Money - 1st Term
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1st Example: Valuate an European 10 years, 5% coupon rate, 100,000 Euros face value German Bond, that is negotiated
5000 0 108110.90 PREMIUM
5000
1 4807.69
2 4622.78
5000
5000
3 4444.98
4 4274.02
5000 5 4109.64
5000 6 3951.57
Pvb= sumatoria Ct / (1+kb)*t + FVn / (1+kb)*n
FV $ 100,000.00 CR 5% Matur 10 years KB 4% PV=? Current Market Price
coupon
$ 5,000.00 Its five per cent of future value
2nd Example: Valuate an European 5 years, 4% coupon rate, 100000 euros face value French Bond, that is negotiated wit
3er Example: Valuate a Ecuadorian Global 8 years, 9% coupon rate, 100.000 dollars face value Bond, discouting it at 9% c
More examples:
1) In Bloomberg you find that a German Bond 10 years Bond, 3% coupon rate 100000 Euros, is negotiated at 98.% of its p 2) Today Global Bonds of Brazil arte negotiated in the New York Stock Exchange in the following conditions: Face Value Maturity 1000000 100000 10000000
Coupon 5 8 10
Yield 6% 8% 10%
5% 9% 12%
What are the current market prices, which Bond would yo buy, why??
ue German Bond, that is negotiated with a required rate of return of 4%
5000 7 3799.59
5000 8 3653.45
5000 9 3512.93
105000 10 70934.24
100000 5000 5000.00
t of future value
French Bond, that is negotiated with a require rate of return of 5%.
ace value Bond, discouting it at 9% coupon rate. What type of Bond is it, why?
Euros, is negotiated at 98.% of its price. What is the yield to maturity of the Bond? e following conditions:
1st exercise Valuate a 10 years bond 100,000 euros that has 1,5% coupon rate semiannually and is negotiated at 7% discounted rate after 3 years the ice recalls the bond offering a 102,5% price, would you accept it? 100000.00 euros 10 years 1.50% semiannual 7.00% YTC manual traditional
71575.19
20 periods 1500.00 coupon
1500.00 1
1500.00 2
1500.00 3
1500.00 4
1500.00 5
1500.00 6
1449.28
1400.27
1352.91
1307.16
1262.96
1220.25
Bo= addition (coupons VA=
-71,575.19 € formula
yield is 7%
after 3 years 100000.00 euros 10 years 1.50% semiannual 7.00%
14 periods 1500.00 coupon
-78,158.96 €
VA=
call date call price coupon YTC
3 102500.00 1500.00 7.99%
102500.00 offered value
2nd exercise analyse a OMC 15 years bond 100 000 dollars, that has a 2,5% quarterly coupon rate, and is negotiated at 96,5% current 2 years later an international broker offers 101,5% of its price would you 100000.00 dollars 15 years 2.50% quarterly 96.50% P ( price) VA=
60 periods 2500.00 coupon 2.62% yield to maturity
$ 96,500.00 call date call price coupon YTC
2 years 101500.00 2500.00 3.17% yield to call
8 periods
In the new york stock exchange today you can negotiate the following securities
homework
6,1 6,2 6,3 6,4 6,5
otiated at 7% discounted rate
1500.00 7
1500.00 8
1500.00 9
1500.00 10
1500.00 11
1500.00 12
1500.00 13
1500.00 14
1500.00 15
1178.99
1139.12
1100.60
1063.38
1027.42
992.67
959.11
926.67
895.34
years
6 periods
yield to call
s negotiated at 96,5% current market price,.
1500.00 16
1500.00 17
1500.00 18
1500.00 19
100000.00 1500.00 20
865.06
835.81
807.54
780.23
51010.44
Karla Trávez 8 "A" International Commerce 1,- Valuate a ECB10 years Bond. 100,000 euros, that has a 1.5% coupon rate semianually and is negotiated at 7% discounted rate. After 3 years the ECB recalls the bond offering a 102,5% price, wouldyou accept it? Why? FV = M= CR = KB = PV =
100000 10 years 2% Semianually 7%
20 periods 1500 3.5%
$ 102,500
? Call Price
1500 0
1500 1
1500 2
1500 3
1500 4
1500 5
1500 6
1500 7
1500 8
1500 9
1500 10
100000 1500 20
1500 11
1500 12
1500 1500 1500 13 14 15
1500 1500 1500 1500 16 17 18 19
1178.99 1139.12 1100.60 1063.38 1027.42
992.67
959.11 926.67 895.34
865.06 835.81 807.54 780.23 51010.44
Bo = Addition [ Coupons t / ( 1 + Kb ) ^ t ] Manually Excell
1449.28
1400.27 1352.91
1307.16
1262.96 1220.25
$ -71,575.19
B) Call Date = Call Price = Coupon = YTC =
3 years
6 periods
102.5% $ 102,500
1500 $ -71,575.19
=
[ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 102,500 / (1+KB) ^6]
7.99% Accepted because the Yield to Call is greater than the yield to maturity
2,- Analyze a GMC 15 years bond, 100,000 dollars that has 2,5% quarterly coupon rate and it is negotiated at 96,5% coupon market price. Two years later an International Broker offer 101,5% of its price, would you accept it QUARTERLY FV = M= CR = PV =
100,000.00 15 years 2.50% 96.50%
FV = 100,000 Periods = 60 periods CR = 2,500 PV = 96,500 Tasa = ? 2.62% YTM Quarterly 10.47% YTM
IN 2 YEARS PV = Call date = CR = Call price = Tasa =
96,500 2 years Periods = 8 2,500 101.5% FV = 101,500 ? 3.17% YTC Quarterly 12.68% YTC
periods
Karla Trávez 8 "A" International Commerce 3,- In the New York Stock Exchange today you can negotiate the following fix - rent securities : Bond a) Telefonica b) Bank of America c) Toyota
Face Value 100,000.00 100,000.00 100,000.00
Maturity 5 10 12
Coupon Rate 1.50% quarter 2.50% semi 1% semi
Price 101.5% 99% 100%
YTM 5.65% 5.13% 2.00%
YTC 6.14% 6.49% 2.98%
Calculate the yield to maturity according to the information at the current market price. Assume that 2 years later you can negotiate the bonds at 102% of their values, which bond would you negotiate, why? a)
TODAY
IN 2 YEARS
FV = 100,000 M = 5 years 20 periods CR = 1.50% quarterly 1500 PV = 101.50% 101500 Tasa = ? 1.41% YTM Quarterly 5.65% YTM
PV = Call date = CR = Call price =
b)
IN 2 YEARS
TODAY
Tasa =
FV = 100,000 M = 10 years 20 periods CR = 2.50% semi 2500 PV = 99.00% 99000 Tasa = ? 2.56% YTM Semianually 5.13% YTM
PV =
b)
IN 2 YEARS
TODAY
FV = 100,000 M = 12 years 24 periods CR = 1.00% semi 1000 PV = 100.00% 100000 Tasa = ? 1.00% YTM Semianually 2.00% YTM
101,500 2 years 1,500 102.0%
?
PV =
102.0%
?
Periods =
periods
4
periods
FV = 102,000
3.25% YTC Semianually 6.49% YTC
100,000 2 years
CR =
Tasa =
4
FV = 102,000
2,500
Call date = Call price =
periods
1.54% YTC Quarterly 6.14% YTC
2 years
CR =
Tasa =
8
99,000
Call date = Call price =
Periods =
Periods =
1,000 102.0%
?
FV = 102,000
1.49% YTC Semianually 2.98% YTC
Karla Trávez 8 "A" International Commerce BOOK'S EXERCISES 6.1.- Compton Computer bonds pay $80 annual interest , mature in 10 years, and pay $1,000 at maturity. What will their value be if the market rate of interest is 1) 6 percent, or 2) 10 percent, and interests is paid a) annually, b) semiannually? CR = M= FV = KB = PV =
80 10 years 1000 6% annually ? 0
PV = CR = M= FV = KB = PV =
80 2 71.20
80 3 67.17
80 4 63.37
80 80 5 6 59.78 56.40
80 7 53.20
80 10 years 1000 6% semiannually ? 80 0 1 75.47
20 periods
80 2 71.20
80 3 67.17
80 4 63.37
80 80 5 6 59.78 56.40
80 7 53.20
80 80 80 8 9 10 50.19 47.35 44.67
80 80 11 12 42.14 39.76
-$1,229.40 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^20]
80 10 years 1000 10% annually ? 0
PV =
1000 80 80 80 8 9 10 50.19 47.35 603.07
-$1,147.20 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^10]
PV = CR = M= FV = KB = PV =
80 1 75.47
80 1 72.73
80 2 66.12
80 3 60.11
80 4 54.64
80 80 5 6 49.67 45.16
80 7 41.05
1000 80 80 80 8 9 10 37.32 33.93 416.39
-$877.11 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^10]
80 80 80 13 14 15 37.51 35.38 33.38
1000 80 80 80 80 80 16 17 18 19 20 31.49 29.71 28.03 26.44 336.75
Karla Trávez 8 "A" International Commerce CR = M= FV = KB = PV =
80 10 years 1000 10% semiannually ? 80 0 1 72.73 PV =
20 periods
80 2 66.12
80 3 60.11
80 4 54.64
80 80 5 6 49.67 45.16
80 7 41.05
80 80 80 8 9 10 37.32 33.93 30.84
80 80 11 12 28.04 25.49
80 80 80 13 14 15 23.17 21.07 19.15
-$829.73 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^20]
6.3.- Greenman Engineering has some 15-years $1,000 par bonds outstanding, when have coupon interest rate of 9 percent and pay interest annually. What is the yield to maturity on the bonds if thier current market price is: a. $1,181.72 b. $795.99 c. Would you be wiling to pay $795.99 if you minimum required rate of return was 11 percent? Why or why not? A) PV = 1181.72 CR = 9% M= 15 years FV = 1000 YTM = ? YTM =
90.00
B) PV = 795.99 CR = 9% M= 15 years FV = 1000 YTM = ?
7.00%
90.00
YTM = 11.99%
6.4.- A $1,000 par value bond has a 12 percent coupon rate, pays interests annually, and has 15 years ramaining until it matures. a. If Bo = $1,151.72, what is its yield to maturity (YTM)? b. If the bond can be called in 6 years at $1,030, what is the bond's yield to call (YTC)? A) FV = 1000 CR = 12% M= 15 years PV = 1151.72 YTM = ? YTM =
10.00%
120
Call Price = CR = Call time= PV = YTM = ? YTM =
1030 120 6
years ###
9.01%
1000 80 80 80 80 80 16 17 18 19 20 17.41 15.83 14.39 13.08 160.54
Karla Trávez 8 "A" International Commerce 6.6.- Kamath Brithers has a $1,000 par, 9 percent coupon rate bond oustanding. The has 14 years to maturity. a. If the current market value of the bond is $1,200, and interest is paid annually, what is the bond's yield to maturity? b. What if everthing is as in (a), but interest is paid semiannually? a) ANNUALLY FV = 1000 CR = 9% M= 14 years PV = 1200 YTM = ? YTM =
6.75%
b) SEMIANNUALLY FV = 1000 CR = 9% M= 14 years PV = 1200 YTM = ?
90
YTM =
7.30%
90 28 periods
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 1
PROBLEMS: 1) Valuate a British 10 years, 100000 Z with a 2% semiannually coupon rate that is negotiated at 6% discounted rate. Assume 2 years later The British Central Bank recalls the bond at its Face Value. What is the YTC? Would you accept the offering? 1ST PART
N= FV = CR = K= Coupon = Coupon =
DATA 10 100000 2% 6%
years Z semiannually annually
2000 1
t=0
2000 2
2000 3 N= CR= K=
CR * FV 2000 Bond =
(85,122.53)
2000 … 20 periods 2% semiannually 3% semiannually
(Discounted Bond)
2ND PART DATA N= 2 CR = 2% PV = Bo = 85122.53 FV = 100000 Coupon = Coupon =
years semiannually Z Z
2000 1
t=0
2000 2
2000 3 N= CR= YTC =
CR * FV 2000 YTC = YTC =
6.33% 12.65%
semiannually annually
100000 FV 2000 Coupon 4 Periods 4 periods 2% semiannually ?
100000 FV 2000 Coupon 20 Periods
R//. Yes, because YTC represents a better percentage (6,33% semiannually) than K (3% semiannually) 2) The Bobl German 5 years bond is negotiated today at 98,5% of its value. If the bond is 100000 euros and 1% quarterly coupon rate, How much is the YTM? After 3 years The European Central Bank recalls bonds at 102.5%. Would you accept it? Why? 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 1% 98500 100000
years quarterly 98.5%
1000 1
t=0
1000 2
1000 3 N= CR= YTM =
CR * FV 1000 YTM = YTM = YTM =
1.08% 2.17% 4.34%
1000 …
100000 FV 1000 Coupon 20 Quarters
20 quarters 1% quarterly ?
quarterly semiannually annually
2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1% 98500 102500
years quarterly 98.5% 102.5%
1000 1
t=0
1000 2
1000 3 N= CR= YTC =
CR * FV 1000 YTC = YTC = YTC =
1.33% 2.66% 5.32%
quarterly semiannually annually
R//. Yes, because YTC represents a better percentage (1,33% quarterly) than YTM (1,08% quarterly)
1000 … 12 quarters 1% quarterly ?
102500 FV 1000 Coupon 12 Quarters
3) The following fix-rent financial information is taken from Bloomberg: Bond Brazil Mexico Canada USA
FV 10000000 1000000 100000 100000
YTM = YTC =
? ?
Maturity 10 years 5 years 12 years 10 years
3.50% 1.50% 5% 2.50%
CR semiannually quarterly annually semiannually
Price 101.50% 97.50% 98% 100%
Assume After 4 years 102.50% After 3 years 99.50% After 5 years 101% After 5 years 103%
BRAZILIAN BOND - 1ST PART
N= CR = PV = FV =
DATA 10 3.50% 10150000 10000000
Coupon = Coupon =
CR * FV 350000
years semiannually 101.5%
t=0
350000 1
350000 2
350000 3 N= CR= YTM =
YTM = YTM =
3.40% 6.79%
350000 …
10000000 FV 350000 Coupon 20 Periods
20 periods 3,5% semiannually ?
semiannually annually
BRAZILIAN BOND - 2ND PART
N= CR = PV = FV =
DATA 4 3.50% 10150000 10250000
Coupon = Coupon =
CR * FV 350000
years semiannually 101.5% 102.5%
t=0
350000 1
350000 2
350000 3 N= CR= YTC =
350000 … 8 periods 3,5% semiannually ?
10250000 FV 350000 Coupon 8 Periods
YTC = YTC =
3.56% 7.11%
semiannually annually
MEXICAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 1.50% 975000 1000000
years quarterly 97.5%
15000 1
t=0
15000 2
15000 3 N= CR= YTM =
CR * FV 15000 YTM = YTM = YTM =
1.65% 3.30% 6.59%
15000 …
1000000 FV 15000 Coupon 20 Quarters
20 quarters 1,5% quarterly ?
quarterly semiannually annually
MEXICAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1.50% 975000 995000
years quarterly 97.5% 99.5%
15000 1
t=0
15000 2
15000 3 N= CR= YTC =
CR * FV 15000 YTC = YTC = YTC =
1.69% 3.39% 6.78%
quarterly semiannually annually
15000 … 12 quarters 1,5% quarterly ?
995000 FV 15000 Coupon 12 Quarters
CANADIAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 12 5.00% 98000 100000
years annually 98%
5000 1
t=0
5000 2
5000 3 N= CR= YTM =
CR * FV 5000 YTM =
5.23%
5000 …
100000 FV 5000 Coupon 12 Years
12 years 5% annually ?
annually
CANADIAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 5.00% 98000 101000
years annually 98% 101%
5000 1
t=0
5000 2
5000 3 N= CR= YTC =
CR * FV 5000 YTC =
5.65%
annually
5000 4 5 years 5% annually ?
101000 FV 5000 Coupon 5 Years
AMERICAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 2.50% 100000 100000
years semiannually 100%
2500 1
t=0
2500 2
2500 3 N= CR= YTM =
CR * FV 2500 YTM = YTM =
2.50% 5.00%
2500 …
100000 FV 2500 Coupon 20 Periods
20 periods 2,5% semiannually ?
semiannually annually
AMERICAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 2.50% 100000 103000
years semiannually 100% 103%
2500 1
t=0
2500 2
2500 3 N= CR= YTC =
CR * FV 2500 YTC = YTC =
2.76% 5.53%
semiannually annually
2500 … 10 periods 2,5% semiannually ?
103000 FV 2500 Coupon 10 Periods
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 2
MORE PROBLEMS: 1) In the New York Stock Exchange you can buy a 5 years FEDBOND, 100000 Dollars, 2.5% semiannually coupon rate at 98.5% current market price. If you could renegotiate them 2 years later at its Face Value. Would you accept it? Why? 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 2.50% 98500 100000
years semiannually 98.5%
2500 1
t=0
2500 2
2500 3 N= CR= YTM =
CR * FV 2500 YTM = YTM =
2.67% 5.35%
2500 … 10 periods 2,5% semiannually ?
semiannually annually
2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 2.50% 98500 100000
years semiannually 98.5% 100%
2500 1
t=0
2500 2
2500 3 N= CR= YTC =
CR * FV 2500 YTC = YTC =
2.90% 5.81%
semiannually annually
100000 FV 2500 Coupon 4 Periods 4 periods 2,5% semiannually ?
100000 FV 2500 Coupon 10 Periods
R//. Yes, because YTC represents a better percentage (2,90% semiannually) than YTM (2,67% semiannually) 2) The Bond of America has the following portfolio: Bond GMC ADIDAS Petrobras Mitsubishi
FV 1000000 100000 10000000 1000000
Maturity 10 years 5 years 3 years 12 years
4% 1.5% 0.5% 1.5%
CR semiannually quarterly monthly semiannually
Price 97.50% 95.81% 102.78% 101%
YTM 8.37% 7% 5% 2.90%
YTC 10.34% 9.24% 5.48% 3.45%
Analyze the current market prices given and the YTM and the YTC, consider a renegotiation of all bonds 2 years later when FED and ECB have decided to decrease interest rate policies to 2.5% and the new Bond Price reference is 102% of its value . Would you accept it to renegotiate it. Why??? GMC BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 4% 975000 1000000
years semiannually 97.50%
40000 1
t=0
40000 2
40000 3 N= CR= YTM =
CR * FV 40000 YTM = YTM =
4.19% 8.37%
40000 … 20 periods 4% semiannually ?
semiannually annually
GMC BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 4% 975000 1020000
years semiannually 97.50% 102%
40000 1
t=0
40000 2
40000 3 N= CR= YTC =
CR * FV 40000 YTC = YTC =
5.17% 10.34%
semiannually annually
1020000 FV 40000 Coupon 4 Periods 4 periods 4% semiannually ?
1000000 FV 40000 Coupon 20 Periods
R//. Yes, because YTC (10,34% annually) is more than YTM (8,37% annually) ADIDAS BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 5 1.50% 7% ? 100000
years quarterly annually
1500 1
t=0
1500 2
1500 3 N= CR= YTM =
CR * FV 1500 Price =
(95,811.78)
1500 …
100000 FV 1500 Coupon 20 Quarters
20 quarters 1,5% quarterly 1,75% quarterly
(Discounted Bond)
ADIDAS BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 1.50% 95811.78 102000
years quarterly 95.81% 102%
1500 1
t=0
1500 2
1500 3 N= CR= YTC =
CR * FV 1500 YTC = YTC = YTC =
2.31% 4.62% 9.24%
quarterly semiannually annually
R//. Yes, because YTC (9,24% annually) is more than YTM (7,00% annually)
1500 … 8 quarters 1,5% quarterly ?
102000 FV 1500 Coupon 8 Quarters
PETROBRAS BOND - 1ST PART
N= CR = YTM = PV = FV =
DATA 3 0.50% 5% ? 10000000
Coupon = Coupon =
CR * FV 50000
years monthly annually
50000 1
t=0
50000 2
50000 3 N= CR= YTM =
Price =
(10,278,047.51)
50000 …
10000000 FV 50000 Coupon 36 Months
36 months 0,5% monthly 0,42% monthly
(Premium Bond)
PETROBRAS BOND - 2ND PART
N= CR = PV = FV =
DATA 2 0.50% 10278047.51 10200000
Coupon = Coupon =
CR * FV 50000
years monthly 102.78% 102%
50000 1
t=0
50000 2
50000 3 N= CR= YTC =
YTC = YTC = YTC = YTC =
0.46% 1.37% 2.74% 5.48%
monthly quarterly semiannually annually
R//. Yes, because YTC (5,48% annually) is more than YTM (5,00% annually)
50000 … 24 months 0,5% monthly ?
10200000 FV 50000 Coupon 24 Months
MITSUBISHI BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 12 1.50% 1010000 1000000
years semiannually 101%
15000 1
t=0
15000 2
15000 3 N= CR= YTM =
CR * FV 15000 YTM = YTM =
1.45% 2.90%
15000 … 24 periods 1,5% semiannually ?
semiannually annually
MITSUBISHI BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 1.50% 1010000 1020000
years semiannually 101% 102%
15000 1
t=0
15000 2
15000 3 N= CR= YTC =
CR * FV 15000 YTC = YTC =
1.73% 3.45%
semiannually annually
R//. Yes, because YTC (3,45% annually) is more than YTM (2,90% annually)
1020000 FV 15000 Coupon 4 Periods 4 periods 1,5% semiannually ?
1000000 FV 15000 Coupon 24 Periods
3) Valuate the following Bonds according to the information: Bond Gol Telefonica England Mitsubishi
FV 100000 1000000 10000000 1000000
Maturity 8 years 10 years 12 years 5 years
4% 1% 2% 0.50%
CR semiannually quarterly semiannually quarterly
Price 94.38% 100.50% 99.50% 102.40%
YTM 9% 3.94% 4.05% 1.50%
YTC 10.22% 3.82% 4.18% 1.18%
Analyze the current market prices given and the YTM and the YTC, consider a renegotiation of all bonds 3 years later when FED and ECB have decided to decrease interest rate policies to 6% and the new Bond Price reference is its face value . Would you accept it to renegotiate it. Why??? GOL BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 8 4% 9% ? 100000
years semiannually annually
t=0
4000 1
4000 2
4000 3 N= CR= YTM =
CR * FV 4000 Price =
(94,382.99)
4000 …
100000 FV 4000 Coupon 16 Periods
16 periods 4% semiannually 4,5% semiannually
(Discounted Bond)
GOL BOND - 2ND PART
N= CR = PV = FV =
DATA 3 4% 94382.99 100000
years semiannually 94.38% 100%
t=0
4000 1
4000 2
4000 3 N=
4000 … 6 periods
100000 FV 4000 Coupon 6 Periods
Coupon = Coupon =
CR * FV 4000
CR= YTC = YTC = YTC =
5.11% 10.22%
4% semiannually ?
semiannually annually
R//. Yes, because YTC (10,22% annually) is more than YTM (9,00% annually) TELEFONICA BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 1% 1005000 1000000
years quarterly 100.50%
10000 1
t=0
10000 2
10000 3 N= CR= YTM =
CR * FV 10000 YTM = YTM = YTM =
0.98% 1.97% 3.94%
10000 …
1000000 FV 10000 Coupon 40 Quarters
40 quarters 1% quarterly ?
quarterly semiannually annually
TELEFONICA BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1% 1005000 1000000
years quarterly 100.50% 100%
10000 1
t=0
10000 2
10000 3 N= CR= YTC =
CR * FV 10000 YTC = YTC = YTC =
0.96% 1.91% 3.82%
quarterly semiannually annually
R//. No, because YTC (3,82% annually) is less than YTM (3,94% annually)
10000 … 12 quarters 1% quarterly ?
1000000 FV 10000 Coupon 12 Quarters
ENGLAND BOND - 1ST PART
N= CR = PV = FV =
DATA 12 2% 9950000 10000000
Coupon = Coupon =
CR * FV 200000
years semiannually 99.50%
t=0
200000 1
200000 2
200000 3 N= CR= YTM =
YTM = YTM =
2.03% 4.05%
200000 …
10000000 FV 200000 Coupon 24 Periods
24 periods 2% semiannually ?
semiannually annually
ENGLAND BOND - 2ND PART
N= CR = PV = FV =
DATA 3 2% 9950000 10000000
Coupon = Coupon =
CR * FV 200000
years semiannually 99.50% 100%
t=0
200000 1
200000 2
200000 3 N= CR= YTC =
YTC = YTC =
2.09% 4.18%
semiannually annually
R//. Yes, because YTC (4,18% annually) is more than YTM (4,05% annually)
200000 … 6 periods 2% semiannually ?
10000000 FV 200000 Coupon 6 Periods
MITSUBISHI BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 5 0.50% 1.50% ? 1000000
years quarterly annually
5000 1
t=0
5000 2
5000 3 N= CR= YTM =
CR * FV 5000 Price =
(1,024,042.12)
5000 …
1000000 FV 5000 Coupon 20 Quarters
20 quarters 0,5% quarterly 0,375% quarterly
(Premium Bond)
MITSUBISHI BOND - 2ND PART
N= CR = PV = FV =
DATA 3 0.50% 1024042.12 1000000
Coupon = Coupon =
CR * FV 5000
years quarterly 102.40% 100%
5000 1
t=0
5000 2
5000 3 N= CR= YTC =
YTC = YTC = YTC =
0.30% 0.59% 1.18%
quarterly semiannually annually
R//. No, because YTC (1,18% annually) is less than YTM (1,50% annually)
5000 … 12 quarters 0,5% quarterly ?
1000000 FV 5000 Coupon 12 Quarters
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 3
6.3.- Cavalier industries has a current (Do) cash dividen of $2 per share. You estimate that cash dividends will grow at 12% per year for each of 3 years (t1,t2,t3), and then a 6% oer year for each of 2 more years (t4 and t5). After t5 you expect them to grow at 2% per year to infinity. a.- What is the current market value of Cavalier Industries common stock if the required rate of return is 14%? b.- What is the market price if evereything is the same as in a) except that after year 5 there is no expected growth in cash dividends
Do = g1 = g2 = g3 = Ks =
Data (Section A) 2 12% 6% 2% 14%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
12% 6% 2%
D1 = Do(1+g1)^1 D1 = 2(1+0,12)^1 D1 = 2,24
D2 = Do(1+g1)^2 D2 = 2(1+0,12)^2 D2 = 2,51
D3 = Do(1+g1)^3 D3 = 2(1+0,12)^3 D3 = 2,81
D4 = D3(1+g2)^1 D4 = 2,81(1+0,06)^1 D4 = 2,98
D5 = D3(1+g2)^2 D5 = 2,81(1+0,06)^2 D5 = 3,16
D6 = D5(1+g3)^1 D6 = 3,16(1+0,02)^1 D6 = 3,22
d1 d2 d3 d4 d5 d6 P5 Po
2.24 2.51 2.81 2.98 3.16 3.22 26.84 23.13
P5 = D6 / (Ks-g3) P5 = 3,22 / (0,14-0,02) P5 = 26,84 Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,24/(1,14)^1 + 2,51/(1,14)^2 + 2,81/(1,14)^3 + 2,98/(1,14)^4 + 3,16/(1,14)^5 + 26,84/(1,14)^5 Po = 1,96 + 1,93 + 1,90 + 1,76 + 1,64 + 13,94 R//. Po = $23,13
Do = g1 = g2 = Ks =
Data (Section B) 2 12% 6% 14%
P5 Po=? t=0
d1=2,24 1
d2=2,51 2
d3=2,81 3
d4=2,98 4
d5=3,16 5
12% P5 = D1 / Ks P5 = d5 / Ks P5 = 3,16 / 0,14 P5 = 22,55
6% P5 Po
22.55 20.90
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,24/(1,14)^1 + 2,51/(1,14)^2 + 2,81/(1,14)^3 + 2,98/(1,14)^4 + 3,16/(1,14)^5 + 22,55/(1,14)^5 Po = 1,96 + 1,93 + 1,90 + 1,76 + 1,64 + 11,71 R//. Po = $20,9
No-Growth
6.7.- You are interested in buying 100 shares of a &60 par value preferred stock that has an 8,5% dividend rate a.- If you required return is 11%, how much would you willing to pay to acquire its 100 shares? b.- What if no dividend will be paid until t = 3? At the same required return, how much would you now be willing to pay?
Po = dr = Ks = D1 =
Data (Section A) 60 8.50% 11% ?
D4 = Ks =
Data (Section B) 5.10 11% P3 = D4 / Ks P3 = 5,10 / 11% P3 = 46,36
D1 = Po * dr D1 = 60 * 8,5% D1 = 5,10
Po = D1 / Ks Po = 5,10 / 11% Po = 46,36 Po = $4636,36
D1 Po x 100 shares
Po=? t=0 Po = P3 / (1+Ks)^3 Po = 46,36 / (1+0,11)^3 Po = 33,90 Po = 3390,07
d1 = 0 1
d2 = 0 2 P3 Po
x 100 shares
5.10 4636.36
P3 = 46,36 d3 = 0 d4=5,10 3 Infinity 46.36 3390.07
6.9.- A stock currently pays cash dividends of $4 oer share (Do = $4), and the required rate of return is 12%. What is its market value in the following cases? a.- There is o future growth in dividends. b.- Dividends grow at 8% per year to infinity. c.- Dividends grow at 5% for each of 2 years; and there is no growth expected after D2. d.- Growth will be 10% for each of 2 years (n = 2) after which growth will be 5% per year until infinity. e.- Recalculate d) where growth is now 7% for 5 years ( n = 5 ), after which growth will be 3% per year until infinity. f.- Finally, now suppose the required rate of return is 15% and Do = $2.50. Recalculate a), b), d) and e) with these new values.
Do = Ks =
Data (Section A) 4 12%
Do = g1 = Ks =
Data (Section B) 4 8% 12%
Do = g1 = Ks =
Data (Section C) 4 5% 12% D1 = Do(1+g1)^1 D1 = 4(1+0,05)^1 D1 = 4,20
Po = D1 / Ks Po = 4 / 0,12 Po = $33,33
Po
33.33
Po = D1 / (Ks-g) Po = 4 / (0,12-0,08) Po = $100
Po
100
d1 1
d2 2
d1 d2 P2 Po
4.20 4.41 36.75 36.57
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 4(1+0,05)^2 D2 = 4,41
P2 = D1 / Ks P2 = d2 / Ks P2 = 4,41 / 0,12 P2 = 36,75
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,20/(1,12)^1 + 4,41/(1,12)^2 + 36,75/(1,12)^2 Po = 3,75 + 3,52 + 29,30 R//. Po = $36,57
No-Growth
Do = g1 = g2 = Ks =
Data (Section D) 4 10% 5% 12% D1 = Do(1+g1)^1 D1 = 4(1+0,10)^1 D1 = 4,40
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 4(1+0,10)^2 D2 = 4,84
D3 = D2(1+g2)^1 D3 = 4,84(1+0,05)^1 D3 = 5,08
P2 = D3 / (Ks-g2) P2 = 5,08 / (0,12-0,05) P2 = $72,60
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,40/(1,12)^1 + 4,84/(1,12)^2 + 72,60/(1,12)^2 Po = 3,93 + 3,86 + 57,88 R//. Po = $65,67
d1 1
d2 2
d1 d2 d3 P2 Po
4.40 4.84 5.08 72.60 65.67
d3
Do = g1 = g2 = Ks =
Data (Section E) 4 7% 3% 12%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
7% 3% D1 = Do(1+g1)^1 D1 = 4(1+0,07)^1 D1 = 4,28
D2 = Do(1+g1)^2 D2 = 4(1+0,07)^2 D2 = 4,58
D3 = Do(1+g1)^3 D1 = 4(1+0,07)^3 D3 = 4,90
D4 = Do(1+g1)^4 D4 = 4(1+0,07)^4 D4 = 5,24
D5 = Do(1+g1)^5 D5 = 4(1+0,07)^5 D5 = 5,61
D6 = D5(1+g2)^1 D6 = 5,61(1+0,03)^1 D6 = 5,78
d1 d2 d3 d4 d5 d6 P5 Po
4.28 4.58 4.90 5.24 5.61 5.78 64.21 53.90
P5 = D6 / (Ks-g2) P5 = 5,78 / (0,12-0,03) P5 = $64,21
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,28/(1,12)^1 + 4,58/(1,12)^2 + 4,90/(1,12)^3 + 5,24/(1,12)^4 + 5,61/(1,12)^5 + 64,21/(1,12)^5 Po = 3,82 + 3,65 + 3,49 + 3,33 + 3,18 + 36,43 R//. Po = $53,90
Do = Ks =
Data (Section F) 2.50 15%
Po = D1 / Ks Po = 2,50 / 0,15 Po = $16,67
Po
16.67
Do = g1 = Ks =
Data (Section F) 2.50 8% 15%
Do = g1 = g2 = Ks =
Data (Section F) 2.50 10% 5% 15% D1 = Do(1+g1)^1 D1 = 2,50(1+0,10)^1 D1 = 2,75
Po = D1 / (Ks-g) Po = 2,50 / (0,15-0,08) Po = $36
Po
36
d1 1
d2 2
d1 d2 d3 P2 Po
2.75 3.03 3.18 31.76 28.70
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 2,50(1+0,10)^2 D2 = 3,03
D3 = D2(1+g2)^1 D3 = 3,03(1+0,05)^1 D3 = 3,18
P2 = D3 / (Ks-g2) P2 = 5,08 / (0,15-0,05) P2 = $31,76
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,75/(1,15)^1 + 3,03/(1,15)^2 + 31,76/(1,15)^2 Po = 2,39 + 2,29 + 24,02 R//. Po = $28,70
d3
Do = g1 = g2 = Ks =
Data (Section F) 2.50 7% 3% 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
7% 3% D1 = Do(1+g1)^1 D1 = 2,50(1+0,07)^1 D1 = 2,68
D2 = Do(1+g1)^2 D2 = 2,50(1+0,07)^2 D2 = 2,86
D3 = Do(1+g1)^3 D3 = 2,50(1+0,07)^3 D3 = 3,06
D4 = Do(1+g1)^4 D4 = 2,50(1+0,07)^4 D4 = 3,28
D5 = Do(1+g1)^5 D5 = 2,50(1+0,07)^5 D5 = 3,51
D6 = D5(1+g2)^1 D6 = 3,51(1+0,03)^1 D6 = 3,61
d1 d2 d3 d4 d5 d6 P5 Po
2.68 2.86 3.06 3.28 3.51 3.61 30.10 25.10
P5 = D6 / (Ks-g2) P5 = 3,61 / (0,15-0,03) P5 = $30,10
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,68/(1,15)^1 + 2,86/(1,15)^2 + 3,06/(1,15)^3 + 3,28/(1,15)^4 + 3,51/(1,15)^5 + 30,10/(1,15)^5 Po = 2,33 + 2,16 + 2,01 + 1,88 + 1,75 + 14,97 R//. Po = $25,10
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT - TASK N°4
Share Google Microsoft Petrobras Exxon Mobil Budweiser
MKT Price 250 100 50 1000 10
Current Dividend 40 20 15 150 2
Years 1,2,3 Growth 1 20% 10% 25% 12% 10%
Years 4,5 Growth 2 25% 8% 20% 8% 15%
6 to infinity Growth 3 10% infinity 5% infinity 10% infinity 6% infinity 20% infinity
Ks 30% 15% 20% 10% 15%
1.- According to the information valuate all the shares with the 3 different stages, include current market prices with infinity valuations and with no growth. 2.- Two years later J.P.Morgan Investment Bank of New York wants to buy the Portfolio with the following prices: Share Google Microsoft Petrobras Exxon Mobil Budweiser
MKT Price 450 200 150 1450 18
Data (Google - Infinity) Do = 40 g1 = 20% g2 = 25% g3 = 10% Ks = 30%
Would you recommend to accept the offering, why?
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
Dividends 48.00 57.60 69.12 86.40 108.00 118.80 594.00
PV 36.92 34.08 31.46 30.25 29.09 159.98
Po
321.79
d5 5
d6
20% 25%
D1 = Do(1+g1)^1 D1 = 40(1+0,20)^1 D1 = 48
D2 = Do(1+g1)^2 D2 = 40(1+0,20)^2 D2 = 57.60
D3 = Do(1+g1)^3 D3 = 40(1+0,20)^3 D3 = 69.12
D4 = D3(1+g2)^1 D4 = 69.12(1+0,25)^1 D4 = 86.40
D5 = D3(1+g2)^2 D5 = 69.12(1+0,25)^2 D5 = 108
D6 = D5(1+g3)^1 D6 = 108(1+0,10)^1 D6 = 118.80
P5 = D6/(Ks-g3) P5 = 594
Years d1 d2 d3 d4 d5 d6 P5
10%
Data (Google - No Growth) Do = 40 g1 = 20% g2 = 25% Ks = 30%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
Dividends 48.00 57.60 69.12 86.40 108.00 360.00
PV 36.92 34.08 31.46 30.25 29.09 96.96
Po
258.76
d5 5
20% 25% D1 = Do(1+g1)^1 D1 = 40(1+0,20)^1 D1 = 48
D2 = Do(1+g1)^2 D2 = 40(1+0,20)^2 D2 = 57.60
D3 = Do(1+g1)^3 D3 = 40(1+0,20)^3 D3 = 69.12
D4 = D3(1+g2)^1 D4 = 69.12(1+0,25)^1 D4 = 86.40
D5 = D3(1+g2)^2 D5 = 69.12(1+0,25)^2 D5 = 108
P5 = d5 / Ks P5 = 108 / 0,30 P5 = 360
New Data (Google - No Growth) N= 2 D1 = 48.00 D2 = 57.60 P2 = 450 Po = 258.76
Years d1 d2 d3 d4 d5 P5
P2 Po=258,76 t=0
Valores TIR
-258.76 49.64%
d1 1
d2 2
48.00 507.60 Yes, because TIR (49,64%) is more than K (30%)
No-Growth
Data (Microsoft - Infinity) Do = 20 g1 = 10% g2 = 8% g3 = 5% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
10% 8% 5%
D1 = Do(1+g1)^1 D1 = 20(1+0,10)^1 D1 = 22
D2 = Do(1+g1)^2 D2 = 20(1+0,10)^2 D2 = 24,20
D3 = Do(1+g1)^3 D3 = 20(1+0,10)^3 D3 = 26,62
D4 = D3(1+g2)^1 D4 = 26,62(1+0,08)^1 D4 = 28,75
D5 = D3(1+g2)^2 D5 = 26,62(1+0,08)^2 D5 = 31,05
D6 = D5(1+g3)^1 D6 = 31,05(1+0,05)^1 D6 = 32,60
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 32,60 / (0,15-0,05) P5 = 326,02
Dividends 22.00 24.20 26.62 28.75 31.05 32.60 326.02
162.09
Total
248.90
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $248,90
New Data (Microsoft - Infinity) N= 2 D1 = 22.00 D2 = 24.20 P2 = 200 Po = 248.90
P2 Po=248,90 t=0
Valores TIR
-248.90 -0.57%
d1 1
d2 2
22.00 224.20 No, because TIR (-0,57%) is less than K (15%)
PV 19.13 18.30 17.50 16.44 15.44
Data (Microsoft - No Growth) Do = 20 g1 = 10% g2 = 8% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
10% 8% D1 = Do(1+g1)^1 D1 = 20(1+0,10)^1 D1 = 22
D2 = Do(1+g1)^2 D2 = 20(1+0,10)^2 D2 = 24,20
D3 = Do(1+g1)^3 D3 = 20(1+0,10)^3 D3 = 26,62
D4 = D3(1+g2)^1 D4 = 26,62(1+0,08)^1 D4 = 28,75
D5 = D3(1+g2)^2 D5 = 26,62(1+0,08)^2 D5 = 31,05
P5 = d5 / Ks P5 = 31,05 / 0,15 P5 = 207
Years d1 d2 d3 d4 d5 P5
Dividends 22.00 24.20 26.62 28.75 31.05 207.00
PV 19.13 18.30 17.50 16.44 15.44 102.91
Total
189.72
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $189,72
New Data (Microsoft - No Growth) N= 2 D1 = 22.00 D2 = 24.20 P2 = 200 Po = 189.72
P2 Po=189,72 t=0
Valores TIR
-189.72 14.66%
d1 1
d2 2
22.00 224.20 No, because TIR (14,66%) is less than K (15%)
No-Growth
Data (Petrobras - Infinity) Do = 15 g1 = 25% g2 = 20% g3 = 10% Ks = 20%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
25% 20% 10%
D1 = Do(1+g1)^1 D1 = 15(1+0,25)^1 D1 = 18,75
D2 = Do(1+g1)^2 D2 = 15(1+0,25)^2 D2 = 23,44
D3 = Do(1+g1)^3 D3 = 15(1+0,25)^3 D3 = 29,30
D4 = D3(1+g2)^1 D4 = 29,30(1+0,20)^1 D4 = 35,16
D5 = D3(1+g2)^2 D5 = 29,30(1+0,20)^2 D5 = 42,19
D6 = D5(1+g3)^1 D6 = 42,19(1+0,10)^1 D6 = 46,41
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 46,41 / (0,20-0,10) P5 = 464,06
Dividends 18.75 23.44 29.30 35.16 42.19 46.41 464.06
PV 15.63 16.28 16.95 16.95 16.95 186.50
Total
269.26
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $269,26
New Data (Petrobras - Infinity) N= 2 D1 = 18.75 D2 = 23.44 P2 = 150 Po = 269.26
P2 Po=269,26 t=0
Valores TIR
-269.26 -16.19%
d1 1
d2 2
18.75 173.44 No, because TIR (-16,19%) is less than K (20%)
Data (Petrobras - No Growth) Do = 15 g1 = 25% g2 = 20% Ks = 20%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
25% 20% D1 = Do(1+g1)^1 D1 = 15(1+0,25)^1 D1 = 18,75
D2 = Do(1+g1)^2 D2 = 15(1+0,25)^2 D2 = 23,44
D3 = Do(1+g1)^3 D3 = 15(1+0,25)^3 D3 = 29,30
D4 = D3(1+g2)^1 D4 = 29,30(1+0,20)^1 D4 = 35,16
D5 = D3(1+g2)^2 D5 = 29,30(1+0,20)^2 D5 = 42,19
P5 = d5 / Ks P5 = 42,19 / 0,20 P5 = 210,94
Years d1 d2 d3 d4 d5 P5
Dividends 18.75 23.44 29.30 35.16 42.19 210.94
PV 15.63 16.28 16.95 16.95 16.95 84.77
Total
167.53
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $167,53
New Data (Petrobras - No Growth) N= 2 D1 = 18.75 D2 = 23.44 P2 = 150 Po = 167.53
P2 Po=167,53 t=0
Valores TIR
-167.53 7.50%
d1 1
d2 2
18.75 173.44 No, because TIR (7,50%) is less than K (20%)
No-Growth
Data (Exxon - Infinity) Do = 150 g1 = 12% g2 = 8% g3 = 6% Ks = 10%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
12% 8% 6%
D1 = Do(1+g1)^1 D1 = 150(1+0,12)^1 D1 = 168
D2 = Do(1+g1)^2 D2 = 150(1+0,12)^2 D2 = 188,16
D3 = Do(1+g1)^3 D3 = 150(1+0,12)^3 D3 = 210,74
D4 = D3(1+g2)^1 D4 = 210,74(1+0,08)^1 D4 = 227,60
D5 = D3(1+g2)^2 D5 = 210,74(1+0,08)^2 D5 = 245,81
D6 = D5(1+g3)^1 D6 = 245,81(1+0,06)^1 D6 = 260,55
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 260,55 / (0,10-0,06) P5 = 6513,86
Dividends 168.00 188.16 210.74 227.60 245.81 260.55 6513.86
PV 152.73 155.50 158.33 155.45 152.63 4044.60
Total
4819.24
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $4819,24
New Data (Exxon - Infinity) N= 2 D1 = 168.00 D2 = 188.16 P2 = 1450 Po = 4819.24
P2 Po=4819,24 t=0
Valores TIR
-4819.24 -156.59%
d1 1
d2 2
168.00 1638.16 No, because TIR (-39,33%) is less than K (10%)
Data (Exxon - No Growth) Do = 150 g1 = 12% g2 = 8% Ks = 10%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
12% 8% D1 = Do(1+g1)^1 D1 = 150(1+0,12)^1 D1 = 168
D2 = Do(1+g1)^2 D2 = 150(1+0,12)^2 D2 = 188,16
D3 = Do(1+g1)^3 D3 = 150(1+0,12)^3 D3 = 210,74
D4 = D3(1+g2)^1 D4 = 210,74(1+0,08)^1 D4 = 227,60
D5 = D3(1+g2)^2 D5 = 210,74(1+0,08)^2 D5 = 245,81
P5 = d5 / Ks P5 = 245,81 / 0,10 P5 = 2458,06
Years d1 d2 d3 d4 d5 P5
Dividends 168.00 188.16 210.74 227.60 245.81 2458.06
PV 152.73 155.50 158.33 155.45 152.63 1526.26
Total
2300.91
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $2300,91
New Data (Exxon - No Growth) N= 2 D1 = 168.00 D2 = 188.16 P2 = 1450 Po = 2300.91
P2 Po=2300,91 t=0
Valores TIR
-2300.91 -11.89%
d1 1
d2 2
168.00 1638.16 No, because TIR (-11,89%) is less than K (10%)
No-Growth
Data (Budweiser - Infinity) Do = 2 g1 = 10% g2 = 15% g3 = 20% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
10% 15% 20%
D1 = Do(1+g1)^1 D1 = 2(1+0,10)^1 D1 = 2,20
D2 = Do(1+g1)^2 D2 = 2(1+0,10)^2 D2 = 2,42
D3 = Do(1+g1)^3 D3 = 2(1+0,10)^3 D3 = 2,66
D4 = D3(1+g2)^1 D4 = 2,66(1+0,15)^1 D4 = 3,06
D5 = D3(1+g2)^2 D5 = 2,66(1+0,15)^2 D5 = 3,52
D6 = D5(1+g3)^1 D6 = 3,52(1+0,20)^1 D6 = 4,22
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 4,22 / (0,15-0,20) P5 = -84,49
Dividends 2.20 2.42 2.66 3.06 3.52 4.22 -84.49
PV 1.91 1.83 1.75 1.75 1.75 -42.01
Total
-33.01
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = -$33,01
New Data (Budweiser - Infinity) N= 2 D1 = 2.20 D2 = 2.42 P2 = 18 Po = -33.01
P2 Po=-33,01 t=0
Valores TIR
-33.01 -17.95%
d1 1
d2 2
2.20 20.42 No, because TIR (-17,95%) is less than K (15%)
Data (Budweiser - No Growth) Do = 2 g1 = 10% g2 = 15% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
10% 15% D1 = Do(1+g1)^1 D1 = 2(1+0,10)^1 D1 = 2,20
D2 = Do(1+g1)^2 D2 = 2(1+0,10)^2 D2 = 2,42
D3 = Do(1+g1)^3 D3 = 2(1+0,10)^3 D3 = 2,66
D4 = D3(1+g2)^1 D4 = 2,66(1+0,15)^1 D4 = 3,06
D5 = D3(1+g2)^2 D5 = 2,66(1+0,15)^2 D5 = 3,52
P5 = d5 / Ks P5 = 2,66 / 0,15 P5 = 2458,06
Years d1 d2 d3 d4 d5 P5
Dividends 2.20 2.42 2.66 3.06 3.52 23.47
PV 1.91 1.83 1.75 1.75 1.75 11.67
Total
20.66
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $20,66
New Data (Budweiser - No Growth) N= 2 D1 = 2.20 D2 = 2.42 P2 = 18 Po = 20.66
P2 Po=20,66 t=0
Valores TIR
-20.66 4.88%
d1 1
d2 2
2.20 20.42 No, because TIR (4,88%) is less than K (15%)
No-Growth
Using the following financial information taken from the BVG, analyze it: Security Amazonas Bond GMac Bond Holcim Shares Bolivariano Shares
Price 92% 95% 30 10
FV 100000 100000
Coupon / Dividend 4% semiannually 1,5% quarterly 10% 5%
N 5 years 7 years
Yield ? ? 15% 12%
g1
g2
12% 15%
10% 5%
P3 95% 98% 42 18
g1 = t1, t2, t3 g2 = infinity Valuate the securities according the financial information: a) An investor wants to invest $100000, which of the options are the best for him?, why? b) Assume 3 years after the investor bought all, another bank offers different prices (P3), would you recommend to buy, why?
FV = PV = CR = N= COUPON = YTM =
Amazonas Bond (1st Part) 100000 92000 4% 10
Semi Periods
4000 5.04%
Amazonas Bond (2nd Part) FV = 95000 PV = 92000 CR = 4% Semi N= 6 Periods COUPON = YTC =
4000 4.83%
No, because YTC (4,83%) is less than YTM (5,04%)
FV = PV = CR = N= COUPON = YTM =
GMac Bond (1st Part) 100000 95000 1.50% 28 1500 1.73%
Quarter Periods
GMac Bond (2nd Part) FV = 98000 PV = 95000 CR = 1.50% Semi N= 12 Periods COUPON = YTC =
1500 1.82%
Yes, because YTC (1,82%) is more than YTM (1,73%) Holcim Shares (1st Part) Do = 3 g1 = 12% g2 = 10% Ks = 15%
P3 Po=? t=0
d1 1
d2 2
d3 3
d4
12% D1 = Do(1+g1)^1 D1 = 3(1+0,12)^1 D1 = 3,36
D2 = Do(1+g1)^2 D2 = 3(1+0,12)^2 D2 = 3,76
D4 = D3(1+g2)^1 D1 = 4,21(1+0,10)^1 D4 = 4,64
D3 = Do(1+g1)^3 D3 = 3(1+0,12)^3 D3 = 4,21
10%
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 92,73
Po = 69,51
Dividends 3.36 3.76 4.21 4.64 92.73
PV 2.92 2.85 2.77 60.97
Total Holcim Shares (2nd Part) N= 3 D1 = 3.36 D2 = 3.76 D3 = 4.21 P3 = 42.00 Po = 69.51
P3 Po=69,51 t=0
Valores TIR
-69.51 -8.97%
d1 1
d2 2
d3 3
3.36
3.76
46.21
No, because TIR (-8,97%) is less than Ks (15%)
69.51
Bolivariano Shares (1st Part) Do = 0.5 g1 = 15% g2 = 5% Ks = 12%
P3 Po=? t=0
d1 1
d2 2
d3 3
d4
15% D1 = Do(1+g1)^1 D1 = 0,5(1+0,15)^1 D1 = 0,58
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 0,5(1+0,15)^2 D3 = 0,5(1+0,15)^3 D2 = 0,66 D3 = 0,76
D4 = D3(1+g2)^1 D1 = 0,76(1+0,05)^1 D4 = 0,80
5%
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 11,41
Po = 9,70
Dividends 0.58 0.66 0.76 0.80 11.41
PV 0.51 0.53 0.54 8.12
Total Bolivariano Shares (2nd Part) N= 3 D1 = 0.58 D2 = 0.66 D3 = 0.76 P3 = 18.00 Po = 9.70
P3 Po=9,70 t=0
Valores TIR
-9.70 28.45%
d1 1
d2 2
d3 3
0.58
0.66
18.76
Yes, because TIR (28,45%) is more than Ks (12%)
9.70
1.- In The Bolsa de Valores de Guayaquil there is the following financial information available: Security Global 2015 Bond CFN - Bond Holcim Shares Holcim Shares Tekal Shares Tekal Shares
Po 93.77% 87.44% 66.50 36.13 316.76 255.14
FV 100000 10000
Coupon / Dividend / Do 4,5% semiannually 2% quarterly $3 $3 $40 $40
N 10 years 4 years
Yield 10% 12% 10% 10% 20% 20%
g1
g2
7% 7% 10% 10%
5% 5% 5% 5% g1 = 1,2,3 years g2 = infinity
Analyze the Bonds and Shares and valuate the current market Prices today. In Shares consider g2 (growth rate of 2nd stage) a) % to infinity and b) without growing Assume you bought the bonds and shares at the current market Prices calculated, and 3 years later an important Investment Bank offers different Prices (P3 column) which of them would you accept, Why?
FV = PV = CR = N=
Global 2015 Bond (1st Part) 100000 ? 4.50% 20
COUPON = Kb =
4500 5.00%
PV =
-93,768.89
Semi Periods
Global 2015 Bond (2nd Part) FV = 99500 PV = -93,768.89 CR = 4.50% N= 6 COUPON = YTC =
Semi
Yes, because YTC (5,68%) is higher than Kb (5,00%)
4500 5.68%
CFN Bond (1st Part) 10000 ? 2.00% 16
FV = PV = CR = N= COUPON = Kb =
200 3.00%
PV =
-8,743.89
CFN Bond (2nd Part) 9500 -8,743.89 2.00% 12
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
200 2.90%
Dividends 3.21 3.43 3.68 3.86 77.18
PV 2.92 2.84 2.76 57.98
Total
66.50
3.43
33.68
No, because YTC (2,90%) is lower than Kb (3,00%)
Do = g1 = g2 = Ks =
Holcim Shares (Infinity) 3 7% 5% 10%
D1 = Do(1+g1)^1 D1 = 3(1+0,07)^1 D1 = 3,21
D2 = Do(1+g1)^2 D2 = 3(1+0,07)^2 D2 = 3,43
D4 = D3(1+g2)^1 D4 = 3,68(1+0,05)^1 D4 = 3,86
D3 = Do(1+g1)^3 D3 = 3(1+0,07)^3 D3 = 3,68
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 77,18
Po = 66,50 Valores TIR
-66.50 -16.45%
3.21
No, because TIR (-16,45%) is lower than Ks (10%)
Do = g1 = Ks =
Holcim Shares (No Growth) 3 7% 10%
D1 = Do(1+g1)^1 D1 = 3(1+0,07)^1 D1 = 3,21
D2 = Do(1+g1)^2 D2 = 3(1+0,07)^2 D2 = 3,43
D3 = Do(1+g1)^3 D3 = 3(1+0,07)^3 D3 = 3,68
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 36,75
Dividends 3.21 3.43 3.68 36.75
PV 2.92 2.84 2.76 27.61
Total
36.13
3.43
33.68
Po = 36,13 Valores TIR
-36.13 4.07%
3.21
No, because TIR (4,07%) is lower than Ks (10%)
Do = g1 = g2 = Ks =
Tekal Shares (Infinity) 40 10% 5% 20%
D1 = Do(1+g1)^1 D1 = 40(1+0,10)^1 D1 = 44
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 40(1+0,10)^2 D3 = 40(1+0,10)^3 D2 = 48,40 D3 = 53,24
D4 = D3(1+g2)^1 D4 = 53,24(1+0,05)^1 D4 = 55,90
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 372,68
Dividends 44.00 48.40 53.24 55.90 372.68
PV 36.67 33.61 30.81 215.67
Total
316.76
48.40
903.24
Po = 316,76 Valores TIR
-316.76 50.29%
44.00
Yes, because TIR (50,29%) is higher than Ks (20%)
Do = g1 = Ks =
Tekal Shares (No Growth) 40 10% 20%
D1 = Do(1+g1)^1 D1 = 40(1+0,10)^1 D1 = 44
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 40(1+0,10)^2 D3 = 40(1+0,10)^3 D2 = 48,40 D3 = 53,24
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 266,20
Dividends 44.00 48.40 53.24 266.20
PV 36.67 33.61 30.81 154.05
Total
255.14
48.40
903.24
Po = 255,14 Valores TIR
-255.14 62.68%
44.00
Yes, because TIR (62,68%) is higher than Ks (20%)
2.- In the New York Stock Exchange today, in Bloomberg, there is the following financial information available: Security GM - Bond Boeing - Shares
Po 88.50% 100
FV 100000
Coupon / Dividend / Do 3% quarterly 15%
N 4 years
Yield 15.94% 15%
g1
g2
10%
5% g1 = 1,2,3 years g2 = infinity
An important client of Chase Manhattan bank wants to invest $100000, which of the options in the table could be the best alternative, why? Assume you bought the bonds and shares at the current market Prices, and 2 years later an important investment Bank offers different Prices (P2 column) which of them would you accept, why?
FV = PV = CR = N= COUPON = YTM =
GM - Bond (1st Part) 100000 88500 3% 16 3000 3.99%
GM - Bond (2nd Part) 95000 88500 3% 8
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
3000 4.18%
Yes, because YTC (4,18%) is higher than YTM (3,99%) The best alternative is GM - Bond because it offers a better yield (15.94%) than Boeing - Shares (15%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 15(1+0,10)^1 D1 = 16,50
Boeing - Shares 15 10% 5% 15% D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 15(1+0,10)^2 D3 = 15(1+0,10)^3 D2 = 18,15 D3 = 19,97
D4 = D3(1+g2)^1 D4 = 19,97(1+0,05)^1 D4 = 55,90
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 209,63
Dividends 16.50 18.15 19.97 20.96 209.63
137.84
Total
179.04
Po = 179,04 Valores TIR
-179.04 1.63%
16.50
No, because TIR (1,63%) is lower than Ks (15%)
168.15
PV 14.35 13.72 13.13
P3 99.5% 95% $30 $30 $850 $850 g1 = 1,2,3 years g2 = infinity
15 Bond (2nd Part)
Semi Periods
Semi
Sell / Not Sell Sell Not Sell Not Sell Not Sell Sell Sell
Bond (2nd Part)
Quarterly Periods
Quarterly
P2 95% $150 g1 = 1,2,3 years g2 = infinity
Bond (2nd Part)
Quarterly Periods
Quarterly
oeing - Shares (15%)
Sell / Not Sell Sell Not Sell
1.- There is the following financial information available: Security Bond N° 1 Bond N° 2 Share N° 1 Share N° 1 Share N° 2 Share N° 2
Po 113.80% 96.67% 36.21 28.52 368.80 256.58
FV 100000 100000
Coupon / Dividend / Do 6% semiannually 2% quarterly $3 $3 $30 $30
N 12 years 4 years
Yield 10% 9% 12% 12% 14% 14%
g1
g2
5% 5% 7% 7%
3% 3% 5% 5% g1 = 1,2,3 years g2 = infinity
Analyze the Bonds and Shares and valuate the current market Prices today. In Shares consider g2 (growth rate of 2nd stage) a) % to infinity and b) without growing Assume you bought the bonds and shares at the current market Prices calculated, and 3 years later an important Investment Bank offers different Prices (P3 column) which of them would you accept, Why?
FV = PV = CR = N=
Bond N° 1 (1st Part) 100000 ? 6.00% 24
COUPON = Kb =
6000 5.00%
PV =
-113,798.64
Bond N° 1 (2nd Part) 97500 -113,798.64 6.00% 6
Semi Periods
FV = PV = CR = N=
Semi
COUPON = YTC =
No, because YTC (3,06%) is lower than Kb (5,00%)
6000 3.06%
FV = PV = CR = N=
Bond N° 2 (1st Part) 100000 ? 2.00% 16
COUPON = Kb =
2000 2.25%
PV =
-96,671.84
Bond N° 2 (2nd Part) 99000 -96,671.84 2.00% 12
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
2000 2.25%
Dividends 3.15 3.31 3.47 3.58 39.75
PV 2.81 2.64 2.47 28.29
Total
36.21
3.31
33.47
No, because YTC (2,25%) is equal than Kb (2,25%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 3(1+0,05)^1 D1 = 3,15
Share N° 1 (Infinity) 3 5% 3% 12% D2 = Do(1+g1)^2 D2 = 3(1+0,05)^2 D2 = 3,31
D4 = D3(1+g2)^1 D4 = 3,47(1+0,03)^1 D4 = 3,58
D3 = Do(1+g1)^3 D3 = 3(1+0,05)^3 D3 = 3,47
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 39,75
Po = 36,21 Valores TIR
-36.21 3.62%
3.15
No, because TIR (3,62%) is lower than Ks (12%)
Do = g1 = Ks =
Share N° 1 (No Growth) 3 5% 12%
D1 = Do(1+g1)^1 D1 = 3(1+0,05)^1 D1 = 3,15
D2 = Do(1+g1)^2 D2 = 3(1+0,05)^2 D2 = 3,31
D3 = Do(1+g1)^3 D3 = 3(1+0,05)^3 D3 = 3,47
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 28,94
Dividends 3.15 3.31 3.47 28.94
PV 2.81 2.64 2.47 20.60
Total
28.52
3.31
33.47
Po = 28,52 Valores TIR
-28.52 13.08%
3.15
Yes, because TIR (13,08%) is higher than Ks (12%)
Do = g1 = g2 = Ks =
Share N° 2 (Infinity) 30 7% 5% 14%
D1 = Do(1+g1)^1 D1 = 30(1+0,07)^1 D1 = 32,10
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 30(1+0,07)^2 D3 = 30(1+0,07)^3 D2 = 34,35 D3 = 36,75
D4 = D3(1+g2)^1 D4 = 36,75(1+0,05)^1 D4 = 38,59
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 428,77
Dividends 32.10 34.35 36.75 38.59 428.77
PV 28.16 26.43 24.81 289.40
Total
368.80
34.35
886.75
Po = 368,80 Valores TIR
-368.80 39.30%
32.10
Yes, because TIR (39,30%) is higher than Ks (14%)
Do = g1 = Ks =
Share N° 2 (No Growth) 30 7% 14%
D1 = Do(1+g1)^1 D1 = 30(1+0,07)^1 D1 = 32,10
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 30(1+0,07)^2 D3 = 30(1+0,07)^3 D2 = 34,35 D3 = 36,75
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 262,51
Dividends 32.10 34.35 36.75 262.51
PV 28.16 26.43 24.81 177.19
Total
256.58
34.35
886.75
Po = 256,58 Valores TIR
-256.58 58.51%
32.10
Yes, because TIR (58,51%) is higher than Ks (14%)
2.- There is the following financial information available: Security Telefonica - Bond Vodafone - Shares
Po 100% 10
FV 100000
Coupon / Dividend / Do 1% quarterly 4%
N 5 years
Yield 4% 6%
g1
g2
10%
5% g1 = 1,2,3 years g2 = infinity
An important client of Chase Manhattan bank wants to invest $100000, which of the options in the table could be the best alternative, why? Assume you bought the bonds and shares at the current market Prices, and 2 years later an important investment Bank offers different Prices (P2 column) which of them would you accept, why?
FV = PV = CR = N= COUPON = YTM =
Telefonica - Bond (1st Part) 100000 100000 1% 20 1000 1.00%
Telefonica - Bond (2nd Part) FV = 101500 PV = 100000 CR = 1% N= 8
Quarterly Periods
COUPON = YTC =
Quarterly
1000 1.18%
Yes, because YTC (1,18%) is higher than YTM (1%) The best alternative is Vodafone - Shares because it offers a better yield (6%) than Telefonica - Bonds (4%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 0,4(1+0,10)^1 D1 = 0,44
Vodafone - Shares 0.4 10% 5% 6% D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 0,4(1+0,10)^2 D3 = 0,4(1+0,10)^3 D2 = 0,48 D3 = 0,53
D4 = D3(1+g2)^1 D4 = 0,53(1+0,05)^1 D4 = 0,56
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 55,90
Dividends 0.44 0.48 0.53 0.56 55.90
46.94
Total
48.23
Po = 48,23 Valores TIR
-48.23 -156.21%
0.44
No, because TIR (-42,88%) is lower than Ks (6%)
15.48
PV 0.42 0.43 0.45
P3 97.5% 99% $30 $30 $850 $850 g1 = 1,2,3 years g2 = infinity
N° 1 (2nd Part)
Semi Periods
Semi
Sell / Not Sell Not Sell Not Sell Not Sell Sell Sell Sell
N° 2 (2nd Part)
Quarterly Periods
Quarterly
P2 101.50% $15 g1 = 1,2,3 years g2 = infinity
a - Bond (2nd Part)
Quarterly Periods
Quarterly
Telefonica - Bonds (4%)
Sell / Not Sell Sell Not Sell
5000 0 108110.90 PREMIUM
5000
1 4807.69
2 4622.78
5000
5000
3 4444.98
4 4274.02
5000 5 4109.64
5000 6 3951.57
Pvb= sumatoria Ct / (1+kb)*t + FVn / (1+kb)*n
FV $ 100,000.00 CR 5% Matur 10 years KB 4% PV=? Current Market Price
coupon
$ 5,000.00 Its five per cent of future value
2nd Example: Valuate an European 5 years, 4% coupon rate, 100000 euros face value French Bond, that is negotiated wit
3er Example: Valuate a Ecuadorian Global 8 years, 9% coupon rate, 100.000 dollars face value Bond, discouting it at 9% c
More examples:
1) In Bloomberg you find that a German Bond 10 years Bond, 3% coupon rate 100000 Euros, is negotiated at 98.% of its p 2) Today Global Bonds of Brazil arte negotiated in the New York Stock Exchange in the following conditions: Face Value Maturity 1000000 100000 10000000
Coupon 5 8 10
Yield 6% 8% 10%
5% 9% 12%
What are the current market prices, which Bond would yo buy, why??
ue German Bond, that is negotiated with a required rate of return of 4%
5000 7 3799.59
5000 8 3653.45
5000 9 3512.93
105000 10 70934.24
100000 5000 5000.00
t of future value
French Bond, that is negotiated with a require rate of return of 5%.
ace value Bond, discouting it at 9% coupon rate. What type of Bond is it, why?
Euros, is negotiated at 98.% of its price. What is the yield to maturity of the Bond? e following conditions:
1st exercise Valuate a 10 years bond 100,000 euros that has 1,5% coupon rate semiannually and is negotiated at 7% discounted rate after 3 years the ice recalls the bond offering a 102,5% price, would you accept it? 100000.00 euros 10 years 1.50% semiannual 7.00% YTC manual traditional
71575.19
20 periods 1500.00 coupon
1500.00 1
1500.00 2
1500.00 3
1500.00 4
1500.00 5
1500.00 6
1449.28
1400.27
1352.91
1307.16
1262.96
1220.25
Bo= addition (coupons VA=
-71,575.19 € formula
yield is 7%
after 3 years 100000.00 euros 10 years 1.50% semiannual 7.00%
14 periods 1500.00 coupon
-78,158.96 €
VA=
call date call price coupon YTC
3 102500.00 1500.00 7.99%
102500.00 offered value
2nd exercise analyse a OMC 15 years bond 100 000 dollars, that has a 2,5% quarterly coupon rate, and is negotiated at 96,5% current 2 years later an international broker offers 101,5% of its price would you 100000.00 dollars 15 years 2.50% quarterly 96.50% P ( price) VA=
60 periods 2500.00 coupon 2.62% yield to maturity
$ 96,500.00 call date call price coupon YTC
2 years 101500.00 2500.00 3.17% yield to call
8 periods
In the new york stock exchange today you can negotiate the following securities
homework
6,1 6,2 6,3 6,4 6,5
otiated at 7% discounted rate
1500.00 7
1500.00 8
1500.00 9
1500.00 10
1500.00 11
1500.00 12
1500.00 13
1500.00 14
1500.00 15
1178.99
1139.12
1100.60
1063.38
1027.42
992.67
959.11
926.67
895.34
years
6 periods
yield to call
s negotiated at 96,5% current market price,.
1500.00 16
1500.00 17
1500.00 18
1500.00 19
100000.00 1500.00 20
865.06
835.81
807.54
780.23
51010.44
Karla Trávez 8 "A" International Commerce 1,- Valuate a ECB10 years Bond. 100,000 euros, that has a 1.5% coupon rate semianually and is negotiated at 7% discounted rate. After 3 years the ECB recalls the bond offering a 102,5% price, wouldyou accept it? Why? FV = M= CR = KB = PV =
100000 10 years 2% Semianually 7%
20 periods 1500 3.5%
$ 102,500
? Call Price
1500 0
1500 1
1500 2
1500 3
1500 4
1500 5
1500 6
1500 7
1500 8
1500 9
1500 10
100000 1500 20
1500 11
1500 12
1500 1500 1500 13 14 15
1500 1500 1500 1500 16 17 18 19
1178.99 1139.12 1100.60 1063.38 1027.42
992.67
959.11 926.67 895.34
865.06 835.81 807.54 780.23 51010.44
Bo = Addition [ Coupons t / ( 1 + Kb ) ^ t ] Manually Excell
1449.28
1400.27 1352.91
1307.16
1262.96 1220.25
$ -71,575.19
B) Call Date = Call Price = Coupon = YTC =
3 years
6 periods
102.5% $ 102,500
1500 $ -71,575.19
=
[ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 102,500 / (1+KB) ^6]
7.99% Accepted because the Yield to Call is greater than the yield to maturity
2,- Analyze a GMC 15 years bond, 100,000 dollars that has 2,5% quarterly coupon rate and it is negotiated at 96,5% coupon market price. Two years later an International Broker offer 101,5% of its price, would you accept it QUARTERLY FV = M= CR = PV =
100,000.00 15 years 2.50% 96.50%
FV = 100,000 Periods = 60 periods CR = 2,500 PV = 96,500 Tasa = ? 2.62% YTM Quarterly 10.47% YTM
IN 2 YEARS PV = Call date = CR = Call price = Tasa =
96,500 2 years Periods = 8 2,500 101.5% FV = 101,500 ? 3.17% YTC Quarterly 12.68% YTC
periods
Karla Trávez 8 "A" International Commerce 3,- In the New York Stock Exchange today you can negotiate the following fix - rent securities : Bond a) Telefonica b) Bank of America c) Toyota
Face Value 100,000.00 100,000.00 100,000.00
Maturity 5 10 12
Coupon Rate 1.50% quarter 2.50% semi 1% semi
Price 101.5% 99% 100%
YTM 5.65% 5.13% 2.00%
YTC 6.14% 6.49% 2.98%
Calculate the yield to maturity according to the information at the current market price. Assume that 2 years later you can negotiate the bonds at 102% of their values, which bond would you negotiate, why? a)
TODAY
IN 2 YEARS
FV = 100,000 M = 5 years 20 periods CR = 1.50% quarterly 1500 PV = 101.50% 101500 Tasa = ? 1.41% YTM Quarterly 5.65% YTM
PV = Call date = CR = Call price =
b)
IN 2 YEARS
TODAY
Tasa =
FV = 100,000 M = 10 years 20 periods CR = 2.50% semi 2500 PV = 99.00% 99000 Tasa = ? 2.56% YTM Semianually 5.13% YTM
PV =
b)
IN 2 YEARS
TODAY
FV = 100,000 M = 12 years 24 periods CR = 1.00% semi 1000 PV = 100.00% 100000 Tasa = ? 1.00% YTM Semianually 2.00% YTM
101,500 2 years 1,500 102.0%
?
PV =
102.0%
?
Periods =
periods
4
periods
FV = 102,000
3.25% YTC Semianually 6.49% YTC
100,000 2 years
CR =
Tasa =
4
FV = 102,000
2,500
Call date = Call price =
periods
1.54% YTC Quarterly 6.14% YTC
2 years
CR =
Tasa =
8
99,000
Call date = Call price =
Periods =
Periods =
1,000 102.0%
?
FV = 102,000
1.49% YTC Semianually 2.98% YTC
Karla Trávez 8 "A" International Commerce BOOK'S EXERCISES 6.1.- Compton Computer bonds pay $80 annual interest , mature in 10 years, and pay $1,000 at maturity. What will their value be if the market rate of interest is 1) 6 percent, or 2) 10 percent, and interests is paid a) annually, b) semiannually? CR = M= FV = KB = PV =
80 10 years 1000 6% annually ? 0
PV = CR = M= FV = KB = PV =
80 2 71.20
80 3 67.17
80 4 63.37
80 80 5 6 59.78 56.40
80 7 53.20
80 10 years 1000 6% semiannually ? 80 0 1 75.47
20 periods
80 2 71.20
80 3 67.17
80 4 63.37
80 80 5 6 59.78 56.40
80 7 53.20
80 80 80 8 9 10 50.19 47.35 44.67
80 80 11 12 42.14 39.76
-$1,229.40 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^20]
80 10 years 1000 10% annually ? 0
PV =
1000 80 80 80 8 9 10 50.19 47.35 603.07
-$1,147.20 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^10]
PV = CR = M= FV = KB = PV =
80 1 75.47
80 1 72.73
80 2 66.12
80 3 60.11
80 4 54.64
80 80 5 6 49.67 45.16
80 7 41.05
1000 80 80 80 8 9 10 37.32 33.93 416.39
-$877.11 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^10]
80 80 80 13 14 15 37.51 35.38 33.38
1000 80 80 80 80 80 16 17 18 19 20 31.49 29.71 28.03 26.44 336.75
Karla Trávez 8 "A" International Commerce CR = M= FV = KB = PV =
80 10 years 1000 10% semiannually ? 80 0 1 72.73 PV =
20 periods
80 2 66.12
80 3 60.11
80 4 54.64
80 80 5 6 49.67 45.16
80 7 41.05
80 80 80 8 9 10 37.32 33.93 30.84
80 80 11 12 28.04 25.49
80 80 80 13 14 15 23.17 21.07 19.15
-$829.73 [ Coupon 1 / ( 1+KB ) ^ 1 ] + [ Coupon 2 / ( 1+KB ) ^ 1 ] +,,,,,,, [ 1080 / (1+KB) ^20]
6.3.- Greenman Engineering has some 15-years $1,000 par bonds outstanding, when have coupon interest rate of 9 percent and pay interest annually. What is the yield to maturity on the bonds if thier current market price is: a. $1,181.72 b. $795.99 c. Would you be wiling to pay $795.99 if you minimum required rate of return was 11 percent? Why or why not? A) PV = 1181.72 CR = 9% M= 15 years FV = 1000 YTM = ? YTM =
90.00
B) PV = 795.99 CR = 9% M= 15 years FV = 1000 YTM = ?
7.00%
90.00
YTM = 11.99%
6.4.- A $1,000 par value bond has a 12 percent coupon rate, pays interests annually, and has 15 years ramaining until it matures. a. If Bo = $1,151.72, what is its yield to maturity (YTM)? b. If the bond can be called in 6 years at $1,030, what is the bond's yield to call (YTC)? A) FV = 1000 CR = 12% M= 15 years PV = 1151.72 YTM = ? YTM =
10.00%
120
Call Price = CR = Call time= PV = YTM = ? YTM =
1030 120 6
years ###
9.01%
1000 80 80 80 80 80 16 17 18 19 20 17.41 15.83 14.39 13.08 160.54
Karla Trávez 8 "A" International Commerce 6.6.- Kamath Brithers has a $1,000 par, 9 percent coupon rate bond oustanding. The has 14 years to maturity. a. If the current market value of the bond is $1,200, and interest is paid annually, what is the bond's yield to maturity? b. What if everthing is as in (a), but interest is paid semiannually? a) ANNUALLY FV = 1000 CR = 9% M= 14 years PV = 1200 YTM = ? YTM =
6.75%
b) SEMIANNUALLY FV = 1000 CR = 9% M= 14 years PV = 1200 YTM = ?
90
YTM =
7.30%
90 28 periods
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
Karla Trávez 8 "A" International Commerce
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 1
PROBLEMS: 1) Valuate a British 10 years, 100000 Z with a 2% semiannually coupon rate that is negotiated at 6% discounted rate. Assume 2 years later The British Central Bank recalls the bond at its Face Value. What is the YTC? Would you accept the offering? 1ST PART
N= FV = CR = K= Coupon = Coupon =
DATA 10 100000 2% 6%
years Z semiannually annually
2000 1
t=0
2000 2
2000 3 N= CR= K=
CR * FV 2000 Bond =
(85,122.53)
2000 … 20 periods 2% semiannually 3% semiannually
(Discounted Bond)
2ND PART DATA N= 2 CR = 2% PV = Bo = 85122.53 FV = 100000 Coupon = Coupon =
years semiannually Z Z
2000 1
t=0
2000 2
2000 3 N= CR= YTC =
CR * FV 2000 YTC = YTC =
6.33% 12.65%
semiannually annually
100000 FV 2000 Coupon 4 Periods 4 periods 2% semiannually ?
100000 FV 2000 Coupon 20 Periods
R//. Yes, because YTC represents a better percentage (6,33% semiannually) than K (3% semiannually) 2) The Bobl German 5 years bond is negotiated today at 98,5% of its value. If the bond is 100000 euros and 1% quarterly coupon rate, How much is the YTM? After 3 years The European Central Bank recalls bonds at 102.5%. Would you accept it? Why? 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 1% 98500 100000
years quarterly 98.5%
1000 1
t=0
1000 2
1000 3 N= CR= YTM =
CR * FV 1000 YTM = YTM = YTM =
1.08% 2.17% 4.34%
1000 …
100000 FV 1000 Coupon 20 Quarters
20 quarters 1% quarterly ?
quarterly semiannually annually
2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1% 98500 102500
years quarterly 98.5% 102.5%
1000 1
t=0
1000 2
1000 3 N= CR= YTC =
CR * FV 1000 YTC = YTC = YTC =
1.33% 2.66% 5.32%
quarterly semiannually annually
R//. Yes, because YTC represents a better percentage (1,33% quarterly) than YTM (1,08% quarterly)
1000 … 12 quarters 1% quarterly ?
102500 FV 1000 Coupon 12 Quarters
3) The following fix-rent financial information is taken from Bloomberg: Bond Brazil Mexico Canada USA
FV 10000000 1000000 100000 100000
YTM = YTC =
? ?
Maturity 10 years 5 years 12 years 10 years
3.50% 1.50% 5% 2.50%
CR semiannually quarterly annually semiannually
Price 101.50% 97.50% 98% 100%
Assume After 4 years 102.50% After 3 years 99.50% After 5 years 101% After 5 years 103%
BRAZILIAN BOND - 1ST PART
N= CR = PV = FV =
DATA 10 3.50% 10150000 10000000
Coupon = Coupon =
CR * FV 350000
years semiannually 101.5%
t=0
350000 1
350000 2
350000 3 N= CR= YTM =
YTM = YTM =
3.40% 6.79%
350000 …
10000000 FV 350000 Coupon 20 Periods
20 periods 3,5% semiannually ?
semiannually annually
BRAZILIAN BOND - 2ND PART
N= CR = PV = FV =
DATA 4 3.50% 10150000 10250000
Coupon = Coupon =
CR * FV 350000
years semiannually 101.5% 102.5%
t=0
350000 1
350000 2
350000 3 N= CR= YTC =
350000 … 8 periods 3,5% semiannually ?
10250000 FV 350000 Coupon 8 Periods
YTC = YTC =
3.56% 7.11%
semiannually annually
MEXICAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 1.50% 975000 1000000
years quarterly 97.5%
15000 1
t=0
15000 2
15000 3 N= CR= YTM =
CR * FV 15000 YTM = YTM = YTM =
1.65% 3.30% 6.59%
15000 …
1000000 FV 15000 Coupon 20 Quarters
20 quarters 1,5% quarterly ?
quarterly semiannually annually
MEXICAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1.50% 975000 995000
years quarterly 97.5% 99.5%
15000 1
t=0
15000 2
15000 3 N= CR= YTC =
CR * FV 15000 YTC = YTC = YTC =
1.69% 3.39% 6.78%
quarterly semiannually annually
15000 … 12 quarters 1,5% quarterly ?
995000 FV 15000 Coupon 12 Quarters
CANADIAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 12 5.00% 98000 100000
years annually 98%
5000 1
t=0
5000 2
5000 3 N= CR= YTM =
CR * FV 5000 YTM =
5.23%
5000 …
100000 FV 5000 Coupon 12 Years
12 years 5% annually ?
annually
CANADIAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 5.00% 98000 101000
years annually 98% 101%
5000 1
t=0
5000 2
5000 3 N= CR= YTC =
CR * FV 5000 YTC =
5.65%
annually
5000 4 5 years 5% annually ?
101000 FV 5000 Coupon 5 Years
AMERICAN BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 2.50% 100000 100000
years semiannually 100%
2500 1
t=0
2500 2
2500 3 N= CR= YTM =
CR * FV 2500 YTM = YTM =
2.50% 5.00%
2500 …
100000 FV 2500 Coupon 20 Periods
20 periods 2,5% semiannually ?
semiannually annually
AMERICAN BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 2.50% 100000 103000
years semiannually 100% 103%
2500 1
t=0
2500 2
2500 3 N= CR= YTC =
CR * FV 2500 YTC = YTC =
2.76% 5.53%
semiannually annually
2500 … 10 periods 2,5% semiannually ?
103000 FV 2500 Coupon 10 Periods
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 2
MORE PROBLEMS: 1) In the New York Stock Exchange you can buy a 5 years FEDBOND, 100000 Dollars, 2.5% semiannually coupon rate at 98.5% current market price. If you could renegotiate them 2 years later at its Face Value. Would you accept it? Why? 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 5 2.50% 98500 100000
years semiannually 98.5%
2500 1
t=0
2500 2
2500 3 N= CR= YTM =
CR * FV 2500 YTM = YTM =
2.67% 5.35%
2500 … 10 periods 2,5% semiannually ?
semiannually annually
2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 2.50% 98500 100000
years semiannually 98.5% 100%
2500 1
t=0
2500 2
2500 3 N= CR= YTC =
CR * FV 2500 YTC = YTC =
2.90% 5.81%
semiannually annually
100000 FV 2500 Coupon 4 Periods 4 periods 2,5% semiannually ?
100000 FV 2500 Coupon 10 Periods
R//. Yes, because YTC represents a better percentage (2,90% semiannually) than YTM (2,67% semiannually) 2) The Bond of America has the following portfolio: Bond GMC ADIDAS Petrobras Mitsubishi
FV 1000000 100000 10000000 1000000
Maturity 10 years 5 years 3 years 12 years
4% 1.5% 0.5% 1.5%
CR semiannually quarterly monthly semiannually
Price 97.50% 95.81% 102.78% 101%
YTM 8.37% 7% 5% 2.90%
YTC 10.34% 9.24% 5.48% 3.45%
Analyze the current market prices given and the YTM and the YTC, consider a renegotiation of all bonds 2 years later when FED and ECB have decided to decrease interest rate policies to 2.5% and the new Bond Price reference is 102% of its value . Would you accept it to renegotiate it. Why??? GMC BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 4% 975000 1000000
years semiannually 97.50%
40000 1
t=0
40000 2
40000 3 N= CR= YTM =
CR * FV 40000 YTM = YTM =
4.19% 8.37%
40000 … 20 periods 4% semiannually ?
semiannually annually
GMC BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 4% 975000 1020000
years semiannually 97.50% 102%
40000 1
t=0
40000 2
40000 3 N= CR= YTC =
CR * FV 40000 YTC = YTC =
5.17% 10.34%
semiannually annually
1020000 FV 40000 Coupon 4 Periods 4 periods 4% semiannually ?
1000000 FV 40000 Coupon 20 Periods
R//. Yes, because YTC (10,34% annually) is more than YTM (8,37% annually) ADIDAS BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 5 1.50% 7% ? 100000
years quarterly annually
1500 1
t=0
1500 2
1500 3 N= CR= YTM =
CR * FV 1500 Price =
(95,811.78)
1500 …
100000 FV 1500 Coupon 20 Quarters
20 quarters 1,5% quarterly 1,75% quarterly
(Discounted Bond)
ADIDAS BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 1.50% 95811.78 102000
years quarterly 95.81% 102%
1500 1
t=0
1500 2
1500 3 N= CR= YTC =
CR * FV 1500 YTC = YTC = YTC =
2.31% 4.62% 9.24%
quarterly semiannually annually
R//. Yes, because YTC (9,24% annually) is more than YTM (7,00% annually)
1500 … 8 quarters 1,5% quarterly ?
102000 FV 1500 Coupon 8 Quarters
PETROBRAS BOND - 1ST PART
N= CR = YTM = PV = FV =
DATA 3 0.50% 5% ? 10000000
Coupon = Coupon =
CR * FV 50000
years monthly annually
50000 1
t=0
50000 2
50000 3 N= CR= YTM =
Price =
(10,278,047.51)
50000 …
10000000 FV 50000 Coupon 36 Months
36 months 0,5% monthly 0,42% monthly
(Premium Bond)
PETROBRAS BOND - 2ND PART
N= CR = PV = FV =
DATA 2 0.50% 10278047.51 10200000
Coupon = Coupon =
CR * FV 50000
years monthly 102.78% 102%
50000 1
t=0
50000 2
50000 3 N= CR= YTC =
YTC = YTC = YTC = YTC =
0.46% 1.37% 2.74% 5.48%
monthly quarterly semiannually annually
R//. Yes, because YTC (5,48% annually) is more than YTM (5,00% annually)
50000 … 24 months 0,5% monthly ?
10200000 FV 50000 Coupon 24 Months
MITSUBISHI BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 12 1.50% 1010000 1000000
years semiannually 101%
15000 1
t=0
15000 2
15000 3 N= CR= YTM =
CR * FV 15000 YTM = YTM =
1.45% 2.90%
15000 … 24 periods 1,5% semiannually ?
semiannually annually
MITSUBISHI BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 2 1.50% 1010000 1020000
years semiannually 101% 102%
15000 1
t=0
15000 2
15000 3 N= CR= YTC =
CR * FV 15000 YTC = YTC =
1.73% 3.45%
semiannually annually
R//. Yes, because YTC (3,45% annually) is more than YTM (2,90% annually)
1020000 FV 15000 Coupon 4 Periods 4 periods 1,5% semiannually ?
1000000 FV 15000 Coupon 24 Periods
3) Valuate the following Bonds according to the information: Bond Gol Telefonica England Mitsubishi
FV 100000 1000000 10000000 1000000
Maturity 8 years 10 years 12 years 5 years
4% 1% 2% 0.50%
CR semiannually quarterly semiannually quarterly
Price 94.38% 100.50% 99.50% 102.40%
YTM 9% 3.94% 4.05% 1.50%
YTC 10.22% 3.82% 4.18% 1.18%
Analyze the current market prices given and the YTM and the YTC, consider a renegotiation of all bonds 3 years later when FED and ECB have decided to decrease interest rate policies to 6% and the new Bond Price reference is its face value . Would you accept it to renegotiate it. Why??? GOL BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 8 4% 9% ? 100000
years semiannually annually
t=0
4000 1
4000 2
4000 3 N= CR= YTM =
CR * FV 4000 Price =
(94,382.99)
4000 …
100000 FV 4000 Coupon 16 Periods
16 periods 4% semiannually 4,5% semiannually
(Discounted Bond)
GOL BOND - 2ND PART
N= CR = PV = FV =
DATA 3 4% 94382.99 100000
years semiannually 94.38% 100%
t=0
4000 1
4000 2
4000 3 N=
4000 … 6 periods
100000 FV 4000 Coupon 6 Periods
Coupon = Coupon =
CR * FV 4000
CR= YTC = YTC = YTC =
5.11% 10.22%
4% semiannually ?
semiannually annually
R//. Yes, because YTC (10,22% annually) is more than YTM (9,00% annually) TELEFONICA BOND - 1ST PART
N= CR = PV = FV = Coupon = Coupon =
DATA 10 1% 1005000 1000000
years quarterly 100.50%
10000 1
t=0
10000 2
10000 3 N= CR= YTM =
CR * FV 10000 YTM = YTM = YTM =
0.98% 1.97% 3.94%
10000 …
1000000 FV 10000 Coupon 40 Quarters
40 quarters 1% quarterly ?
quarterly semiannually annually
TELEFONICA BOND - 2ND PART
N= CR = PV = FV = Coupon = Coupon =
DATA 3 1% 1005000 1000000
years quarterly 100.50% 100%
10000 1
t=0
10000 2
10000 3 N= CR= YTC =
CR * FV 10000 YTC = YTC = YTC =
0.96% 1.91% 3.82%
quarterly semiannually annually
R//. No, because YTC (3,82% annually) is less than YTM (3,94% annually)
10000 … 12 quarters 1% quarterly ?
1000000 FV 10000 Coupon 12 Quarters
ENGLAND BOND - 1ST PART
N= CR = PV = FV =
DATA 12 2% 9950000 10000000
Coupon = Coupon =
CR * FV 200000
years semiannually 99.50%
t=0
200000 1
200000 2
200000 3 N= CR= YTM =
YTM = YTM =
2.03% 4.05%
200000 …
10000000 FV 200000 Coupon 24 Periods
24 periods 2% semiannually ?
semiannually annually
ENGLAND BOND - 2ND PART
N= CR = PV = FV =
DATA 3 2% 9950000 10000000
Coupon = Coupon =
CR * FV 200000
years semiannually 99.50% 100%
t=0
200000 1
200000 2
200000 3 N= CR= YTC =
YTC = YTC =
2.09% 4.18%
semiannually annually
R//. Yes, because YTC (4,18% annually) is more than YTM (4,05% annually)
200000 … 6 periods 2% semiannually ?
10000000 FV 200000 Coupon 6 Periods
MITSUBISHI BOND - 1ST PART
N= CR = YTM = PV = FV = Coupon = Coupon =
DATA 5 0.50% 1.50% ? 1000000
years quarterly annually
5000 1
t=0
5000 2
5000 3 N= CR= YTM =
CR * FV 5000 Price =
(1,024,042.12)
5000 …
1000000 FV 5000 Coupon 20 Quarters
20 quarters 0,5% quarterly 0,375% quarterly
(Premium Bond)
MITSUBISHI BOND - 2ND PART
N= CR = PV = FV =
DATA 3 0.50% 1024042.12 1000000
Coupon = Coupon =
CR * FV 5000
years quarterly 102.40% 100%
5000 1
t=0
5000 2
5000 3 N= CR= YTC =
YTC = YTC = YTC =
0.30% 0.59% 1.18%
quarterly semiannually annually
R//. No, because YTC (1,18% annually) is less than YTM (1,50% annually)
5000 … 12 quarters 0,5% quarterly ?
1000000 FV 5000 Coupon 12 Quarters
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT TASK N° 3
6.3.- Cavalier industries has a current (Do) cash dividen of $2 per share. You estimate that cash dividends will grow at 12% per year for each of 3 years (t1,t2,t3), and then a 6% oer year for each of 2 more years (t4 and t5). After t5 you expect them to grow at 2% per year to infinity. a.- What is the current market value of Cavalier Industries common stock if the required rate of return is 14%? b.- What is the market price if evereything is the same as in a) except that after year 5 there is no expected growth in cash dividends
Do = g1 = g2 = g3 = Ks =
Data (Section A) 2 12% 6% 2% 14%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
12% 6% 2%
D1 = Do(1+g1)^1 D1 = 2(1+0,12)^1 D1 = 2,24
D2 = Do(1+g1)^2 D2 = 2(1+0,12)^2 D2 = 2,51
D3 = Do(1+g1)^3 D3 = 2(1+0,12)^3 D3 = 2,81
D4 = D3(1+g2)^1 D4 = 2,81(1+0,06)^1 D4 = 2,98
D5 = D3(1+g2)^2 D5 = 2,81(1+0,06)^2 D5 = 3,16
D6 = D5(1+g3)^1 D6 = 3,16(1+0,02)^1 D6 = 3,22
d1 d2 d3 d4 d5 d6 P5 Po
2.24 2.51 2.81 2.98 3.16 3.22 26.84 23.13
P5 = D6 / (Ks-g3) P5 = 3,22 / (0,14-0,02) P5 = 26,84 Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,24/(1,14)^1 + 2,51/(1,14)^2 + 2,81/(1,14)^3 + 2,98/(1,14)^4 + 3,16/(1,14)^5 + 26,84/(1,14)^5 Po = 1,96 + 1,93 + 1,90 + 1,76 + 1,64 + 13,94 R//. Po = $23,13
Do = g1 = g2 = Ks =
Data (Section B) 2 12% 6% 14%
P5 Po=? t=0
d1=2,24 1
d2=2,51 2
d3=2,81 3
d4=2,98 4
d5=3,16 5
12% P5 = D1 / Ks P5 = d5 / Ks P5 = 3,16 / 0,14 P5 = 22,55
6% P5 Po
22.55 20.90
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,24/(1,14)^1 + 2,51/(1,14)^2 + 2,81/(1,14)^3 + 2,98/(1,14)^4 + 3,16/(1,14)^5 + 22,55/(1,14)^5 Po = 1,96 + 1,93 + 1,90 + 1,76 + 1,64 + 11,71 R//. Po = $20,9
No-Growth
6.7.- You are interested in buying 100 shares of a &60 par value preferred stock that has an 8,5% dividend rate a.- If you required return is 11%, how much would you willing to pay to acquire its 100 shares? b.- What if no dividend will be paid until t = 3? At the same required return, how much would you now be willing to pay?
Po = dr = Ks = D1 =
Data (Section A) 60 8.50% 11% ?
D4 = Ks =
Data (Section B) 5.10 11% P3 = D4 / Ks P3 = 5,10 / 11% P3 = 46,36
D1 = Po * dr D1 = 60 * 8,5% D1 = 5,10
Po = D1 / Ks Po = 5,10 / 11% Po = 46,36 Po = $4636,36
D1 Po x 100 shares
Po=? t=0 Po = P3 / (1+Ks)^3 Po = 46,36 / (1+0,11)^3 Po = 33,90 Po = 3390,07
d1 = 0 1
d2 = 0 2 P3 Po
x 100 shares
5.10 4636.36
P3 = 46,36 d3 = 0 d4=5,10 3 Infinity 46.36 3390.07
6.9.- A stock currently pays cash dividends of $4 oer share (Do = $4), and the required rate of return is 12%. What is its market value in the following cases? a.- There is o future growth in dividends. b.- Dividends grow at 8% per year to infinity. c.- Dividends grow at 5% for each of 2 years; and there is no growth expected after D2. d.- Growth will be 10% for each of 2 years (n = 2) after which growth will be 5% per year until infinity. e.- Recalculate d) where growth is now 7% for 5 years ( n = 5 ), after which growth will be 3% per year until infinity. f.- Finally, now suppose the required rate of return is 15% and Do = $2.50. Recalculate a), b), d) and e) with these new values.
Do = Ks =
Data (Section A) 4 12%
Do = g1 = Ks =
Data (Section B) 4 8% 12%
Do = g1 = Ks =
Data (Section C) 4 5% 12% D1 = Do(1+g1)^1 D1 = 4(1+0,05)^1 D1 = 4,20
Po = D1 / Ks Po = 4 / 0,12 Po = $33,33
Po
33.33
Po = D1 / (Ks-g) Po = 4 / (0,12-0,08) Po = $100
Po
100
d1 1
d2 2
d1 d2 P2 Po
4.20 4.41 36.75 36.57
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 4(1+0,05)^2 D2 = 4,41
P2 = D1 / Ks P2 = d2 / Ks P2 = 4,41 / 0,12 P2 = 36,75
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,20/(1,12)^1 + 4,41/(1,12)^2 + 36,75/(1,12)^2 Po = 3,75 + 3,52 + 29,30 R//. Po = $36,57
No-Growth
Do = g1 = g2 = Ks =
Data (Section D) 4 10% 5% 12% D1 = Do(1+g1)^1 D1 = 4(1+0,10)^1 D1 = 4,40
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 4(1+0,10)^2 D2 = 4,84
D3 = D2(1+g2)^1 D3 = 4,84(1+0,05)^1 D3 = 5,08
P2 = D3 / (Ks-g2) P2 = 5,08 / (0,12-0,05) P2 = $72,60
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,40/(1,12)^1 + 4,84/(1,12)^2 + 72,60/(1,12)^2 Po = 3,93 + 3,86 + 57,88 R//. Po = $65,67
d1 1
d2 2
d1 d2 d3 P2 Po
4.40 4.84 5.08 72.60 65.67
d3
Do = g1 = g2 = Ks =
Data (Section E) 4 7% 3% 12%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
7% 3% D1 = Do(1+g1)^1 D1 = 4(1+0,07)^1 D1 = 4,28
D2 = Do(1+g1)^2 D2 = 4(1+0,07)^2 D2 = 4,58
D3 = Do(1+g1)^3 D1 = 4(1+0,07)^3 D3 = 4,90
D4 = Do(1+g1)^4 D4 = 4(1+0,07)^4 D4 = 5,24
D5 = Do(1+g1)^5 D5 = 4(1+0,07)^5 D5 = 5,61
D6 = D5(1+g2)^1 D6 = 5,61(1+0,03)^1 D6 = 5,78
d1 d2 d3 d4 d5 d6 P5 Po
4.28 4.58 4.90 5.24 5.61 5.78 64.21 53.90
P5 = D6 / (Ks-g2) P5 = 5,78 / (0,12-0,03) P5 = $64,21
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 4,28/(1,12)^1 + 4,58/(1,12)^2 + 4,90/(1,12)^3 + 5,24/(1,12)^4 + 5,61/(1,12)^5 + 64,21/(1,12)^5 Po = 3,82 + 3,65 + 3,49 + 3,33 + 3,18 + 36,43 R//. Po = $53,90
Do = Ks =
Data (Section F) 2.50 15%
Po = D1 / Ks Po = 2,50 / 0,15 Po = $16,67
Po
16.67
Do = g1 = Ks =
Data (Section F) 2.50 8% 15%
Do = g1 = g2 = Ks =
Data (Section F) 2.50 10% 5% 15% D1 = Do(1+g1)^1 D1 = 2,50(1+0,10)^1 D1 = 2,75
Po = D1 / (Ks-g) Po = 2,50 / (0,15-0,08) Po = $36
Po
36
d1 1
d2 2
d1 d2 d3 P2 Po
2.75 3.03 3.18 31.76 28.70
P2 Po=? t=0
D2 = Do(1+g1)^2 D2 = 2,50(1+0,10)^2 D2 = 3,03
D3 = D2(1+g2)^1 D3 = 3,03(1+0,05)^1 D3 = 3,18
P2 = D3 / (Ks-g2) P2 = 5,08 / (0,15-0,05) P2 = $31,76
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,75/(1,15)^1 + 3,03/(1,15)^2 + 31,76/(1,15)^2 Po = 2,39 + 2,29 + 24,02 R//. Po = $28,70
d3
Do = g1 = g2 = Ks =
Data (Section F) 2.50 7% 3% 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
7% 3% D1 = Do(1+g1)^1 D1 = 2,50(1+0,07)^1 D1 = 2,68
D2 = Do(1+g1)^2 D2 = 2,50(1+0,07)^2 D2 = 2,86
D3 = Do(1+g1)^3 D3 = 2,50(1+0,07)^3 D3 = 3,06
D4 = Do(1+g1)^4 D4 = 2,50(1+0,07)^4 D4 = 3,28
D5 = Do(1+g1)^5 D5 = 2,50(1+0,07)^5 D5 = 3,51
D6 = D5(1+g2)^1 D6 = 3,51(1+0,03)^1 D6 = 3,61
d1 d2 d3 d4 d5 d6 P5 Po
2.68 2.86 3.06 3.28 3.51 3.61 30.10 25.10
P5 = D6 / (Ks-g2) P5 = 3,61 / (0,15-0,03) P5 = $30,10
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) Po = 2,68/(1,15)^1 + 2,86/(1,15)^2 + 3,06/(1,15)^3 + 3,28/(1,15)^4 + 3,51/(1,15)^5 + 30,10/(1,15)^5 Po = 2,33 + 2,16 + 2,01 + 1,88 + 1,75 + 14,97 R//. Po = $25,10
BRUNO RAMOS BARCO
8B BANKING MANAGEMENT - TASK N°4
Share Google Microsoft Petrobras Exxon Mobil Budweiser
MKT Price 250 100 50 1000 10
Current Dividend 40 20 15 150 2
Years 1,2,3 Growth 1 20% 10% 25% 12% 10%
Years 4,5 Growth 2 25% 8% 20% 8% 15%
6 to infinity Growth 3 10% infinity 5% infinity 10% infinity 6% infinity 20% infinity
Ks 30% 15% 20% 10% 15%
1.- According to the information valuate all the shares with the 3 different stages, include current market prices with infinity valuations and with no growth. 2.- Two years later J.P.Morgan Investment Bank of New York wants to buy the Portfolio with the following prices: Share Google Microsoft Petrobras Exxon Mobil Budweiser
MKT Price 450 200 150 1450 18
Data (Google - Infinity) Do = 40 g1 = 20% g2 = 25% g3 = 10% Ks = 30%
Would you recommend to accept the offering, why?
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
Dividends 48.00 57.60 69.12 86.40 108.00 118.80 594.00
PV 36.92 34.08 31.46 30.25 29.09 159.98
Po
321.79
d5 5
d6
20% 25%
D1 = Do(1+g1)^1 D1 = 40(1+0,20)^1 D1 = 48
D2 = Do(1+g1)^2 D2 = 40(1+0,20)^2 D2 = 57.60
D3 = Do(1+g1)^3 D3 = 40(1+0,20)^3 D3 = 69.12
D4 = D3(1+g2)^1 D4 = 69.12(1+0,25)^1 D4 = 86.40
D5 = D3(1+g2)^2 D5 = 69.12(1+0,25)^2 D5 = 108
D6 = D5(1+g3)^1 D6 = 108(1+0,10)^1 D6 = 118.80
P5 = D6/(Ks-g3) P5 = 594
Years d1 d2 d3 d4 d5 d6 P5
10%
Data (Google - No Growth) Do = 40 g1 = 20% g2 = 25% Ks = 30%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
Dividends 48.00 57.60 69.12 86.40 108.00 360.00
PV 36.92 34.08 31.46 30.25 29.09 96.96
Po
258.76
d5 5
20% 25% D1 = Do(1+g1)^1 D1 = 40(1+0,20)^1 D1 = 48
D2 = Do(1+g1)^2 D2 = 40(1+0,20)^2 D2 = 57.60
D3 = Do(1+g1)^3 D3 = 40(1+0,20)^3 D3 = 69.12
D4 = D3(1+g2)^1 D4 = 69.12(1+0,25)^1 D4 = 86.40
D5 = D3(1+g2)^2 D5 = 69.12(1+0,25)^2 D5 = 108
P5 = d5 / Ks P5 = 108 / 0,30 P5 = 360
New Data (Google - No Growth) N= 2 D1 = 48.00 D2 = 57.60 P2 = 450 Po = 258.76
Years d1 d2 d3 d4 d5 P5
P2 Po=258,76 t=0
Valores TIR
-258.76 49.64%
d1 1
d2 2
48.00 507.60 Yes, because TIR (49,64%) is more than K (30%)
No-Growth
Data (Microsoft - Infinity) Do = 20 g1 = 10% g2 = 8% g3 = 5% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
10% 8% 5%
D1 = Do(1+g1)^1 D1 = 20(1+0,10)^1 D1 = 22
D2 = Do(1+g1)^2 D2 = 20(1+0,10)^2 D2 = 24,20
D3 = Do(1+g1)^3 D3 = 20(1+0,10)^3 D3 = 26,62
D4 = D3(1+g2)^1 D4 = 26,62(1+0,08)^1 D4 = 28,75
D5 = D3(1+g2)^2 D5 = 26,62(1+0,08)^2 D5 = 31,05
D6 = D5(1+g3)^1 D6 = 31,05(1+0,05)^1 D6 = 32,60
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 32,60 / (0,15-0,05) P5 = 326,02
Dividends 22.00 24.20 26.62 28.75 31.05 32.60 326.02
162.09
Total
248.90
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $248,90
New Data (Microsoft - Infinity) N= 2 D1 = 22.00 D2 = 24.20 P2 = 200 Po = 248.90
P2 Po=248,90 t=0
Valores TIR
-248.90 -0.57%
d1 1
d2 2
22.00 224.20 No, because TIR (-0,57%) is less than K (15%)
PV 19.13 18.30 17.50 16.44 15.44
Data (Microsoft - No Growth) Do = 20 g1 = 10% g2 = 8% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
10% 8% D1 = Do(1+g1)^1 D1 = 20(1+0,10)^1 D1 = 22
D2 = Do(1+g1)^2 D2 = 20(1+0,10)^2 D2 = 24,20
D3 = Do(1+g1)^3 D3 = 20(1+0,10)^3 D3 = 26,62
D4 = D3(1+g2)^1 D4 = 26,62(1+0,08)^1 D4 = 28,75
D5 = D3(1+g2)^2 D5 = 26,62(1+0,08)^2 D5 = 31,05
P5 = d5 / Ks P5 = 31,05 / 0,15 P5 = 207
Years d1 d2 d3 d4 d5 P5
Dividends 22.00 24.20 26.62 28.75 31.05 207.00
PV 19.13 18.30 17.50 16.44 15.44 102.91
Total
189.72
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $189,72
New Data (Microsoft - No Growth) N= 2 D1 = 22.00 D2 = 24.20 P2 = 200 Po = 189.72
P2 Po=189,72 t=0
Valores TIR
-189.72 14.66%
d1 1
d2 2
22.00 224.20 No, because TIR (14,66%) is less than K (15%)
No-Growth
Data (Petrobras - Infinity) Do = 15 g1 = 25% g2 = 20% g3 = 10% Ks = 20%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
25% 20% 10%
D1 = Do(1+g1)^1 D1 = 15(1+0,25)^1 D1 = 18,75
D2 = Do(1+g1)^2 D2 = 15(1+0,25)^2 D2 = 23,44
D3 = Do(1+g1)^3 D3 = 15(1+0,25)^3 D3 = 29,30
D4 = D3(1+g2)^1 D4 = 29,30(1+0,20)^1 D4 = 35,16
D5 = D3(1+g2)^2 D5 = 29,30(1+0,20)^2 D5 = 42,19
D6 = D5(1+g3)^1 D6 = 42,19(1+0,10)^1 D6 = 46,41
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 46,41 / (0,20-0,10) P5 = 464,06
Dividends 18.75 23.44 29.30 35.16 42.19 46.41 464.06
PV 15.63 16.28 16.95 16.95 16.95 186.50
Total
269.26
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $269,26
New Data (Petrobras - Infinity) N= 2 D1 = 18.75 D2 = 23.44 P2 = 150 Po = 269.26
P2 Po=269,26 t=0
Valores TIR
-269.26 -16.19%
d1 1
d2 2
18.75 173.44 No, because TIR (-16,19%) is less than K (20%)
Data (Petrobras - No Growth) Do = 15 g1 = 25% g2 = 20% Ks = 20%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
25% 20% D1 = Do(1+g1)^1 D1 = 15(1+0,25)^1 D1 = 18,75
D2 = Do(1+g1)^2 D2 = 15(1+0,25)^2 D2 = 23,44
D3 = Do(1+g1)^3 D3 = 15(1+0,25)^3 D3 = 29,30
D4 = D3(1+g2)^1 D4 = 29,30(1+0,20)^1 D4 = 35,16
D5 = D3(1+g2)^2 D5 = 29,30(1+0,20)^2 D5 = 42,19
P5 = d5 / Ks P5 = 42,19 / 0,20 P5 = 210,94
Years d1 d2 d3 d4 d5 P5
Dividends 18.75 23.44 29.30 35.16 42.19 210.94
PV 15.63 16.28 16.95 16.95 16.95 84.77
Total
167.53
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $167,53
New Data (Petrobras - No Growth) N= 2 D1 = 18.75 D2 = 23.44 P2 = 150 Po = 167.53
P2 Po=167,53 t=0
Valores TIR
-167.53 7.50%
d1 1
d2 2
18.75 173.44 No, because TIR (7,50%) is less than K (20%)
No-Growth
Data (Exxon - Infinity) Do = 150 g1 = 12% g2 = 8% g3 = 6% Ks = 10%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
12% 8% 6%
D1 = Do(1+g1)^1 D1 = 150(1+0,12)^1 D1 = 168
D2 = Do(1+g1)^2 D2 = 150(1+0,12)^2 D2 = 188,16
D3 = Do(1+g1)^3 D3 = 150(1+0,12)^3 D3 = 210,74
D4 = D3(1+g2)^1 D4 = 210,74(1+0,08)^1 D4 = 227,60
D5 = D3(1+g2)^2 D5 = 210,74(1+0,08)^2 D5 = 245,81
D6 = D5(1+g3)^1 D6 = 245,81(1+0,06)^1 D6 = 260,55
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 260,55 / (0,10-0,06) P5 = 6513,86
Dividends 168.00 188.16 210.74 227.60 245.81 260.55 6513.86
PV 152.73 155.50 158.33 155.45 152.63 4044.60
Total
4819.24
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $4819,24
New Data (Exxon - Infinity) N= 2 D1 = 168.00 D2 = 188.16 P2 = 1450 Po = 4819.24
P2 Po=4819,24 t=0
Valores TIR
-4819.24 -156.59%
d1 1
d2 2
168.00 1638.16 No, because TIR (-39,33%) is less than K (10%)
Data (Exxon - No Growth) Do = 150 g1 = 12% g2 = 8% Ks = 10%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
12% 8% D1 = Do(1+g1)^1 D1 = 150(1+0,12)^1 D1 = 168
D2 = Do(1+g1)^2 D2 = 150(1+0,12)^2 D2 = 188,16
D3 = Do(1+g1)^3 D3 = 150(1+0,12)^3 D3 = 210,74
D4 = D3(1+g2)^1 D4 = 210,74(1+0,08)^1 D4 = 227,60
D5 = D3(1+g2)^2 D5 = 210,74(1+0,08)^2 D5 = 245,81
P5 = d5 / Ks P5 = 245,81 / 0,10 P5 = 2458,06
Years d1 d2 d3 d4 d5 P5
Dividends 168.00 188.16 210.74 227.60 245.81 2458.06
PV 152.73 155.50 158.33 155.45 152.63 1526.26
Total
2300.91
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $2300,91
New Data (Exxon - No Growth) N= 2 D1 = 168.00 D2 = 188.16 P2 = 1450 Po = 2300.91
P2 Po=2300,91 t=0
Valores TIR
-2300.91 -11.89%
d1 1
d2 2
168.00 1638.16 No, because TIR (-11,89%) is less than K (10%)
No-Growth
Data (Budweiser - Infinity) Do = 2 g1 = 10% g2 = 15% g3 = 20% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
d6
10% 15% 20%
D1 = Do(1+g1)^1 D1 = 2(1+0,10)^1 D1 = 2,20
D2 = Do(1+g1)^2 D2 = 2(1+0,10)^2 D2 = 2,42
D3 = Do(1+g1)^3 D3 = 2(1+0,10)^3 D3 = 2,66
D4 = D3(1+g2)^1 D4 = 2,66(1+0,15)^1 D4 = 3,06
D5 = D3(1+g2)^2 D5 = 2,66(1+0,15)^2 D5 = 3,52
D6 = D5(1+g3)^1 D6 = 3,52(1+0,20)^1 D6 = 4,22
Years d1 d2 d3 d4 d5 d6 P5
P5 = D6 / (Ks-g3) P5 = 4,22 / (0,15-0,20) P5 = -84,49
Dividends 2.20 2.42 2.66 3.06 3.52 4.22 -84.49
PV 1.91 1.83 1.75 1.75 1.75 -42.01
Total
-33.01
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = -$33,01
New Data (Budweiser - Infinity) N= 2 D1 = 2.20 D2 = 2.42 P2 = 18 Po = -33.01
P2 Po=-33,01 t=0
Valores TIR
-33.01 -17.95%
d1 1
d2 2
2.20 20.42 No, because TIR (-17,95%) is less than K (15%)
Data (Budweiser - No Growth) Do = 2 g1 = 10% g2 = 15% Ks = 15%
P5 Po=? t=0
d1 1
d2 2
d3 3
d4 4
d5 5
10% 15% D1 = Do(1+g1)^1 D1 = 2(1+0,10)^1 D1 = 2,20
D2 = Do(1+g1)^2 D2 = 2(1+0,10)^2 D2 = 2,42
D3 = Do(1+g1)^3 D3 = 2(1+0,10)^3 D3 = 2,66
D4 = D3(1+g2)^1 D4 = 2,66(1+0,15)^1 D4 = 3,06
D5 = D3(1+g2)^2 D5 = 2,66(1+0,15)^2 D5 = 3,52
P5 = d5 / Ks P5 = 2,66 / 0,15 P5 = 2458,06
Years d1 d2 d3 d4 d5 P5
Dividends 2.20 2.42 2.66 3.06 3.52 23.47
PV 1.91 1.83 1.75 1.75 1.75 11.67
Total
20.66
Po = (€ Dt / (1+Ks)^t) + (Pn / (1+Ks)^n) R//. Po = $20,66
New Data (Budweiser - No Growth) N= 2 D1 = 2.20 D2 = 2.42 P2 = 18 Po = 20.66
P2 Po=20,66 t=0
Valores TIR
-20.66 4.88%
d1 1
d2 2
2.20 20.42 No, because TIR (4,88%) is less than K (15%)
No-Growth
Using the following financial information taken from the BVG, analyze it: Security Amazonas Bond GMac Bond Holcim Shares Bolivariano Shares
Price 92% 95% 30 10
FV 100000 100000
Coupon / Dividend 4% semiannually 1,5% quarterly 10% 5%
N 5 years 7 years
Yield ? ? 15% 12%
g1
g2
12% 15%
10% 5%
P3 95% 98% 42 18
g1 = t1, t2, t3 g2 = infinity Valuate the securities according the financial information: a) An investor wants to invest $100000, which of the options are the best for him?, why? b) Assume 3 years after the investor bought all, another bank offers different prices (P3), would you recommend to buy, why?
FV = PV = CR = N= COUPON = YTM =
Amazonas Bond (1st Part) 100000 92000 4% 10
Semi Periods
4000 5.04%
Amazonas Bond (2nd Part) FV = 95000 PV = 92000 CR = 4% Semi N= 6 Periods COUPON = YTC =
4000 4.83%
No, because YTC (4,83%) is less than YTM (5,04%)
FV = PV = CR = N= COUPON = YTM =
GMac Bond (1st Part) 100000 95000 1.50% 28 1500 1.73%
Quarter Periods
GMac Bond (2nd Part) FV = 98000 PV = 95000 CR = 1.50% Semi N= 12 Periods COUPON = YTC =
1500 1.82%
Yes, because YTC (1,82%) is more than YTM (1,73%) Holcim Shares (1st Part) Do = 3 g1 = 12% g2 = 10% Ks = 15%
P3 Po=? t=0
d1 1
d2 2
d3 3
d4
12% D1 = Do(1+g1)^1 D1 = 3(1+0,12)^1 D1 = 3,36
D2 = Do(1+g1)^2 D2 = 3(1+0,12)^2 D2 = 3,76
D4 = D3(1+g2)^1 D1 = 4,21(1+0,10)^1 D4 = 4,64
D3 = Do(1+g1)^3 D3 = 3(1+0,12)^3 D3 = 4,21
10%
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 92,73
Po = 69,51
Dividends 3.36 3.76 4.21 4.64 92.73
PV 2.92 2.85 2.77 60.97
Total Holcim Shares (2nd Part) N= 3 D1 = 3.36 D2 = 3.76 D3 = 4.21 P3 = 42.00 Po = 69.51
P3 Po=69,51 t=0
Valores TIR
-69.51 -8.97%
d1 1
d2 2
d3 3
3.36
3.76
46.21
No, because TIR (-8,97%) is less than Ks (15%)
69.51
Bolivariano Shares (1st Part) Do = 0.5 g1 = 15% g2 = 5% Ks = 12%
P3 Po=? t=0
d1 1
d2 2
d3 3
d4
15% D1 = Do(1+g1)^1 D1 = 0,5(1+0,15)^1 D1 = 0,58
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 0,5(1+0,15)^2 D3 = 0,5(1+0,15)^3 D2 = 0,66 D3 = 0,76
D4 = D3(1+g2)^1 D1 = 0,76(1+0,05)^1 D4 = 0,80
5%
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 11,41
Po = 9,70
Dividends 0.58 0.66 0.76 0.80 11.41
PV 0.51 0.53 0.54 8.12
Total Bolivariano Shares (2nd Part) N= 3 D1 = 0.58 D2 = 0.66 D3 = 0.76 P3 = 18.00 Po = 9.70
P3 Po=9,70 t=0
Valores TIR
-9.70 28.45%
d1 1
d2 2
d3 3
0.58
0.66
18.76
Yes, because TIR (28,45%) is more than Ks (12%)
9.70
1.- In The Bolsa de Valores de Guayaquil there is the following financial information available: Security Global 2015 Bond CFN - Bond Holcim Shares Holcim Shares Tekal Shares Tekal Shares
Po 93.77% 87.44% 66.50 36.13 316.76 255.14
FV 100000 10000
Coupon / Dividend / Do 4,5% semiannually 2% quarterly $3 $3 $40 $40
N 10 years 4 years
Yield 10% 12% 10% 10% 20% 20%
g1
g2
7% 7% 10% 10%
5% 5% 5% 5% g1 = 1,2,3 years g2 = infinity
Analyze the Bonds and Shares and valuate the current market Prices today. In Shares consider g2 (growth rate of 2nd stage) a) % to infinity and b) without growing Assume you bought the bonds and shares at the current market Prices calculated, and 3 years later an important Investment Bank offers different Prices (P3 column) which of them would you accept, Why?
FV = PV = CR = N=
Global 2015 Bond (1st Part) 100000 ? 4.50% 20
COUPON = Kb =
4500 5.00%
PV =
-93,768.89
Semi Periods
Global 2015 Bond (2nd Part) FV = 99500 PV = -93,768.89 CR = 4.50% N= 6 COUPON = YTC =
Semi
Yes, because YTC (5,68%) is higher than Kb (5,00%)
4500 5.68%
CFN Bond (1st Part) 10000 ? 2.00% 16
FV = PV = CR = N= COUPON = Kb =
200 3.00%
PV =
-8,743.89
CFN Bond (2nd Part) 9500 -8,743.89 2.00% 12
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
200 2.90%
Dividends 3.21 3.43 3.68 3.86 77.18
PV 2.92 2.84 2.76 57.98
Total
66.50
3.43
33.68
No, because YTC (2,90%) is lower than Kb (3,00%)
Do = g1 = g2 = Ks =
Holcim Shares (Infinity) 3 7% 5% 10%
D1 = Do(1+g1)^1 D1 = 3(1+0,07)^1 D1 = 3,21
D2 = Do(1+g1)^2 D2 = 3(1+0,07)^2 D2 = 3,43
D4 = D3(1+g2)^1 D4 = 3,68(1+0,05)^1 D4 = 3,86
D3 = Do(1+g1)^3 D3 = 3(1+0,07)^3 D3 = 3,68
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 77,18
Po = 66,50 Valores TIR
-66.50 -16.45%
3.21
No, because TIR (-16,45%) is lower than Ks (10%)
Do = g1 = Ks =
Holcim Shares (No Growth) 3 7% 10%
D1 = Do(1+g1)^1 D1 = 3(1+0,07)^1 D1 = 3,21
D2 = Do(1+g1)^2 D2 = 3(1+0,07)^2 D2 = 3,43
D3 = Do(1+g1)^3 D3 = 3(1+0,07)^3 D3 = 3,68
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 36,75
Dividends 3.21 3.43 3.68 36.75
PV 2.92 2.84 2.76 27.61
Total
36.13
3.43
33.68
Po = 36,13 Valores TIR
-36.13 4.07%
3.21
No, because TIR (4,07%) is lower than Ks (10%)
Do = g1 = g2 = Ks =
Tekal Shares (Infinity) 40 10% 5% 20%
D1 = Do(1+g1)^1 D1 = 40(1+0,10)^1 D1 = 44
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 40(1+0,10)^2 D3 = 40(1+0,10)^3 D2 = 48,40 D3 = 53,24
D4 = D3(1+g2)^1 D4 = 53,24(1+0,05)^1 D4 = 55,90
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 372,68
Dividends 44.00 48.40 53.24 55.90 372.68
PV 36.67 33.61 30.81 215.67
Total
316.76
48.40
903.24
Po = 316,76 Valores TIR
-316.76 50.29%
44.00
Yes, because TIR (50,29%) is higher than Ks (20%)
Do = g1 = Ks =
Tekal Shares (No Growth) 40 10% 20%
D1 = Do(1+g1)^1 D1 = 40(1+0,10)^1 D1 = 44
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 40(1+0,10)^2 D3 = 40(1+0,10)^3 D2 = 48,40 D3 = 53,24
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 266,20
Dividends 44.00 48.40 53.24 266.20
PV 36.67 33.61 30.81 154.05
Total
255.14
48.40
903.24
Po = 255,14 Valores TIR
-255.14 62.68%
44.00
Yes, because TIR (62,68%) is higher than Ks (20%)
2.- In the New York Stock Exchange today, in Bloomberg, there is the following financial information available: Security GM - Bond Boeing - Shares
Po 88.50% 100
FV 100000
Coupon / Dividend / Do 3% quarterly 15%
N 4 years
Yield 15.94% 15%
g1
g2
10%
5% g1 = 1,2,3 years g2 = infinity
An important client of Chase Manhattan bank wants to invest $100000, which of the options in the table could be the best alternative, why? Assume you bought the bonds and shares at the current market Prices, and 2 years later an important investment Bank offers different Prices (P2 column) which of them would you accept, why?
FV = PV = CR = N= COUPON = YTM =
GM - Bond (1st Part) 100000 88500 3% 16 3000 3.99%
GM - Bond (2nd Part) 95000 88500 3% 8
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
3000 4.18%
Yes, because YTC (4,18%) is higher than YTM (3,99%) The best alternative is GM - Bond because it offers a better yield (15.94%) than Boeing - Shares (15%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 15(1+0,10)^1 D1 = 16,50
Boeing - Shares 15 10% 5% 15% D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 15(1+0,10)^2 D3 = 15(1+0,10)^3 D2 = 18,15 D3 = 19,97
D4 = D3(1+g2)^1 D4 = 19,97(1+0,05)^1 D4 = 55,90
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 209,63
Dividends 16.50 18.15 19.97 20.96 209.63
137.84
Total
179.04
Po = 179,04 Valores TIR
-179.04 1.63%
16.50
No, because TIR (1,63%) is lower than Ks (15%)
168.15
PV 14.35 13.72 13.13
P3 99.5% 95% $30 $30 $850 $850 g1 = 1,2,3 years g2 = infinity
15 Bond (2nd Part)
Semi Periods
Semi
Sell / Not Sell Sell Not Sell Not Sell Not Sell Sell Sell
Bond (2nd Part)
Quarterly Periods
Quarterly
P2 95% $150 g1 = 1,2,3 years g2 = infinity
Bond (2nd Part)
Quarterly Periods
Quarterly
oeing - Shares (15%)
Sell / Not Sell Sell Not Sell
1.- There is the following financial information available: Security Bond N° 1 Bond N° 2 Share N° 1 Share N° 1 Share N° 2 Share N° 2
Po 113.80% 96.67% 36.21 28.52 368.80 256.58
FV 100000 100000
Coupon / Dividend / Do 6% semiannually 2% quarterly $3 $3 $30 $30
N 12 years 4 years
Yield 10% 9% 12% 12% 14% 14%
g1
g2
5% 5% 7% 7%
3% 3% 5% 5% g1 = 1,2,3 years g2 = infinity
Analyze the Bonds and Shares and valuate the current market Prices today. In Shares consider g2 (growth rate of 2nd stage) a) % to infinity and b) without growing Assume you bought the bonds and shares at the current market Prices calculated, and 3 years later an important Investment Bank offers different Prices (P3 column) which of them would you accept, Why?
FV = PV = CR = N=
Bond N° 1 (1st Part) 100000 ? 6.00% 24
COUPON = Kb =
6000 5.00%
PV =
-113,798.64
Bond N° 1 (2nd Part) 97500 -113,798.64 6.00% 6
Semi Periods
FV = PV = CR = N=
Semi
COUPON = YTC =
No, because YTC (3,06%) is lower than Kb (5,00%)
6000 3.06%
FV = PV = CR = N=
Bond N° 2 (1st Part) 100000 ? 2.00% 16
COUPON = Kb =
2000 2.25%
PV =
-96,671.84
Bond N° 2 (2nd Part) 99000 -96,671.84 2.00% 12
Quarterly Periods
FV = PV = CR = N=
Quarterly
COUPON = YTC =
2000 2.25%
Dividends 3.15 3.31 3.47 3.58 39.75
PV 2.81 2.64 2.47 28.29
Total
36.21
3.31
33.47
No, because YTC (2,25%) is equal than Kb (2,25%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 3(1+0,05)^1 D1 = 3,15
Share N° 1 (Infinity) 3 5% 3% 12% D2 = Do(1+g1)^2 D2 = 3(1+0,05)^2 D2 = 3,31
D4 = D3(1+g2)^1 D4 = 3,47(1+0,03)^1 D4 = 3,58
D3 = Do(1+g1)^3 D3 = 3(1+0,05)^3 D3 = 3,47
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 39,75
Po = 36,21 Valores TIR
-36.21 3.62%
3.15
No, because TIR (3,62%) is lower than Ks (12%)
Do = g1 = Ks =
Share N° 1 (No Growth) 3 5% 12%
D1 = Do(1+g1)^1 D1 = 3(1+0,05)^1 D1 = 3,15
D2 = Do(1+g1)^2 D2 = 3(1+0,05)^2 D2 = 3,31
D3 = Do(1+g1)^3 D3 = 3(1+0,05)^3 D3 = 3,47
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 28,94
Dividends 3.15 3.31 3.47 28.94
PV 2.81 2.64 2.47 20.60
Total
28.52
3.31
33.47
Po = 28,52 Valores TIR
-28.52 13.08%
3.15
Yes, because TIR (13,08%) is higher than Ks (12%)
Do = g1 = g2 = Ks =
Share N° 2 (Infinity) 30 7% 5% 14%
D1 = Do(1+g1)^1 D1 = 30(1+0,07)^1 D1 = 32,10
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 30(1+0,07)^2 D3 = 30(1+0,07)^3 D2 = 34,35 D3 = 36,75
D4 = D3(1+g2)^1 D4 = 36,75(1+0,05)^1 D4 = 38,59
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 428,77
Dividends 32.10 34.35 36.75 38.59 428.77
PV 28.16 26.43 24.81 289.40
Total
368.80
34.35
886.75
Po = 368,80 Valores TIR
-368.80 39.30%
32.10
Yes, because TIR (39,30%) is higher than Ks (14%)
Do = g1 = Ks =
Share N° 2 (No Growth) 30 7% 14%
D1 = Do(1+g1)^1 D1 = 30(1+0,07)^1 D1 = 32,10
D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 30(1+0,07)^2 D3 = 30(1+0,07)^3 D2 = 34,35 D3 = 36,75
Years d1 d2 d3 P3
P3 = D3 / Ks P3 = 262,51
Dividends 32.10 34.35 36.75 262.51
PV 28.16 26.43 24.81 177.19
Total
256.58
34.35
886.75
Po = 256,58 Valores TIR
-256.58 58.51%
32.10
Yes, because TIR (58,51%) is higher than Ks (14%)
2.- There is the following financial information available: Security Telefonica - Bond Vodafone - Shares
Po 100% 10
FV 100000
Coupon / Dividend / Do 1% quarterly 4%
N 5 years
Yield 4% 6%
g1
g2
10%
5% g1 = 1,2,3 years g2 = infinity
An important client of Chase Manhattan bank wants to invest $100000, which of the options in the table could be the best alternative, why? Assume you bought the bonds and shares at the current market Prices, and 2 years later an important investment Bank offers different Prices (P2 column) which of them would you accept, why?
FV = PV = CR = N= COUPON = YTM =
Telefonica - Bond (1st Part) 100000 100000 1% 20 1000 1.00%
Telefonica - Bond (2nd Part) FV = 101500 PV = 100000 CR = 1% N= 8
Quarterly Periods
COUPON = YTC =
Quarterly
1000 1.18%
Yes, because YTC (1,18%) is higher than YTM (1%) The best alternative is Vodafone - Shares because it offers a better yield (6%) than Telefonica - Bonds (4%)
Do = g1 = g2 = Ks = D1 = Do(1+g1)^1 D1 = 0,4(1+0,10)^1 D1 = 0,44
Vodafone - Shares 0.4 10% 5% 6% D2 = Do(1+g1)^2 D3 = Do(1+g1)^3 D2 = 0,4(1+0,10)^2 D3 = 0,4(1+0,10)^3 D2 = 0,48 D3 = 0,53
D4 = D3(1+g2)^1 D4 = 0,53(1+0,05)^1 D4 = 0,56
Years d1 d2 d3 d4 P3
P3 = D4/(Ks-g2) P3 = 55,90
Dividends 0.44 0.48 0.53 0.56 55.90
46.94
Total
48.23
Po = 48,23 Valores TIR
-48.23 -156.21%
0.44
No, because TIR (-42,88%) is lower than Ks (6%)
15.48
PV 0.42 0.43 0.45
P3 97.5% 99% $30 $30 $850 $850 g1 = 1,2,3 years g2 = infinity
N° 1 (2nd Part)
Semi Periods
Semi
Sell / Not Sell Not Sell Not Sell Not Sell Sell Sell Sell
N° 2 (2nd Part)
Quarterly Periods
Quarterly
P2 101.50% $15 g1 = 1,2,3 years g2 = infinity
a - Bond (2nd Part)
Quarterly Periods
Quarterly
Telefonica - Bonds (4%)
Sell / Not Sell Sell Not Sell
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