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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
2012 Yes Yes Yes Yes
2013 Yes Yes Yes Yes
2014 Yes Yes Yes Yes
2015 No Yes No Yes
2016 Yes Yes Yes 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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SFM COMPILER Mutual Funds
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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Mutual Funds SFM COMPILER
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
R2 = Return from the Fund
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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SFM COMPILER Mutual Funds
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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Mutual Funds SFM COMPILER
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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SFM COMPILER Mutual Funds
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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Mutual Funds SFM COMPILER
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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SFM COMPILER Mutual Funds
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.
Question 7 May 2010 Paper – 6 Marks
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
Amount payable on shares 6.32
Expenditure accrued 0.75
Sub total liabilities (B) 7.07
Net Assets Value (A) – (B) 54.26
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Mutual Funds SFM COMPILER
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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SFM COMPILER Mutual Funds
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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Mutual Funds SFM COMPILER
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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SFM COMPILER Mutual Funds
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 = Dividend Dist. + Capital Gain Dist. + Capital Appreciation
Purchase Price x 100
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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Mutual Funds SFM COMPILER
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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SFM COMPILER Mutual Funds
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
Mutual Funds SFM COMPILER
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
SFM COMPILER Mutual Funds
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
Question 16 Nov 2012 Paper – 5 Marks
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
Question 17 May 2013 RTP
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
Mutual Funds SFM COMPILER
R2 = R1
1 – Initial Expense + Re
R2 = Return from the Fund
R1 = Direct Return
Re = Recurring Expenses
In the above Question
R2 = Return from the Fund
R1 = 16%
Re = 1.5%
Initial Expenses = 5.5%
R2 = 16
1 – 0.055 + 1.5 = 18.43%
Question 18 May 2013 Paper – 10 Marks
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
SFM COMPILER Mutual Funds
EAY (1 + 0.0142878)3– 1
= 4.34787%
(1.0285)4 – 1
= 10.321%
(1.01)12 – 1
= – 12.6825%
Question 19 May 2013 Paper – 8 Marks
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
Mutual Funds SFM COMPILER
Question 20 Nov 2013 - RTP – Similar to - Question 15 - May 2012 Paper
Question 21 Nov 2013 Paper – 5 Marks
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%
HPY = Dividend Dist. + Capital Gain Dist. + Capital Appreciation
Purchase Price x 100
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
SFM COMPILER Mutual Funds
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
Question 22 May 2013 RTP
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
Mutual Funds SFM COMPILER
Solution :
i) Payout Plan
HPY = Dividend Dist. + Capital Gain Dist. + Capital Appreciation
Purchase Price x 100
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
Question 23 May 2014 Paper – 8 Marks
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
Amount payable on shares 13.54
Expenditure accrued 1.76
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
SFM COMPILER Mutual Funds
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
Sub total assets (A) 87.664
Less: Liabilities
Amount payable on shares 13.54
Expenditure accrued 1.76
Sub total liabilities (B) 15.30
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
Question 25 Nov 2014 Paper – 4 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
Mutual Funds SFM COMPILER
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
SFM COMPILER Mutual Funds
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 Price = 22.98 – 0.2% = 22.93
Redemption Proceeds = 37,500 x 22.93 = 8,60,027
– short term Capital Gain tax @10%
7,500 (22.93 – Nil) 17,198
Net Realization 8,42,829
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 Price = 82.07 – 0.2% = 81.90586
Redemption Proceeds = 10,000 x 81.90586 = 8,19,059
– short term Capital Gain tax @10% NIL
Net Realization 8,19,059
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
Mutual Funds SFM COMPILER
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
SFM COMPILER Mutual Funds
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
Mutual Funds SFM COMPILER
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
SFM COMPILER Mutual Funds
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
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Mutual Funds SFM COMPILER
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
Sub total assets (A) 53.078
Less: Liabilities
Amount payable on shares
Expenditure accrued
8.32
1.00
Sub total liabilities (B) 9.32
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
Question 33 Nov 2016 – RTP
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
Amount payable on shares
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.
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 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
SFM COMPILER Mutual Funds
Dividend accrued
Fixed income securities
1.950
9.409
Sub total assets (A) 87.664
Less: Liabilities
Amount payable on shares
Expenditure accrued
13.54
1.76
Sub total liabilities (B) 15.30
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
Question 34 Nov 2016 – Paper – 8 Marks
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
Mutual Funds SFM COMPILER
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
SFM COMPILER Mutual Funds
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
Question 36 Nov 2017 – RTP
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
Mutual Funds SFM COMPILER
8.5%
SGL 2025
100 91.36 30th June, 2025 20,000 30th June 6.5205
Number of Units (Rs.10 face value each): 100000
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
SFM COMPILER Mutual Funds
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
Question 37 Nov 2017 – Paper
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%
Question 38 Nov 2017 – Paper
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
Mutual Funds SFM COMPILER
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
Question 39 May 2018 – RTP
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
SFM COMPILER Mutual Funds
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%
Question 40 May 2018 – RTP
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
Mutual Funds SFM COMPILER
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
Question 41 May 2018 – Paper – 5 Marks
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%
Question 42 May 2018 – Paper – 8 Marks
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
SFM COMPILER Mutual Funds
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
Question 46 Nov 2018 – Paper – 5 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
Mutual Funds SFM COMPILER
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
Question 47 Nov 2018 – Paper – 8 Marks
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
SFM COMPILER Mutual Funds
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
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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 ? ? ?
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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%.