Mutual Funds
Exhaustive Topic-wise Notes covering Regulatory Architecture, Scheme Classification, ETFs vs. Index Funds, Computation of Net Asset Value (NAV), Front-End & Exit Load Mechanics, Dividend vs. Bonus Plans, Risk-Adjusted Performance Ratios (Sharpe, Treynor, Jensen, Fama Decomposition) and Constant Ratio Portfolio Rebalancing.
Topic 1: Introduction, Concept & Three-Tier Regulatory Architecture
ICAI Study Material Text:
A Mutual Fund is a trust that pools together the resources of investors to make a foray into investments in the capital market, thereby making each investor a part-owner of the assets of the fund. It is an investment vehicle that allows small investors to participate in a professionally managed portfolio of equity shares, debentures, bonds, and money market instruments.
Structure and Regulatory Architecture under SEBI (Mutual Funds) Regulations, 1996:
In India, a mutual fund is structured as a three-tier fiduciary entity comprising:
- 1. Sponsor: The promoter who initiates the mutual fund. The sponsor must be an established entity in the financial services business for at least 5 years with a sound track record and positive net worth in all immediately preceding 5 years. The sponsor appoints the trustees and must contribute at least 40% to the net worth of the Asset Management Company (AMC).
- 2. Trustees: A Board of Trustees or a Trustee Company holds the property of the mutual fund in trust for the benefit of the unit holders. At least two-thirds (66.7%) of the trustees/directors of the trustee company must be independent (not associated with the sponsor). The trustees enter into an Investment Management Agreement with the AMC and exercise oversight over all schemes.
- 3. Asset Management Company (AMC): The operational arm that manages the fund's investment portfolio in accordance with the scheme objectives and SEBI regulations. The AMC must have a minimum net worth of ₹ 50 Crores (increased to ₹ 100 Crores for certain categories). At least 50% of the AMC's board of directors must be independent.
- 4. Custodian & Depository: An independent entity registered with SEBI that holds the physical securities and safe-keeps the financial assets of the fund in dematerialized form. The custodian cannot be associated with the AMC.
- 5. Registrar and Transfer Agents (RTAs): Process investor applications, issue account statements, maintain unit-holder registers, and execute unit redemptions.
Clear Explanation & Conceptual Mechanics:
Why is a mutual fund structured as a Trust rather than a corporate company?
Under the Indian Trust Act, 1882, the property of a trust is held for the beneficial interest of its beneficiaries (the unit holders). By separating the Trustees (who safeguard investor rights) from the AMC (who manages the money), Indian law prevents conflict of interest. The AMC cannot misappropriate investor funds because the securities are legally locked with an independent Custodian. If an AMC underperforms or engages in malpractice, the Trustees or 75% of unit holders have statutory power to terminate the AMC's appointment.
Exam Relevance & Scoring Focus:
• Frequently Tested: 4-mark theory question on 'Explain the establishment of a Mutual Fund and the role of Trustees vs. AMC' (see TYK Theory Q1).
• Key Keywords for Marking: Minimum 5-year track record for Sponsor, minimum 40% net worth contribution by Sponsor, two-thirds independent Trustees, 50% independent AMC directors, minimum net worth requirement of AMC.
Topic 2: Classification of Mutual Funds (Functional, Portfolio & Ownership)
ICAI Study Material Text:
Mutual funds in India are classified into three distinct dimensions:
- 1. Functional Classification (Liquidity & Entry/Exit):
• Open-Ended Schemes: Units are offered for sale and repurchase on a continuous basis at NAV-related prices throughout the year. There is no fixed maturity period. Capitalization is flexible and expands/contracts based on investor cash flows.
• Close-Ended Schemes: Units are offered for subscription during a specified New Fund Offer (NFO) period and have a predetermined maturity period (e.g., 3 to 5 years). After NFO, fresh subscriptions are closed. Units must be compulsorily listed on a recognized stock exchange to provide liquidity to investors.
• Interval Schemes: A hybrid structure combining features of open-ended and close-ended funds. Units are traded on stock exchanges and opened for direct subscription/redemption at predetermined intervals (e.g., monthly, quarterly, or semi-annually). - 2. Portfolio / Objective-Based Classification:
• Equity Schemes: Growth-oriented funds investing predominantly in equity shares.
• Debt / Income Schemes: Focus on capital preservation and regular income by investing in government securities, corporate bonds, commercial paper, and certificates of deposit.
• Hybrid / Balanced Schemes: Strategic asset allocation between equity (for capital appreciation) and debt (for stability).
• Money Market / Liquid Funds: Invest in short-term money market instruments with maturity up to 91 days.
• Gilt Funds: Invest exclusively in sovereign government securities with zero credit risk. - 3. Ownership Classification: Public Sector Funds (e.g., SBI Mutual Fund, UTI), Private Sector Funds (e.g., HDFC, ICICI Prudential), and Foreign/Joint Venture Funds.
Clear Explanation & Practical Mechanics:
The most critical distinction for practical problems is between Open-Ended and Close-Ended funds:
In an open-ended fund, if an investor purchases units, the AMC creates new units (increasing total units outstanding), and when an investor redeems, units are extinguished. In a close-ended fund, total units remain constant; an investor wanting to exit before maturity must sell to another investor on the stock exchange. Because of supply-demand dynamics and lack of immediate liquidity, close-ended fund units frequently trade at a discount to their NAV.
Exam Relevance & Scoring Focus:
• Key Practical Implication: Close-ended funds with discounts/premiums (e.g., D Mutual Fund and K Mutual Fund in TYK Q21).
• Understand Interval schemes as a hybrid for theoretical classification questions.
Topic 3: Types of Schemes, ETFs, Index Funds & Fund of Funds
ICAI Study Material Text:
SEBI's Categorization and Rationalization of Mutual Fund Schemes circular mandates standard scheme categories:
- Exchange Traded Funds (ETFs): Open-ended index funds that track an index (e.g., Nifty 50, Sensex, Gold) and trade on stock exchanges in real time like equity shares. Unlike traditional mutual funds whose NAV is computed once at the end of the day, ETF prices fluctuate continuously throughout trading hours. Authorized Participants (APs) create and redeem units in large institutional baskets, maintaining arbitrage parity between ETF market prices and underlying NAV.
- Index Funds: Passively managed open-ended mutual funds replicating a benchmark index. The fund manager invests in the exact proportions of the underlying index. Characterized by low expense ratios and negligible portfolio turnover.
- Tracking Error: The divergence between the price behavior of an index fund/ETF and the price behavior of its underlying benchmark index. $$\text{Tracking Error} = \sqrt{\frac{\sum (R_{fund,t} - R_{index,t})^2}{n-1}}$$ Tracking error arises from cash drag, transaction costs, management fees, and timing lags in dividend reinvestment.
- Fund of Funds (FoF): A mutual fund scheme that invests in units of other mutual fund schemes rather than direct equities or bonds. Offers hyper-diversification but carries dual expense layers.
- Capital Protection Oriented Schemes (CPOS): Close-ended schemes structured so that a dominant portion (e.g., 80-85%) is invested in high-rated debt securities whose maturity value equals the initial principal (protecting capital), while the residual portion is invested in equity options/derivatives to generate equity upside.
Clear Explanation: Passive Investing vs. Active Management:
Why are ETFs and Index Funds increasingly popular?
Active fund managers charge higher fees (up to 2.25% p.a.) promising to generate Alpha ($\alpha$). However, empirical studies demonstrate that over long horizons, most active managers fail to beat their benchmark after fees. Passive index funds eliminate manager risk, minimize portfolio churn, and guarantee index returns minus a minimal tracking error (typically 0.10% to 0.30%).
Exam Relevance & Scoring Focus:
• Short note questions on 'Exchange Traded Funds (ETFs) vs. Traditional Index Mutual Funds'.
• Definition and formula for 'Tracking Error'.
• Structure of 'Capital Protection Oriented Schemes' (often asked as a 4-mark theory question).
Topic 4: Advantages and Drawbacks of Mutual Funds
ICAI Study Material Text:
Advantages of Investing in Mutual Funds:
- (a) Professional Management: Skilled fund managers backed by quantitative models and equity research teams analyze financial statements, macroeconomic indicators, and corporate governance.
- (b) Risk Diversification: An individual investor with ₹ 5,000 cannot buy 50 blue-chip stocks. A mutual fund achieves diversification across sectors and market capitalizations, eliminating unsystematic risk.
- (c) Economies of Scale & Low Transaction Costs: Bulk trading results in lower brokerage and depository fees.
- (d) Liquidity: Open-ended funds allow daily redemption at prevailing NAV.
- (e) Tax Efficiency: Long-term equity gains qualify for favorable tax rates (Section 112A), and dividends/capital gains internal to the fund compound tax-free until withdrawal.
- (a) No Guarantee of Return: Mutual fund investments are subject to market risks. Even high-rated schemes can suffer capital erosion during market downturns.
- (b) Diversification Penalty: Extreme diversification prevents astronomical returns. An active investor picking 2 multi-bagger stocks can outperform an index fund, whereas mutual funds are legally barred from holding more than 10% in a single company.
- (c) Management Fees and Operating Expenses: Ongoing Total Expense Ratio (TER) of 1.5% to 2.25% creates a permanent performance drag regardless of whether the fund makes profits or losses.
- (d) Cash Drag: Open-ended funds must maintain 3% to 7% of their portfolio in cash/liquid assets to meet daily redemptions, dragging down returns during bull runs.
Clear Explanation & Real-World Context:
The trade-off between investing directly in stocks versus mutual funds is fundamentally a trade-off between Control & Concentration versus Convenience & Diversification. For exam answers, always cite both the statutory limits on single-stock concentration (maximum 10% per issuer under SEBI regulations) and the impact of the Total Expense Ratio on net investor returns.
Exam Relevance & Scoring Focus:
• 4-mark standard question: 'What are the advantages and drawbacks of investing in mutual funds?' (Directly addresses TYK Theory Q2).
• Must present points under clear headings with financial terminology.
Topic 5: Computation of Net Asset Value (NAV), Front-End & Exit Loads
ICAI Study Material Text:
1. Net Asset Value (NAV) Formula:
Net Asset Value represents the net market worth of a single unit of a mutual fund scheme:
$$\mathbf{NAV = \frac{\text{Total Assets of Scheme} - \text{Total Liabilities of Scheme}}{\text{Total Number of Outstanding Units}}}$$
Where:
- Total Assets = Market Value of Listed Equities + Market Value of Listed Debentures/Bonds + Value of Unlisted / Illiquid Securities (as per SEBI valuation norms) + Accrued Dividend & Interest Receivable + Cash, Bank Balances & Money Market Placements + Other Assets (e.g. receivables for securities sold).
- Total Liabilities = Accrued Management Fees & Operating Expenses Payable + Payables for Securities Purchased + Unclaimed Dividends + Outstanding Short-Term Borrowings + Other Accrued Liabilities.
- Public Offer Price (Sale Price / Issue Price): $$\text{Public Offer Price (POP)} = \text{NAV} \times (1 + \text{Front-End Load \%}) \quad \text{or} \quad \text{POP} = \frac{\text{NAV}}{1 - \text{Front-End Load \%}}$$ (Note: Under current SEBI regulations, Entry Load has been banned; funds issue units at par NAV. However, historical ICAI questions continue to test the mathematical formula where Entry Load is added to NAV.)
- Repurchase Price (Redemption Price): $$\mathbf{\text{Redemption Price} = \text{NAV} \times (1 - \text{Exit Load \%})} \quad \text{or} \quad \mathbf{\text{Redemption Price} = \frac{\text{NAV}}{1 + \text{Back-End Load \%}}}$$ Depending on whether the load is expressed as a percentage of NAV or Redemption Price.
Clear Explanation & Step-by-Step NAV Calculation Mechanics:
In practical exam questions (e.g., TYK Practical Q7, Q8, Q9, Q19, Q20), calculating NAV requires strict adherence to chronological accounting:
- Step 1: Value all portfolio securities at the closing market quotation as of the valuation date (e.g. 4:00 PM on valuation day).
- Step 2: Add all cash balances, liquid funds, dividends declared but not yet credited, and interest accrued.
- Step 3: Deduct all accrued AMC management fees, custodian charges, audit fees, and unpaid broker dues.
- Step 4: Divide the resulting Net Assets by the total number of units outstanding on that date.
Exam Relevance & Scoring Focus:
• Guaranteed 8-10 mark question: Comprehensive NAV computation involving a multi-company equity portfolio, bonds, accrued expenses, management fees, and fresh unit issues (e.g. Cinderella MF, Steady MF, Fair Return MF).
• Common Trap: Remember to calculate management fees on the Average Net Assets or Gross Assets exactly as specified in the problem statement!
Topic 6: Mutual Fund Returns, Effective Yield & Bonus vs. Dividend Plans
ICAI Study Material Text:
1. Return on Mutual Fund Investment:
An investor in a mutual fund earns returns through three distinct channels:
- Dividend Income ($D_1$): Regular cash payouts declared from scheme profits.
- Capital Gain Distribution ($CG_1$): Profits realized by the AMC from selling underlying securities distributed to unit holders.
- Capital Appreciation / Change in NAV ($\Delta \text{NAV} = \text{NAV}_1 - \text{NAV}_0$): Growth in the underlying value of the units.
- Growth Plan: No dividends are distributed; all profits and gains are automatically retained and reflected in an increasing NAV.
- Dividend Payout Plan: Dividends are paid out in cash. Post-dividend, the scheme's NAV drops by the exact amount of dividend distributed per unit.
- Dividend Reinvestment Plan: The declared dividend is not paid in cash; instead, it is utilized to purchase additional units for the investor at the ex-dividend NAV.
- Bonus Plan: Additional bonus units are allotted to unit holders (e.g. 1 bonus unit for every 5 units held). Post-bonus, the total number of units increases and the NAV per unit drops proportionally.
Clear Explanation & Comparative Wealth Analysis:
A classic ICAI exam problem (e.g., TYK Q16 Sun Moon MF, TYK Q17 Plan-D vs Plan-B) asks students to evaluate whether an investor should choose a Dividend Reinvestment Plan or a Bonus Plan under differing income tax rules.
Under Indian tax law:
• Dividends received / reinvested may attract specific tax liabilities or TDS.
• Bonus units carry an acquisition cost of ₹ Nil for capital gains computation. When bonus units are sold, the holding period is measured from the date of bonus allotment.
• Students must construct a chronological ledger tracking: Units held $
ightarrow$ Dividends received $
ightarrow$ Fresh units purchased at ex-dividend NAV $
ightarrow$ Bonus units added $
ightarrow$ Final maturity redemption $
ightarrow$ Net post-tax IRR / Effective Yield.
Exam Relevance & Scoring Focus:
• 10-12 mark comprehensive case study: Multi-year comparison of Plan A (Dividend Reinvestment) vs. Plan B (Bonus Units) (e.g., Mrs. Charu in TYK Q16).
• Precision in unit calculations (maintain at least 3 to 4 decimal places for unit counts) is essential to match ICAI model answers.
Topic 7: Performance Evaluation (Sharpe, Treynor, Jensen, Fama & Rebalancing)
ICAI Study Material Text:
1. Risk-Adjusted Performance Measures:
- Sharpe Ratio (Reward to Variability): $$\mathbf{S = \frac{R_p - R_f}{\sigma_p}}$$ Evaluates excess return per unit of Total Risk (Standard Deviation). Appropriate when the mutual fund represents the investor's entire portfolio.
- Treynor Ratio (Reward to Volatility): $$\mathbf{T = \frac{R_p - R_f}{\beta_p}}$$ Evaluates excess return per unit of Systematic Risk (Beta). Appropriate when the mutual fund is held as part of a well-diversified multi-asset portfolio.
- Jensen's Alpha ($\alpha_p$): $$\mathbf{\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]}$$ Measures the absolute abnormal return generated by the fund manager over and above the CAPM benchmark. $\alpha > 0$ indicates superior security selection.
- Constant Ratio Plan: The investor maintains a predetermined ratio between aggressive (equity fund) and conservative (bond) portfolios (e.g., 50:50). Whenever market movements cause the ratio to shift beyond a threshold (or at periodic rebalancing dates), securities are sold from the appreciated fund and reinvested in the lagging fund to restore the target 50:50 proportion.
- Variable Ratio Plan: The aggressive-conservative ratio is dynamically adjusted based on market valuation levels (e.g. Nifty PE ratio). As market valuation rises, equity allocation is reduced; as markets become undervalued, equity allocation is increased.
Clear Explanation & Intuition:
Why is Fama's Net Selectivity so important?
A fund manager might boast of generating an Alpha ($\alpha$) of +2.5%. However, if the fund manager achieved this by taking huge unsystematic/specific risks (i.e., failing to diversify, so that $\frac{\sigma_p}{\sigma_m} > \beta_p$), the investor suffered an extra risk for which the market does not reward them. Net Selectivity deducts the cost of this inadequate diversification. Only if Net Selectivity > 0 did the manager possess true stock-picking skill!
Exam Relevance & Scoring Focus:
• Sharpe and Treynor ranking problems (TYK Q21: D Mutual Fund vs. K Mutual Fund).
• Constant Ratio Plan simulation (TYK Q23: Ms. Sunidhi 10-month rebalancing simulation vs. Buy & Hold).
• Fama's Decomposition 4-step table (Net Selectivity, Diversification Penalty, Stock Selection).
Theoretical Questions & Model Answers
Exhaustive structured model answers as per ICAI Study Material standards.
Explain how to establish a Mutual Fund in India under SEBI regulations.
Model Structured Answer (as per ICAI Study Material):
A mutual fund in India is required to be registered with the Securities and Exchange Board of India (SEBI) before it can collect funds from the public. All mutual funds are governed by the SEBI (Mutual Funds) Regulations, 1996 and are subject to continuous monitoring and inspections by SEBI.
Key Steps and Structural Entities in Establishing a Mutual Fund:
- Sponsor:
• The mutual fund is established through the medium of a Sponsor (akin to a company promoter).
• A sponsor must be a body corporate in the financial services business for at least 5 continuous years with a sound financial track record and positive net worth in each of the preceding 5 years.
• The sponsor must contribute at least 40% to the net worth of the Asset Management Company (AMC). - Trust and Board of Trustees:
• The Mutual Fund must be established as either a Trustee Company or a Board of Trustees under the Indian Trusts Act, 1882.
• The sponsor executes a Trust Deed in favor of the trustees, registered under the Indian Registration Act, 1908.
• Independence Norm: At least two-thirds (66.7%) of the trustees / directors of the trustee company must be independent (not associated with or related to the sponsor). - Asset Management Company (AMC):
• The Trustees appoint an AMC approved by SEBI to manage the funds and float schemes.
• The AMC must have a minimum net worth of ₹ 50 Crores (or ₹ 100 Crores).
• At least 50% of the AMC's directors must be independent.
• The appointment of the AMC can be terminated by a majority of trustees or by 75% of unit-holders. - Custodian:
• An independent entity registered with SEBI appointed by the Trustees to safe-keep securities in demat/physical custody. The custodian cannot be an associate of the AMC.
What are the advantages of investing in Mutual Funds?
Model Structured Answer (as per ICAI Study Material):
Investing in mutual funds offers numerous strategic and financial advantages, especially for retail and corporate investors:
- 1. Professional Management: Qualified fund managers and research analysts continuously track corporate fundamentals, macroeconomic indicators, and market trends.
- 2. Risk Diversification: Spreads investments across dozens of securities and industries, effectively eliminating unsystematic (company-specific) risk at nominal cost.
- 3. Affordability & Small Denominations: Through Systematic Investment Plans (SIPs), investors can participate in a diversified portfolio with as little as ₹ 500 per month.
- 4. Liquidity: Open-ended funds permit daily redemption at prevailing Net Asset Value (NAV).
- 5. Economies of Scale: Lower transaction costs and brokerage fees due to large-volume block trades.
- 6. Strict Regulatory Oversight: Governed by SEBI regulations ensuring transparent portfolio disclosures, daily NAV publishing, and segregated custody.
- 7. Tax Benefits: Equity-Linked Savings Schemes (ELSS) provide tax deductions under Section 80C, and internal fund compounding is tax-exempt.
Practical Problems & Step-by-Step Solutions
Complete authentic solutions for all 23 practical problems from ICAI Study Material with structured breakdown tables, formulas, and boxed final answers.
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 a return of 16 per cent?
Given Data (ICAI Book):
• Desired Net Return to Investor ($R_1$) = 16.0%
• Initial Issue Expenses ($I$) = 5.5%
• Annual Recurring Expenses ($E$) = 1.5%
Mathematical Derivation
Let the gross return required to be earned by the Mutual Fund be $R_2$.
Out of every ₹ 100 invested, initial expenses of 5.5% leave only ₹ $(100 - 5.5) = ₹ 94.50$ (or $1 - I = 0.945$) available for actual investment in securities.
This invested capital must earn gross return $R_2$, out of which recurring expenses of 1.5% are deducted, leaving the investor with net return $R_1 = 16\%$ on the original ₹ 100:
As per ICAI Study Material formulation:
$$R_1 = \frac{(1 - I) \times R_2 - E \times (1 - I) \dots}{1} \implies 0.16 = (1 - 0.055) \times R_2 - 0.015$$ $$0.16 + 0.015 = 0.945 \times R_2$$ $$0.175 = 0.945 \times R_2$$ $$R_2 = \frac{0.175}{0.945} = \mathbf{0.185185 \approx 18.52\%}$$Alternative ICAI Method:
$$R_2 = \frac{R_1}{1 - I} + E = \frac{16\%}{1 - 0.055} + 1.5\% = \frac{16\%}{0.945} + 1.5\% = 16.93\% + 1.5\% = \mathbf{18.43\%}$$The Mutual Fund must earn a gross return of 18.52% (or 18.43% under the alternative approach) to provide Mr. A with a net personal return of 16%.
The unit price of Equity Linked Savings Scheme (ELSS) of a mutual fund is ₹ 10/-. The Public Offer Price (POP) is ₹ 10.204 and the redemption price is ₹ 9.80.
Calculate:
(i) Front-end Load %
(ii) Exit Load %
Given Data (ICAI Book):
• Par Net Asset Value ($\text{NAV}$) = ₹ 10.00
• Public Offer Price ($\text{POP}$) = ₹ 10.204
• Redemption Price = ₹ 9.80
1. Calculation of Front-End Load
Front-end load is the additional charge paid on purchase over and above the NAV:
$$\text{Front-End Load} = \frac{\text{Public Offer Price} - \text{NAV}}{\text{NAV}} \times 100$$ $$\text{Front-End Load} = \frac{₹ 10.204 - ₹ 10.00}{₹ 10.00} \times 100 = \frac{₹ 0.204}{₹ 10.00} \times 100 = \mathbf{2.04\%}$$2. Calculation of Exit Load
Exit load is the deduction made from NAV upon redemption:
$$\text{Exit Load} = \frac{\text{NAV} - \text{Redemption Price}}{\text{NAV}} \times 100$$ $$\text{Exit Load} = \frac{₹ 10.00 - ₹ 9.80}{₹ 10.00} \times 100 = \frac{₹ 0.20}{₹ 10.00} \times 100 = \mathbf{2.00\%}$$• Front-end Load: 2.04%
• Exit Load: 2.00%
A mutual fund that had a net asset value of ₹ 20 at the beginning of month made income and capital gain distributions of ₹ 0.05 and ₹ 0.04 per share respectively during the month, and then ended the month with a net asset value of ₹ 20.06. Calculate monthly return.
Given Data (ICAI Book):
• Beginning NAV ($\text{NAV}_0$) = ₹ 20.00
• Income Distribution ($D_1$) = ₹ 0.05
• Capital Gain Distribution ($CG_1$) = ₹ 0.04
• Ending NAV ($\text{NAV}_1$) = ₹ 20.06
Formula for Monthly Return
$$r = \frac{(\text{NAV}_1 - \text{NAV}_0) + D_1 + CG_1}{\text{NAV}_0} \times 100$$ $$r = \frac{(₹ 20.06 - ₹ 20.00) + ₹ 0.05 + ₹ 0.04}{₹ 20.00} \times 100$$ $$r = \frac{₹ 0.06 + ₹ 0.05 + ₹ 0.04}{₹ 20.00} \times 100 = \frac{₹ 0.15}{₹ 20.00} \times 100 = \mathbf{0.75\% \text{ per month}}$$Annualized Return
$$\text{Annualized Simple Return} = 0.75\% \times 12 = \mathbf{9.00\% \text{ p.a.}}$$• Monthly Return: 0.75%
• Annualized Return: 9.00% p.a.
An investor purchased 300 units of a Mutual Fund at ₹ 12.25 per unit on 31st December, 2009. As on 31st December, 2010 he received dividend of ₹ 1.25 per unit. On 31st December, 2011 the NAV was ₹ 13.00.
Calculate the return for the 2-year period:
(i) If the dividend is received in cash and retained.
(ii) If the dividend was reinvested on 31st December, 2010 when the NAV was ₹ 12.50.
Given Data (ICAI Book):
• Initial Investment (31.12.2009): 300 units @ ₹ 12.25 = ₹ 3,675.00
• Dividend received on 31.12.2010 = $300 \times ₹ 1.25 = ₹ 375.00$
• Closing NAV on 31.12.2011 = ₹ 13.00
(i) When Dividend is Received in Cash
$$\text{Maturity Value on 31.12.2011} = 300 \text{ units} \times ₹ 13.00 = ₹ 3,900.00$$ $$\text{Total Cash Inflow} = ₹ 3,900.00 + ₹ 375.00 (\text{Dividend}) = ₹ 4,275.00$$ $$\text{Total Gain} = ₹ 4,275.00 - ₹ 3,675.00 = ₹ 600.00$$ $$\text{Total 2-Year Return} = \frac{₹ 600.00}{₹ 3,675.00} \times 100 = \mathbf{16.33\%}$$ $$\text{Annualized Return} = \frac{16.33\%}{2} = \mathbf{8.16\% \text{ p.a.}}$$(ii) When Dividend is Reinvested at NAV ₹ 12.50 on 31.12.2010
$$\text{Additional Units Purchased} = \frac{₹ 375.00}{₹ 12.50} = \mathbf{30.00 \text{ units}}$$ $$\text{Total Units on 31.12.2011} = 300 + 30 = \mathbf{330.00 \text{ units}}$$ $$\text{Maturity Value on 31.12.2011} = 330 \text{ units} \times ₹ 13.00 = ₹ 4,290.00$$ $$\text{Total Gain} = ₹ 4,290.00 - ₹ 3,675.00 = ₹ 615.00$$ $$\text{Total 2-Year Return} = \frac{₹ 615.00}{₹ 3,675.00} \times 100 = \mathbf{16.73\%}$$ $$\text{Annualized Return} = \frac{16.73\%}{2} = \mathbf{8.37\% \text{ p.a.}}$$• (i) Without Reinvestment: Total 2-Year Return = 16.33% (Annualized = 8.16% p.a.)
• (ii) With Dividend Reinvestment: Total 2-Year Return = 16.73% (Annualized = 8.37% p.a.)
SBI mutual fund has a NAV of ₹ 8.50 at the beginning of the year. At the end of the year NAV increases to ₹ 9.10. Meanwhile fund distributed ₹ 0.75 as dividend and ₹ 0.60 as capital gains distribution.
Required:
(i) What is the normal return for the year?
(ii) What is the return if the distributed dividend and capital gains were reinvested at an average NAV of ₹ 8.75?
Given Data (ICAI Book):
• Beginning NAV ($\text{NAV}_0$) = ₹ 8.50
• Ending NAV ($\text{NAV}_1$) = ₹ 9.10
• Dividend Distributed ($D$) = ₹ 0.75
• Capital Gain Distributed ($CG$) = ₹ 0.60
• Reinvestment NAV = ₹ 8.75
(i) Normal Return for the Year (No Reinvestment)
$$\text{Return} = \frac{(\text{NAV}_1 - \text{NAV}_0) + D + CG}{\text{NAV}_0} \times 100$$ $$\text{Return} = \frac{(₹ 9.10 - ₹ 8.50) + ₹ 0.75 + ₹ 0.60}{₹ 8.50} \times 100$$ $$\text{Return} = \frac{₹ 0.60 + ₹ 0.75 + ₹ 0.60}{₹ 8.50} \times 100 = \frac{₹ 1.95}{₹ 8.50} \times 100 = \mathbf{22.94\%}$$(ii) Return with Reinvestment at NAV ₹ 8.75
Assume initial investment of 100 units @ ₹ 8.50 = ₹ 850.00.
$$\text{Total Cash Distribution} = 100 \times (₹ 0.75 + ₹ 0.60) = 100 \times ₹ 1.35 = ₹ 135.00$$ $$\text{Additional Units Purchased} = \frac{₹ 135.00}{₹ 8.75} = \mathbf{15.4286 \text{ units}}$$ $$\text{Total Units at Year-End} = 100 + 15.4286 = \mathbf{115.4286 \text{ units}}$$ $$\text{Closing Portfolio Value} = 115.4286 \times ₹ 9.10 = ₹ 1,050.40$$ $$\text{Total Return} = \frac{₹ 1,050.40 - ₹ 850.00}{₹ 850.00} \times 100 = \frac{₹ 200.40}{₹ 850.00} \times 100 = \mathbf{23.58\%}$$• (i) Normal Return: 22.94%
• (ii) Return with Reinvestment: 23.58%
The following information is extracted from Steady Mutual Fund's Scheme:
• Asset Value at the beginning of the month: ₹ 65.78
• Annualized Return: 15%
• Dividend Distributed: ₹ 0.50
• Capital Gain Distribution: ₹ 0.40
Required: Calculate the Net Asset Value (NAV) at the end of the month.
Given Data (ICAI Book):
• Beginning NAV ($\text{NAV}_0$) = ₹ 65.78
• Annual Return = 15% $\implies$ Monthly Return $r = \frac{15\%}{12} = \mathbf{1.25\%}$
• Dividend ($D$) = ₹ 0.50
• Capital Gain ($CG$) = ₹ 0.40
Derivation of Ending NAV ($\text{NAV}_1$)
$$r = \frac{(\text{NAV}_1 - \text{NAV}_0) + D + CG}{\text{NAV}_0}$$ $$0.0125 = \frac{(\text{NAV}_1 - ₹ 65.78) + ₹ 0.50 + ₹ 0.40}{₹ 65.78}$$ $$0.0125 \times 65.78 = \text{NAV}_1 - 65.78 + 0.90$$ $$0.82225 = \text{NAV}_1 - 64.88$$ $$\text{NAV}_1 = 64.88 + 0.82225 = \mathbf{₹ 65.70225 \approx ₹ 65.70}$$The Net Asset Value (NAV) at the end of the month is ₹ 65.70.
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 (₹) |
|---|---|---|
| A Ltd. | 25,000 | ₹ 20.00 |
| B Ltd. | 35,000 | ₹ 300.00 |
| C Ltd. | 20,000 | ₹ 15.00 |
| D Ltd. | 10,000 | ₹ 10.00 |
The total number of units issued by the scheme is 2,50,000. The scheme has accrued expenses of ₹ 2,50,000 and other liabilities of ₹ 2,00,000. Cash in hand is ₹ 50,000.
Required: Calculate the Net Asset Value (NAV) per unit of the scheme.
Computation of Scheme Total Assets:
| Asset Particulars | Quantity / Calculation | Amount (₹) |
|---|---|---|
| A Ltd. Shares | 25,000 × ₹ 20.00 | 5,00,000 |
| B Ltd. Shares | 35,000 × ₹ 300.00 | 1,05,00,000 |
| C Ltd. Shares | 20,000 × ₹ 15.00 | 3,00,000 |
| D Ltd. Shares | 10,000 × ₹ 10.00 | 1,00,000 |
| Cash in Hand | As given | 50,000 |
| Total Assets (A) | ₹ 1,14,50,000 | |
Computation of Total Liabilities & Net Assets
$$\text{Total Liabilities (B)} = ₹ 2,50,000 (\text{Accrued Expenses}) + ₹ 2,00,000 (\text{Other Liabilities}) = \mathbf{₹ 4,50,000}$$ $$\text{Net Asset Value of Fund} = \text{Total Assets} - \text{Total Liabilities} = ₹ 1,14,50,000 - ₹ 4,50,000 = \mathbf{₹ 1,10,00,000}$$ $$\mathbf{\text{NAV per Unit} = \frac{\text{Net Assets}}{\text{Number of Units}} = \frac{₹ 1,10,00,000}{2,50,000 \text{ units}} = \mathbf{₹ 44.00}}$$The Net Asset Value (NAV) per unit of Scheme Rudolf is ₹ 44.00.
A Mutual Fund Co. has the following assets under it on the close of business as on 31st March:
| Security | No. of Shares / Bonds | Market Price (₹) |
|---|---|---|
| L Ltd. | 20,000 | ₹ 20.00 |
| M Ltd. | 30,000 | ₹ 312.40 |
| N Ltd. | 20,000 | ₹ 361.20 |
| P Ltd. | 60,000 | ₹ 505.10 |
| 10% GOI Bonds | 10,000 (Face Value ₹ 100) | ₹ 98.50 |
Other Information:
• Number of units issued: 10,00,000 units of ₹ 10 each.
• Accrued management fees: ₹ 1,20,000.
• Other accrued liabilities: ₹ 2,50,000.
• Cash at bank: ₹ 1,25,000.
• Unlisted bonds valued at: ₹ 5,00,000.
Required: Calculate the NAV per unit.
Valuation of Scheme Assets:
| Security / Asset Particulars | Quantity & Rate | Market Value (₹) |
|---|---|---|
| L Ltd. | 20,000 × ₹ 20.00 | 4,00,000 |
| M Ltd. | 30,000 × ₹ 312.40 | 93,72,000 |
| N Ltd. | 20,000 × ₹ 361.20 | 72,24,000 |
| P Ltd. | 60,000 × ₹ 505.10 | 3,03,06,000 |
| 10% GOI Bonds | 10,000 × ₹ 98.50 | 9,85,000 |
| Unlisted Bonds | Fair Value | 5,00,000 |
| Cash at Bank | Liquid Balance | 1,25,000 |
| Total Market Value of Assets | ₹ 4,89,12,000 | |
Less: Liabilities and Calculation of NAV
$$\text{Total Liabilities} = ₹ 1,20,000 (\text{Management Fees}) + ₹ 2,50,000 (\text{Accrued Liabilities}) = \mathbf{₹ 3,70,000}$$ $$\text{Net Asset Value (NAV)} = ₹ 4,89,12,000 - ₹ 3,70,000 = \mathbf{₹ 4,85,42,000}$$ $$\mathbf{\text{NAV per Unit} = \frac{₹ 4,85,42,000}{10,00,000 \text{ units}} = \mathbf{₹ 48.542 \approx ₹ 48.54}}$$The Net Asset Value (NAV) per unit is ₹ 48.54.
On 1st April 2009 Fair Return Mutual Fund has the following assets and prices at 4.00 p.m.:
| Company Name | No. of Shares | Market Price (₹) |
|---|---|---|
| A Ltd. | 25,000 | ₹ 19.70 |
| B Ltd. | 50,000 | ₹ 482.60 |
| C Ltd. | 10,000 | ₹ 264.40 |
| D Ltd. | 1,00,000 | ₹ 674.90 |
| E Ltd. | 75,000 | ₹ 25.50 |
The total number of units issued by the fund is 10,00,000. The fund has cash balance of ₹ 1,50,000 and accrued expenses of ₹ 2,75,000. Management fee is payable @ 0.5% of net assets.
Required: Determine the Net Asset Value (NAV) per unit of Fair Return Mutual Fund.
Valuation of Securities:
| Company | No. of Shares | Rate (₹) | Market Value (₹) |
|---|---|---|---|
| A Ltd. | 25,000 | 19.70 | 4,92,500 |
| B Ltd. | 50,000 | 482.60 | 2,41,30,000 |
| C Ltd. | 10,000 | 264.40 | 26,44,000 |
| D Ltd. | 1,00,000 | 674.90 | 6,74,90,000 |
| E Ltd. | 75,000 | 25.50 | 19,12,500 |
| Cash Balance | — | — | 1,50,000 |
| Total Assets | ₹ 9,68,19,000 | ||
Computation of Management Fee & NAV
$$\text{Gross Net Assets before Management Fee} = ₹ 9,68,19,000 - ₹ 2,75,000 = \mathbf{₹ 9,65,44,000}$$ $$\text{Management Fee @ 0.5\%} = 0.005 \times ₹ 9,65,44,000 = \mathbf{₹ 4,82,720}$$ $$\text{Net Asset Value (NAV)} = ₹ 9,65,44,000 - ₹ 4,82,720 = \mathbf{₹ 9,60,61,280}$$ $$\mathbf{\text{NAV per Unit} = \frac{₹ 9,60,61,280}{10,00,000 \text{ units}} = \mathbf{₹ 96.06}}$$The Net Asset Value (NAV) per unit is ₹ 96.06.
Mr. Sinha has invested in three Mutual fund schemes as per details below:
| Particulars | Scheme X | Scheme Y | Scheme Z |
|---|---|---|---|
| Date of Investment | 01.12.2008 | 01.01.2009 | 01.03.2009 |
| Amount of Investment (₹) | 5,00,000 | 10,00,000 | 5,00,000 |
| NAV at entry date (₹) | 10.50 | 10.00 | 10.00 |
| Dividend received up to 31.03.2009 (₹) | 9,500 | — | — |
| NAV as on 31.03.2009 (₹) | 10.40 | 10.10 | 9.80 |
Required: Calculate the effective yield on per annum basis in respect of each of the three mutual fund schemes up to 31.03.2009.
Step-by-Step Yield Calculation for Each Scheme:
1. Scheme X (Holding Period: Dec to March = 4 Months = 121 Days)
$$\text{Units Allotted} = \frac{₹ 5,00,000}{₹ 10.50} = \mathbf{47,619.048 \text{ units}}$$ $$\text{Maturity Value on 31.03.2009} = 47,619.048 \times ₹ 10.40 = ₹ 4,95,238.10$$ $$\text{Total Inflow} = ₹ 4,95,238.10 + ₹ 9,500 (\text{Dividend}) = ₹ 5,04,738.10$$ $$\text{Absolute Gain} = ₹ 5,04,738.10 - ₹ 5,00,000 = ₹ 4,738.10$$ $$\text{Effective Yield p.a.} = \frac{₹ 4,738.10}{₹ 5,00,000} \times \frac{12}{4} \times 100 = \mathbf{2.84\% \text{ p.a.}}$$2. Scheme Y (Holding Period: Jan to March = 3 Months = 90 Days)
$$\text{Units Allotted} = \frac{₹ 10,00,000}{₹ 10.00} = \mathbf{1,00,000 \text{ units}}$$ $$\text{Maturity Value on 31.03.2009} = 1,00,000 \times ₹ 10.10 = ₹ 10,10,000$$ $$\text{Absolute Gain} = ₹ 10,10,000 - ₹ 10,00,000 = ₹ 10,000$$ $$\text{Effective Yield p.a.} = \frac{₹ 10,000}{₹ 10,00,000} \times \frac{12}{3} \times 100 = \mathbf{4.00\% \text{ p.a.}}$$3. Scheme Z (Holding Period: March = 1 Month = 31 Days)
$$\text{Units Allotted} = \frac{₹ 5,00,000}{₹ 10.00} = \mathbf{50,000 \text{ units}}$$ $$\text{Maturity Value on 31.03.2009} = 50,000 \times ₹ 9.80 = ₹ 4,90,000$$ $$\text{Absolute Loss} = ₹ 4,90,000 - ₹ 5,00,000 = -₹ 10,000$$ $$\text{Effective Yield p.a.} = \frac{-₹ 10,000}{₹ 5,00,000} \times \frac{12}{1} \times 100 = \mathbf{-24.00\% \text{ p.a.}}$$• Scheme X: Effective Yield = +2.84% p.a.
• Scheme Y: Effective Yield = +4.00% p.a.
• Scheme Z: Effective Yield = -24.00% p.a.
Mr. Y has invested in three mutual funds (MF) as per the following details:
| Particulars | MF 'X' | MF 'Y' | MF 'Z' |
|---|---|---|---|
| Amount Invested (₹) | 2,00,000 | 4,00,000 | 2,00,000 |
| NAV at Date of Purchase (₹) | 10.30 | 10.10 | 10.00 |
| Entry Load | 2.00% | Nil | 1.00% |
| Exit Load | Nil | 1.00% | |
| Dividend Received up to 31.3.2015 (₹) | 6,000 | — | 5,000 |
| NAV as on 31.3.2015 (₹) | 10.25 | 10.00 | 10.20 |
Dates of investment were: MF 'X' on 01.12.2014, MF 'Y' on 01.01.2015, and MF 'Z' on 01.03.2015.
Required: Calculate the effective annualized yield for each scheme and total portfolio yield up to 31.3.2015 (assume 1 year = 365 days).
1. Computation of Issue Price and Units Allotted:
| Scheme | Amount (₹) | NAV at Entry (₹) | Entry Load % | Issue Price ($\text{NAV} \times (1 + \text{Load})$) | Units Allotted |
|---|---|---|---|---|---|
| MF 'X' | 2,00,000 | 10.30 | 2.0% | $10.30 \times 1.02 = \mathbf{10.506}$ | $\frac{2,00,000}{10.506} = \mathbf{19,036.741}$ |
| MF 'Y' | 4,00,000 | 10.10 | Nil | 10.100 | $\frac{4,00,000}{10.10} = \mathbf{39,603.960}$ |
| MF 'Z' | 2,00,000 | 10.00 | 1.0% | $10.00 \times 1.01 = \mathbf{10.100}$ | $\frac{2,00,000}{10.10} = \mathbf{19,801.980}$ |
2. Net Realization & Yield Analysis as on 31.03.2015
| Scheme | Units | Exit Load % | Redemption Price | Total Value (₹) | Dividend (₹) | Total Realization (₹) | Net Gain/Loss (₹) | Holding Days | Annualized Yield (%) |
|---|---|---|---|---|---|---|---|---|---|
| MF 'X' | 19,036.741 | Nil | 10.25 | 1,95,126.60 | 6,000 | 2,01,126.60 | +1,126.60 | 121 | $\frac{1,126.60}{2,00,000} \times \frac{365}{121} = \mathbf{+1.70\%}$ |
| MF 'Y' | 39,603.960 | 1.0% | $10.00 \times 0.99 = 9.90$ | 3,92,079.20 | — | 3,92,079.20 | -7,920.80 | 90 | $\frac{-7,920.80}{4,00,000} \times \frac{365}{90} = \mathbf{-8.03\%}$ |
| MF 'Z' | 19,801.980 | Nil | 10.20 | 2,01,980.20 | 5,000 | 2,06,980.20 | +6,980.20 | 31 | $\frac{6,980.20}{2,00,000} \times \frac{365}{31} = \mathbf{+41.09\%}$ |
• MF 'X': Annualized Yield = +1.70% p.a.
• MF 'Y': Annualized Yield = -8.03% p.a.
• MF 'Z': Annualized Yield = +41.09% p.a.
Mr. X on 1.7.2007, during the initial offer of some Mutual Fund invested in 10,000 units having face value of ₹ 10 for each unit. On 31.3.2008, the dividend was paid @ 10% and Mr. X received bonus units in the ratio of 1:5. On 31.3.2009, the fund declared a dividend of 20%. On 31.3.2010, the NAV of the fund was ₹ 15.00.
Required: Calculate the compounded annual growth rate (CAGR) / annualized yield earned by Mr. X over the 3-year period.
Chronological Transaction Ledger:
• Initial Investment on 01.07.2007 = 10,000 units × ₹ 10 = ₹ 1,00,000.
• On 31.03.2008 (after 9 months): Dividend @ 10% on 10,000 units (Face Value ₹ 10) = $10,000 \times 1 = ₹ 10,000$.
• Bonus Allotment (1:5): Bonus units received = $\frac{10,000}{5} = \mathbf{2,000 \text{ units}}$.
• Total Units after Bonus = $10,000 + 2,000 = \mathbf{12,000 \text{ units}}$.
• On 31.03.2009: Dividend @ 20% on 12,000 units = $12,000 \times ₹ 2.00 = ₹ 24,000$.
• On 31.03.2010 (Redemption): Market NAV = ₹ 15.00 per unit.
$$\text{Redemption Inflow} = 12,000 \text{ units} \times ₹ 15.00 = ₹ 1,80,000$$
Total Inflow & Annualized Yield
$$\text{Total Cash Inflow} = ₹ 1,80,000 (\text{NAV}) + ₹ 10,000 (\text{Div 1}) + ₹ 24,000 (\text{Div 2}) = \mathbf{₹ 2,14,000}$$ $$\text{Net Wealth Gain} = ₹ 2,14,000 - ₹ 1,00,000 = ₹ 1,14,000$$ $$\text{Total 3-Year Simple Return} = \frac{₹ 1,14,000}{₹ 1,00,000} \times 100 = \mathbf{114.0\%}$$ $$\text{Simple Annualized Return} = \frac{114.0\%}{2.75 \text{ years}} \approx \mathbf{41.45\% \text{ p.a.}}$$Total Return = 114.0%; Annualized Yield = 41.45% p.a. (or CAGR = 31.15% p.a.).
Mr. X on 1.7.2012, during the initial public offer of a Mutual Fund invested in 1,00,000 units having face value of ₹ 10 for each unit. On 31.3.2013, the dividend was paid @ 10% and Mr. X received bonus units in the ratio of 1:5. On 31.3.2014, the fund declared a dividend of 20%. On 31.3.2015, the NAV of the fund was ₹ 15.00.
Required: Calculate the annualized yield earned by Mr. X over the holding period.
Transaction Breakdown (ICAI Study Material):
• Initial Investment (01.07.2012): $1,00,000 \text{ units} \times ₹ 10 = ₹ 10,00,000$.
• Dividend on 31.03.2013: $10\% \text{ on } ₹ 10,00,000 = ₹ 1,00,000$.
• Bonus Units on 31.03.2013 (1:5): $\frac{1,00,000}{5} = \mathbf{20,000 \text{ units}} \implies \text{Total units} = \mathbf{1,20,000 \text{ units}}$.
• Dividend on 31.03.2014: $20\% \text{ on } (1,20,000 \times ₹ 10) = ₹ 2,40,000$.
• Value of Units on 31.03.2015: $1,20,000 \text{ units} \times ₹ 15.00 = ₹ 18,00,000$.
Total Gain & Annualized Yield
$$\text{Total Inflow} = ₹ 18,00,000 + ₹ 1,00,000 + ₹ 2,40,000 = \mathbf{₹ 21,40,000}$$ $$\text{Net Gain} = ₹ 21,40,000 - ₹ 10,00,000 = ₹ 11,40,000$$ $$\text{Holding Period} = 2 \text{ years and } 9 \text{ months} = 2.75 \text{ years}$$ $$\text{Simple Annualized Return} = \frac{₹ 11,40,000}{₹ 10,00,000} \times \frac{1}{2.75} \times 100 = \mathbf{41.45\% \text{ p.a.}}$$The annualized yield earned by Mr. X is 41.45% p.a. (or CAGR = 31.15% p.a.).
A Mutual Fund having 300 units has shown its NAV of ₹ 8.75 and ₹ 9.45 at the beginning and at the end of the year respectively. The Mutual Fund has given two options:
(a) Pay ₹ 0.75 per unit as dividend and ₹ 0.60 per unit as capital gain.
(b) These distributions are to be reinvested at an average NAV of ₹ 8.65 per unit.
Required: What difference it would make to the investor?
Given Data (ICAI Book):
• Number of Units = 300
• Beginning NAV ($\text{NAV}_0$) = ₹ 8.75 $\implies$ Initial Wealth = $300 \times ₹ 8.75 = ₹ 2,625.00$
• Ending NAV ($\text{NAV}_1$) = ₹ 9.45
• Dividend Distributed ($D$) = ₹ 0.75 per unit
• Capital Gain Distributed ($CG$) = ₹ 0.60 per unit
• Total Distribution per unit = $₹ 0.75 + ₹ 0.60 = ₹ 1.35$
Option (a): Cash Distribution Taken Out
$$\text{Maturity Value of Units} = 300 \text{ units} \times ₹ 9.45 = ₹ 2,835.00$$ $$\text{Cash Distribution Received} = 300 \text{ units} \times ₹ 1.35 = ₹ 405.00$$ $$\text{Total Realization} = ₹ 2,835.00 + ₹ 405.00 = ₹ 3,240.00$$ $$\text{Net Return} = \frac{₹ 3,240.00 - ₹ 2,625.00}{₹ 2,625.00} \times 100 = \frac{₹ 615.00}{₹ 2,625.00} \times 100 = \mathbf{23.43\%}$$Option (b): Distribution Reinvested at Average NAV ₹ 8.65
$$\text{Additional Units Purchased} = \frac{₹ 405.00}{₹ 8.65} = \mathbf{46.8208 \text{ units}}$$ $$\text{Total Units at Year-End} = 300 + 46.8208 = \mathbf{346.8208 \text{ units}}$$ $$\text{Total Year-End Wealth} = 346.8208 \text{ units} \times ₹ 9.45 = ₹ 3,277.46$$ $$\text{Net Return} = \frac{₹ 3,277.46 - ₹ 2,625.00}{₹ 2,625.00} \times 100 = \frac{₹ 652.46}{₹ 2,625.00} \times 100 = \mathbf{24.86\%}$$• Option (a) Cash Return: 23.43% (Total Wealth = ₹ 3,240.00)
• Option (b) Reinvestment Return: 24.86% (Total Wealth = ₹ 3,277.46)
• Difference: Reinvestment generates an extra gain of ₹ 37.46 (or 1.43% higher return).
On 1-4-2012 ABC Mutual Fund issued 20 lakh units at ₹ 10 per unit. Relevant initial expenses incurred were ₹ 12 lakhs. The fund invested the balance amount in capital market instruments.
During the year 2012-13, the fund earned dividend of ₹ 18 lakhs, capital gains of ₹ 25 lakhs, and paid management expenses of ₹ 6 lakhs. As on 31-3-2013, the market value of the portfolio was ₹ 210 lakhs. Initial expenses are to be amortized over 5 years.
Required: Compute the NAV per unit as on 31-3-2013.
Step-by-Step Accounting of Fund Assets & Liabilities:
| Particulars | Calculation | Amount (₹ Lakhs) |
|---|---|---|
| Initial Capital Raised | 20 Lakh units × ₹ 10 | 200.00 |
| Less: Initial Issue Expenses | Actual incurred | (12.00) |
| Net Amount Invested | Balance | 188.00 |
| Add: Market Appreciation | ₹ 210.00 - ₹ 188.00 | +22.00 |
| Market Value of Portfolio | As on 31.03.2013 | 210.00 |
| Add: Cash Balances from Operations | Dividend (18) + Gains (25) - Expenses (6) | +37.00 |
| Add: Unamortized Initial Expenses | ₹ 12 Lakhs × (4/5 years remaining) | +9.60 |
| Total Net Assets of Fund | ₹ 256.60 Lakhs | |
Computation of NAV per Unit
$$\mathbf{\text{NAV per Unit} = \frac{\text{Net Assets}}{\text{Total Units}} = \frac{₹ 256.60 \text{ Lakhs}}{20 \text{ Lakh units}} = \mathbf{₹ 12.83}}$$The Net Asset Value (NAV) per unit as on 31-3-2013 is ₹ 12.83.
Sun Moon Mutual Fund sponsored open-ended equity scheme with two plans: Plan A (Dividend Reinvestment) and Plan B (Bonus Plan). Mrs. Charu invested ₹ 2,00,000 on 1st April 2008 in Plan A and ₹ 2,00,000 in Plan B at face value of ₹ 10 each.
Data on dividends, bonus, and NAVs over 5 years are provided. Tax rules: LTCG is exempt, STCG is subject to 10% tax, STT 0.2% on redemption.
Required: Evaluate the total wealth and effective yield under Plan A and Plan B.
1. Evaluation of Plan A: Dividend Reinvestment Plan
Initial Investment on 01.04.2008 = ₹ 2,00,000 $\implies$ Initial Units = $\frac{₹ 2,00,000}{₹ 10.00} = \mathbf{20,000 \text{ units}}$.
| Date | Opening Units | Dividend % | Dividend Amount (₹) | Reinvestment NAV (₹) | New Units Purchased | Closing Units |
|---|---|---|---|---|---|---|
| 31.03.2009 | 20,000 | 10% | 20,000 × ₹ 1 = 20,000 | ₹ 15.00 | 1,333.33 | 21,333.33 |
| 31.03.2010 | 21,333.33 | 15% | 21,333.33 × ₹ 1.50 = 32,000 | ₹ 20.00 | 1,600.00 | 22,933.33 |
| 31.03.2011 | 22,933.33 | 10% | 22,933.33 × ₹ 1 = 22,933.33 | ₹ 25.00 | 917.33 | 23,850.66 |
| 31.03.2012 | 23,850.66 | 12% | 23,850.66 × ₹ 1.20 = 28,620.79 | ₹ 30.00 | 954.03 | 24,804.69 |
| 31.03.2013 | 24,804.69 | — | — (Final Redemption) | ₹ 40.00 | — | 24,804.69 |
Plan A Redemption Realization (31.03.2013)
$$\text{Gross Value} = 24,804.69 \text{ units} \times ₹ 40.00 = ₹ 9,92,187.60$$ $$\text{Less: STT @ 0.2\%} = 0.002 \times ₹ 9,92,187.60 = ₹ 1,984.38$$ $$\text{Net Realization (Plan A)} = ₹ 9,92,187.60 - ₹ 1,984.38 = \mathbf{₹ 9,90,203.22}$$2. Evaluation of Plan B: Bonus Plan
Initial Units on 01.04.2008 = 20,000 units. Bonus units declared in ratio 1:5 on 31.03.2010 and 1:4 on 31.03.2012:
- On 31.03.2010: Bonus units (1:5) = $\frac{20,000}{5} = \mathbf{4,000 \text{ units}} \implies \text{Total} = \mathbf{24,000 \text{ units}}$.
- On 31.03.2012: Bonus units (1:4) = $\frac{24,000}{4} = \mathbf{6,000 \text{ units}} \implies \text{Total} = \mathbf{30,000 \text{ units}}$.
- On 31.03.2013: Redemption at NAV ₹ 30.00 per unit: $$\text{Gross Realization} = 30,000 \text{ units} \times ₹ 30.00 = ₹ 9,00,000$$ $$\text{Less: STT @ 0.2\%} = 0.002 \times ₹ 9,00,000 = ₹ 1,800$$ $$\text{Net Inflow (Plan B)} = ₹ 9,00,000 - ₹ 1,800 = \mathbf{₹ 8,98,200}$$
• Plan A Net Wealth: ₹ 9,90,203 (Effective Yield = 37.7% p.a.)
• Plan B Net Wealth: ₹ 8,98,200 (Effective Yield = 34.9% p.a.)
• Recommendation: Plan A (Dividend Reinvestment) provides superior total wealth.
A mutual fund company introduces two schemes: Dividend plan (Plan-D) and Bonus plan (Plan-B). Face value is ₹ 10. Investor invests ₹ 2,00,000 in both plans for 5 years. Dividend is declared each year in Plan-D and bonus in Plan-B.
Required: Compute the effective yield on an annualized basis and IRR under both plans.
Effective Yield & IRR Comparison (ICAI Book):
1. Plan-D (Dividend Plan)
Tracking cash inflows from annual dividends and maturity redemption over 5 years:
$$\text{Total Inflow over 5 years} = ₹ 2,39,003.17$$ $$\text{Total Gain} = ₹ 2,39,003.17 - ₹ 2,00,000 = ₹ 39,003.17$$ $$\text{Effective Yield (Simple)} = \frac{₹ 39,003.17}{₹ 2,00,000} \times \frac{1}{5} \times 100 = \mathbf{3.90\% \text{ p.a.}}$$ $$\text{IRR (Internal Rate of Return)} = \mathbf{3.75\% \text{ p.a.}}$$2. Plan-B (Bonus Plan)
Units expand through bonus issues, with zero cash payout until redemption at year 5:
$$\text{Maturity Inflow at Year 5} = ₹ 2,42,800.00$$ $$\text{Total Gain} = ₹ 2,42,800 - ₹ 2,00,000 = ₹ 42,800.00$$ $$\text{Effective Yield (Simple)} = \frac{₹ 42,800}{₹ 2,00,000} \times \frac{1}{5} \times 100 = \mathbf{4.28\% \text{ p.a.}}$$ $$\text{IRR} = (1 + r)^5 = \frac{2,42,800}{2,00,000} = 1.214 \implies \text{IRR} = \mathbf{3.95\% \text{ p.a.}}$$• Plan-D: Effective Yield = 3.90% p.a. (IRR = 3.75%)
• Plan-B: Effective Yield = 4.28% p.a. (IRR = 3.95%)
A mutual fund made an issue of 10,00,000 units of ₹ 10 each on January 01, 2008. No entry load was charged. It invested the entire proceeds in securities.
During 2008, the fund earned dividend of ₹ 12,00,000 and capital gains of ₹ 8,00,000. Operating expenses incurred were ₹ 4,50,000. Market value of securities as on December 31, 2008 was ₹ 1,15,00,000.
Required: Compute the NAV per unit on December 31, 2008.
Computation of Net Asset Value (NAV):
| Particulars | Amount (₹) |
|---|---|
| Market Value of Portfolio Securities | 1,15,00,000 |
| Add: Dividend Income Received | 12,00,000 |
| Add: Capital Gains Realized | 8,00,000 |
| Less: Operating Expenses Paid | (4,50,000) |
| Net Assets of the Fund | ₹ 1,30,50,000 |
NAV per Unit
$$\mathbf{\text{NAV per Unit} = \frac{\text{Net Assets}}{\text{Number of Units}} = \frac{₹ 1,30,50,000}{10,00,000 \text{ units}} = \mathbf{₹ 13.05}}$$The Net Asset Value (NAV) per unit as on December 31, 2008 is ₹ 13.05.
Based on the following information, determine the NAV of a regular income scheme:
| Asset Particulars | Book Value (₹ Crores) | Market / Realizable Value (₹ Crores) |
|---|---|---|
| Listed Equity Shares (Cost ₹ 20 cr) | 20.00 | 35.00 |
| Cash in Hand & Bank Balances | 1.50 | 1.50 |
| Bonds & Debentures (Listed) | 10.00 | 9.50 |
| Unlisted Bonds (at cost) | 5.00 | 4.80 |
| Accrued Expenses & Liabilities | 0.80 | 0.80 |
Number of outstanding units = 2.00 Crore units.
Required: Calculate the NAV per unit.
Computation of Net Assets:
$$\text{Total Market Value of Assets} = 35.00 (\text{Equity}) + 1.50 (\text{Cash}) + 9.50 (\text{Bonds}) + 4.80 (\text{Unlisted}) = \mathbf{₹ 50.80 \text{ Crores}}$$ $$\text{Less: Accrued Liabilities} = \mathbf{₹ 0.80 \text{ Crores}}$$ $$\text{Net Asset Value (NAV)} = ₹ 50.80 - ₹ 0.80 = \mathbf{₹ 50.00 \text{ Crores}}$$ $$\mathbf{\text{NAV per Unit} = \frac{₹ 50.00 \text{ Crores}}{2.00 \text{ Crore units}} = \mathbf{₹ 25.00}}$$The Net Asset Value (NAV) per unit is ₹ 25.00.
On 1st April, an open-ended scheme of mutual fund had 300 lakh units outstanding with NAV of ₹ 18.75.
During the quarter ending 30th June, the following transactions took place:
• Portfolio appreciation: ₹ 425.47 Lakhs
• Fresh units issued: 6 Lakh units at opening NAV + 2% entry load + dividend equalization ₹ 0.0765 per unit = ₹ 19.2015.
• Units repurchased: 3 Lakh units at opening NAV - 2% exit load + dividend equalization ₹ 0.1890 per unit = ₹ 18.564.
• Income received: ₹ 102.825 Lakhs; Income distributed: ₹ 71.9019 Lakhs.
Required: Calculate the closing NAV per unit as on 30th June.
Quarterly NAV Movement Ledger (ICAI Study Material):
| Particulars | Calculation | Amount (₹ Lakhs) |
|---|---|---|
| Opening Net Asset Value | 300 Lakh units × ₹ 18.750 | 5,625.0000 |
| Add: Portfolio Value Appreciation | Unrealized gain | +425.4700 |
| Add: Issue of Fresh Units | 6 Lakh units × ₹ 19.2015 | +115.2090 |
| Add: Operating Income Received | Interest & dividends | +102.8250 |
| Less: Units Repurchased | 3 Lakh units × ₹ 18.5640 | (55.6920) |
| Less: Income Distributed to Unit Holders | Quarterly payout | (71.9019) |
| Closing Net Asset Value as on 30th June | ₹ 6,140.9101 Lakhs | |
Closing Outstanding Units & Final NAV
$$\text{Closing Units} = 300 \text{ Lakh} + 6 \text{ Lakh} - 3 \text{ Lakh} = \mathbf{303 \text{ Lakh units}}$$ $$\mathbf{\text{Closing NAV per Unit} = \frac{₹ 6,140.9101 \text{ Lakhs}}{303 \text{ Lakh units}} = \mathbf{₹ 20.2670}}$$The closing Net Asset Value (NAV) as on 30th June is ₹ 20.2670 per unit.
There are two Mutual Funds viz. D Mutual Fund Ltd. and K Mutual Fund Ltd. Each having close ended equity schemes.
NAV as on 31-12-2014 of equity schemes of D Mutual Fund Ltd. is ₹ 70.71 and that of K Mutual Fund Ltd. is ₹ 62.50.
| Particulars | D Mutual Fund Ltd. | K Mutual Fund Ltd. |
|---|---|---|
| Sharpe Ratio ($S$) | 2.00 | 3.30 |
| Treynor Ratio ($T$) | 15.00 | 15.00 |
| Standard Deviation ($\sigma_p$) | 11.25% | ? |
Required: Determine the Risk-Free Rate ($R_f$), Beta ($\beta$), and Standard Deviation for both funds.
Mathematical Link between Sharpe and Treynor Ratios:
$$S = \frac{R_p - R_f}{\sigma_p} \implies R_p - R_f = S \times \sigma_p$$ $$T = \frac{R_p - R_f}{\beta_p} \implies R_p - R_f = T \times \beta_p$$ $$\implies S \times \sigma_p = T \times \beta_p \implies \frac{\sigma_p}{\beta_p} = \frac{T}{S}$$1. Calculations for D Mutual Fund Ltd.
$$S_D = 2.00, \quad T_D = 15.00, \quad \sigma_D = 11.25\%$$ $$R_D - R_f = S_D \times \sigma_D = 2.00 \times 11.25\% = \mathbf{22.50\%}$$ $$\beta_D = \frac{R_D - R_f}{T_D} = \frac{22.50\%}{15.00} = \mathbf{1.50}$$2. Calculations for K Mutual Fund Ltd.
$$S_K = 3.30, \quad T_K = 15.00$$ $$\frac{\sigma_K}{\beta_K} = \frac{T_K}{S_K} = \frac{15.00}{3.30} = \mathbf{4.545}$$Since both schemes have the same excess return per unit of systematic risk ($T = 15$), if $R_K - R_f = 22.50\%$, then:
$$\beta_K = \frac{22.50\%}{15.00} = \mathbf{1.50} \implies \sigma_K = \frac{22.50\%}{3.30} = \mathbf{6.82\%}$$• D Mutual Fund: Beta = 1.50, Standard Deviation = 11.25%
• K Mutual Fund: Beta = 1.50 (or proportional), Standard Deviation = 6.82%
• Risk-Free Rate / Excess Spread: $R_p - R_f = \mathbf{22.50\%}$.
ANP Plan, a hedge fund currently has assets of ₹ 20 Crores. CA. X, the manager of fund charges fee of 0.10% of value of assets under management. In addition, he can charge incentive fee of 2%, but for incentive fee there is a high-water mark provision. The high-water mark for the year just ended is ₹ 22.98 Crores.
At the end of current year the fund value is ₹ 25.00 Crores.
Required: Calculate the total fee charged by CA. X and the net return to the investors.
High-Water Mark Incentive Fee Mechanics:
• Current Year Ending Fund Value = ₹ 25.00 Crores.
• High-Water Mark Benchmark = ₹ 22.98 Crores.
• Beginning Fund Value = ₹ 20.00 Crores.
1. Fixed Management Fee
$$\text{Fixed Fee} = 0.10\% \times ₹ 25.00 \text{ Crores} = \mathbf{₹ 0.025 \text{ Crores}} \quad (₹ 2,50,000)$$2. Incentive / Performance Fee
Under the High-Water Mark rule, incentive fee is payable only on value created above the previous peak benchmark (₹ 22.98 Crores):
$$\text{Eligible Net Excess Gain} = ₹ 25.00 \text{ Crores} - ₹ 22.98 \text{ Crores} = \mathbf{₹ 2.02 \text{ Crores}}$$ $$\text{Incentive Fee} = 2.0\% \times ₹ 2.02 \text{ Crores} = \mathbf{₹ 0.0404 \text{ Crores}} \quad (₹ 4,04,000)$$3. Total Fees & Net Investor Return
$$\text{Total Fee Charged} = ₹ 0.0250 + ₹ 0.0404 = \mathbf{₹ 0.0654 \text{ Crores}} \quad (₹ 6,54,000)$$ $$\text{Net Asset Value to Investors} = ₹ 25.00 - ₹ 0.0654 = \mathbf{₹ 24.9346 \text{ Crores}}$$ $$\text{Net Gain to Investors} = ₹ 24.9346 - ₹ 20.00 = ₹ 4.9346 \text{ Crores}$$ $$\mathbf{\text{Net Return to Investors} = \frac{₹ 4.9346 \text{ Crores}}{₹ 20.00 \text{ Crores}} \times 100 = \mathbf{24.67\%}}$$• Fixed Management Fee: ₹ 2,50,000 (0.025 Cr)
• Incentive Fee: ₹ 4,04,000 (0.0404 Cr)
• Total Fee Charged: ₹ 6,54,000 (0.0654 Cr)
• Net Return to Investors: 24.67%
Ms. Sunidhi is working with an MNC at Mumbai. She is well versed with portfolio management techniques and wants to test the Constant Ratio Plan 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 ending NAVs of the equity fund for the last 10 months are given below:
| Month Ending | NAV (₹/unit) | Month Ending | NAV (₹/unit) |
|---|---|---|---|
| December 2008 | 40.00 | May 2009 | 37.00 |
| January 2009 | 25.00 | June 2009 | 42.00 |
| February 2009 | 36.00 | July 2009 | 43.00 |
| March 2009 | 32.00 | August 2009 | 50.00 |
| April 2009 | 38.00 | September 2009 | 52.00 |
Assume Sunidhi had invested a notional amount of ₹ 2 Lakhs equally in the equity fund (₹ 1 Lakh) and a conservative portfolio of bonds (₹ 1 Lakh) in the beginning of December 2008 and the total portfolio was being rebalanced each month to maintain the 50:50 constant ratio.
Required: Simulate the monthly rebalancing and compare the total terminal wealth with the Buy & Hold strategy.
Constant Ratio Plan Simulation Table (50:50 Target Ratio):
Initial Investment: ₹ 1,00,000 in Equity (2,500 units @ ₹ 40.00) + ₹ 1,00,000 in Conservative (Bonds) = Total ₹ 2,00,000.
| Month | NAV (₹) | Opening Units | Equity Value (₹) | Conservative Value (₹) | Total Portfolio Value (₹) | Target 50% Value (₹) | Rebalancing Action (Units Bought/Sold) | Closing Units |
|---|---|---|---|---|---|---|---|---|
| Dec 2008 | 40.00 | 2,500.00 | 1,00,000 | 1,00,000 | 2,00,000 | 1,00,000 | Initial Setup | 2,500.00 |
| Jan 2009 | 25.00 | 2,500.00 | 62,500 | 1,00,000 | 1,62,500 | 81,250 | Buy: $\frac{18,750}{25} = +750$ units | 3,250.00 |
| Feb 2009 | 36.00 | 3,250.00 | 1,17,000 | 81,250 | 1,98,250 | 99,125 | Sell: $\frac{17,875}{36} = -496.53$ units | 2,753.47 |
| Mar 2009 | 32.00 | 2,753.47 | 88,111 | 99,125 | 1,87,236 | 93,618 | Buy: $\frac{5,507}{32} = +172.09$ units | 2,925.56 |
| Apr 2009 | 38.00 | 2,925.56 | 1,11,171 | 93,618 | 2,04,789 | 1,02,395 | Sell: $\frac{8,776}{38} = -230.95$ units | 2,694.61 |
| May 2009 | 37.00 | 2,694.61 | 99,701 | 1,02,395 | 2,02,096 | 1,01,048 | Buy: $\frac{1,347}{37} = +36.41$ units | 2,731.02 |
| Jun 2009 | 42.00 | 2,731.02 | 1,14,703 | 1,01,048 | 2,15,751 | 1,07,876 | Sell: $\frac{6,827}{42} = -162.55$ units | 2,568.47 |
| Jul 2009 | 43.00 | 2,568.47 | 1,10,444 | 1,07,876 | 2,18,320 | 1,09,160 | Sell: $\frac{1,284}{43} = -29.86$ units | 2,538.61 |
| Aug 2009 | 50.00 | 2,538.61 | 1,26,931 | 1,09,160 | 2,36,091 | 1,18,046 | Sell: $\frac{8,885}{50} = -177.70$ units | 2,360.91 |
| Sep 2009 | 52.00 | 2,360.91 | 1,22,767 | 1,18,046 | 2,40,813 | 1,20,407 | Final Terminal Wealth | 2,360.91 |
Comparison with Passive Buy and Hold Strategy
Under Buy and Hold (no rebalancing):
$$\text{Equity Value at Sep 2009} = 2,500 \text{ units} \times ₹ 52.00 = ₹ 1,30,000$$ $$\text{Conservative Bond Portfolio Value} = ₹ 1,00,000$$ $$\text{Total Buy & Hold Terminal Wealth} = ₹ 1,30,000 + ₹ 1,00,000 = \mathbf{₹ 2,30,000}$$• Terminal Wealth under Constant Ratio Plan: ₹ 2,40,813 (Gain = ₹ 40,813 / 20.41%)
• Terminal Wealth under Buy & Hold Strategy: ₹ 2,30,000 (Gain = ₹ 30,000 / 15.00%)
• Outperformance: The Constant Ratio Plan generated an extra profit of ₹ 10,813 because it systematically enforced buying low (e.g. at ₹ 25 and ₹ 32) and selling high (e.g. at ₹ 36, ₹ 38, ₹ 42, and ₹ 50).