iapm selected numericals
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Illustration 4:
An Investor buys 75 unit
receives dividend at the rate of
2010 the funds NAV was 15.
Solution:
The Beginning Value of In
Number of Units Reinveste
Total No. of Units
End Period Value and Inves
Return on Investment
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s of a fund at 9.5 on 1st
January, 2010. On 3
10%. The ex-dividend NAV was 10.25. O
5. Calculate the return on Investment.
estment = 9.5 x 75
= 712.50
= units31.725.10
75
= 75 + 7.31 = 82.31
tment = 82.31 x 15.25
= 1,255.23= 100x
MV
MVMV
b
be
= 10050.712
50.71223.1255x
= 10050.712
73.542x
= 76.17%
3 :- INVESTMENT ALTERNATIVES
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ay of teaching
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College Patkar
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0th
June, 2010 he
31st
December,
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Illustration 2:
The details of three portfolios are given below. Compare these portfolios on performance using
the Sharpe, Treynor and Jensen's measures.
Portfolio Average Return Standard Deviation Beta
1 15% 0.25 1.252 12% 0.30 0.75
3 10% 0.20 1.10
Market Index 12% 0.25 1.00
The risk-free rate of return is 9%.
Solution:-
Sharpe Measure =
FRR
Portfolio 1 = )1(....2425.0
915
Portfolio 2 = )3(...1030.0
912
Portfolio 3 = )4(...520.0
910
MarketIndex = )2(...1225.0
912
As per Sharpe Measure, Portfolio 1 is better than 2, 3 and market Index.
Treynors Measure
FRR
Portfolio 1 = )1(...%8.425.1
915
Portfolio 2 = )2(...%4
75.0
912
Portfolio 3 = )4(...%90.010.1
910
MarketIndex = )3(...%5.220.1
912
CHAPTER 4: PORTFOLIO MANAGEMENT FRAMEWORK
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As per Treynors Measure, Portf
Jensens Measures :-
R = RF + (RPortfolio 1 = 9 + 1.25 (
= 9 + 3.75= 12.75
Portfolio 2 = 9 + 0.75 (
= 9 + 2.25= 11.25
Portfolio 3 = 9 + 1.10 (
= 9 + 3.3= 12.3
Now,Portfolio 1 = 15 12.75
Portfolio 2 = 12 11.25
Portfolio 3 = 10 12.3Market Index = 0 (by defi
As per Jensens Measure, Portfo
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olio 1 is better than 2, 3 and market Index.
RF)2 9)
2 9)
2 9)
= 2.25 (1)
= 0.75 (2)
= - 2.3 (3)ition)
io 1 is better than portfolio 2, and portfolio 3.
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Illustration 1:
Four equal annual payments of 5,000 are made into a deposit account that pays 8
percent interest per year. What is the future value of this annuity at the end of 4 years?
Solution:
R
1)R1(AFVannuityofvaluefutureThe
t
A
= 5,000 x FVIFA @ 8%
= 5,000 x 4.5061= 22530.50
Illustration 4:
A bank promises to give you 10,000 after 3 years at the rate of 10% interest. How much
should you deposit today?
Solution:
nR
x)1(
1FVPV
3)10.01(
1000,10
x
3)1.1(
1
000,10 x
331.1
1000,10 x
= 7513
ORPVCIF = CIF x DF
= 10,000 x 0.7513
= 7513.
Illustration 21:Krishnamurthy has inherited 1,000 a year for next 20 years. First payment being made in one
years time. However he is need of money immediately and would like to sell his income to any
buyer who would pay him the right price. Assume that the current market rate of interest is 10%.
(a) What should be the right price he should accept?
(b) How much of his income should he sell if he wants only 2,500 at present.
CHAPTER 8: - TIME VALUE OF MONEY
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(c) If you have invested in buyi
be your proposal.
Solution:
(a) PV = 1,000 x PVIF (10% of= 1,000 x 8.514
= 8514
Comment: The right price he sh
(b) PV
8,514 1,000
2,500 (?)
Comment: He should sell 29
(c) 8,514 1,000
5,000 (?)Comment: My proposal will be
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3) SCOrE is shortcutJhabak Sir who mix
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imp.
(IAPM NUMERICALS) M:
g the income but if you had only 5,000 to i
0 years)
ould accept is 8514.
.63 of his income.
to receive minimum 587.27 of his income.
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vest what would
eat leaderwith
given
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CHAPTER : 9 RISK AND RETURN
Illustration 3:
Given below are the likely returns in case of shares of VCC Ltd. and LCC Ltd. in the various
economic conditions. Both the shares are presently quoted at Rs. 100 per share.Economic
ConditionsProbability
Returns of
VCC Ltd.
Returns of
LCC Ltd.
High Growth
Low Growth
StagnationRecession
0.3
0.4
0.20.1
100
110
120140
150
130
9060
Which of the two companies are risky investments?
Solution:-
VCC Ltd.
Economic
ConditionP R PxR=R )RR(
2)RR( 2)RR(P
High
Growth0.3 100 30 12 144 43.2
Low
Growth0.4 110 44 2 4 1.6
Stagnation 0.2 120 24 8 64 12.8
Recession 0.1 140 14 28 784 78.4
112 Variance 136
Expected Return = 112%
Risk = Standard deviation = V = 136 = 11.66%
LCC Ltd.
Economic
ConditionP R PxR=R )RR(
2)RR( 2)RR(P
High
Growth0.3 150 45 29 841 252.30
Low
Growth0.4 130 52 9 81 32.40
Stagnation 0.2 90 18 31 961 192.20
Recession 0.1 60 6 61 3721 372.10
121 Variance 849
Expected Return = 121%
Risk = Standard deviation = V = 849 = 29.14%
CHAPTER : 9 RISK AND RETURN
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VCC Ltd. LCC Ltd.
Return
Risk ()112%11.66%
121%29.14%
Comment :1. The risk in LCC is more than VCC Ltd.
2. The choice of an Investor totally depends upon the risk return profile of the Investors.An Investor, who is willing to take risk, would invest in LCC, since the return is higher.
An Investor who is willing to take less risk, will Invest in VCC Ltd.
Illustration 8:
In January 2008, Mr. Dhimant Kapadia purchased the following 5 scrips:
Co.'s Name No. of Shares Purchase price
H Ltd.
C Ltd.S Ltd.F Ltd.
M Ltd.
100
100100100
100
250
18080240
260
He paid brokerage of Rs. 1,500
During the year 2008, Mr. Dhimant Kapadia received the following.
Co's Name Dividend Bonus Shares
H Ltd.
C Ltd.S Ltd.F Ltd.
M Ltd.
300
290450500
600
1:2
In January 2009, Mr. Dhimant Kapadia sold all his holdings at the following prices.
Co's Name Market Price
H Ltd. 275
C Ltd. 240S Ltd. 108
F Ltd. 200M Ltd. 400
He paid brokerage of Rs. 1,865.Calculate the holding period return.
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Solution:-
Formula :-
Holding period Return = 100xbeginningat thePrice
Dividend+beginningat thePrice-YearLastofendat thePrice
100x102500
2140102500134185
= 33%
W.N.1) Price at beginning:-
NameNo. of
Shares
Purchase
Price
Brokerage
Purchase Price
H Ltd.
C. Ltd.S. Ltd.
F. Ltd.
M Ltd.
100
100100
100
100
250
18080
240
260
25,000
18,0008,000
24,000
26,000
1,01,000+ Brokerage 1,500
1,02,500
W.N. 2) Price at the end:-
NameNo. of
Shares
Purchase
PriceAmount
H. Ltd.
C. Ltd.S. Ltd.
F. Ltd.
M. Ltd.
150
100100
100
100
275
240108
200
400
41,250
24,00010,800
20,000
40,0001,36,050
- Brokerage 1,865
1,34,185
Illustration 14:
The common stocks of Bajaj and TVS have expected returns of 15% and 20% respectively,
while the standard deviations are 20% and 40%. The excepted correlation coefficient betweenthe two stocks is 0.36. What is the excepted value of return and the standard deviation of a
portfolio consisting of (a) 40% Bajaj and 60% TVS? (b) 40% TVS and 60% Bajaj?
Solution:-
(a)
Bajaj TVS
Return
W
150.20
0.40
200.40
0.60
Correlation Co efficient between two stocks = 0.36
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Expected Return of Portfolio = WB x RB + WT RT= 0.40 x 15 + 0.60 x 20= 6 + 12
= 18%
Riskof Portfolio =BTTTBBTTBB CxxWxxWxxWxW 2)()()()(
2222
36.040.060.020.040.02)40.0()60.0()20.0()40.0(2222
xxxxxxx
36.040.060.020.040.0216.036.004.016.0 xxxxxxx
014.0058.0006.0
078.0= 0.2792
= 0.2792 x 100
= 27.92% or 0.28
(b)
Bajaj TVS
Return
W
15
0.20
0.60
20
0.40
0.40
Expected Return of Portfolio = WB x RB + WT x RT= 0.60 x 15 + 0.40 x 20
= 9 + 8
= 17%
Risk of Portfolio () =BTTTBBTTBB CxxWxxWxxWxW 2)()()()(
2222
= 36.040.040.020.060.02)40.0()40.0()20.0()60.0( 2222 xxxxxxx
= 36.040.040.020.060.0216.016.004.036.0 xxxxxxx
= 014.0025.0014.0
= 053.0 = 23.0
= 100x23.0
= 23% or 0.23
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RATIO ILLUSTRATION
Illustration 2:
Following information is available relating to Beena Ltd. and Meena Ltd:( in lacs)
Beena Ltd. Meena Ltd.
Equity share capital (Rs. 10) 200 250
12% preference shares 80 100
Profit after tax 50 70
Proposed dividend 35 40
Market price per share 25 35
You are required to calculate: (i) Earning per share. (ii) P/E Ratio (iii) Dividend Payout Ratio.(iv) Return on Equity Shares. As an analyst, advice the investor which of the two companies is
worth investing.
Solution:-
Beena Ltd. Meena Ltd.
(i)SharesEquityof.No
PDNPATEPS
20
6.950
= 2.02 per shares
25
1270
= 2.32 per shares
EPS Signifies that the profit earned by each Equity Shareholder. A higher ratio is favorable.
Based on EPS Meena Ltd. is better than Beena Ltd.
Beena Ltd. Meena Ltd.
(ii)MPS
EPSRatioE/P
02.2
25
= 12.38 times32.2
35
= 15.086 times
P/E Ratio signifies that the market price is how many times the earning. A Lower ratio is
generally favorable. From the point of view of the Investor, Beena Ltd. is better than Meena Ltd,
based on P/E Ratio.
Beena Ltd. Meena Ltd.
(iii) 100xEPS
DPSRatioPayoutDividend 100x
02.2
75.1
= 86.63%
100x32.2
6.1
= 68.97%
CHAPTER :- 10 FUNDAMENTAL AND TECHNICAL ANALYSIS
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Sharesof.No
DividEquityTotalDPS
Dividend Payout Ratio signifies
higher Ratio is favorable, for di
appreciation seeking Investor.
(iv)NPAT
SharesEquityonReturn
Return on Equity Signifies that
Therefore Meena is better than
Conclusion:- Based on P/E ratio
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nd75.1
20
35
25
40
that the dividend is how much percent of E
vidend seeking Investor & Lower ratio is favo
Beena Ltd.
100xCapitalEquity
dividendeferencePr1x
200
6.950
= 20.2%
he profit earned on equity Capital. A higher R
eena Ltd.
, it is recommended to purchase shares of Been
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6.1
uity earnings. A
rable for Capital
Meena Ltd.
00 100x250
1270
= 23.2%
atio is favorable.
Ltd.
is
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CHAPTER :- 11 VALUATION OF DEBENTURES
Illustration 5:
A GOI bond of 1000 each has a coupon rate of 8 percent annum and maturity period is 20
years. If the current market prices is 1050, find YTM?
Solution:-
100x
2
MR
n
MRI
YTMPV
PV
Where,
YTM = Yield to maturity
I = Interest
RX = Redemption ValueMP = Market Price
n = no. of years
100x
2
MR
n
MRI
YTMPV
PV
100x
2
10501000
20
10501000
80
100x
1025
5.280
100x1025
5.77
= 7.56%
Illustration 9:
Calculate the present value of Debenture of Mahesh ltd.
Year Coupon rate
1-2 8%
3-4 10%
5-7 12%
CHAPTER :- 11 VALUATION OF DEBENTURES
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The face value of the debenture is 100. Debentures are redeemed at 5% premium. The required
rate of return 16%.
Solution:-
Year Interest/Cash Inflow PVIF 16% PV of Cash Inflow1
2
3
45
6
7
8
8
10
1012
12
117
0.862
0.743
0.641
0.5520.476
0.410
0.354
6.896
5.944
6.41
5.525.712
4.92
41.418
(12 + 105) PV of Bond 76.82
Present Value of Bond = 76.82
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Illustration 7 :
Sunrise Ltd. is currently paying dividend of 1.50 on its face value of 10. Earnings and
dividends are expected to grow at 5% annual rate indefinitely. Investors require 9% rate of return
on their investments. The company is considering several business strategies and wishes to
determine the effect to these strategies on the market price of its share.
(a) Continuing the present strategy will result in the expected growth rate and required rate
of return as above.(b) Expanding sales will increase the expected dividend growth rate to 7% but will increase
the risk of the company. As a result, the investors required rate of return will increase to
12%.(c) Integrating into retail stores will increase the dividend growth rate to 6 per cent and
increase the required rate of return to 10 per cent.
You are required to find out the best strategy from the point of view of the market price.
Solution:-
D1 = Do (1 + g)= 1.50 (1 + 0.05)
= 1.575
(a) V =gke
D1
05.009.0575.1
= 39.375 per share
b) D1 = Do (1 + g)
= 1.50 (1 + 0.06)
= 1.605
V =gke
D1
07.012.0
605.1
= 32.1 per share
(C) D1 = Do (1 + g)
= 1.50 (1 + 0.06)
= 1.59
CHAPTER :- 12 VALUATION OF EQUITY
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06.010.0
59.1
V
= 39.75 per share
Comment: Strategy C is the best since it results into highest market price.
Illustration 12:
As per the financial accounts for the last year, the company has paid dividend @ 20% . The paid
up equity capital is 6,00,000 and 10% preference share capital 1,00,000. Operating profit is
4,00,000. The tax rate is 32%. The company expects a growth rate of 5%. Compute Value per
Equity Share.
(a) Dividend Growth Approach.
(b) Dividend Approach.(c) Earnings Growth Approach.
(d) Earning Approach.
Solution:-
D1 = D0 (1 + g)
= 2 (1 + 0.05)= 2.1
(a) Dividend Growth Approach:-
V =gke
D1
=
05.010.0
1.2
= 42 per share
(b) Dividend Approach
Ke
DV 1
10.0
2
= 20 per share
(c) Earning Growth Approach
Rs.
Operating Profit 4,00,000(-) Interest -
NPBT 4,00,000
(-) Tax @ 32% 1,28,000
NPAT 2,72,000
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ShareEquityof.No
DividendeferencedPrNPATEPS
000,60
000,10000,72,2
= 4.37 per share
E1 = E0 (1 + g)
= 4.37 (1 + 0.05)
= 4.59
V =gke
E
1
=05.010.0
59.4
=
5.0
59.4
= 91.8 per share
(d) Earning Approach
Ke
EV 1
10.0
37.4
= 43.7 per share
Note: In absence of F.V, It is taken as 10.
In absence of Ke, it is assumed 10 or any value above than growth rate.
Illustration : 17
The chemical and fertilizers ltd has been growing at the rate of 18% in the recent years This
abnormal growth rate is expected to continue for another 4 years and then likely to grow at
normal rate of 6%. Dividend paid last year was 3 per share. Find out the intrinsic value of
share if the required rate of return is 12%.
Solution:-
D1 = D0 (1 + g)
= 3 (1 + 0.18)= 3.54
V =gke
D1
Year Dividend PVIF 12% PV of Dividend
1 3.54 0.893 3.16
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23
4
4.184.93
5.82
0.7970.712
0.636
3.333.51
3.70
(A) 13.70
gKegDP
)1(
44
06.012.0
)6.01(82.5
06.0
)06.1(82.5
= 102.82 x 0.636= 65.39 Rs. (B)
Now,
(A + B) = 13.70 + 65.39= 79.09
Note: When two growth are given calculate as above.
Illustration:20
The Balance Sheet of Ganesh Ltd. as on 31-3-2009 was as under:
Liabilities Rs. Assets Rs.
2,000 Equity share of Rs.100 eachGeneral Reserve
Profit & Loss A/cCreditors
Provision for TaxationProvident Fund
2,00,00050,000
25,00045,000
20,00017,500
Land and BuildingMachinery
Investment at Cost(Market Value Rs.37,500)
DebtorsStock
Cash & Bank
1,25,00075,000
45,000
50,00037,500
25,000
Total 3,57,500 Total 3,57,500
Additional Information:
i) Land and Building & Machinery are valued at 1,37,500 and Rs. 55,000 respectively.
ii) Of the total debts 2,500 are bad.iii) Goodwill is to be valued at 25,500.
iv) The normal dividend declared and paid by such type of companies is 15% on the paidup capital.
v) The average rate of dividend, declared and paid up by the company is 18% on its paid-up
capital.
Calculate the fair value of an equity share of the company.
Solution :-
Calculation of N.A.V / Shares
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Particulars
Market Value of all Real Assets
Land and BuildingMachinery
Investment
DebtorsStock
Cash and Bank
Goodwill
A greed value of outsiders LiabilitiesCreditors
Prov. for Tax
Provident fundNet assets available to all SH.
= Net assets available to all ESH
1,37,50055,000
37,500
47,50037,500
25,000
25,500 3,65,500
45,000
20,00017,500 82,500
2,83,000
NAV / Share =SharesEqofNo
ESHforassetsNet..
=000,2
000,83,2
= 141.5
Yield Value / Share = sharevaluePaidupxNRR
ARR/
= 10015
18x
= 120
Fair Value / Share =2
.. YieldVAN
=2
1205.141
= 130.75
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