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

CHAPTE

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(IAPM NUMERICALS) M:

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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0th

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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


2) Neither an institand every student i

where there are chi


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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ute nor an education centredifferentiated, but like a

dren equally treated.

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College Lala

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where eachhouse


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4

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


3) SCOrE is shortcutJhabak Sir who mix

syllabus wer over a

imp.


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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to Success headed by the grp practical knowledge nicely

l development of students is

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vest what would

eat leaderwith

given


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6

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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7

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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8

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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9

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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10

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:-


(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.


(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.


(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

E-mail Contes "What is S

4) The fruits recei

SCOrE!!


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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ed after hard core studying

Pooja D. Prabhu

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6.1

uity earnings. A

rable for Capital

Meena Ltd.

00 100x250

1270

= 23.2%

atio is favorable.

Ltd.

is


12/18


12

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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13

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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14

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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15

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


16/18


16

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


17/18


17

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


18/18


18

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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