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SFM COMPILER Mutual Funds

Years May Nov

RTP Paper RTP Paper

2008 NA NA Yes No

2009 Yes Yes Yes Yes

2010 Yes Yes Yes No

2011 No Yes Yes Yes




2015 No Yes No Yes


2017 Yes No Yes Yes

2018 (Old) Yes Yes Yes Yes

2018 (New) Yes Yes Yes Yes

2019 (Old)

2019 (New)

2008

Question 1 Nov 2008 – RTP

Arun has invested in three Mutual Fund Schemes as per details below:

MF X MF Y MF Z

Date of investment 01.12.2006 01.01.2007 01.03.2007

Amount of investment 50,000 1,00,000 50,000

Net Asset Value (NAV) at entry date 10.50 10 10

Dividend received upto 31.03.2007 950 1,500 Nil

NAV as at 31.03.2007 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. Arun

upto 31.03.2007?

Solution :

MF A MF B MF C

Date of Investments 1/12/06 1/1/07 1/3/07

Amount of Investment 50,000 1,00,000 50,000

NAV on entry Date 10.50 10 10

CHP - 3 MUTUAL FUNDS

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Mutual Funds SFM COMPILER

Units Received 50,000 10.50 = 4761.9

1,00,000 10 = 10,000

50,000 10 = 5,000

Dividend Received 950 1,500 Nil

Dividend Per Unit 950 4761.9 = 0.1995

1,500 10,000 = 0.15

Nil

NAV at 31/3/2007 10.4 10.10 9.80

Holding Period 4 months 3 months 1 month

HPY 0.1995 – 0.1 10.5 x 100 =

0.9475%

0.15 + 0.1 10 x 100

= 2.5%

–0.2 10 x 100

= 2%

MMY 0.9475 x 3 = 2.8425% 2.5 x 4 = 10% 2 x 12 = - 24%

EAY (1 + 0.009475)3 – 1

= 2.8695%

(1.025)4 – 1

= 10.38%

(1.02)12 – 1

= –26.82%

2009

Question 2 May 2009 - RTP

On 01.07.2005 Mr. A invested in 10,000 units of face value of Rs.10 per unit. On 31.03.2006 dividend

was paid @ 10% and annualized yield was 140%. On 31.03.2007, 20% dividend was given. On

31.03.2008, Mr. A redeemed his all his 11,270.56 units when his annualized yield was 75.45% over

the period of his holding. What are the NAVs as on 31.03.2006,31.03.2007 and 31.03.2008?

Solution

9 months 1 yr 1 Yr

1/7/2005 31/3/2006 31/3/2007 31/3/2008

Yield P.A 140% ? 75.45%

Units 10000 ? ? 11,270.56

Dividend NA 10% 20% NIL

NAV 10 X Y Z

Before we start calculation for NAV, first we need to understand that investor is following dividend

reinvestment plan because units are seen to be increasing from 10,000 to 11,270.56 at the end of

the period.

1) Calculation for First 9 months

Let the NAV on 31.3.2006 be X

Return from 1/7/2005 to 31.3.2006 (9 months) = 140 / 12 x 9 = 105%

HPY = Dividend Dist. + Capital Gain Dist. + Capital Appreciation

Purchase Price x 100

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105 = 1(10% of 10) + (X – 10)

10 x 100

Therefore X = 19.5

Dividend = 10,000 x 1 = 10,000

Amount Reinvested = 10,000

Units Received = 10,000 / 19.5 = 512.82 units

Total Units = 10,000 + 512.82 = 10,512.82

2) Calculation for First 1 yr 9 months

1 yr 1 Yr

31/3/2006 31/3/2007 31/3/2008

Units 10,512.82 ? 11,270.56

Dividend 10% 20% NIL

NAV 19.5 Y Z

Note : Units standing on 31/3/2007 would be the same as on 31/3/2008 because dividend

was received on 31/3/2007 which would have been reinvested and units would have

increased.

Dividend Received = 10,512.82 x 10 x 20% = 21,025.64

Units added = 11,270.56 – 10,512.82 = 757.74

Amount at which it was reinvested, which would the NAV

= 21,025.64 / 757.74 = 27.7478 NAV

3) Last 3 months

1 yrs

31/3/2007 31/3/2008

Yield P.A 75.45%

11,270.56 11,270.56

NIL

NAV 27.7478 Z

Return = 75.45%

75.45 = Z – 27.7478

27.7478 x 100

Z = 48.6835

Question 3 May 2009 Paper – 2 Marks

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Mr. X earns 10% on his investments in equity shares. He is considering a recently floated scheme of

a Mutual Fund where the initial expenses are 6% and annual recurring expensed are expected to be

2%. How much the Mutual Fund scheme should earn to provide a return of 10% to Mr. X?

Solution :

Indifference Point between direct return from the Fund

R2 = R1

1 – Initial Expense + Re

R2 = Return from the Fund

R1 = Direct Return

Re = Recurring Expenses

In the above Question


R1 = 10%

Re = 2%

Initial Expenses = 6%

R2 = 10

1 – 0.06 + 2 = 12.64%

Question 4 Nov 2009 - RTP

Consider the following information about the return on Classic Mutual Fund, the market return and

the T-bill returns:

Year Classic Mutual Fund Market Index T-bills

1994 17.1 10.8 5.4

1995 –14.6 –8.5 6.7

1996 1.7 3.5 6.5

1997 8.0 14.1 4.3

1998 11.5 18.7 4.1

1999 –5.8 –14.5 7.0

2000 –15.6 –26.0 7.9

2001 38.5 36.9 5.8

2002 33.2 23.6 5.0

2003 –7.0 –7.2 5.3

2004 2.9 7.4 6.2

2005 27.4 18.2 10.0

2006 23.0 31.5 11.4

2007 –0.6 –4.9 14.1

2008 21.4 20.4 10.7

The following additional information is available regarding the comparative performance of five

mutual funds:

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Return (%) Standard Deviation (%) Beta

Alpha 1.95 20.03 0.983 0.819

Beta 11.57 18.33 0.971 0.881

Gama 8.41 22.92 1.169 0.816

Rho 9.05 24.04 1.226 0.816

Theta 7.86 15.46 0.666 0.582

From the above information, calculate all the inputs required for determining the Sharpe’s Ratio,

Treynor’s ratio and Jensen’s ratio.

Solution :

Classic (Ri) Market Index (Rm) T-bills (Rp) Ri – Rp Rm – Rp

17.1 10.8 5.4 11.7 5.4

–14.6 –8.5 6.7 –21.30 –15.20

1.7 3.5 6.5 –4.8 –3.00

8 14.1 4.3 3.7 9.8

11.5 18.7 4.1 7.4 14.6

–5.8 –14.5 7 –12.8 –21.5

–15.6 –26.0 7.9 –23.5 –33.9

38.5 36.9 5.8 32.7 31.1

33.2 23.6 5 28.2 18.6

–7.0 –7.2 5.3 –12.3 –12.5

2.9 7.4 6.2 –3.3 1.2

27.4 18.2 10 17.4 8.2

23 31.5 11.4 11.6 20.1

–0.6 –4.9 14.1 –14.7 –19.0

21.4 20.4 10.7 10.7 9.7

Average 9.406 Average 8.267 Average 7.36

Standard Standard Standard

Deviation 16.40 Deviation 17.126 Deviation 2.815

Sharpe’s measure index

S =(R – Rf)/σp

Where,

Rp = Average Return on portfolio

Rf = Risk-free rate of return

σp = Standard deviation of portfolio

Classic Mutual Fund- Sp = Rp - Rf/σp = 9.407– 7.360/16.4 = 0.125

Market Index- Sp = Rm – Rf/σm = 8.267– 7.360/17.126 = 0.053

Classic Mutual Fund is better on the basis of the Sharpe’s measure.

Treynor’s measure

T =(Rp – Rf)/βp

βp = Beta value of portfolio.

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Using regression technique to fine Beta

After making calculation by taking Market Index as (x) and Classic Mutual Fund as (y)the values are

Market Index (x) (x)2 Classic (y) (y)2 (xy)

10.8 116.64 17.1 292.41 184.68

–8.5 72.25 –14.6 213.16 124.1

3.5 12.25 1.7 2.89 5.95

14.1 198.81 8.0 64.00 112.8

18.7 349.69 11.5 132.25 215.05

–14.5 210.25 –5.8 33.64 84.1

–26.0 676.00 –15.6 243.36 405.6

36.9 1361.61 38.5 1482.25 1420.65

23.6 556.96 33.2 1102.24 783.52

–7.2 51.84 –7.0 49.00 50.4

7.4 54.76 2.9 8.41 21.46

18.2 331.24 27.4 750.76 498.68

31.5 992.25 23.0 529.00 724.5

–4.9 24.01 –0.6 0.36 2.94

20.4 416.16 21.4 457.96 436.56

Σx2 = 5424.72 y = 9.406

Σy = 141.1 x = 8.267

Σy2 = 5361.69 n =15

Σxy = 5070.99.

Substituting values in the above equation

b = 5070.99 – 15 x 9.406 x 8.267

5424.72 – 15 x 8.2622 = 3904.59 4399.57 = 0.88

a = 9.406 – 0.88 x 8.267 = 2.13

From above calculation Beta value of security = 0.88

Treynor’s measure of Classic Mutual Fund - T1 = 9.407– 7.360/0.88 = 2.32

Treynor’s measure of Market Index- Tm = 8.267– 7.360/1.00 = 0.907

Jensen’s performance measure

Rjt - Rij = αj + βj ( Rmt - Rft)

Where,

Rjt = Average return on portfolio j for period t

Rft = Risk less rate of interest for period t

αj = Intercept that measures the forecasting ability of the portfolio manager

βj = A measure of systematic risk

Rmt = Average return of a market portfolio for period t.

Substituting values in the above equation = 9.406 – 7.360 = αj + 0.88 (8.267 – 7.360)

αi = 2.046– 0.798 = 1.248

Question 5 Nov Paper – 8 Marks

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A mutual fund made an issue of 10,00,000 units of Rs.10 each on January 01, 2008. No entry load was

charged. It made the following investments:

Rs.

50,000 Equity shares of Rs.100 each @ Rs.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 Rs.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. Other investments are at par.

Find out the Net Asset Value (NAV) per unit given that operating expenses paid during the year

amounted to Rs.5,00,000. Also find out the NAV, if the Mutual fund had distributed a dividend of

Rs.0.80 per unit during the year to the unit holders.

Solution :

1) Opening = 10,00,000 x 10 = Rs.1,00,00,000 crore

Investments 98,00,000 Cash Rs.2,00,000

2) Position of fund

50,000 Equity shares of Rs.100 each @ Rs.175

7% Government Securities

9% Debentures (Unlisted)

10% Debentures (Listed) (90%)

87,50,000

8,00,000

5,00,000

4,50,000

Total 1,05,00,000

3) Cash Position

Opening Balance

Add Dividend Received

Add Interest Received

7% Government Security

9% Debentures

10% Debentures

Less Operating Expenses

2,00,000

12,00,000

56,000

45,000

50,000

(5,00,000)

Total 10,51,000

4) Net Asset Value (NAV) = 1,05,00,000 + 10,51,000

10,00,000 = Rs.11.551

Net Asset Value (NAV) with Dividend

Dividend = 10,00,000 x 0.80 = 8,00,000

= 1,05,00,000 + 10,51,000 – 8,00,000

10,00,000 = Rs.10.751

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2010

Question 6 May 2010 RTP

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 (Rs./unit) Month Ending NAV (Rs./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 Rs.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.

Solution :

Stock

Port-

Folio

NAV

Value of

buy-hold

Strategy

(Rs.)

Value of

Conservative

Portfolio (Rs.)

Value of

aggressive

Portfolio (Rs.)

Total value of

Constand Ratio

Plan (Rs.)

Revaluation

Action

Total No. of

units in

Aggressive

portfolio

40.00 2,00,000 1,00,000 1,00,000 2,00,000 - 2500

25.00 1,25,000 1,00,000 62,500 1,62,500 - 2500

1,25,000 81,250 81,250 1,62,500 Buy 750

units

3250

36.00 1,80,000 81,250 1,17,000 1,98,250 - 3250

1,80,000 99,125 99,125 1,98,250 Sell 496.53 2753.47

32.00 1,60,000 99,125 88,111.04 1,87,236.04 - 2753.47

38.00 1,90,000 99,125 1,04,631.86 2,03,756.86 - 2753.47

1,90,000 1,01,878.43 1,01,878.43 2,03,756.86 Sell 72.46 2681.01

37.00 1,85,000 1,01,878.50 99,197.37 2,01,075.87 - 2681.01

42.00 2,10,000 1,01,878.50 1,12,602.42 2,14,480.92 - 2681.01

43.00 2,15,000 1,01,878.50 1,15,283.43 2,17,161.93 - 2681.01

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50.00 2,50,000 1,01,878.50 1,34,050.50 2,35,929 - 2681.01

2,50,000 1,17,964.50 1,17,964.50 2,35,929 Sell 321.72 2359.29

52.00 2,60,000 1,17,964.50 1,22,683.08 2,40,647.58 - 2356.29

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

Rs.2,60,000.


Based on the following information, determine the NAV of a regular income scheme on per unit basis:

Rs.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 (Rs.10 face value) 20 lacs

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.

Solution :

Particulars Adjustment Value

Rs.crores

Equity Shares 46.00

Cash in hand 1.23

Bonds and debentures not listed (1 – 0.20) 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



Sub total liabilities (B) 7.07

Net Assets Value (A) – (B) 54.26

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No of units 20,00,000

Net Assets Value per unit (Rs.54.26 crore / 20,00,000) Rs.271.30

Question 8 Nov 2010 RTP

Mr. X, an investor purchased 200 units of ABC Mutual Fund at rate of Rs.8.50 p.u., one year ago. Over

the year Mr. X received Rs.0.90 as dividend and had received a capital gains distribution of Rs.0.75

per unit.

You are required to find out:

(a) Mr. X’s holding period return assuming that this no load fund has a NAV of Rs.9.10 as on today.

(b) Mr. X’s holding period return, assuming all the dividends and capital gains distributions are

reinvested into additional units as at average price of Rs.8.75 per unit.

Solution :

(a) Return for Payout Plan :

HPY = Price Purchase

onAppreciati Cap. dist.gain Cap. Div.dist. 100

= 8.5

0.60.750.9 100

= 26.47%

(b) When all dividends and capital gains distributions are reinvested into additional units of the

fund (Rs.8.75/unit):

Dividends and capital gains per unit: Rs.0.90 + Rs. 0.75 = Rs.1.65

Total amount received from 200 units: Rs.1.65 X 200 = Rs.330.00

Additional units added: Rs.330/Rs.8.75 = 37.7 units

Value of 237.7 units held at end of year: 237.7 units X Rs. 9.10 = Rs.2,163

Price paid for 200 units at beginning of year 200 units X Rs. 8.50 = Rs.1,700

Thus, the Holding Period Return =

(No of Units at the end x Ending Price) – (No of units at Beg x Initial Prices)

No of Unis at the Beg xc Initial Price

= 2,163 – 1,700

1,700 x 100 = 27.24%

Question 9 Nov 2010 RTP

Following is the historical performance information is available of the capital market and a Tomplan

Mutual Fund.

Year Tomplan Mutual

Fund Beta

Tomplan Mutual

Fund return %

Return on

Market index%

Return on Govt.

securities%

2001 0.90 –3.00 -8.50 6.50

2002 0.95 1.50 4.00 6.50

2003 0.95 18.00 14.00 6.00

2004 1.00 22.00 18.50 6.00

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2005 1.00 10.00 5.70 5.75

2006 0.90 7.00 1.20 5.75

2007 0.80 18.00 16.00 6.00

2008 0.75 24.00 18.00 5.50

2009 0.75 15.00 10.00 5.50

2010 0.70 –2.00 8.00 6.00

(a) From above information you are required to calculate the following risk adjusted return

measures for the measures for the Tomplan:

(i) Reward-to-variability ratio

(ii) Reward-to-volatility ratio

(b) Comment on the mutual fund’s performance.

Solution :

(1) Calculation of average of these four variables

Year Tomplan Mutual

Fund Beta

Tomplan Mutual

Fund return %

Return on market

index %

Return on Govt.

securities %

2001 0.90 –3.00 -8.50 6.50

2002 0.95 1.50 4.00 6.50

2003 0.95 18.00 14.00 6.00

2004 1.00 22.00 18.50 6.00

2005 1.00 10.00 5.70 5.75

2006 0.90 7.00 1.20 5.75

2007 0.80 18.00 16.00 6.00

2008 0.75 24.00 18.00 5.50

2009 0.75 15.00 10.00 5.50

2010 0.70 –2.00 8.00 6.00

Total 8.7 110.5 86.9 59.5

Average 0.87 11.05 8.69 5.95

Thus, the averages are as follows:

Mutual fund beta = 0.87

Mutual fund return = 11.05 per cent

Return on market index = 8.69 per cent

Return on Govt. securities = 5.95 per cent

(2) Standard deviation of returns of Tomplan Mutual fund

Year Mutual fund returns (X) 𝑿𝟐

1 –3.00 9.00

2 1.50 2.25

3 18.00 324.00

4 22.00 484.00

5 10.00 100.00

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6 7.00 49.00

7 18.00 324.00

8 24.00 576.00

9 15.00 225.00

10 -2.00 4.00

Total 110.50 2097.25

σp = N∑x2 – (∑x)2

N 2 = 9.36

(3) Standard deviation of returns on the market index

Year Return on market index (X) 𝑿𝟐

1 –8.50 72.25

2 4.00 16.00

3 14.00 196.00

4 18.50 342.25

5 5.70 32.49

6 1.20 1.44

7 16.00 256.00

8 18.00 324.00

9 10.00 100.00

10 8.00 64.00

Total 86.90 1404.43

σm = N∑X2 – (∑x)2

N 2 = 8.06

(a) (i) Reward to variability ratio or Sharpe ratio

For Tomplan Mutual Fund

SR =rp – rf

p =

11.05 – 5.95 9.36

= 0.545

For Market

SR = rp – rf

p =

8.69 – 5.95 8.06 = 0.34

(ii) Reward to volatility ratio or Treynor ratio

For Tomplan Mutual Fund

TR = rp – rf

bp =

11.05 – 5.95 0.87 = 5.86

For Market

TR = rp – rf

bp =

8.69 – 5.95 1 = 2.74

(b) Mutual fund performance

Ratios of the mutual fund and the market is as follows:

Ratio Mutual fund Market index

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Sharpe ratio 0.545 0.34

Treynor ratio 5.86 2.74

Thus from above it is clear that the Tomplan Mutual fund has performed better than the market.

2011

Question 10 May 2011 Paper - 8 Marks

An investor purchased 300 units of a Mutual Fund at Rs.12.25 per unit on 31st December, 2009. As

on 31st December, 2010 he has received Rs.1.25 as dividend and Rs.1.00 as capital gains distribution

per unit.

Required :

a. The return on the investment if the NAV as on 31st December, 2010 is

Rs.13.00.

b. 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 Rs.12.50 per unit.

Solution :

i) Payout Plan



HPY = 1.25 + 1 + 0.75

12.25 = 24.49 % P.A

ii) Reinvestment Plan

Amount Reinvested = (1.25 + 1) x 300 units = 675

Units at the beginning = 300 units

No. of units Received = 675

12.50 = 54 units

Total Units = 300 + 54 units = 354 units

Return = 354 x 13 - 300 x 12.25

300 x 12.25 = 25.22% P.A

Decision : Dividend Reinvestment Plan is better than dividend payout Plan

Question 11 Nov RTP – Nov 2011 RTP

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

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

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 fund 8,00,000

Please calculate :

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1. NAV of the Fund.

2. Assuming Mr. X, a HNI, send a cheque of Rs.50,00,000 to the Fund and Fund Manager

purchases 18000 shares of C Ltd. and balance is held in bank. Then what will be position of

fund.

3. Now suppose on 2 April 2009 at 4.00 p.m. the market price of shares is as follows :

Shares Rs.

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.

Solution :

1) NAV on 1st April 2009

Stocks Value

A 10,000 x 19.70 1,97,000

B 50,000 x 482.60 2,41,30,000

C 10,000 x 264.40 26,44,000

D 1,00,000 x 674.90 6,74,90,000

E 30,000 x 25.90 7,77,000

Total 9,52,38,000

NAV = 9,52,38,000

8,00,000 = Rs.119.0475 per unit

2) Revised Fund Position

Cheque of Rs.50,00,000 from Mr. A which was invested in 18000 shares in C Ltd.

Value of shares in C Ltd. = 18000 x 264.40 = 47,59,200

Cash (50,00,000 – 47,59,200) = Rs.2,40,800

Total Fund Value = Rs.9,52,38,000 + Rs.50,00,000 = Rs.10,02,38,000

Units Issued = 50,00,000 119.0475 = 42,000 units

Total Units = 8,00,000 + 42,000 = 8,42,000

NAV = 10,02,38,000

8,42,000 = Rs.119.0475 per unit

3) NAV on 2nd April 2009

Stocks Value

A 10,000 x 20.30 2,03,000

B 50,000 x 513.70 2,56,85,000

C 28,000 x 290.80 81,42,400

D 1,00,000 x 671.90 6,71,90,000

E 30,000 x 44.20 13,26,000

Cash 2,40,800

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Total 10,27,87,200

NAV = 10,27,87,200

8,42,000 = Rs.122.08 per unit

Question 12 Nov 2011 Paper – 5 Marks

Orange purchased 200 units of Oxygen Mutual Fund at Rs.45 per unit on 31st December, 2009. In

2010, he received Rs.1.00 as dividend per unit and a capital gains distribution of Rs.2 per unit.

Required:

i. Calculate the return for the period of one year assuming that the NAV as on 31st December

2010 was Rs.48 per unit.

ii. Calculate the return for the period of one year assuming that the NAV as on 31st December

2010 was Rs.48 per unit and all dividends and capital gains distributions have been reinvested

at an average price of ` 46.00 per unit.

Ignore taxation.

Solution :

(i) Returns for the year

HPY = icePurchasePr

onAppreciati Cap. dist.gain Cap. dist. Div.

= 45

321 100 = 13.33%

(ii) When all dividends and capital gains distributions are re-invested into additional units of the

fund @ (Rs.46/unit)

Dividend + Capital Gains per unit = Rs.1.00+Rs.2.00 = Rs.3.00

Total received from 200 units = Rs.3.00 x 200 = Rs.600

Additional Units Acquired = 600

46 =13.04 Units.

Total No. of Units = 200 units + 13.04 units = 213.04 units.

Value of 213.04 units held at the end of the year

= 213.04 units x Rs.48 = Rs.10225.92

Price Paid for 200 Units at the beginning of the year

= 200 units x Rs.45 = Rs.9000.00

Thus, the Holding Period Return would be:

= (No of Units at the end x Ending Price) – (No of units at Beg x Initial Price)

(No of Units at the Beg x Initital Price)

= 1,225.92 – 9,000

9,000 x 100 = 13.62%

2012

Question 13 May 2012 RTP – Similar to - Question 9 : Nov 2010 RTP

Question 14 May 2012 Paper

16 | P a g e


A Mutual Fund Co. has the following assets under it on the close of business as on:

Company No. of Shares 1st February 2012 Market price

per share (Rs)

2nd February, 2012 Market

price per share (Rs)

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 Rs.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.

Solution :

1) NAV on 1st Feb 2012

Stocks Value

L

M

N

P

20,000 x 20

30,000 x 312.40

20,000 x 361.20

60,000 x 505.10

4,00,000

93,72,000

72,24,000

3,03,06,000

Total 4,73,02,000

NAV = 4,73,02,000

6,00,000 = Rs.78.8367 per unit

2) Revised Fund Position

Cheque of Rs.30,00,000 from Mr. A which was invested in 8000 shares in M Ltd.

Value of shares in M Ltd. = 8000 x 312.40 = 24,99,200

Cash (30,00,000 – 24,99,200) = Rs.5,00,800

Total Fund Value = 4,73,02,000 + 30,00,000 = 5,03,02,000

Units Issued = 30,00,000 78.8367

= 38,053.34 units

Total Units = 6,00,000 + 38,053.34 = 6,38,053.34

NAV = 5,03,02,000 6,38,053.34 = Rs.78.8367 per unit

3) NAV on 2nd Feb 2012

Stocks Value

17 | P a g e


L

M

N

P

Cash

20,000 x 20.50

38,000 x 360

20,000 x 383.10

60,000 x 503.90

4,10,000

1,36,80,000

76,62,000

3,02,34,000

5,00,800

Total 5,24,86,800

NAV = 5,24,86,800 6,38,053.34 = Rs.82.26 per unit

Question 15 Nov 2012 RTP – Similar to Question 1 – Nov 2008 – RTP


The following information is extracted from Steady Mutual Fund’s Scheme:

- Asset Value at the beginning of the month - Rs.65.78

- Annualised return - 15 %

- Distributions made in the nature of Income - Rs.0.50 and Rs.0.32

& Capital gain (per unit respectively).

You are required to:

(1) Calculate the month end net asset value of the mutual fund scheme (limit your answers to

two decimals).

(2) Provide a brief comment on the month end NAV.

Solution :

(1) Calculation of NAV at the end of month:

Given Annual Return = 15%

Hence Monthly Return = 1.25%

HPY = (NAV at end – NAV at beg) – Capital Dist + Capital Gain

Nav at Beg

0.0125 = 65.78

0.32 0.50 Rs.65.78) - Endat (NAV

Nav at End = Rs.65.78

(2) There are no change in NAV

2013


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?

Solution

Indifference Point between direct return from the Fund

18 | P a g e


R2 = R1

1 – Initial Expense + Re


R1 = Direct Return

Re = Recurring Expenses

In the above Question


R1 = 16%

Re = 1.5%

Initial Expenses = 5.5%

R2 = 16

1 – 0.055 + 1.5 = 18.43%


Mr. Suhail has invested in three Mutual fund schemes as per details below:

Scheme X Scheme Y Scheme Z

Date of Investment 01.04.11 01.05.11 01.07.2011

Amount of Investment 12,00,000 4,00,000 2,50,000

Net Asset Value at entry date 10.25 10.15 10.00

Dividend received up to 31.07.2011 23,000 6,000 Nil

NAV as at 31.7.2011 10.20 10.25 9.90

You are required to calculate the effective yield on per annum basis in respect of each of the three

schemes to Mr. Suhail up to 31.07.2011.

Solution :

MF A MF B MF C

Date of Investments 1/4/11 1/5/11 1/7/07

Amount of Investment 12,00,000 4,00,000 2,50,000

NAV on entry Date 10.25 10.15 10

Units Received 12,00,000 10.25

= 1,17,073.17

4,00,000 10.15

= 39,408.86

2,50,000 10

= 25,000

Dividend Received 23,000 6,000 Nil

Dividend Per Unit 23,000 1,17,073 = 0.19645

6,000 39,408.86 = 0.15225

Nil

NAV at 31/3/2007 10.2 10.25 9.90

Holding Period 4 months 3 months 1 month

HPY 0.19645 – 0.05 10.25 x 100

= 1.42878%

0.15 + 0.1 10.15 x 100

= 2.485%

–0.1 10 x 100

= 1%

MMY 1.42878 x 3 = 4.28463% 2.485 x 4 = 9.94% 1 x 12 = – 12%

19 | P a g e


EAY (1 + 0.0142878)3– 1

= 4.34787%

(1.0285)4 – 1

= 10.321%

(1.01)12 – 1

= – 12.6825%


On 1-4-2012 ABC Mutual Fund issued 20 lakh units at Rs.10 per unit. Relevant initial expenses

involved were Rs.12 lakhs. It invested the fund so raised in capital market instruments to build a

portfolio of Rs.185 lakhs. During the month of April 2012 it disposed off some of the instruments

costing Rs.60 lakhs for Rs.63 lakhs and used the proceeds in purchasing securities for Rs.56 lakhs.

Fund management expenses for the month of April 2012 was Rs.8 lakhs of which 10% was in arrears.

In April 2012 the fund earned dividends amounting to Rs.2 lakhs and it distributed 80% of the realized

earnings. On 30-4-2012 the market value of the portfolio was Rs.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?

Solution :

Amount in Amount in Amount

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 67.2

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 9.90

Rate of Earning (Per Unit)

Amount

Income received (2.40 + 1.60)/20 Rs.0.20

Loss: Loss on disposal (200 - 198)/20 Rs.0.10

Net earning Rs.0.10

Initial investment Rs.10.00

Rate of earning (monthly) 1%

Rate of earning (Annual) 12%

20 | P a g e


Question 20 Nov 2013 - RTP – Similar to - Question 15 - May 2012 Paper


On 01-07-2010, Mr. X Invested Rs.50,000/- at initial offer in Mutual Funds at a face value of Rs.10

each per unit. On 31-03-2011, a dividend was paid @ 10% and annualized yield was 120%. On

31-03-2012, 20% dividend and capital gain of Rs.0.60 per unit was given.

Mr. X redeemed all his 6271.98 units when his annualized yield was 71.50% over the period of

holding.

Calculate NAV as on 31-03-2011, 31-03-2012 and 31-03-2013. For calculations consider a year of 12

months.

Solution :

9 months 1 yr 1 Yr

1/7/2010 31/3/2011 31/3/2012 31/3/2013

Yield P.A 120% ? 71.50%

Units 5000 ? ? 6,271.98

Dividend NA 10% 20% NIL

(0.6 Capital Gain)

NAV 10 X Y

Z

Before we start calculation for NAV, first we need to understand that investor is following dividend

reinvestment plan because units are seen to be increasing from 5,000 to 6,271.98 at the end of the

period.

Calculation for First 9 months

Let the NAV on 31.3.2011 be X

Return from 1/7/2010 to 31.3.2011 (9 months) = 120 / 12 x 9 = 90%



90 = 1(10% of 10) + (X – 10)

10 x 100

Therefore X = 18

Dividend = 5,000 x 1 = 5,000

Amount Reinvested = 5,000

Units Received = 5,000 / 18 = 277.78 units

Total Units = 5,000 + 277.77 = 5,277.78

Calculation for First 1 yr

21 | P a g e


1 yr 1 Yr

31/3/2011 31/3/2012 31/3/2008

Units 5,277.78 ? 6,271.98

Dividend 10% 20% NIL

(0.6 Capital Gain)

NAV Z 18 Y

Note : Units standing on 31/3/2012 would be the same as on 31/3/2013 because dividend was

received on 31/3/2012 which would have been reinvested and units would have increased.

Dividend Received = 5,277.78 x 10 x 20% = 10,555.56

Capital Gain = 5,277.78 x 0.6 = 3,166.668

Total Amount Reinvested = 10,555.56 + 3,166.668 = 13,722.228

Units added = 6,271.98 – 5,277.78 = 994.2

Amount at which it was reinvested, which would the NAV

= 13,722.228 / 994.2 = 13.80 NAV

Last 3 months 1 yrs

31/3/2012 31/3/2013

Yield P.A 71.50%

6,271.98 6,271.98

NIL

NAV 13.80 Z

Return = 71.50%

71.50 = Z – 13.80

13.80 x 100

Z = 23.667

2014


A Mutual Fund having 300 units has shown its NAV of Rs.8.75 and Rs.9.45 at the beginning and at the

end of the year respectively. The Mutual Fund has given two options:

i. Pay Rs.0.75 per unit as dividend and Rs.0.60 per unit as a capital gain, or

ii. These distributions are to be reinvested at an average NAV of Rs.8.65 per unit. What

difference it would make in terms of return available and which option is preferable?

22 | P a g e


Solution :

i) Payout Plan



HPY = 0.75 + 0.60 + 0.70

8.75 = 23.43 % P.A

ii) Reinvestment Plan

Amount Reinvested = (0.75 + 0.60) x 300 units = 405

Units at the beginning = 300 units

No of units Received = 405

8.65 = 46.8208 units

Total Units = 300 + 46.8208 units = 346.8208 units

Return = 346.8208 x 9.45 - 300 x 8.75

300 x 8.75 = 24.86% P.A

Decision : Dividend Reinvestment Plan is better than dividend payout Plan


Based on the following data, estimate the Net Asset Value (NAV) on per unit basis of a Regular Income

Scheme of a Mutual Fund:

Rs. (in lakhs)

Listed Equity shares at cost (ex-dividend) 40.00

Cash in hand 2.76

Bonds & Debentures at cost of these, Bonds not listed 8.96

& not quoted 2.50

Other fixed interest securities at cost 9.75

Dividend accrued 1.95



Current realizable value of fixed income securities of face value of Rs.100 is Rs.96.50.

Number of Units (Rs.10 face value each): 275000

All the listed equity shares were purchased at a time when market portfolio index was 12,500. On

NAV date, the market portfolio index is at 19,975.

There has been a diminution of 15% in unlisted bonds and debentures valuation.

Listed bonds and debentures carry a market value of Rs.7.5 lakhs, on NAV date.

Operating expenses paid during the year amounted to Rs.2.24 lakhs.

Solution :

Particulars Adjustment Value

Rs.lakhs

Equity Shares 63.920

23 | P a g e


Cash in hand 2.760

Bonds and debentures not listed 2.125

Bonds and debentures listed 7.500

Dividends accrued 1.950

Fixed income securities 9.409


Less: Liabilities




Net Assets Value (A) – (B) 72.364

No. of units 2,75,000

Net Assets Value per unit (Rs.72.364 lakhs / 2,75,000) Rs.26.3142

Question 24 Nov 2014 RTP – Similar to - Question 20 - May 2013 Paper – 8 Marks


Cinderella Mutual Fund has the following assets in Scheme Rudolf at the close of business on 31st

March, 2014.

Company No. of Shares Market Price Per Share

Nairobi Ltd. 25000 Rs.20

Dakar Ltd. 35000 Rs.300

Senegal Ltd. 29000 Rs.380

Cairo Ltd. 40000 Rs.500

The total number of units of Scheme Rudolf are 10 lacs. The Scheme Rudolf has accrued expenses of

Rs.2,50,000 and other liabilities of Rs.2,00,000. Calculate the NAV per unit of the Scheme Rudolf.

Solution :

Shares No of Shares Price Amount (Rs.)

Nairobi Ltd.

Dakar Ltd.

Senegal Ltd.

Cairo Ltd.

25,000

35,000

29,000

40,000

20

300

380

500

5,00,000

1,05,00,000

1,10,20,000

2,00,00,000

Less : Accrued Expenses

Other Liabilities

Total Value

No of Units

NAV Per unit (4,15,70,000 / 10,00,000)

4,20,20,000

2,50,000

2,00,000

4,15,70,000

10,00,000

41,57

2015

24 | P a g e


Question 26 May 2015 Paper – Similar to - Question 1 – Nov 2008 – RTP

Question 27 Nov 2015 Paper – 8 Marks – Similar to - Question 2 - May 2009 - RTP

Question 28 Nov 2005 – 12 Marks

Note : This question is inserted because author feels this is important for students to solve – Thanks

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 1-4-1995, Mr. Anand, Mr. Bachhan & Mrs. Charu, three investors

invested Rs. 1,00,000 each and chose 'B', 'C' & 'A' Plan respectively.

The History of the Fund is as follows :

Date Dividend (%) Bonus Net Asset Value per Unit Ratio (FV Rs, 10)

Plan A Plan B Plan C

28-07-1999 20 30.70 31.40 33.42

31-03-2000 70 5:4 58.42 31.05 70.05

31-10-2003 40 42.18 25.02 56.1$

15-03-2004 25 44.45 29.10 64.28

31-03-2004 1:3 42.18 20.05 60.12

24-03-2005 40 1:4 48.10 19.95 72.40

31-07-2005 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:

a. Long-term Capital Gain is exempt from Income tax.

b. Short-term Capital Gain is subject to 10% Income tax.

c. Security Transaction Tax 0.2 percent only on sale/redemption of units.

d. Ignore Education Cess.

Solution :

Plan A – Dividend Reinvestment Plan

Date NAV Dividend

Amount

Units Received Cumulative Units Held

1/4/95

28/7/99

31/3/2000

30/10/2003

15/3/2004

24/03/2005

10

30.7

58.42

42.18

44.45

48.10

-

20,000

74,560

47,711

32,647.20

55,173.4

10,000

651.47

1276.28

1131.13

734.47

1147.06

10,000

10,651.47

11,927.75

13,058.88

13,793.35

14940.41

25 | P a g e


Redemption Price = 53.75 – 0.2% = 53.6425

Redemption Proceeds = 14,940.11 x 53.6425 = 8,01,425

- short term Capital Gain tax @10%

1147.06 (53.64 – 48.10) 636

Net Realization 8,00,789

Return = 1,00,000 = 124

121

789,00,8

r

Return = 31

3

000,00,1

789,00,8

– 1 = 22.31%

Plan B – Bonus Plan

Date Bonus Units Purchased Cumulative Units Held

1/4/99

31/3/2000

31/3/2004

24/3/2005

-

5 : 4

1 : 3

1 : 4

10,000

12,500

7,500

7,500

10,000

22,500

30,000

37,500


Redemption Proceeds = 37,500 x 22.93 = 8,60,027

– short term Capital Gain tax @10%

7,500 (22.93 – Nil) 17,198


Return 1,00,000 = 8,42,829

(1 + r)124

12

Return = 31

3

000,00,1

829,42,8

– 1 = 22.92%

Plan C – Growth Plan


Redemption Proceeds = 10,000 x 81.90586 = 8,19,059

– short term Capital Gain tax @10% NIL


Return 1,00,000 = 8,19,059

(1 + r)124

12

Return = 31

3

000,00,1

059,19,8

– 1 = 22.58%

Question 29 Nov 2015 – Paper

26 | P a g e


Mr. X on 1.7.2012, during the initial public offer of a Mutual Fund (MF) invested Rs.1,00,000 at Face

Value of Rs.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.

Solution :

Yield for 9 months = 115%

Market value of Investments as on 31.03.2013

= 1,00,000/- + (1,00,000x 115%)

= Rs.2,15,000/-

Therefore, NAV as on 31.03.2013 = (2,15,000-10,000)/10,000

= Rs.20.50

(NAV would stand reduced to the extent of dividend payout, being

(Rs.100,000 x 10%) = Rs.10,000)

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

= 10,000

20.50 = 487.80 units

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

= Rs.20,975.60

Let X be the NAV on 31.03.2014, then number of new units reinvested will be Rs.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:

11296.11 = 20975.60

X + 10487.80

Therefore, NAV as on 31.03.2014 = 20,975.60/(11,296.11- 10,487.80)

= Rs.25.95

NAV as on 31.03.2015 = Rs.1,00,000 (1+2.0217)/11296.11

= Rs.26.75

Question 30 Nov 2015 – Paper – 8 Marks

On 1st April, an open ended scheme of mutual fund had 300 lakh units outstanding with Net Assets

Value (NAV) of Rs.18.75. At the end of April, it issued 6 lakh units at opening NAV plus 2% load,

27 | P a g e


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:

Rs.in lakhs

Portfolio value appreciation

Income of April

Income for May

Income for June

425.47

22.950

34.425

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.

Solution :

Calculation of Income available for Distribution

Units (Lakh) Per Unit

(Rs.)

Total (Rs.in

lakh)

Income from April

Add: Dividend equalization collected on issue

300

6

0.0765

0.0765

0.0765

0.1125

22.9500

0.4590

Add: Income from May

306 23.4090

34.4250

Less: Dividend equalization paid on repurchase

306

3

0.1890

0.1890

57.8340

(0.5670)

Add: Income from June

303 0.1890

0.1500

0.3390

0.2373

57.2670

45.4500

Less: Dividend Paid

303 102.7170

(71.9019)

303 0.1017 30.8151

Calculation of Issue Price at the end of April

Rs.

Opening NAV

Add: Entry load 2% of Rs.18.750

18.750

(0.375)

Add: Dividend Equalization paid on Issue Price

19.125

0.0765

19.2015

Calculation of Repurchase Price at the end of May

28 | P a g e


Rs.

Opening NAV

Less: Exit load 2% of Rs.18.750

18.750

(0.375)

Add: Dividend Equalization paid on Issue Price

18.375

0.1890

18.564

Closing NAV

Rs.(Lakh)

Opening Net asset value (Rs.18.75 x 300)

Portfolio Value Appreciation

Issue of Fresh Units (6 x 19.2015)

Income Received (22.950 + 34.425 + 45.450)

5625.0000

425.4700

115.2090

102.8250

Less: Units repurchased (3 x 18.564)

Income Distributed

-55.692

-71.9019

6268.504

(-127.5939)

Closing Net Asset Value 6140.9101

Closing Units (300 + 6 - 3) lakh

Closing NAV as on 30th June ؞

303 lakh

Rs.20.2670

Question 31 May 2016 – RTP

Orange purchased 200 units of Oxygen Mutual Fund at Rs.45 per unit on 31st December,2009. In

2010, he received Rs.1.00 as dividend per unit and a capital gains distribution of Rs.2 per unit.

Required:

(i) Calculate the return for the period of one year assuming that the NAV as on 31st December

2010 was Rs.48 per unit.

(ii) Calculate the return for the period of one year assuming that the NAV as on 31st December

2010 was Rs.48 per unit and all dividends and capital gains distributions have been reinvested

at an average price of Rs.46.00 per unit.

Ignore taxation.

Solution

(i) Returns for the year

(All changes on a Per -Unit Basis)

Change in Price: Rs.48 – Rs.45 = Rs.3.00

Dividends received: Rs.1.00

Capital gains distribution Rs.2.00

Total reward Rs.6.00

Holding period reward: 6.00

45 x 100 = 13.33%

(ii) When all dividends and capital gains distributions are re-invested into additional units of the

fund @ (Rs.46/unit)

29 | P a g e


Dividend + Capital Gains per unit = Rs.1.00 + Rs.2.00 = Rs.3.00

Total received from 200 units = Rs.3.00 x 200 = Rs.600/-

Additional Units Acquired = 600/46

= 13.04 Units.

Total No. of Units = 200 + 13.04

= 213.04 units.

Value of 213.04 units held at the end of the year

= 213.04 units x Rs.48

= Rs.10225.92

Price Paid for 200 Units at the beginning of the year

= 200 units x Rs.45

= Rs.9000.00

Holding Period Reward Rs.(10225.92 – 9000.00) = Rs.1225.92

Holding Period Reward = 𝟏𝟐𝟐𝟓.𝟗𝟐

𝟗𝟎𝟎𝟎 x 100 = 13.62%

Question 32 May 2016 – Paper – 6 Marks

Calculate the NAV of a regular income scheme on per unit basis of Red Bull mutual fund from the

following information:

Particulars Rs.in crores

Listed shares at cost (ex - dividend)

Cash in hand

Bonds & Debentures at cost (ex - interest)

Of these, bonds not listed & not quoted

Other fixed interest securities at cost

Dividend accrued

Amount payable on shares

Expenditure accrued

Value of listed bonds & debentures at NAV date

30

0.75

2.30

1.0

2.50

0.8

8.32

1.00

10

Number of units (Rs.10 face value) 30 lakhs

Current realizable value of fixed income securities

of face value of Rs.100 is 106.50

The listed shares were purchased when index was 7100

and the Present index is 9000

Unlisted bonds and debentures are at cost. Other fixed interest securities are also at cost.

Solution :

Particulars Adjusted Value

Rs. crores

Equity shares (30 x 9000/7100) 38.028

30 | P a g e


Cash in hand

Bonds & Debentures not listed

Bonds & Debentures listed

Dividend accrued

Fixed income securities

0.75

1.00

10.00

0.80

2.50


Less: Liabilities


Expenditure accrued

8.32

1.00


Net assets value (A) – (B) 43.758

No. of units

Net assets value per unit (43.758 crore/30,00,000)

30,00,000

Rs.145.86


Based on the following data, estimate the Net Asset Value (NAV) on per unit basis of a Regular Income

Scheme of a Mutual Fund on 31-3-2015:

Rs. (in lakhs)

Listed Equity shares at cost (ex-dividend)

Cash in hand (As on 1-4-2014)

Bonds & debentures at cost of these, Bonds not listed

& not quoted

Other fixed interest securities at cost

Dividend accrued


Expenditure accrued

40.00

5.00

8.96

2.50

9.75

1.95

13.54

1.76

Current realizable value of fixed income securities of face value of Rs.100 is Rs.96.50.


All the listed equity shares were purchased at a time when market portfolio index was 12,500. On

NAV date, the market portfolio index is at 19,975.

There has been a diminution of 15% in unlisted bonds and debentures valuation.

Listed bonds and debentures carry a market value of Rs.7.5 lakhs, on NAV date.

Operating expenses paid during the year amounted to Rs.2.24 lakhs.

Solution :

Particulars Adjusted Value

Rs. crores

Equity shares

Cash in hand (5.500 – 2.240)

Bonds & Debentures not listed

Bonds & Debentures listed

63.920

2.760

2.125

7.500

31 | P a g e


Dividend accrued

Fixed income securities

1.950

9.409


Less: Liabilities


Expenditure accrued

13.54

1.76


Net assets value (A) – (B) 72.364

No. of units

Net assets value per unit (72.364 lakhs/2,75,000)

2,75,000

Rs.26.314


Mr. Abhishek is interested in investing Rs.2,00,000 for which he is considering following three

alternatives:

(i) Invest Rs.2,00,000 in Mutual Fund X (MFX)

(ii) Invest Rs.2,00,000 in Mutual Fund Y (MFY)

(iii) Invest Rs.1,20,000 in Mutual Fund X (MFX) and ` 80,000 in Mutual Fund Y (MFY)

Average annual return earned by MFX and MFY is 15% and 14% respectively. Risk free rate of return

is 10% and market rate of return is 12%.

Covariance of returns of MFX, MFY and market portfolio Mix are as follow:

MFX MFY Mix

MFX 4.800 4.300 3.370

MFY 4.300 4.250 2.800

M 3.370 2.800 3.100

You are required to calculate:

(i) variance of return from MFX, MFY and market return,

(ii) portfolio return, beta, portfolio variance and portfolio standard deviation,

(iii) expected return, systematic risk and unsystematic risk; and

(iv) Sharpe ratio, Treynor ratio and Alpha of MFX, MFY and Portfolio Mix

Solution :

(i) Variance of Returns

𝐂𝐨𝐫𝐢,𝐣 = 𝐂𝐨𝐯 (𝐢.𝐣)

𝛔𝐢𝛔𝐣

Accordingly, for MFX

1 = 𝐂𝐨𝐯 (𝐗,𝐗)

𝛔𝐗𝛔𝐗

𝛔𝐱𝟐 = 4.800

Accordingly, for MFY

1 = 𝐂𝐨𝐯(𝐘,𝐘)

𝛔𝐘𝛔𝐘

𝛔𝐲𝟐 = 4.250

32 | P a g e


Accordingly, for Market return

1 = 𝐂𝐨𝐯 (𝐌,𝐌)

𝛔𝐌𝛔𝐌

𝛔𝐌𝟐 = 3.100

(ii) Portfolio return, beta, variance and standard deviation

Weight of MFX in portfolio = 𝟏,𝟐𝟎,𝟎𝟎𝟎

𝟐,𝟎𝟎,𝟎𝟎𝟎 = 0.60

Weight of MFY in portfolio = 𝟖𝟎,𝟎𝟎𝟎

𝟐,𝟎𝟎,𝟎𝟎𝟎 = 0.40

Accordingly Portfolio Return

0.60 × 15% + 0.40 × 14% = 14.60%

Beta of each Fund

β = 𝐂𝐨𝐯 (𝐅𝐮𝐧𝐝,𝐌𝐚𝐫𝐤𝐞𝐭)

𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞 𝐨𝐟 𝐌𝐚𝐫𝐤𝐞𝐭

𝛃𝐗= 𝟑.𝟑𝟕𝟎

𝟑.𝟏𝟎𝟎 = 1.087

𝛃𝐘 = 𝟐.𝟖𝟎𝟎

𝟑.𝟏𝟎𝟎 = 0.903

Portfolio Beta

0.60 x 1.087 + 0.40 x 0.903

= 1.013

Portfolio Variance

σXY2 = WX

2σX2 +WY

2σY2 + 2WXWYCOVX.Y

= (0.60)2 (4.800) + (0.40)2 (4.250) + 2(0.60) (0.40) (4.300)

= 4.472

Or Portfolio Standard Deviation

σXY = √4.472

= 2.115

(iii) Expected Return, Systematic and Unsystematic Risk of Portfolio

Portfolio Return = 10% + 1.0134(12% - 10%) = 12.03%

MF X Return = 10% + 1.087(12% - 10%) = 12.17%

MF Y Return = 10% + 0.903(12% - 10%) = 28.06%

Systematic Risk = β2σ2

Accordingly,

Systematic Risk of MFX = (1.087)2 x 3.10 = 3.663

Systematic Risk of MFY = (0.903)2 x 3.10 = 2.528

Systematic Risk of Portfolio = (1.013)2 x 3.10 = 3.181

Unsystematic Risk = Total Risk – Systematic Risk

Accordingly,

Unsystematic Risk of MFX = 4.80 – 3.663 = 1.137

33 | P a g e


UnSystematic Risk of MFY = 4.250 – 2.528 = 1.722

UnSystematic Risk of Portfolio = 4.472 – 3.181 = 1.291

(iv) Sharpe and Treynor Ratios and Alpha

Sharpe Ratio

MFX = 𝟏𝟓%−𝟏𝟎%

√𝟒.𝟖𝟎𝟎 = 2.282

MFY = 𝟏𝟒%−𝟏𝟎%

√𝟒.𝟐𝟓𝟎 = 1.94

Portfolio = 𝟏𝟒.𝟔%−𝟏𝟎%

𝟐.𝟏𝟏𝟓 = 2.175

Treynor Ratio

MFX = 𝟏𝟓%−𝟏𝟎%

𝟏.𝟎𝟖𝟕 = 4.60

MFY = 𝟏𝟒%−𝟏𝟎%

𝟎.𝟗𝟎𝟑 = 4.43

Portfolio = 𝟏𝟒.𝟔%−𝟏𝟎%

𝟏.𝟎𝟏𝟑𝟒 = 4.54

Alpha

MFX = 15% - 12.17% = 2.83%

MFY = 14% - 11.81% = 2.19%

Portfolio = 14.6% - 12.03% = 2.57%

Question 35 May 2017 – RTP – Similar to - Question 5 - Nov 2009 Paper


Based on the following data, estimate the Net Asset Value (NAV) 1st July 2016 on per unit basis of a

Debt Fund:

Name of

Security

Face

Value

Rs.

Purchase

Price

Rs.

Maturity Date No. of

Securities

Coupon Date(s) Duration

of Bonds

10.71%

GOI 2028

100 104.78 31st March,

2028

1,00,000 31st March 7.3494

10.%

GOI 2023

100 100.00 31st March,

2023

50,000 31st March &

30th September

5.086

9.5%

GOI 2021

100 97.93 31st December,

2021

40,000 30th June & 31st

December

4.3949

34 | P a g e


8.5%

SGL 2025

100 91.36 30th June, 2025 20,000 30th June 6.5205


All securities were purchased at a time when applicable Yield to Maturity (YTM) was 10%. On NAV

date, the required yield increased by 75 basis point and Cash in hand and accrued expenses were

Rs.6,72,800 and Rs.2,37,400 respectively.

Solution :

Working Notes:

(i) Calculation of Interest Accrued

Name of Security Maturity Date Amount (Rs.)

10.71% GOI 2028 100 x 100000 x 10.71% x 3

12 2,67,750

10% GOI 2022 100 x 50000 x 10.00% x 3

12 1,25,000

Total 3,92,750

Note: Interests on two remaining securities shall not be considered as last interest was paid

on 30.06.2016

(ii) Valuation of Securities

Name of

Security

Purchase

Price

Rs.

Duration

of Bonds

Volatility (+)/(-) Total Amount

(Rs.)

10.71%

GOI 2028

1,04,78,000 7.3494 7.3494

1.10 × 0.75

= 5.0110

-5,25,053 99,52,947

10.%

GOI 2023

50,00,000 5.086 5.086

1.05 × 0.75

= 3.6329

-1,81,645 48,18,355

9.5%

GOI 2021

39,17,200 4.3949 4.3949

1.05 × 0.75

= 3.1392

-1,22,969 37,94,231

8.5%

SGL 2025

18,27,200 6.5205 6,5205

1.10 × 0.75

= 4.4456

-81,230 17,45,970

2,03,11,503

Calculation of NAV

Particulars Rs.Crores

Value of Securities as computed above

Cash in Hand

Interest accrued

2,03,11,503

6,72,800

3,92,750

Sub total assets (A) 2,13,77,053

Less: Liabilities

Expenditure accrued

2,37,400

35 | P a g e


Sub total liabilities (B) 2,37,400

Net Assets Value (A) – (B) 2,11,39,653

No. of units

Net Assets Value per unit (Rs.2,11,39,653/1,00,000)

1,00,000

Rs.211.40


SBI mutual fund has a NAV of Rs.8.50 at the beginning of the year. At the end of the year NAV

increases to Rs.9.10. Meanwhile fund distributes Rs.0.90 as dividend and Rs.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 Rs.8.75 assuming 200 units

were purchased originally? What is the return?

Solution :

Return for the year (all changes on a per year basis)

Particulars Rs./unit

Changes in price (Rs.9.10 – Rs.8.50)

Dividend Received

Capital gain Distribution

0.60

0.90

0.75

Total Return 2.25

Return on investment = 2.25

8.50 x 100 = 26.47%

If all dividends and capital gain are reinvested into additional units at Rs.8.75 per unit the position

would be.

Total amount reinvested = Rs.1.65 x 200 = Rs.330

Additional units added = Rs.330

8.75 = 37.71 units

Value of 237.71 units at end of year = Rs.2,163.16

Price paid for 200 units in beginning of the year (200 x Rs.8.50) = Rs.1,700

Return = 𝐑𝐬.𝟐,𝟏𝟔𝟑.𝟏𝟔−𝐑𝐬.𝟏,𝟕𝟎𝟎

𝐑𝐬.𝟏,𝟕𝟎𝟎 =

𝐑𝐬.𝟒𝟔𝟑.𝟏𝟔

𝐑𝐬.𝟏,𝟕𝟎𝟎 = 27.24%


A reputed financial institution of the country floated a Mutual fund having a corpus of Rs.10 crores

consisting of 1 crore units of Rs.10 each. Mr. Vijay invested Rs.10,000 for 1000 units of Rs.10 each on

1st July 2014. For the financial year ended 31st March 2015, the fund declared a dividend of 10% and

Mr. Vijay found that his annualized yield from the fund was 153.33%. The mutual fund during the

financial year ended 31st March 2016, declared a dividend of 20%. Mr. Vijay has reinvested the entire

dividend in acquiring units of this mutual fund at its appropriate NAV. On 31st march 2017 Mr. Vijay

redeemed all his balances of 1129.61 units when his annualized yield was 73.52%.

You are required to find out NAV as on 31st March 2015, 31st March 2016 and 31st March 2017.

Solution :

Yield for 9 months = (153.33 x 9/12) = 115%

36 | P a g e


Market value of Investments as on 31.03.2015 = 10,000+(10,000×115%)

= Rs.21,500/-

Therefore, NAV as on 31.03.2015 = (21,500 - 1,000)/1,000

= Rs.20.50

NAV would stand reduced to the extent of dividend payout, being (1,000×10×10%)

= Rs.1,000)

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

= Rs.1,000

Rs.20.50 = 48.78 units

Therefore, units as on 31.03.2015 = 1,000+ 48.78 = 1048.78

[Alternately, units as on 31.03.2015 = (21,500/20.50) = 1048.78]

Dividend as on 31.03.2016 = 1048.78 x 10 x 0.2 = Rs.2,097.56

Let X be the NAV on 31.03.2016, then number of new units reinvested will be Rs.2097.56/X.

Accordingly 1129.61 units shall consist of reinvested units and 1048.78 (as on 31.03.2015). Thus, by

way of equation it can be shown as follows:

1129.61 = 2097.56

X + 1048.78

Therefore, NAV as on 31.03.2016 = 2097.56/(1,129.61- 1,048.78) = Rs.25.95

NAV as on 31.03.2017 = Rs.10,000 (1+0.7352x33/12)/1129.61 = Rs.26.75


On 1-4-2012 ABC Mutual Fund issued 20 lakh units at Rs.10 per unit. Relevant initial expenses

involved were Rs.12 lakhs. It invested the fund so raised in capital market instruments to build a

portfolio of Rs.185 lakhs. During the month of April 2012 it disposed off some of the instruments

costing Rs.60 lakhs for Rs.63 lakhs and used the proceeds in purchasing securities for Rs.56 lakhs.

Fund management expenses for the month of April 2012 were Rs.8 lakhs of which 10% was in arrears.

In April 2012 the fund earned dividends amounting to Rs.2 lakhs and it distributed 80% of the realized

earnings. On 30-4-2012 the market value of the portfolio was Rs.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?

Solution :

Amount in

Rs.lakhs

Amount in

Rs.lakhs

Amount in

Rs.lakhs

Opening Bank (200-185-12)

Add: Proceeds from sale of securities

Add: Dividend received

Deduct:

Cost of securities purchased

Fund management expenses paid

(90% of 8)

3.00

63.00

2.00

56.00

7.20

68.00

37 | P a g e


Capital gains distributed

= 80% of (63-60)

Dividend distributed

= 80% of 2.00

Closing Bank

Closing market value of portfolio

2.40

1.60

67.20

0.80

198.00

Less Arrears of expenses

198.80

0.80

Closing Net Assets 198.00

Number of units (Lakhs)

Closing NAV per unit (198.00/20)

20

9.90

Rate of Earning (Per Unit)

Amount

Income received (Rs.2.40+0Rs.1.60)/20

Loss: Loss on disposal (Rs.200 – Rs.198)/20

Rs.0.20

Rs.0.10

Net earnings Rs.0.10

Initial investment

Rate of earning (Monthly)

Rate of earning (Annual)

Rs.10.00

1%

12%


A mutual fund made an issue of 10,00,000 units of Rs.10 each on January 01, 2008. No entry load was

charged. It made the following investments:

Particulars Amount

50,000 Equity shares of Rs.100 each @ Rs.160

7% Government Securities

9% Debentures (Unlisted)

10% Debentures (Listed)

80,00,000

8,00,000

5,00,0000

5,00,000

98,00,000

During the year, dividends of Rs.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. Other investments are at par.

Find out the Net Asset Value (NAV) per unit given that operating expenses paid during the year

amounted to Rs.5,00,000. Also find out the NAV, if the Mutual fund had distributed a dividend of

Rs.0.80 per unit during the year to the unit holders.

Solution :

Particulars Rs.

Cash balance in the beginning

(Rs.100 lakhs – Rs.98 lakhs)

2,00,000

38 | P a g e


Dividend Received

Interest on 7% Govt. Securities

Interest on 9% Debentures

Interest on 10% Debentures

12,00,000

56,000

45,000

50,000

(-) Operating expenses

15,51,000

5,00,000

Net cash balance at the end 10,51,000

Calculation of NAV Rs.

Cash Balance

7% Govt. Securities (at par)

50,000 equity shares @ Rs175 each

9% Debentures (Unlisted) at cost

10% Debentures @ 90%

10,51,000

8,00,000

87,50,000

5,00,000

4,50,000

Total Assets 1,15,51,000

No. of Unit

NAV per Unit

10,00,000

Rs.11.55

Calculation of NAV, if dividend of Rs.0.80 is paid –

Net Assets (Rs.1,15,51,000 – Rs.8,00,000) Rs.1,07,51,000

No. of Units 10,00,000

NAV per unit Rs.10.75


The unit price of Equity Linked Savings Scheme (ELSS) of a mutual fund is Rs.10/-. The public offer

price (POP) of the unit is Rs.10.204 and the redemption price is Rs.9.80.

Calculate:

(i) Front-end Load

(ii) Back end Load

Solution

i. Front End Load 10.204−10

10 × 100 = 2.04%

ii. Back End Load 10−9.8

10 × 100 = 2%


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 (Rs.) 2,00,000 4,00,000 2,00,000

Net Assets Value (NAV) at the time of

purchase (Rs.)

10.30 10.10 10

39 | P a g e


Dividend Received up to 31.03.2018 (Rs.) 6,000 0 5,000

NAV as on 31.03.2018 (Rs.) 10.25 10 10.20

Effective Yield per annum as on

31.03.2018 (Percent)

9.66 -11.66 24.15

Assume 1 Year =365 days

Mr. Y has misplaced the documents of his investment. Held him in finding the date of his original

investment after ascertaining the following:

(i) Number of units in each scheme;

(ii) Total NPV;

(iii) Total Yield; and

(iv) Number of days investment held.

Solution :

Particulars MF ‘X’ MF ‘Y’ MF ‘Z’

1. No. of Units

= Amount

NAV

200000

10.30

= 19,417.475

400000

10.10

= 39,603.96

200000

10

= 20,000

2. Net Asset at End

= Units × Closing NAV

19,417.475 × 10.25

= 1,99,029

39,603 × 10 =

3,96,040

20,000 × 10.2 =

2,04,000

3. Dividend Per Unit 6000

19417.475 = 0.309 NIL 5000

20000 = 0.25

4. Yield

Div.dist.+Capital App

Purchase Price × 100

(10.25−10.30)+0.309

10.30 ×

100 = 2.515%

(10−10.10)

10.10 × 100 =

0.99%

(10.25 − 10) + 0.25

10

× 100 = 4.5%

5. No of days investment held 2.515 ×365

𝑛 = 9.66

N = 95 days

0.99×365

𝑛= 11.66

N = 31 days

4.5 × 365

𝑛 = 24.15

N = 68 days

Question 43 May 2018 (New) – RTP – Similar to - Question 28 - Nov 2005 – 12 Marks

Question 44 May 2018 (New) – Paper - 10 marks – Similar t0 - Question 14 - May 2012 - Paper

Question 45 Nov 2018 – RTP – Similar to - Question 30 - Nov 2015 – Paper – 8 Marks


During the year 2017 an investor invested in a mutual fund. The capital gain and dividend for the year

was Rs.3.00 per unit, which were re-invested at the year end NAV of Rs.23.75. The investor had a

total units of 26,750 as at the end of the year. The NAV had appreciated by 18.75% during the year

and there was an entry load of Rs.0.05 at the time when the investment was made.

The investor lost his records and wants to find out the amount of investment made and the entry

load in the mutual fund.

Solution :

40 | P a g e


Closing NAV = 23.75 which is 118.75%

Opening NAV = 23.75/118.75% = 20

Entry Load = 0.05

Therefore Purchase Price = 20 + 0.05 = 20.05

Let the opening units be X

؞𝐱×𝟑

𝟐𝟑.𝟕𝟓 = 26,750 – x

3x = 6,35,312.5 – 23.75x؞

X = 23,750؞

Amount invested = 23,750 x 20.05 = Rs.4,76,187.5

Entry Load = 23,750 x 0.05 = Rs.1,187.5


A Mutual fund raised Rs.150 lakhs on April 1, 2018 by issue of 15 lakh units at Rs.10 per unit. The

fund invested in several capital market instruments to build a portfolio of Rs.140 lakhs. The initial

expenses amounted to Rs.8 lakhs. During the month of April, the fund sold certain instruments

costing Rs.44.75 lakhs for Rs.47 lakhs and used the proceeds to purchase certain other securities for

Rs.41.6 lakhs. The fund management expenses for the month amounted to Rs.6 lakhs of which

Rs.50,000 was in arrears. The fund earned dividends amounting to Rs.1.5 lakhs and it distributed 80%

of the realized earnings. The market value of the portfolio on 30th April, 2018 was Rs.147.84 lakhs.

An investor subscribed to 1000 units on April 1 and disposed it off at closing NAV on 30th April.

Determine his annual rate of earnings.

Solution :

Issue = 15 lakhs units x 10 = 150

Portfolio 140 Cash 10

Less: Sold (44.75) Less: Exp (8)

Add: Purch 41.6 Add: Sale 47

Balance 136.85 Less: Purchase (41.6)

Less: Exp (5.5)

Market Value 147.85 Add: Div 1.5

Less: Div

(1.5 x 80%) (1.2)

(2.25 x 80%) (1.8)

Balance 0.4

NAV at End = (𝟏𝟒𝟕.𝟖𝟓+𝟎.𝟒)−𝟎.𝟓

𝟏𝟓 = 9.85

HPY = 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧+𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐆𝐚𝐢𝐧 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧+𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐀𝐩𝐩𝐫𝐞𝐜𝐢𝐚𝐭𝐢𝐨𝐧

𝐏𝐮𝐫𝐜𝐡𝐚𝐬𝐞 𝐏𝐫𝐢𝐜𝐞 x 100

Dividend Distribution = 𝟏.𝟐

𝟏𝟓 = 0.08 per unit

Capital gain distribution =𝟏.𝟖

𝟏𝟓 = 0.12 per unit

41 | P a g e


HPY = 𝟎.𝟎𝟖+𝟎.𝟏𝟐+(𝟗.𝟖𝟓−𝟏𝟎)

𝟏𝟎 x 100 = 0.5% per month

BEY = 0.5 x 𝟏𝟐

𝟏 = 6% P.A.

EAY (𝟏. 𝟎𝟎𝟓)𝟏𝟐 – 1 = 6.17% P.A.

Question 48 Nov 2018 (New) – RTP – Similar to - Question 7 - May 2010 - Paper – 6 Marks

Question 49 Nov 2018 – New – Paper – 8 Marks - Similar to – Question no 22 – May 2013 RTP

Question 50 May 2019 (New) - RTP

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 Rs.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:

Particular Equity Schemes

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 Rs.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.

Solution :

D MF K MF

NAV (31/12/14) 70.71 62.50

Equity 99% 96%

Cash 1% 4%

Equity (70.71 0.99) 70 60

Cash 0.71 2.5

1) Calculation of

Sharpe Ratio =

RfR

For D MF For K MF

2 = 25.11

RfR 3.3 =

5

RfR

42 | P a g e


R – Rf = 22.50 R – Rf = 16.5

Treynor Ratio

For D MF For K MF

15 =

22.5 15 =

16.5

= 1.5 = 1.1

2) Decrease in value of Equity

DMF KMF

Market down 5% 5%

1.5% 1%

in Equity 7.5% 5.5%

Value 70 – 7.5% 60 – 5.5%

= 64.75 = 56.70

3) Cash Balance

DMF KMF

OP 0.71 2.5

Exp. 0.25 0.25

0.46 2.25

4) NAV at end of month

DMF KMF

Equity 64.75 56.70

Cash 0.46 2.25

Total 65.21 58.95

Question 51 May 2019 (Old) - RTP

Mr. X on 1.7.2015, during the initial offer of some Mutual Fund invested in 10,000 units having face

value of Rs.10 for each unit. On 31.3.2016, the dividend paid by the M.F. was

10% and Mr. X found that his annualized yield was 153.33%. On 31.12.2017, 20% dividend was given.

On 31.3.2018, Mr. X redeemed all his balance of 11,296.11 units when his annualized yield was

73.52%. What are the NAVs as on 31.3.2016, 31.3.2017 and 31.3.2018?

Solution :

9 month 1 Year

1/7/15 31/3/16 31/3/17 31/3/18

Units 10,000 11,296.11

FV 10 ? ? ?

43 | P a g e


Div. 10% 20% –

Red. 153.33% P.A. 73.52%

1) Calculation of 9 months

Red. for 9 months = 12

33.153 9 = 1155

HPY = Price Purchase

onAppreciati Cap. dist.gain Cap. dist. Div. 100

Dividend dist. = 10 10% = 1

Let the NAV at end be x

115 = 10

101 x 100

x = 20.5

2) Calculation of 1 year (31/3/17)

Div. = 10,000 10 10% = 10,000

Amt. is reinvested @ Rs.20.5 unit

Units received = 5.20

000,10 = 487.8

Total units = 10,000 + 487.8 = 10487.8

Div. on 31/3/17

= 10487.8 10 20% = Rs.20,976

Units received

= 11,292.11 – 10,487.8 = 808.31

NAV at end

= 31.308

976,20 = Rs.25.95 / untis

3) Calculation for 1 year (31/3/18)

Alt 1

Return = 73.52% P.A.

i.e. from 1/17/15 to 31/3/18 = 73.52 P.A.

10000,00,1

10000,00,1211.96,112

100

33

12= 73.52

2 = 26.5

Alt 2

NAV at end = 25.95 + 73.52%

= Rs.45.03

Question 52 May 2019 (Old) - RTP

On 1st April, an open-ended scheme of mutual fund had 300 lakh units outstanding with Net Assets

Value (NAV) of Rs.18.75. At the end of April, it issued 6 lakh units at opening NAV plus 2% load,

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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:

Rs. in lakh

Portfolio value appreciation 425.470

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.

Solution :

1) Income available for alist

Units Amt. Per unit

Income from April 300 22.95 0.0765

+ New Units 6 0.459 0.0765

306 23.409 0.0765

Income from May 306 34.425 0.1125

306 57.834 0.1890

-Recd. 3 (0.567) 0.1890

303 57.267 0.1890

Income from June 303 45.45 0.15

303 102.7170 0.3390

- Paid (70%) 303 71.9019 0.2373

Balance 303 30.8151 0.1017

2) Calculation of Issue price at end of April

Opening NAV 18.75

+ Entry load (2%) 0.375

19.125

+ Div. Equalisation 0.0765

19.2015

3) Calculation of Red. price at end of May

Opening NAV 18.75

- Exit load (2%) 0.375

18.375

+ Div. Equilisation 0.1890

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18.564

4) Closing NAV

Op. Net Asset (300 18.75) 5625

+ Portfolio App. 425.47

+ Units Issued (6 19.125) 115.209

+ Income Rec. (22.95 + 34.425 + 45.45) 102.825

6268.504

Less

Red. (3 18.564) 55.692

Income Distribution 71.9019

Net Bal. (Net Asset) 6140.9101

Units 303

NAV 20.2670

Question 53 May 2019 (New) - Paper

A Mutual Fund company introduces two schemes – Dividend Plan and Bonus Plan. The face value of

the Unit is Rs.10 on 1-4-2014. Mr.R invested Rs.5 lakh in Dividend Plant and Rs.10 lakh in Bonus Plan.

The NAV of Dividend Plan is Rs.46 and NAV of Bonus Plan is Rs.42. Both the plans matured on 31-03-

2019. The particulars of Dividend and Bonus declared over the period are as follows :

Date Dividend % Bonus Ratio NAV of Dividend Plan NAV of Bonus Plan

Rs. Rs.

31-12.2014 12% - 47.0 42.0

30-09.2015 - 1 : 4 48.0 43.0

31-03-2016 15% - 49.5 41.5

30-09-2017 - 1 : 6 50.0 44.0

31-03-2018 10% - 48.0 43.5

31-03-2019 - - 49.0 44.0

You are required to calculate the effective yield per annum in respect of the above two plans.

Solution :

1) Dividend Reinvestment plan

Date NAV Op. Units Div. Units Rec. Closing

1/4/14 46 - - 10,869.57 10,869.57

31/12/14 47 10,869.57 13043 277.52 11,147.10

31/3/16 49.5 11,147.10 16721 379.79 11,484.89

31/3/18 48 11,484.89 11485 239.27 11,724.16

Redemption value = 11,724.16 = 5,74,484

Return = 5

1

000,00,5

484,74,5

– 1 = 2.816%

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2) Bonus plan

Date Op. Units Bonus Units Rec. Closing

1/4/14 - - 23,809.52 23,809.52

30/9/15 23,809.52 1 : 4 5,952.38 29,761.90

30/9/17 29,761.90 1 : 6 4,960.32 34,722.22

Redemption value = 34,722.22 44 = 15,27,777.54

Return = 5

1

000,00,10

778,27,15

– 1 = 8.846

Question 54 May 2019 (Old) - Paper

The following particulars relating to Vishnu Fund Scheme :

Particular Value

Rs. in Crores

1 Investments in Shares (at cost)

a. Pharmaceutical companies 79

b. Construction Industries 31

c. Service Sector Companies 56

d. IT Companies 34

e. Real Estate Companies 10

2 Investments in Bonds (Fixed Income)

a. Listed Bonds (8000, 14% Bonds of Rs.15,000 each) 12

b. Unlisted Bonds 7

3 No. of Units outstanding (crores) 4.2

4 Expenses Payable 3.5

5 Cash and Cash equivalents 1.5

6 Market expectations on listed bonds 8.842%

Particulars relating to each sector are as follows :

Sector Index on Purchase date Index on Valuation date

Pharmaceutical companies 260 65

Construction Industries 210 450

Service Sector Companies 275 480

IT Companies 240 495

Real Estate Companies 255 410

You are required to calculate the following :

(i) Net Asset Value of the fund

(ii) Net Asset Value per unit

(iii) If the period of consideration is 2 years, and the fund has distributed Rs.3 per unit per year as

cash dividend, ascertain the Net return (Annualized).

(iv) Ascertain the Expenses ratio.

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Solution : 1) Net Assets Investments in Shares

Pharmaceutical (79/260 465) 141.29

Construction (31/210 450) 66.43

Service Sector (56/275 480) 97.75

IT Companies (34/240 495) 70.12

Real estate (10/255 410) 16.08 Investments in Bonds

Listed

08842.0

14.012 19

Unlisted 7 Cash 1.5 419.17 – Expenses payable 3.5 415.67

2) NAV = 2.4

67.415= Rs.98.969/ unit

3) Opening NAV Assets Investments in Shares Pharma 79 Construction 31 Service 56 IT Companies 34 Real Estate 10 Investments in Bonds Listed 12 Unlisted 7

Cash (1.5 + 4.8 + 1.5 + 0.38 – 3.5) + (6 4.2) 29.88 258.88

NAV = 2.4

88.258= 61.64

Return over 2 years

=

64.61

64.61969.986 100 = 70.29%

Assuming Simple Interest

= 2

29.70= 35.15

4) Expenses Ratios

= 88.258

68.6 100 = 2.58%

Question 55 May 2019 (Old) - Paper

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A mutual fund has two scheme i.e. Dividend plan (Plan-A) and Bonus plan (Plan-B). The face value of the unit is Rs.10. On 01/04/2016 Mr.Anand invested Rs.5,00,000 each in Plan-A and Plan-B when the NAV was Rs.46.00 and Rs.43.50 respectively. Both the Plans matured on 31/03/2019. Particulars of dividend and bonus declared over the period are as follows :

Date Dividend (%) Bonus Ratio Net Asset Value (Rs.)

Plan-A Plan-B

30-06-2016 15% 46.80 44.00

31-08-201 6 1 : 6 47.20 45.40

31-03.2017 10% 48.00 46.60

17-09-2017 1 : 8 48.40 47.00

21-11-2017 14% 49.60 47.20

25-02.2018 15% 50.00 47.80

31-03-2018 1 : 10 50.50 48.80

30-06-2018 12% 51.80 49.00

31-03-2019 52.40 50.00

You are required to calculate the Effective Yield Per annum in respective of the above two plans. Solution : 1) Dividend Reinvestment Plan

Date Op. units NAV Div. Units Rec. Closing

1/4/16 - 46 - 10869.57 10,869.57

30/6/16 10,869.57 46.80 16,304 348.38 11,217.95

31/3/17 11,217.95 48 11,218 233.71 11,451.66

21/11/17 11,451.66 49.60 16,032 323.23 11,774.89

25/2/18 11,774.89 50 17,662.33 353.25 12,128.14

30/6/18 12,128.14 51.80 14,554 280.96 12,409.1

Redemption value = 12,409.1 52.40 = 6,50,237

Return = 3

1

000,00,5

237,50,6

– 1 = 9.15%

2) Bonus plan

Date Op. Units Bonus Units Rec. Closing

1/4/16 - - 11,494.25 11,494.25

31/8/16 11,494.25 1 : 6 1,915.71 13,409.96

17/9/17 13,409.96 1 : 8 1,676.24 15,086.20

31/318 150,86.20 1 : 10 1508.62 165,94.83

Redemption value = 165,94.83 50 = 8,29,741

Return = 3

1

000,00,5

741,26,8

– 1 = 18.39%.

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