MUTUAL FUNDS 77.

19

TEST YOUR KNOWLEDGE

Theoretical Questions
1. Explain how to establish a Mutual Fund.
2. What are the advantages of investing in Mutual Funds?
Practical Questions
1. Mr. A can earn a return of 16 per cent by investing in equity shares on his own. Now he is
considering a recently announced equity based mutual fund scheme in which initial
expenses are 5.5 per cent and annual recurring expenses are 1.5 per cent. How much
should the mutual fund earn to provide Mr. A return of 16 per cent?
2. The unit price of Equity Linked Savings Scheme (ELSS) of a mutual fund is ` 10/-. The
public offer price (POP) of the unit is ` 10.204 and the redemption price is ` 9.80.
Calculate:
(i) Front-end Load
(ii) Back end Load
3. A mutual fund that had a net asset value of ` 20 at the beginning of month - made income and
capital gain distribution of ` 0.0375 and ` 0.03 per share respectively during the month, and
then ended the month with a net asset value of ` 20.06. Calculate monthly return.
4. An investor purchased 300 units of a Mutual Fund at ` 12.25 per unit on 31st December,
2009. As on 31st December, 2010 he has received ` 1.25 as dividend and ` 1.00 as capital
gains distribution per unit.
Required :
(i) The return on the investment if the NAV as on 31st December, 2010 is ` 13.00.
(ii) The return on the investment as on 31st December, 2010 if all dividends and capital
gains distributions are reinvested into additional units of the fund at ` 12.50 per unit.
5. SBI mutual fund has a NAV of ` 8.50 at the beginning of the year. At the end of the year
NAV increases to ` 9.10. Meanwhile fund distributes ` 0.90 as dividend and ` 0.75 as
capital gains.
(i) What is the fund’s return during the year?
(ii) Had these distributions been re-invested at an average NAV of ` 8.75 assuming 200
units were purchased originally. What is the return?
6. The following information is extracted from Steady Mutual Fund’s Scheme:
- Asset Value at the beginning of the month - ` 65.78

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 7.20 STRATEGIC FINANCIAL MANAGEMENT

- Annualised return -15 %

- Distributions made in the nature of Income - ` 0.50 and ` 0.32
& Capital gain (per unit respectively).
You are required to:
(i) Calculate the month end net asset value of the mutual fund scheme (limit your
answers to two decimals).
(ii) Provide a brief comment on the month end NAV.
7. Cinderella Mutual Fund has the following assets in Scheme Rudolf at the close of business
on 31 s t March,2014.
Company No. of Shares Market Price Per Share
Nairobi Ltd. 25000 ` 20
Dakar Ltd. 35000 ` 300
Senegal Ltd. 29000 ` 380
Cairo Ltd. 40000 ` 500

The total number of units of Scheme Rudol fare 10 lacs. The Scheme Rudolf has accrued
expenses of ` 2,50,000 and other liabilities of ` 2,00,000. Calculate the NAV per unit of the
Scheme Rudolf.
8. A Mutual Fund Co. has the following assets under it on the close of business as on:
1st February 2012 2nd February 2012
Company No. of Shares Market price per share Market price per share
` `
L Ltd 20,000 20.00 20.50
M Ltd 30,000 312.40 360.00
N Ltd 20,000 361.20 383.10
P Ltd 60,000 505.10 503.90

Total No. of Units 6,00,000

(i) Calculate Net Assets Value (NAV) of the Fund.
(ii) Following information is given:
Assuming one Mr. A, submits a cheque of ` 30,00,000 to the Mutual Fund and the
Fund manager of this company purchases 8,000 shares of M Ltd; and the balance
amount is held in Bank. In such a case, what would be the position of the Fund?
(iii) Find new NAV of the Fund as on 2nd February 2012.

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 MUTUAL FUNDS 77.21

9. On 1st April 2009 Fair Return Mutual Fund has the following assets and prices at 4.00 p.m.

Shares No. of Shares Market Price Per Share (`)

A Ltd. 10000 19.70
B Ltd. 50000 482.60
C Ltd. 10000 264.40
D Ltd. 100000 674.90
E Ltd. 30000 25.90
No. of units of funds 8,00,000

Please calculate:
(a) NAV of the Fund on 1st April 2009.
(b) Assuming that on 1st April 2009, Mr. X, a HNI, send a cheque of ` 50,00,000 to the
Fund and Fund Manager immediately purchases 18000 shares of C Ltd. and balance
is held in bank. Then what will be position of fund.
(c) Now suppose on 2 April 2009 at 4.00 p.m. the market price of shares is as follows:
Shares `
A Ltd. 20.30
B Ltd. 513.70
C Ltd. 290.80
D Ltd. 671.90
E Ltd. 44.20
Then what will be new NAV.
10. A has invested in three Mutual Fund Schemes as per details below:
Particulars MF A MF B MF C
Date of investment 01.12.2009 01.01.2010 01.03.2010
Amount of investment ` 50,000 ` 1,00,000 ` 50,000
Net Asset Value (NAV) at entry date ` 10.50 ` 10 ` 10
Dividend received upto 31.03.2010 ` 950 ` 1,500 Nil
NAV as at 31.03.2010 ` 10.40 ` 10.10 ` 9.80
Required:
What is the effective yield on per annum basis in respect of each of the three schemes to
Mr. A upto 31.03.2010?

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 7.22 STRATEGIC FINANCIAL MANAGEMENT

11. Mr. Sinha has invested in three Mutual fund schemes as per details below:
Scheme X Scheme Y Scheme Z
Date of Investment 01.12.2008 01.01.2009 01.03.2009
Amount of Investment ` 5,00,000 ` 1,00,000 ` 50,000
Net Asset Value at entry date ` 10.50 ` 10.00 ` 10.00
Dividend received upto 31.03.2009 ` 9,500 ` 1,500 Nil
NAV as at 31.3.2009 ` 10.40 ` 10.10 ` 9.80
You are required to calculate the effective yield on per annum basis in respect of each of
the three schemes to Mr. Sinha upto 31.03.2009.
12. Mr. Y has invested in the three mutual funds (MF) as per the following details:
Particulars MF ‘X’ MF ‘Y’ MF ‘Z’
Amount of Investment (`) 2,00,000 4,00,000 2,00,000
Net Assets Value (NAV) at the time of purchase (`) 10.30 10.10 10
Dividend Received up to 31.03.2018 (`) 6,000 0 5,000
NAV as on 31.03.2018 (`) 10.25 10 10.20
Effective Yield per annum as on 31.03.2018 9.66 -11.66 24.15
(percent)
Assume 1 Year =365 days
Mr. Y has misplaced the documents of his investment. Help him in finding the date of his
original investment after ascertaining the following:
(i) Number of units in each scheme;
(ii) Total NAV;
(iii) Total Yield; and
(iv) Number of days investment held.
13. Mr. X on 1.7.2007, during the initial offer of some Mutual Fund invested in 10,000 units
having face value of ` 10 for each unit. On 31.3.2008, the dividend paid by the M.F. was
10% and Mr. X found that his annualized yield was 153.33%. On 31.12.2009, 20% dividend
was given. On 31.3.2010, Mr. X redeemed all his balance of 11,296.11 units when his
annualized yield was 73.52%. What are the NAVs as on 31.3.2008, 31.3.2009 and
31.3.2010?
14. Mr. X on 1.7.2012, during the initial public offer of a Mutual Fund (MF) invested
` 1,00,000 at Face Value of ` 10. On 31.3.2013, the MF declared a dividend of 10% when
Mr. X calculated that his holding period return was 115%. On 31.3.2014, MF again declared
a dividend of 20%. On 31.3.2015, Mr. X redeemed all his investment which had
accumulated to 11,296.11 units when his holding period return was 202.17%.
Calculate the NAVs as on 31.03.2013, 31.03.2014 and 31.03.2015.

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 MUTUAL FUNDS 77.23

15. A Mutual Fund having 300 units has shown its NAV of ` 8.75 and ` 9.45 at the beginning
and at the end of the year respectively. The Mutual Fund has given two options:
(i) Pay ` 0.75 per unit as dividend and ` 0.60 per unit as a capital gain, or
(ii) These distributions are to be reinvested at an average NAV of ` 8.65 per unit.
What difference it would make in terms of return available and which option is preferable?
16. On 1-4-2012 ABC Mutual Fund issued 20 lakh units at ` 10 per unit. Relevant initial
expenses involved were ` 12 lakhs. It invested the fund so raised in capital market
instruments to build a portfolio of ` 185 lakhs. During the month of April 2012 it disposed
off some of the instruments costing ` 60 lakhs for ` 63 lakhs and used the proceeds in
purchasing securities for ` 56 lakhs. Fund management expenses for the month of April
2012 was ` 8 lakhs of which 10% was in arrears. In April 2012 the fund earned dividends
amounting to ` 2 lakhs and it distributed 80% of the realized earnings. On 30-4-2012 the
market value of the portfolio was ` 198 lakhs.
Mr. Akash, an investor, subscribed to 100 units on 1-4-2012 and disposed off the same at
closing NAV on 30-4-2012. What was his annual rate of earning?
17. Sun Moon Mutual Fund (Approved Mutual Fund) sponsored open-ended equity oriented
scheme “Chanakya Opportunity Fund”. There were three plans viz. ‘A’ – Dividend Re-
investment Plan, ‘B’ – Bonus Plan & ‘C’ – Growth Plan.
At the time of Initial Public Offer on 1.4.1999, Mr. Anand, Mr. Bacchan & Mrs. Charu, three
investors invested ` 1,00,000 each & chosen ‘B’, ‘C’ & ‘A’ Plan respectively.
The History of the Fund is as follows:
Date Dividend % Bonus Ratio Net Asset Value per Unit (F.V. ` 10)
Plan A Plan B Plan C
28.07.2003 20 30.70 31.40 33.42
31.03.2004 70 5:4 58.42 31.05 70.05
31.10.2007 40 42.18 25.02 56.15
15.03.2008 25 46.45 29.10 64.28
31.03.2008 1:3 42.18 20.05 60.12
24.03.2009 40 1:4 48.10 19.95 72.40
31.07.2009 53.75 22.98 82.07

On 31st July all three investors redeemed all the balance units.
Calculate annual rate of return to each of the investors.
Consider:
1. Long-term Capital Gain is exempt from Income tax.
2. Short-term Capital Gain is subject to 10% Income tax.

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 7.24 STRATEGIC FINANCIAL MANAGEMENT

3. Security Transaction Tax 0.2 per cent only on sale/redemption of units.

4. Ignore Education Cess.
18. A mutual fund company introduces two schemes i.e. Dividend plan (Plan-D) and Bonus plan
(Plan-B). The face value of the unit is ` 10. On 1-4-2005 Mr. K invested ` 2,00,000 each in
Plan-D and Plan-B when the NAV was ` 38.20 and ` 35.60 respectively. Both the plans
matured on 31-3-2010.
Particulars of dividend and bonus declared over the period are as follows:
Date Dividend Bonus Net Asset Value (`)
% Ratio Plan D Plan B
30-09-2005 10 39.10 35.60
30-06-2006 1:5 41.15 36.25
31-03-2007 15 44.20 33.10
15-09-2008 13 45.05 37.25
30-10-2008 1:8 42.70 38.30
27-03-2009 16 44.80 39.10
11-04-2009 1:10 40.25 38.90
31-03-2010 40.40 39.70

What is the effective yield per annum in respect of the above two plans?
19. A mutual fund made an issue of 10,00,000 units of ` 10 each on January 01, 2008. No
entry load was charged. It made the following investments:
Particulars `
50,000 Equity shares of ` 100 each @ ` 160 80,00,000
7% Government Securities 8,00,000
9% Debentures (Unlisted) 5,00,000
10% Debentures (Listed) 5,00,000
98,00,000

During the year, dividends of ` 12,00,000 were received on equity shares. Interest on all
types of debt securities was received as and when due. At the end of the year equity shares
and 10% debentures are quoted at 175% and 90% respectively of face value. Other
investments are at par.
Find out the Net Asset Value (NAV) per unit given that operating expenses paid during the
year amounted to ` 5,00,000. Also find out the NAV, if the Mutual fund had distributed a
dividend of ` 0.80 per unit during the year to the unit holders.

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 MUTUAL FUNDS 77.25

20. Based on the following information, determine the NAV of a regular income scheme on per
unit basis:
Particulars ` Crores
Listed shares at Cost (ex-dividend) 20
Cash in hand 1.23
Bonds and debentures at cost 4.3
Of these, bonds not listed and quoted 1
Other fixed interest securities at cost 4.5
Dividend accrued 0.8
Amount payable on shares 6.32
Expenditure accrued 0.75
Number of units (` 10 face value) 20 lacs
Current realizable value of fixed income securities of face value of ` 100 106.5
The listed shares were purchased when Index was 1,000
Present index is 2,300
Value of listed bonds and debentures at NAV date 8
There has been a diminution of 20% in unlisted bonds and debentures. Other fixed interest
securities are at cost.
21. On 1st April, an open ended scheme of mutual fund had 300 lakh units outstanding with Net
Assets Value (NAV) of ` 18.75. At the end of April, it issued 6 lakh units at opening NAV
plus 2% load, adjusted for dividend equalization. At the end of May, 3 Lakh units were
repurchased at opening NAV less 2% exit load adjusted for dividend equalization. At the
end of June, 70% of its available income was distributed.
In respect of April-June quarter, the following additional information are available:
` in lakh
Portfolio value appreciation 425.47
Income of April 22.950
Income for May 34.425
Income for June 45.450
You are required to calculate
(i) Income available for distribution;
(ii) Issue price at the end of April;
(iii) repurchase price at the end of May; and
(iv) net asset value (NAV) as on 30th June.

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 7.26 STRATEGIC FINANCIAL MANAGEMENT

22. Five portfolios experienced the following results during a 7- year period:
Average Annual Standard Correlation with the
Portfolio
Return (Rp) (%) Deviation (Sp) market returns (r)
A 19.0 2.5 0.840
B 15.0 2.0 0.540
C 15.0 0.8 0.975
D 17.5 2.0 0.750
E 17.1 1.8 0.600
Market Risk (σm) 1.2
Market rate of Return (Rm) 14.0
Risk-free Rate (Rf) 9.0

Rank the portfolios using (a) Sharpe’s method, (b) Treynor’s method and (c) Jensen’s Alpha
23. There are two Mutual Funds viz. D Mutual Fund Ltd. and K Mutual Fund Ltd. Each having
close ended equity schemes.
NAV as on 31-12-2014 of equity schemes of D Mutual Fund Ltd. is ` 70.71 (consisting 99%
equity and remaining cash balance) and that of K Mutual Fund Ltd. is 62.50 (consisting 96%
equity and balance in cash).
Following is the other information:

Equity Schemes
Particular
D Mutual Fund Ltd. K Mutual Fund Ltd.
Sharpe Ratio 2 3.3
Treynor Ratio 15 15
Standard deviation 11.25 5

There is no change in portfolios during the next month and annual average cost is ` 3 per
unit for the schemes of both the Mutual Funds.
If Share Market goes down by 5% within a month, calculate expected NAV after a month for
the schemes of both the Mutual Funds.
For calculation, consider 12 months in a year and ignore number of days for particular
month.
24. ANP Plan, a hedge fund currently has assets of ` 20 crore. CA. X, the manager of fund
charges fee of 0.10% of portfolio asset. In addition to it he charges incentive fee of 2%. The
incentive will be linked to gross return each year in excess of the portfolio maximum value

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 MUTUAL FUNDS 77.27

since the inception of fund. The maximum value the fund achieved so far since inception of
fund about one and half year ago was ` 21 crores.

You are required to compute the fee payable to CA. X, if return on the fund this year turns out to be
(a) 29%, (b) 4.5%, (c) -1.8%
25. Ms. Sunidhi is working with an MNC at Mumbai. She is well versant with the portfolio
management techniques and wants to test one of the techniques on an equity fund she has
constructed and compare the gains and losses from the technique with those from a
passive buy and hold strategy. The fund consists of equities only and the ending NAVs of
the fund he constructed for the last 10 months are given below:
Month Ending NAV (`/unit) Month Ending NAV (`/unit)
December 2008 40.00 May 2009 37.00
January 2009 25.00 June 2009 42.00
February 2009 36.00 July 2009 43.00
March 2009 32.00 August 2009 50.00
April 2009 38.00 September 2009 52.00
Assume Sunidhi had invested a notional amount of ` 2 lakhs equally in the equity fund and
a conservative portfolio (of bonds) in the beginning of December 2008 and the total portfolio
was being rebalanced each time the NAV of the fund increased or decreased by 15%.
You are required to determine the value of the portfolio for each level of NAV following the
Constant Ratio Plan.
Answers to Theoretical Questions
1. Establishment of a Mutual Fund: A mutual fund is required to be registered with the
Securities and Exchange Board of India (SEBI) before it can collect funds from the public.
All mutual funds are governed by the same set of regulations and are subject to monitoring
and inspections by the SEBI. The Mutual Fund has to be established through the medium of
a sponsor. A sponsor means any body corporate who, acting alone or in combination with
another body corporate, establishes a mutual fund after completing the formalities
prescribed in the SEBI's Mutual Fund Regulations.
The role of sponsor is akin to that of a promoter of a company, who provides the initial
capital and appoints the trustees. The sponsor should be a body corporate in the business
of financial services for a period not less than 5 years, be financially sound and be a fit
party to act as sponsor in the eyes of SEBI.

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 7.28 STRATEGIC FINANCIAL MANAGEMENT

The Mutual Fund has to be established as either a trustee company or a Trust, under the
Indian Trust Act and the instrument of trust shall be in the form of a deed. The deed shall be
executed by the sponsor in favour of the trustees named in the instrument of trust. The trust
deed shall be duly registered under the provisions of the Indian Registration Act, 1908. The
trust deed shall contain clauses specified in the Third Schedule of the Regulations.
An Asset Management Company, who holds an approval from SEBI, is to be appointed to
manage the affairs of the Mutual Fund and it should operate the schemes of such fund. The
Asset Management Company is set up as a limited liability company, with a minimum net
worth of ` 10 crores.
The sponsor should contribute at least 40% to the networth of the Asset Management
Company. The Trustee should hold the property of the Mutual Fund in trust for the benefit of
the unit holders.
SEBI regulations require that at least two-thirds of the directors of the Trustee Company or
board of trustees must be independent, that is, they should not be associated with the
sponsors. Also, 50 per cent of the directors of AMC must be independent. The appointment
of the AMC can be terminated by majority of the trustees or by 75% of the unit holders of
the concerned scheme.
The AMC may charge the mutual fund with Investment Management and Advisory fees
subject to prescribed ceiling. Additionally, the AMC may get the expenses on operation of
the mutual fund reimbursed from the concerned scheme.
The Mutual fund also appoints a custodian, holding valid certificate of registration issued by
SEBI, to have custody of securities held by the mutual fund under different schemes. In
case of dematerialized securities, this is done by Depository Participant. The custodian
must be independent of the sponsor and the AMC.

2. Please refer paragraph 5

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 MUTUAL FUNDS 77.29

Answers to the Practical Questions

1. Personal earnings of Mr. A = R1 = 16%
Mutual Fund earnings = R2
1
R2 = R 1 + Recurring expenses (%)
1 − Initial expenses (%)

1
= × 16% + 1.5%
1 − 0.055
= 18.43%
Mutual Fund earnings = 18.43%
2. Public Offer Price = NAV/ (1 – Front end Load)
Public Offer Price: ` 10.204 and NAV: ` 10
Accordingly,
10.204 = 10/(1 – F)
F = 0.0199 say 2%
Redemption Price = NAV/ (1 – Back End Load)
` 9.80 = 10/ (1 – Back End Load)
B = 0.0204 i.e. 2.04%
Alternative
10.204 − 10.00
(i) Front End Load = = 0.0204 or 2.04%
10.00
10.00 − 9.80
(ii) Exit Load = = 0.020 or 2.00%
10.00
3. Calculation of Monthly Return on the Mutual Funds
 (NAV - NAV ) + I + G 
r =  t t- 1 t t

 NAV 
t- 1

Where,
r = Return on the mutual fund
NAVt = Net assets value at time period t
NAVt – 1 = Net assets value at time period t – 1

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 7.30 STRATEGIC FINANCIAL MANAGEMENT

It = Income at time period t

Gt = Capital gain distribution at time period t
 ( ` 20.06 − ` 20.00 ) + ( ` 0.0375 + ` 0.03 ) 
r =  
 20 
0.06 + 0.0675
=
20
0.1275
= = 0.006375
20
Or, r = 0.6375% p.m.
Or = 7.65% p.a.
4. Return for the year (all changes on a per year basis)
Particulars ` /Unit
Change in price (` 13.00 – ` 12.25) 0.75
Dividend received 1.25
Capital gain distribution 1.00
Total Return 3.00
3.00
Return on investment = × 100 = 24.49%
12.25
Alternatively, it can also be computed as follows:
(NAV1 - NAV0 )+ D1 + CG1
X100
NAV0

(13 -12.25) + 1.25 + 1.00

= X 100
12.25
= 24.49%
If all dividends and capital gain are reinvested into additional units at ` 12.50 per unit the
position would be.
Total amount reinvested = ` 2.25 × 300 = ` 675
` 675
Additional units added = = 54 units
12.50
Value of 354 units as on 31-12-2010 = ` 4,602

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 MUTUAL FUNDS 77.31

Price paid for 300 units on 31-12-2009 (300 × ` 12.25) = ` 3,675

` 4,602 - ` 3,675 ` 927
Return = = = 25.22%
` 3,675 ` 3,675

5. (i) Normal Return for the year (all changes on a per year basis)
Particulars ` /Unit
Change in price (` 9.10 – ` 8.50) 0.60
Dividend received 0.90
Capital gain distribution 0.75
Total Return 2.25

2.25
Return on investment = × 100 = 26.47%
8.50
(ii) If all dividends and capital gain are reinvested into additional units at ` 8.75 per unit
the position would be.
Total amount reinvested = ` 1.65 × 200 = ` 330
` 330
Additional units added = = 37.71 units
8.75
Value of 237.71 units at end of year = ` 2,163.16
Price paid for 200 units in beginning of the year (200 × ` 8.50) = ` 1,700
` 2,163.16 - ` 1,700 ` 463.16
Return = = = 27.24%
` 1,700 ` 1,700

6. (i) Calculation of NAV at the end of month:

Given Annual Return = 15%
Hence Monthly Return = 1.25% (r)
(NAV t - NAVt -1 ) + I t +G t
r=
NAVt -1

0.0125 =
(NAVt − ` 65.78) + ` 0.50 + ` 0.32
` 65.78
0.82 = NAVt - ` 64.96

NAVt = ` 65.78
(ii) There is no change in NAV.

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 7.32 STRATEGIC FINANCIAL MANAGEMENT

7.

Shares No. of shares Price Amount (`)

Nairobi Ltd. 25,000 20.00 5,00,000
Dakar Ltd. 35,000 300.00 1,05,00,000
Senegal Ltd. 29,000 380.00 1,10,20,000
Cairo Ltd. 40,000 500.00 2,00,00,000
4,20,20,000
Less: Accrued Expenses 2,50,000
Other Liabilities 2,00,000
Total Value 4,15,70,000
No. of Units 10,00,000
NAV per Unit (4,15,70,000/10,00,000) 41.57

8. (i) NAV of the Fund

` 4,00,000 + ` 93,72,000 + ` 72,24,000 + ` 3,03,06,000
=
6,00,000
` 4,73,02,000
= = ` 78.8366 rounded to ` 78.84
6,00,000
(ii) The revised position of fund shall be as follows:
Shares No. of shares Price Amount (`)
L Ltd. 20,000 20.00 4,00,000
M Ltd. 38,000 312.40 1,18,71,200
N Ltd. 20,000 361.20 72,24,000
P Ltd. 60,000 505.10 3,03,06,000
Cash 5,00,800
5,03,02,000
30,00,000
No. of units of fund = 6,00,000 + = 6,38,053
78.8366
(iii) On 2nd February 2012, the NAV of fund will be as follows:
Shares No. of shares Price Amount (`)
L Ltd. 20,000 20.50 4,10,000
M Ltd. 38,000 360.00 1,36,80,000

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 MUTUAL FUNDS 77.33

N Ltd. 20,000 383.10 76,62,000

P Ltd. 60,000 503.90 3,02,34,000
Cash 5,00,800
5,24,86,800
` 5,24,86,800
NAV as on 2nd February 2012 = = ` 82.26 per unit
6,38,053
9. (a) NAV of the Fund.
` 1,97,000 + ` 2,41,30,000 + ` 26,44,000 + ` 6,74,90,000 + ` 7,77,000
=
800000
` 9,52,38,000
= = ` 119.0475 rounded to ` 119.05
800000
(b) The revised position of fund shall be as follows:
Shares No. of shares Price Amount (Rs.)
A Ltd. 10000 19.70 1,97,000
B Ltd. 50000 482.60 2,41,30,000
C Ltd. 28000 264.40 74,03,200
D Ltd. 100000 674.90 674,90,000
E Ltd. 30000 25.90 7,77,000
Cash 2,40,800
10,02,38,000
5000000
No. of units of fund = 800000 + = 842000
119.0475
(c) On 2nd April 2009, the NAV of fund will be as follows:
Shares No. of shares Price Amount (`)
A Ltd. 10000 20.30 2,03,000
B Ltd. 50000 513.70 2,56,85,000
C Ltd. 28000 290.80 81,42,400
D Ltd. 100000 671.90 6,71,90,000
E Ltd. 30000 44.20 13,26,000
Cash 2,40,800
10,27,87,200
` 10,27,87,200
NAV as on 2nd April 2009 = = ` 122.075 per unit
842000

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 7.34 STRATEGIC FINANCIAL MANAGEMENT

10.

Scheme Investment Unit Nos. Unit NAV Total NAV 31.3.2010

(Investment/NAV at entry 31.3.2010 (Unit Nos. X Unit
date) NAV as on
31.3.2010)
` ` `
MF A 50,000 4761.905 10.40 49,523.812
MF B 1,00,000 10,000 10.10 1,01,000
MF C 50,000 5,000 9.80 49,000

Scheme NAV Dividend Total Yield Number Effective Yield

(+) / (–) Received Change in of days (% P.A.) (Total
NAV Yield/
(NAV as on 31.3.2010
+Dividend Investment) X
–Investment)
(365/No. of
days)
X 100
` ` `
MF A (–)476.188 950 473.812 121 2.858%
MF B (+)1,000 1,500 2,500 90 10.139%
MF C (–)1,000 Nil (–)1,000 31 (–)24%

11. Calculation of effective yield on per annum basis in respect of three mutual fund schemes to
Mr. Sinha up to 31-03-2009:
Particulars MF X MF Y MF Z
(a) Investments ` 5,00,000 ` 1,00,000 ` 50,000
(b) Opening NAV `10.50 `10.00 `10.00
(c) No. of units (a/b) 47,619.05 10,000 5,000
(d) Unit NAV ON 31-3-2009 ` 10.40 ` 10.10 ` 9.80
(e) Total NAV on 31-3-2009 (c x d) ` 4,95,238.12 ` 1,01,000 ` 49,000
(f) Increase / Decrease of NAV (e - a) (` 4,761.88) ` 1,000 (` 1,000)
(g) Dividend Received ` 9,500 ` 1,500 Nil
(h) Total yield (f + g) ` 4,738.12 ` 2,500 (` 1,000)
(i) Number of Days 121 90 31
(j) Effective yield p.a. (h/a x 365/i x 100) 2.859% 10.139% (-) 23.55%

© The Institute of Chartered Accountants of India

 MUTUAL FUNDS 77.35

12. (i) Number of Units in each Scheme

MF ‘X’ ` 2,00,000
= 19,417.48
` 10.30
MF ‘Y’ ` 4,00,000
= 39,603.96
` 10.10
MF ‘Z’ ` 2,00,000
= 20,000.00
` 10.00

(ii) Total NAV on 31.03.2018

MF ‘X’ = 19,417.48 x ` 10.25 ` 1,99,029.17
MF ‘Y’ = 39,603.96 x ` 10.00 ` 3,96,039.60
MF ‘Z’ = 20,000.00 x ` 10.20 ` 2,04,000.00
Total ` 7,99,068.77
(iii) Total Yield
Capital Yield Dividend Yield Total
MF ‘X’ ` 1,99,029.17- ` 2,00,000 ` 6,000 ` 5,029.17
= - ` 970.83
MF ‘Y’ ` 3,96,039.60 - ` 4,00,000 Nil - ` 3,960.40
= - ` 3,960.40
MF ‘Z’ ` 2,04,000 - ` 2,00,000 ` 5,000 ` 9,000.00
= ` 4,000
Total ` 10,068.77
` 10,068.77
Total Yield = × 100 = 1.2586%
` 8,00,000

(iv) No. of Days Investment Held

MF ‘X’ MF ‘Y’ MF ‘Z’

Let No. of days be X Y Z
Initial Investment (`) 2,00,000 4,00,000 2,00,000
Yield (`) 5,029.17 -3,960.40 9,000.00
Yield (%) 2.5146 - 0.9901 4.5
Period of Holding (Days) 2.5146 − 0.9901 4.5
× 365 × 365 × 365
9.66 − 11.66 24.15
= 95 Days = 31 Days = 68 Days

© The Institute of Chartered Accountants of India

 7.36 STRATEGIC FINANCIAL MANAGEMENT

Date of Original Investment 27.12.17 01.03.18 23.01.18

Alternatively following dates can also be considered:
Date of Original Investment 26.12.17 28.02.18 22.01.18
13. Yield for 9 months = (153.33 x 9/12) = 115%
Market value of Investments as on 31.03.2008 = 1,00,000/- + (1,00,000x 115%)
= `2,15,000/-
Therefore, NAV as on 31.03.2008 = (2,15,000-10,000)/10,000= `20.50
(NAV would stand reduced to the extent of dividend payout, being (10,000x10x10%) = `10,000)
`10,000
Since dividend was reinvested by Mr. X, additional units acquired = = 487.80 units
` 20.50
Therefore, units as on 31.03.2008 = 10, 000+ 487.80 = 10,487.80
[Alternately, units as on 31.03.2008 = (2,15,000/20.50) = 10,487.80]
Dividend as on 31.03.2009 = 10,487.80 x 10 x 0.2 = `20,975.60
Let X be the NAV on 31.03.2009, then number of new units reinvested will be `
20,975.60/X. Accordingly 11296.11 units shall consist of reinvested units and 10487.80 (as
on 31.03.2008). Thus, by way of equation it can be shown as follows:
20975.60
11296.11 = + 10487.80
X
Therefore, NAV as on 31.03.2009 = 20,975.60/(11,296.11- 10,487.80)
= `25.95
NAV as on 31.03.2010 = ` 1,00,000 (1+0.7352x33/12)/11296.11
= ` 26.75
14. Yield for 9 months = 115%
Market value of Investments as on 31.03.2013 = 1,00,000/- + (1,00,000x 115%)
= ` 2,15,000/-
Therefore, NAV as on 31.03.2013 = (2,15,000 -10,000)/10,000 = ` 20.50
(NAV would stand reduced to the extent of dividend payout, being (`100,000 x 10%)
= ` 10,000)

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 MUTUAL FUNDS 77.37

Since dividend was reinvested by Mr. X, additional units acquired

` 10,000
= = 487.80 units
` 20.50
Therefore, units as on 31.03.2013 = 10,000+ 487.80 = 10,487.80
[Alternately, units as on 31.03.2013 = (2,15,000/20.50) = 10,487.80]
Dividend as on 31.03.2014 = 10,487.80 x 10 x 0.2 = ` 20,975.60
Let X be the NAV on 31.03.2014, then number of new units reinvested will be
` 20,975.60/X. Accordingly 11296.11 units shall consist of reinvested units and 10487.80
(as on 31.03.2013). Thus, by way of equation it can be shown as follows:
20975.60
11296.11 = + 10487.80
X
Therefore, NAV as on 31.03.2014 = 20,975.60/(11,296.11- 10,487.80)
= ` 25.95
NAV as on 31.03.2015 = ` 1,00,000 (1+2.0217)/11296.11
= ` 26.75
15. (i) Returns for the year
(All changes on a Per -Unit Basis)
Change in Price: ` 9.45 – `8.75 = ` 0.70
Dividends received: ` 0.75
Capital gains distribution ` 0.60
Total reward ` 2.05
` 2.05
Holding period reward: × 100 = 23.43%
` 8.75
(ii) When all dividends and capital gains distributions are re-invested into additional
units of the fund @ (` 8.65/unit)
Dividend + Capital Gains per unit
= ` 0.75 + ` 0.60 = ` 1.35
Total received from 300 units = `1.35 x 300 = `405/-.

© The Institute of Chartered Accountants of India

 7.38 STRATEGIC FINANCIAL MANAGEMENT

Additional Units Acquired

= `405/`8.65 = 46.82 Units.
Total No.of Units = 300 units + 46.82 units = 346.82 units.
Value of 346.82 units held at the end of the year
= 346.82 units x `9.45 = `3277.45
Price Paid for 300 Units at the beginning of the year
= 300 units x `8.75 = `2,625.00
Holding Period Reward
` (3277.45 – 2625.00) = `652.45
` 652.45
Holding Period Reward = × 100 = 24.85%
` 2625.00
Conclusion: Since the holding period reward is more in terms of percentage in
option-two i.e., reinvestment of distributions at an average NAV of `8.65 per unit,
this option is preferable.
16.

Amount in Amount in Amount in

` lakhs ` lakhs ` lakhs
Opening Bank (200 - 185 -12) 3.00
Add: Proceeds from sale of securities 63.00
Add: Dividend received 2.00 68.00
Deduct:
Cost of securities purchased 56.00
Fund management expenses paid (90% of 8) 7.20
Capital gains distributed = 80% of (63 – 60) 2.40
Dividend distributed =80% of 2.00 1.60 67.20
Closing Bank 0.80
Closing market value of portfolio 198.00
198.80
Less: Arrears of expenses 0.80
Closing Net Assets 198.00
Number of units (Lakhs) 20
Closing NAV per unit (198.00/20) 9.90
Rate of Earning (Per Unit)

© The Institute of Chartered Accountants of India

 MUTUAL FUNDS 77.39

Amount
Income received (` 2.40 + ` 1.60)/20 ` 0.20
Loss: Loss on disposal (` 200 - ` 198)/20 ` 0.10
Net earning ` 0.10
Initial investment ` 10.00
Rate of earning (monthly) 1%
Rate of earning (Annual) 12%

17. Mrs. Charu Plan A Dividend Reinvestment

(Amount in ` )
Date Investment Dividend Dividend Re- NAV Units Closing
payout invested (Closing Unit
(%) Units X Face value Balance
of ‘10 X Dividend ∑ Units
Payout %)
01.04.1999 1,00,000.00 10.00 10,000.00 10,000.00
28.07.2003 20 20,000.00 30.70 651.47 10,651.47
31.03.2004 70 74,560.29 58.42 1,276.28 11,927.75
30.10.2007 40 47,711.00 42.18 1,131.13 13,058.88
15.03.2008 25 32,647.20 46.45 702.85 13,761.73
24.03.2009 40 55,046.92 48.10 1,144.43 14,906.16
Redemption value 14,906.16 × 53.75 8,01,206.10
Less: Security Transaction Tax (STT) is 0.2% 1,602.41
Net amount received 7,99,603.69
Less: Short term capital gain tax @ 10% on 1,144.43 (53.64* – 48.10≈) = 634
6,340
Net of tax 7,98,969.69
Less: Investment 1,00,000.00
6,98,969.69
*(53.75 – STT @ 0.2%)
≈ This value can also be taken as zero
6,98,969.69 12
Annual average return (%) × × 100 = 67.64 %
1,00,000 124

© The Institute of Chartered Accountants of India

 7.40 STRATEGIC FINANCIAL MANAGEMENT

Mr. Anand Plan B – Bonus

(Amount in `)
Date Units Bonus units Total Balance NAV per unit
01.04.1999 10,000 10,000 10
31.03.2004 12,500 22,500 31.05
31.03.2008 7,500 30,000 20.05
24.03.2009 7,500 37,500 19.95
Redemption value 37,500 × 22.98 8,61,750.00
Less: Security Transaction Tax (STT) is 0.2% 1,723.50
Net amount received 8,60,026.50
Less: Short term capital gain tax @ 10%
7,500 × (22.93† – 19.95≈) = 22,350 2,235.00
Net of tax 8,57,791.50
Less: Investment 1,00,000.00
Net gain 7,57,791.50
†(22.98 – STT @ 0.2%)
≈ This value can also be taken as zero.

7,57,791.50 12
Annual average return (%) × × 100 = 73.33 %
1,00,000 124

Mr. Bacchan Plan C – Growth

Particulars (Amount in `)
Redemption value 10,000 × 82.07 8,20,700.00
Less: Security Transaction Tax (S.T.T) is .2% 1,641.40
Net amount received 8,19,058.60
Less: Short term capital gain tax @ 10% 0.00
Net of tax 8,19,058.60
Less: Investment 1,00,000.00
Net gain 7,19,058.60
7,19,058 12
Annual average return (%) × × 100 = 69.59 %
1,00,000 124

© The Institute of Chartered Accountants of India

 MUTUAL FUNDS 77.41

Note: Alternatively, figure of * and † can be taken as without net of Tax because, as per
Proviso 5 of Section 48 of IT Act, no deduction of STT shall be allowed in computation of
Capital Gain.
18. Plan – D
2,00,000
Unit acquired = = 5235.60
38.20
Date Units held Dividend Reinvestment New Total
% Amount Rate Units Units
01.04.2005 5235.60
30.09.2005 5235.60 10 5235.60 39.10 133.90 5369.50
31.03.2007 5369.50 15 8054.25 44.20 182.22 5551.72
15.09.2008 5551.72 13 7217.24 45.05 160.20 5711.92
27.03.2009 5711.92 16 9139.07 44.80 204 5915.92
31.03.2010 Maturity Value (` 40.40 X 5915.92) ` 2,39,003.17
Less: Cost of Acquisition ` 2,00,000.00
Total Gain ` 39,003.17

` 39,003.17 1
∴Effective Yield = × × 100 = 3.90%
` 2,00,000 5

Alternatively, it can be computed by using the IRR method as follows:

NPV at 4% = -2,00,000 + 1,96,443 = -3,557
NPV at 2% = -2,00,000 + 2,16,473 = 16,473
NPV at LR 16473
IRR= LR + (HR -LR) = 2% + ( 4% - 2%) = 3.645%
NPV at LR -NPV at HR 16473 - (-3557)

Plan – B

Date Particulars Calculation Working No. of Units NAV (`)

1.4.05 Investment `2,00,000/35.60= 5617.98 35.60
30.6.06 Bonus 5617.98/5 = 1123.60 36.25
6741.58
30.10.08 " 6741.58/8 = 842.70 38.30
7584.28

© The Institute of Chartered Accountants of India

 7.42 STRATEGIC FINANCIAL MANAGEMENT

11.4.09 " 7584.28/10 = 758.43 38.90

8342.71
31.3.10 Maturity Value 8342.71 x ` 39.70= 3,31,205.59
Less: Investment 2,00,000.00
Gain 1,31,205.59

1,31,205.59 1
∴Effective Yield x x100 = 13.12%
2,00,000 5
Alternatively, it can be computed by using the IRR method as follows:
NPV at 13% = -2,00,000 + 1,79,765 = -20,235
NPV at 8% = -2,00,000 + 2,25,413 = 25,413
NPV at LR 25413
IRR= LR + (HR - LR) = 8% + (13% − 8%) = 10.78%
NPV at LR - NPV at HR 25413 − ( −20235)
19. In order to find out the NAV, the cash balance at the end of the year is calculated as
follows-
Particulars `
Cash balance in the beginning
(` 100 lakhs – ` 98 lakhs) 2,00,000
Dividend Received 12,00,000
Interest on 7% Govt. Securities 56,000
Interest on 9% Debentures 45,000
Interest on 10% Debentures 50,000
15,51,000
(-) Operating expenses 5,00,000
Net cash balance at the end 10,51,000
Calculation of NAV `
Cash Balance 10,51,000
7% Govt. Securities (at par) 8,00,000
50,000 equity shares @ ` 175 each 87,50,000
9% Debentures (Unlisted) at cost 5,00,000

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 MUTUAL FUNDS 77.43

10% Debentures @90% 4,50,000

Total Assets 1,15,51000
No. of Units 10,00,000
NAV per Unit ` 11.55

Calculation of NAV, if dividend of ` 0.80 is paid –

Net Assets (` 1,15,51,000 – ` 8,00,000) ` 1,07,51,000
No. of Units 10,00,000
NAV per unit ` 10.75
20.
Particulars Adjusted Values
` crores
Equity Shares 46.00
Cash in hand 1.23
Bonds and debentures not listed 0.80
Bonds and debentures listed 8.00
Dividends accrued 0.80
Fixed income securities 4.50
Sub total assets (A) 61.33
Less: Liabilities
Amount payable on shares 6.32
Expenditure accrued 0.75
Sub total liabilities (B) 7.07
Net Assets Value (A) – (B) 54.26
No. of units 20,00,000
Net Assets Value per unit (` 54.26 crore / 20,00,000) ` 271.30
21. Calculation of Income available for Distribution
Units Per Unit Total
(Lakh) (`) (` In lakh)
Income from April 300 0.0765 22.9500
Add: Dividend equalization collected on issue 6 0.0765 0.4590
306 0.0765 23.4090
Add: Income from May 0.1125 34.4250

© The Institute of Chartered Accountants of India

 7.44 STRATEGIC FINANCIAL MANAGEMENT

306 0.1890 57.8340

Less: Dividend equalization paid on repurchase 3 0.1890 (0.5670)
303 0.1890 57.2670
Add: Income from June 0.1500 45.4500
303 0.3390 102.7170
Less: Dividend Paid 0.2373 (71.9019)
303 0.1017 30.8151
Calculation of Issue Price at the end of April
`
Opening NAV 18.750
Add: Entry Load 2% of ` 18.750 (0.375)
19.125
Add: Dividend Equalization paid on Issue Price 0.0765
19.2015

Calculation of Repurchase Price at the end of May

`
Opening NAV 18.750
Less: Exit Load 2% of ` 18.750 (0.375)
18.375
Add: Dividend Equalization paid on Issue Price 0.1890
18.564

Closing NAV
` (Lakh)
Opening Net Asset Value (` 18.75 × 300) 5625.0000
Portfolio Value Appreciation 425.4700
Issue of Fresh Units (6 × 19.2015) 115.2090
Income Received (22.950 + 34.425 + 45.450) 102.8250
6268.504
Less: Units repurchased (3 × 18.564) -55.692

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 MUTUAL FUNDS 77.45

Income Distributed -71.9019 (-127.5939)

Closing Net Asset Value 6140.9101
Closing Units (300 + 6 – 3) lakh 303 lakh
∴ Closing NAV as on 30th June ` 20.2670

22. Let portfolio standard deviation be σp

Market Standard Deviation = σm
Coefficient of correlation = r
σ pr
Portfolio beta (βp) =
σm

Required portfolio return (Rp) = Rf + βp (Rm – Rf)

Portfolio Beta Return from the portfolio (Rp) (%)

A 1.75 17.75
B 0.90 13.50
C 0.65 12.25
D 1.25 15.25
E 0.90 13.50

Portfolio Sharpe Method Treynor Method Jensen's Alpha

Ratio Rank Ratio Rank Ratio Rank
A 4.00 IV 5.71 V 1.25 V
B 3.00 V 6.67 IV 1.50 IV
C 7.50 I 9.23 I 2.75 II
D 4.25 III 6.80 III 2.25 III
E 4.50 II 9.00 II 3.60 I

23. Working Notes:

(i) Decomposition of Funds in Equity and Cash Components

D Mutual Fund Ltd. K Mutual Fund Ltd.

NAV on 31.12.14 ` 70.71 ` 62.50
% of Equity 99% 96%

© The Institute of Chartered Accountants of India

 7.46 STRATEGIC FINANCIAL MANAGEMENT

Equity element in NAV ` 70 ` 60

Cash element in NAV ` 0.71 ` 2.50

(ii) Calculation of Beta

(a) D Mutual Fund Ltd.
E(R) - R f E(R) - R f
Sharpe Ratio = 2 = =
σD 11.25

E(R) - Rf = 22.50
E(R) - R f 22.50
Treynor Ratio = 15 = =
βD βD

βD = 22.50/15 = 1.50
(b) K Mutual Fund Ltd.
E(R) - R f E(R) - R f
Sharpe Ratio = 3.3 = =
σK 5

E(R) - Rf = 16.50
E(R) - R f 16.50
Treynor Ratio = 15 = =
βK βK

βK = 16.50/15 = 1.10
(iii) Decrease in the Value of Equity
D Mutual Fund Ltd. K Mutual Fund Ltd.
Market goes down by 5.00% 5.00%
Beta 1.50 1.10
Equity component goes down 7.50% 5.50%

(iv) Balance of Cash after 1 month

D Mutual Fund Ltd. K Mutual Fund Ltd.
Cash in Hand on 31.12.14 ` 0.71 ` 2.50
Less: Exp. Per month ` 0.25 ` 0.25
Balance after 1 month ` 0.46 ` 2.25

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 MUTUAL FUNDS 77.47

NAV after 1 month

D Mutual Fund Ltd. K Mutual Fund Ltd.

Value of Equity after 1 month
70 x (1 - 0.075) ` 64.75 -
60 x (1 - 0.055) - ` 56.70
Cash Balance 0.46 2.25
65.21 58.95
24. (a) If return is 29%

`
Fixed fee (A) 0.10% of ` 20 crore 2,00,000
New Fund Value (1.29 x ` 20 crore) 25.80 crore
Excess Value of best achieved (25.8 crore – 21.0 crore) 4.80 crore
Incentive Fee (2% of 4.80 crores) (B) 9,60,000
Total Fee (A)+(B) 11,60,000

(b) If return is 4.5%

`
Fixed (A) 0.10% of ` 20 crore 2,00,000
New Fund Value (1.045 x ` 20 crore) 20.90 crore
Excess Value of best achieved (20.90 crore –21.00 crore) (` 0.10 crore)
Incentive Fee (as does not exceed best achieved) (B) Nil
Total Fee (A)+(B) 2,00,000

(c) If return is (-1.8%)

No incentive only fixed fee of ` 2,00,000 will be paid
25. Constant Ratio Plan:

Stock Value of Value of Total value Revaluation Total No.

Portfolio Conservative aggressive of Constant Action of units in
NAV Portfolio Portfolio Ratio Plan aggressive
(`) (`) (`) portfolio
(`)
40.00 1,00,000 1,00,000 2,00,000 - 2500

© The Institute of Chartered Accountants of India

 7.48 STRATEGIC FINANCIAL MANAGEMENT

25.00 1,00,000 62,500 1,62,500 - 2500

81,250 81,250 1,62,500 Buy 750 units 3250
36.00 81,250 1,17,000 1,98,250 - 3250
99,125 99,125 1,98,250 Sell 496.53 units 2753.47
32.00 99,125 88,111.04 1,87,236.04 - 2753.47
38.00 99,125 1,04,631.86 2,03,756.86 - 2753.47
1,01,878.43 1,01,878.43 2,03,756.86 Sell 72.46 units 2681.01
37.00 1,01,878.50 99,197.37 2,01,075.87 - 2681.01
42.00 1,01,878.50 1,12,602.42 2,14,480.92 - 2681.01
43.00 1,01,878.50 1,15,283.43 2,17,161.93 - 2681.01
50.00 1,01,878.50 1,34,050.50 2,35,929 - 2681.01
1,17,964.50 1,17,964.50 2,35,929 Sell 321.72 units 2359.29
52.00 1,17,964.50 1,22,683.08 2,40,647.58 - 2359.29

Hence, the ending value of the mechanical strategy is ` 2,40,647.58 and buy & hold strategy is
` 2,60,000.

© The Institute of Chartered Accountants of India