑
i
=
1
n
p
i
(
r
i
−
^
r
)
2
A
0.1(-0.03-0.07)
2
+0.2(0.02-0.07)
2
+0.4(0.07-0.07)
2
+0.2(0.12-0.07)
2
+0.1(0.17-0.07)
2
0.1(-0.1)
2
+0.2(-0.05)
2
+0.4(0)
2
+0.2(0.05)
2
+0.1(0.1)
2
0.1*0.01+0.2*0.0025+0+0.2*0.0025+0.1*0.01
0.001+0.0005+0.0005+0.001=0.003
√
0.003
=
0.054772255
B
0.1(-0.10-0.08)
2
+0.2(0.01-0.08)
2
+0.4(0.08-0.08)
2
+0.2(0.16-0.08)
2
+0.1(0.24-0.08)
2
0.1(-0.18)
2
+0.2(-0.07)
2
+0.4(0)
2
+0.2(0.08)
2
+0.1(0.16)
2
0.1*0.0324+0.2*0.0049+0+0.2*0.0064+0.1*0.0256
0.00324+0.00098+0.00128+0.00256=0.00806
√
0.00806
=
0.089777502
Coefficient of Variation
CV=
σ
/
E
(
r
A
)
A
0.0548/0.07
=0.7829
B
0.0898/0.08
=
1.1225
(7-8)
Based on the information in Problem 7-7, if a portfolio is made up of 40% of Stock A and 60% of Stock B:
a.
Calculate the portfolio’s expected rate of return.
E(r
P
)=W
A
*E(r
A
)+ W
B
*E(r
B
)
E(R
P
)= (0.4*0.07)+(0.6*0.08)
W
A
=0.4E(r
A
)=0.07
E(R
P
)=0.028+0.048
W
B
=0.6E(r
B
)=0.08
E(R
P
)=0.076
E(R
P
)=
7.6%
b.
Calculate the portfolio's standard deviation. Assume that the correlation between the two stocks is 0.40.
σ
2
P
=(W
A
*σ
A
)
2
+( W
B
*σ
B
)
2
+2(W
A
)(W
B
)(σ
A
)(σ
B
)(P
AB
)
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7
σ
2
P
=(0.4*0.054772255)
2
+(0.6*0.089777502)
2
+2(0.4)(0.6)(0.054772255)
(0.089777502)(0.4)
σ
2
P
=0.000479999+0.002901599+0.000944124
σ
2
P
=0.004325722
σ
P
=
√
0.004325722
σ
P
=
0.06577
(7-12)
Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between stocks A and B is 0.2. What is the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?
E(r
A
)=0.12
E(r
P
)=W
A
*E(r
A
)+ W
B
*E(r
B
)
E(r
B
)=0.18
E(r
P
)=(0.3*0.12)+(0.7*0.18)
σ
A
=0.4
E(r
P
)=0.036+0.126
σ
B
=0.6
E(r
P
)=
0.162
P
AB
=0.2
W
A
=0.3
σ
2
P
=(W
A
*σ
A
)
2
+( W
B
*σ
B
)
2
+2(W
A
)(W
B
)(σ
A
)(σ
B
)(P
AB
)
W
B
=0.7
σ
2
P
=(0.3*0.4)
2
+(0.7*0.6)
2
+2(0.3)(0.7)(0.4)(0.6)(0.2)
σ
2
P
=0.0144+0.1764+0.02016
σ
2
P
=0.21096
σ
P
=
√
0.21096
σ
P
=
0.4593
(7-14)
Meera has the following portfolio:
Stock
Amount Invested
Beta
Expected Return
Bio-Eng Inc.
$75,000
1.90
12.50%
Canada Pipelines Co.
$125,000
0.75
6.75%
Industrial Auto Parts
$200,000
1.20
9%
Upon further analysis, she determines that the current risk-free rate is 3%, while the market risk premium is 5%.
a.
What return does Meera expect on her portfolio, based on the individual stocks’ expected returns?
Total Portfolio: $75,000+$125,000+$200,000=$400,000
W
A
=75,000/400,000=0.1875
8
W
B
=125,000/400,000=0.3125
W
C
=200,000/400,000=0.5
E(r
P
)=W
A
*E(r
A
)+ W
B
*E(r
B
)+ W
C
*E(r
C
)
E(r
P
)=(0.1875*0.1250)+(0.3125*0.0675)+(0.5*0.09)
E(r
P
)=0.0234375+0.02109375+0.045
E(r
P
)=
0.08953125
b.
What is the required return on the portfolio? What do the answers in parts a and b tell you about the stocks.
CAPM: r
P
=r
RF
+β
P
(RP
M
)
β
P
=W
A
β
A
+W
B
β
B
+W
C
β
C
β
P
=(0.1875*1.90)+( 0.3125*0.75)+(0.5*1.20)
β
P
=0.35625+0.234375+0.6
β
P
=1.190325
r
P
=0.03+1.190325(0.05)
r
P
=0.03+0.05951625
r
P
=
0.08951625
c.
Meera is thinking of adding another stock, Offshore Oil Co., to her portfolio. Offshore has a beta of 2.3 and an expected return of 14%. Should she add this stock? Briefly explain why or why not.
r
i
=r
RF
+β
i
(RP
M
)
r
i
=14.5%
r
i
=0.03+2.3(0.05)
r
D
=14%
r
i
=0.03+0.115
Meera should not add this stock to her portfolio because r
i
=0.145 (14.5%)
the market does not give a high enough return to compensate for the risk that is being taken. d.
Assuming that Offshore Oil does provide the expected return required and that Meera invests another $100,000 in offshore Oil, what will be her portfolio’s new expected return?
New Portfolio total: $500,000
New weights:
9
W
A
=75,000/500,000=0.15
W
B
=125,000/500,000=0.25
W
C
=200,000/500,000=0.4
W
D
=100,000/500,000=0.2
E(r
P
)=W
A
*E(r
A
)+ W
B
*E(r
B
)+ W
C
*E(r
C
)+ W
D
*E(r
D
)
E(r
P
)=(0.15*0.1250)+(0.25*0.0675)+(0.4*0.09)+(0.2*.14)
E(r
P
)=0.01875+0.016875+0.036+0.028
E(r
P
)=
0.099625
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10
Chapter Eight
(8-6)
EMC Corporation’s current free cash flow is $400,000 and is expected to grow at a constant rate of 5%. The weighted average cost of capital, WACC=12%. Calculate EMC’s estimated value of operations.
V
=
FCF
(
1
+
g
)
WACC
−
g
V
=
400,000
(
1
+
0.05
)
0.12
−
0.05
V
=
400,000
(
1.05
)
0.07
V
=
420,000
0.07
V=6,000,000
(8-12)
What must be a company’s dividend growth rate for its stock to have an expected value of $13.25, assuming its most recently paid dividend was $0.50 and the stock’s required return is 10%?
P
0
=
D
1
r
S
−
g
P
0
=
D
0
(
1
+
g
)
r
S
−
g
13.25
=
0.5
(
1
+
g
)
0.1
−
g
(
0.1
−
g
)
13.25
=
0.5
(
1
+
g
)
(
0.1
)
13.25
−
13.25
g
=
0.5
(
1
)+
0.5
g
1.325
−
13.25
g
=
0.5
+
0.5
g
−
13.25
g
=
0.5
−
1.325
+
0.5
g
−
13.25
g
=
0.5
g
−
0.825
−
13.25
g
−
0.5
g
=−
0.825
−
13.75
g
=−
0.825
g
=
−
0.825
−
13.75
g=0.06=6%
11
(8-14)
The beta coefficient for Stock C is b
c
=0.4, whereas that for Stock D is b
D
=-0.3. (Stock D’s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative beta stocks, although collection agency stocks are sometimes cited as an example)
a.
If the risk-free rate is 4% and the expected rate of return on an average stock is 13%, what are the required rates of return on Stocks C and D.
CAPM:SML R
i
=r
RF
+β
i
(E(R
M
)-r
RF
)
R
c
=0.04+0.4(0.13-0.04)
R
c
=0.04+0.4(0.09)
R
c
=0.04+0.036
R
c
=
0.076
R
D
=0.04+(-0.3)(0.13-0.04)
R
D
=0.04+(-0.3)(0.09)
R
D
=0.04+(-0.027)
R
D
=
0.013
b.
For Stock C, suppose the current price, P
0
is $30; the next expected dividend, D
1
is $1.00;
and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium? Explain, and describe what will happen if the stock is not in equilibrium.
E
(
r
C
)
=
D
1
P
0
+
g
E
(
r
C
)
=
1
30
+
0.04
E
(
r
C
)
=
0.07
The expected return on stock C is 7% and the required return on Stock C is 7.6%. If the stock is not in equilibrium, it means the stock is priced too high which causes people to start selling which in turn declines the price of the stock. The price will drop until it is approximately $27.78, which will put the stock in equilibrium.
12
(8-16)
Simpkins Ltd. is expanding rapidly, and it currently needs to retain all of its earnings; hence it does not pay any dividends. However, investors expect Simpkins to begin paying dividends, with the first dividend of $0.5 coming 3 years from today. The dividend should grow rapidly at a rate of 80% per year- during years 4 and 5. After year 5, the company should grow at a constant rate of 7% per year. If the required return n the stock is 16%, what is the value of the stock today?
D
4
=0.5(1+0.8)=0.9
D
5
=0.9(1+0.8)=1.62
D
6
=1.62(1+0.07)=1.7334
P
5
=
1.7334
(
0.16
−
0.07
)
P
5
=
1.7334
0.09
P
5
=19.26
Cash flows
Yr1:$0
Yr2:$0
Yr3:$0.5
Yr4:$0.9
Yr5:$20.88
Rate=16%
NPV=10.7586 P
0
=
10.76
5
6
4
2
3
1
g
n
=7%
g
s
=80%
g
s
=80%
D
5
$1.62
P
5
$19.26
D
6
$1.73
D
4
$0.90
$0.5
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13
(8-18)
You buy a share of Ludwig Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years.
D
o
=x, D
1
=$1.07, D
2
=$1.1449, D
3
=$1.2250, P
o
=$21.40, P
3
=$26.22
a.
Calculate the growth rate in dividends.
g
=
D
2
−
D
1
D
1
∗
100
g
=
1.1449
−
1.07
1.07
∗
100
g
=
0.0749
1.07
∗
100
g=0.07
g=
7%
b.
Calculate the expected dividend yield.
D
1
P
0
1.07
21.40
=0.05
Expected dividend yield: 5%
c.
Assuming that the calculated growth rate is expected to continue, what is this stock’s expected total rate of return?
r
s
=
D
1
P
0
+
g
5%+7%
Expected total rate of return: 12%
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(%)
248
a. What is the yield to maturity of each bond?
b. What is the duration of each bond?
Price (%)
80.36
96.95
135.22
Complete this question by entering your answers in the tabs below.
Required A
Bond Coupon
(%)
2
4
8
Required B
What is the yield to maturity of each bond?
Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.
YTM
%
%
%
Saved
22255
35445
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Assume that you are choosing between 3 bonds that mature in 5 years and have a face value of $1,000. The first one pays annual coupon of $70. The second one pays $17 every three months, and the third one pays $5.5 every month. Assuming that all three bonds are selling at the same price in the market, which one would you buy?
Bond 1
Bond 2
Bond 3
Blank
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Last Part of Question D and question E please
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Please answer in typing format
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son.2
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do ? correct will be upvote
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Please need help to calculate attached 2 questions in excel formula
Thanks
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Fingen's 16-year, $1 comma 000 par value bonds pay 14 percent interest annually. The market price of the bonds is $1 comma 070 and the market's required yield to maturity on a comparable-risk bond is 11 percent. a. Compute the bond's yield to maturity. b. Determine the value of the bond to you, given your required rate of return. c. Should you purchase the bond? Question content area bottom Part 1 a. What is your yield to maturity on the Fingen bonds given the market price of the bonds? enter your response here%
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Related to Checkpoint 9.2) (Yield to maturity) The Saleemi Corporation's
$1,000
bonds pay
8
percent interest annually and have
15
years until maturity. You can purchase the bond for
$1,075.
a. What is the yield to maturity on this bond?
b. Should you purchase the bond if the yield to maturity on a comparable-risk bond is
6
percent?
Question content area bottom
Part 1
a. The yield to maturity on the Saleemi bonds is
enter your response here%.
(Round to two decimal places.)
Part 2
b. You
▼
should
should not
purchase the bonds because your yield to maturity on the Saleemi bonds is
▼
greater
less
than the one on a comparable risk bond. (Select from the drop-down menus.)
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TABLE 3.9
END-OF-YEAR PAYMENTS
Bond A
Bond B
Bond C
Bond D
Year 1
100
50
0+1,000
Year 2
Year 3
100
50
100 +1,000
50+1,000
0+ 1,000
Consider the four bonds having annual payments as shown in Table 3.9. All of the bonds have a 15%
yield.
Which bond has the highest price?
Bond A
Bond B
Bond C
Bond D
O ooO
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Question 2
Two bonds are available for purchase in the financial markets. The first bond is a two-year,
50,000 AUD bond that pays an annual coupon of 6 per cent. The second bond is a two-
year, 10,000 AUD, zero-coupon bond.
(a) What is the duration of the coupon bond if the current yield-to-maturity (R) is 6
per cent? And 8 per cent? How does the change in the current yield to maturity affect
the duration of this coupon bond?
(b) Calculate the duration of the zero-coupon bond with a yield to maturity of 5 per
cent, and 8 per cent.
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- aj.4arrow_forward* Assignment 3 i Assume coupons are paid annually. Here are the prices of three bonds with 10-year maturities. Assume face value is $100. Bond Coupon (%) 248 a. What is the yield to maturity of each bond? b. What is the duration of each bond? Price (%) 80.36 96.95 135.22 Complete this question by entering your answers in the tabs below. Required A Bond Coupon (%) 2 4 8 Required B What is the yield to maturity of each bond? Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. YTM % % % Saved 22255 35445arrow_forwardAssume that you are choosing between 3 bonds that mature in 5 years and have a face value of $1,000. The first one pays annual coupon of $70. The second one pays $17 every three months, and the third one pays $5.5 every month. Assuming that all three bonds are selling at the same price in the market, which one would you buy? Bond 1 Bond 2 Bond 3 Blankarrow_forward
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