Dean's Office Official Model Question Paper

Answer: Bank Discount Yield (BDY / $r_{bd}$): An annualized measure of return on a short-term discount instrument (such as a Treasury Bill) that calculates yield as a percentage of the instrument’s face value (par) rather than its actual purchase price, assuming a 360-day commercial year.

Formula:

$$r_{bd} = \frac{F - P}{F} \times \frac{360}{t} = \frac{D}{F} \times \frac{360}{t}$$

Where $F$ is face value, $P$ is purchase price, $D = F - P$ is discount amount, and $t$ is days to maturity.

Answer:

• Repo (Repurchase Agreement): A short-term transaction in which a commercial bank sells government securities to the central bank (Nepal Rastra Bank) with a commitment to repurchase them at an agreed higher price on a specified future date. It serves as a liquidity injection mechanism into the banking system.
• Reverse Repo: A transaction in which the central bank sells government securities to commercial banks with an agreement to buy them back, serving to absorb excess liquidity from the financial system.

Answer: Book Building Method: A capital market price discovery mechanism authorized by the Securities Board of Nepal (SEBON) where the issuer sets a price band instead of a fixed par value (Rs. 100). Qualified Institutional Buyers (QIBs) submit competitive bids across the band. A mathematical cut-off price is determined based on aggregate demand, and retail individual investors are subsequently allotted shares at a statutory 10% discount to this cut-off price.

Answer: Net Asset Value (NAV): The net rupee worth of a single unit of a mutual fund scheme, representing the fair market value of all underlying investments less accrued scheme liabilities.

Per-Unit Formula:

$$\text{NAV per Unit} = \frac{\text{Market Value of Portfolio Securities} + \text{Cash \& Receivables} - \text{Accrued Operating Liabilities}}{\text{Total Number of Scheme Units Outstanding}}$$

Answer:

1. Pure Expectations Theory: Asserts that long-term yields represent an unbiased geometric average of current and expected future short-term interest rates.
2. Liquidity Preference Theory: Argues that investors prefer short-term liquidity, requiring a positive liquidity risk premium to commit capital to longer maturities, making upward-sloping yield curves standard.
3. Market Segmentation Theory: Asserts that financial markets are compartmentalized by maturity segments determined by institutional asset-liability requirements (e.g., commercial banks in short-term vs. pension funds in long-term).

Solution: Money Market Instruments & Treasury Bill Yields

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Step 1: Identification of Given Parameters

• Face Value ($F$) = Rs. 100,000
• Purchase Price ($P$) = Rs. 98,250
• Absolute Discount ($D = F - P$) = $100,000 - 98,250 = \text{Rs. } 1,750$
• Days to Maturity ($t$) = 91 days

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Part (a): Bank Discount Yield ($r_{bd}$) (3 Marks)

$$r_{bd} = \frac{D}{F} \times \frac{360}{t} = \frac{1,750}{100,000} \times \frac{360}{91} = 0.017500 \times 3.956044 = 0.069231 = \mathbf{6.923\%}$$

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Part (b): Money Market / Investment Yield ($r_{mm}$) (3 Marks)

The money market yield calculates return on the actual purchase price ($P$) over a 360-day year:

$$r_{mm} = \frac{D}{P} \times \frac{360}{t} = \frac{1,750}{98,250} \times \frac{360}{91} = 0.0178117 \times 3.956044 = 0.070464 = \mathbf{7.046\%}$$

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Part (c): Bond Equivalent Yield & Effective Annual Yield (4 Marks)

1. Bond Equivalent Yield (BEY / $r_{bey}$):

BEY annualizes the holding period return using actual capital invested ($P$) over a standard 365-day year:

$$r_{bey} = \frac{D}{P} \times \frac{365}{t} = \frac{1,750}{98,250} \times \frac{365}{91} = 0.0178117 \times 4.010989 = 0.071443 = \mathbf{7.144\%}$$

2. Effective Annual Yield (EAY):

EAY accounts for compound interest by reinvesting the proceeds across all sub-periods:

$$\text{Holding Period Return } (HPR) = \frac{D}{P} = \frac{1,750}{98,250} = 0.0178117$$

$$\text{EAY} = (1 + HPR)^{\frac{365}{t}} - 1 = (1 + 0.0178117)^{\frac{365}{91}} - 1 = (1.0178117)^{4.010989} - 1$$

$$\text{EAY} = 1.073413 - 1 = 0.073413 = \mathbf{7.341\%}$$

3. Comparative Yield Summary & Explanation:

$$\mathbf{r_{bd} (6.923\%) < r_{mm} (7.046\%) < r_{bey} (7.144\%) < \text{EAY} (7.341\%)}$$

Analytical Rationale:

• $r_{bd}$ is the lowest because it understates true return by dividing discount by par value ($F$) rather than actual cash outlay ($P$), and it assumes a 360-day year.
• $r_{mm}$ corrects the denominator bias by dividing by $P$.
• $r_{bey}$ corrects the calendar bias by utilizing 365 days.
• $\text{EAY}$ is highest because it fully reflects the power of quarterly compounding.

Solution: Secondary Market Operations & Margin Trading

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Part (a): Initial Margin Balance Sheet at Day 0 (2 Marks)

• Total Market Value of Shares = $1,000 \text{ shares} \times \text{Rs. } 800 = \text{Rs. } 800,000$
• Investor’s Initial Equity ($50\% \times 800,000$) = Rs. 400,000
• Margin Borrowing from Broker ($50\% \times 800,000$) = Rs. 400,000

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Part (b): Margin Call Trigger Price ($P^*$) (3 Marks)

A margin call is triggered when actual margin equals the maintenance margin ($MM = 30\%$):

$$\text{Actual Margin} = \frac{\text{Total Market Value} - \text{Loan}}{\text{Total Market Value}} = MM$$

$$\frac{1,000 \times P^* - 400,000}{1,000 \times P^*} = 0.30$$

$$1,000 P^* - 400,000 = 300 P^*$$

$$700 P^* = 400,000 \implies P^* = \frac{400,000}{700} = \mathbf{\text{Rs. } 571.43}$$

Conclusion: If the market price falls below Rs. 571.43, the broker will issue a margin call.

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Part (c): Position Evaluation at $P = \text{Rs. } 500$ After 6 Months (5 Marks)

1. Accrued Loan, Equity, and Actual Margin:

• Market Value of Stock = $1,000 \times 500 = \text{Rs. } 500,000$
• Accrued Loan Interest (6 months @ 10%) = $400,000 \times 10\% \times \frac{6}{12} = \text{Rs. } 20,000$
• Total Broker Debt = $400,000 + 20,000 = \text{Rs. } 420,000$
• Account Equity = $\text{Market Value} - \text{Total Debt} = 500,000 - 420,000 = \mathbf{\text{Rs. } 80,000}$
• Actual Margin Percentage:
  $$\text{Actual Margin} = \frac{80,000}{500,000} = 0.16 = \mathbf{16.00\%}$$
  Since $16\% < 30\%$, a margin call is immediately triggered.

2. Margin Call Amount to Restore to Initial Margin (50%):

• Required Equity = $50\% \times \text{Current Value} = 0.50 \times 500,000 = \text{Rs. } 250,000$
• Current Equity = Rs. 80,000
• Cash Deposit Required:
  $$\text{Margin Call Deposit} = \text{Required Equity} - \text{Current Equity} = 250,000 - 80,000 = \mathbf{\text{Rs. } 170,000}$$

3. Rate of Return on Invested Capital:

$$\text{Rate of Return} = \frac{\text{Ending Equity} - \text{Initial Equity}}{\text{Initial Equity}} = \frac{80,000 - 400,000}{400,000} = \frac{-320,000}{400,000} = \mathbf{-80.00\%}$$

(While the underlying stock dropped 37.5%, the leveraged investor suffered an 80% loss due to financial leverage and interest costs).

Solution: Mutual Funds Valuation & Performance Attribution

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Part (a): Portfolio Valuation and NAV Computation (4 Marks)

$$\text{NAV per Unit} = \frac{\text{Net Assets}}{\text{Outstanding Units}} = \frac{\text{Rs. } 65,000,000}{5,000,000 \text{ units}} = \mathbf{\text{Rs. } 13.00 \text{ per unit}}$$

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Part (b): Trading Discount / Premium on NEPSE (2 Marks)

• Market Price ($P$) = Rs. 11.50
• Net Asset Value ($NAV$) = Rs. 13.00

$$\text{Discount / Premium Rate} = \frac{P - NAV}{NAV} \times 100\% = \frac{11.50 - 13.00}{13.00} \times 100\% = \frac{-1.50}{13.00} \times 100\% = \mathbf{-11.54\%}$$

Conclusion: NIBL Growth Fund is trading at a discount of 11.54% relative to its underlying Net Asset Value. Such closed-end fund discounts are common in emerging markets due to illiquidity and management expense drags.

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Part (c): Risk-Adjusted Performance Measures (4 Marks)

Parameters: $R_p = 18\%, \sigma_p = 22\%, \beta_p = 1.20, R_m = 14\%, \sigma_m = 18\%, R_f = 6\%$.

1. Sharpe Ratio ($S$):

$$S_p = \frac{R_p - R_f}{\sigma_p} = \frac{18 - 6}{22} = \frac{12}{22} = \mathbf{0.545}$$

$$S_m = \frac{R_m - R_f}{\sigma_m} = \frac{14 - 6}{18} = \frac{8}{18} = \mathbf{0.444}$$

2. Treynor Ratio ($T$):

$$T_p = \frac{R_p - R_f}{\beta_p} = \frac{18 - 6}{1.20} = \frac{12}{1.20} = \mathbf{10.00\%}$$

$$T_m = \frac{R_m - R_f}{\beta_m} = \frac{14 - 6}{1.00} = \mathbf{8.00\%}$$

3. Jensen’s Alpha ($\alpha$):

$$\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)] = 18\% - [6\% + 1.20(14\% - 6\%)]$$

$$\alpha_p = 18\% - [6\% + 9.60\%] = 18\% - 15.60\% = \mathbf{+2.40\%}$$

4. Managerial Evaluation:

• Superior Performance: The fund achieved a positive Jensen’s Alpha of +2.40%, outperforming the CAPM benchmark return by 240 basis points.
• Both the Sharpe Ratio ($0.545 > 0.444$) and Treynor Ratio ($10.00\% > 8.00\%$) surpass the NEPSE benchmark, proving that the fund manager successfully added value after adjusting for both total risk and systematic risk.

Solution: Merchant Banking Functions & Issue Underwriting

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Part (a): Core Functions of Merchant Bankers in Nepal (5 Marks)

Under SEBON regulations, merchant bankers perform five essential statutory activities:

1. Issue Management: Managing initial public offerings (IPOs), rights issues, debenture offerings, and book-building processes—including drafting the prospectus, regulatory liaison with SEBON and ROC, and managing the public subscription.
2. Underwriting Services: Guaranteeing to purchase and absorb unsubscribed securities in a public offering in exchange for an underwriting commission, eliminating issue failure risk for corporate issuers.
3. Portfolio Management Services (PMS): Managing customized discretionary and non-discretionary investment portfolios for high-net-worth individuals and institutional clients.
4. Registrar to Shares (RTS) / Share Transfer Agent: Maintaining the statutory register of shareholders, managing physical-to-demat verification, handling dividend disbursements, rights allotments, and CDS & Clearing reconciliations.
5. Corporate Advisory Services: Advising corporate clients on financial restructuring, capital structure optimization, mergers and acquisitions (M&A), asset valuation, and project financing.

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Part (b): Underwriting Syndicate Calculations (5 Marks)

1. Issue Parameters:

• Total Shares Offered = 2,000,000 shares @ Rs. 100 = Rs. 200,000,000
• Public Applications Received = 1,400,000 shares
• Unsubscribed Shortfall = $2,000,000 - 1,400,000 = \mathbf{600,000 \text{ shares}}$ (Shortfall Value = Rs. 60,000,000)
• Underwriting Commission Rate = 2.5% on total underwritten commitment.

2. Underwriting Commitments & Commissions:

• Merchant Bank X (40%):
  • Commitment = $2,000,000 \times 40\% = 800,000 \text{ shares}$ (Rs. 80,000,000)
  • Commission = $\text{Rs. } 80,000,000 \times 2.5\% = \mathbf{\text{Rs. } 2,000,000}$
• Merchant Bank Y (35%):
  • Commitment = $2,000,000 \times 35\% = 700,000 \text{ shares}$ (Rs. 70,000,000)
  • Commission = $\text{Rs. } 70,000,000 \times 2.5\% = \mathbf{\text{Rs. } 1,750,000}$
• Merchant Bank Z (25%):
  • Commitment = $2,000,000 \times 25\% = 500,000 \text{ shares}$ (Rs. 50,000,000)
  • Commission = $\text{Rs. } 50,000,000 \times 2.5\% = \mathbf{\text{Rs. } 1,250,000}$

3. Absorption of Shortfall Shares & Net Cash Settlement:

Each merchant bank absorbs its proportional quota of unsubscribed shares and pays the net purchase amount after deducting its earned underwriting commission.

Case Solution: Nepal Banking Liquidity & Monetary Framework

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Part (a): Regulatory Metric Computations & Compliance Evaluation (6 Marks)

1. Computations for Year 1 and Year 2:

2. Regulatory Compliance Analysis:

• Year 1: NCBL breached the statutory 90% CD ratio ceiling by 200 basis points (92.00%). Under NRB unified directives, the bank was subject to penal interest fines on the Rs. 4 Billion excess lending and faced regulatory restrictions on opening new branches and declaring dividends.
• Year 2: Deposits grew rapidly (+15%) while credit demand stalled (+5%), causing the CD ratio to decline to 84.00%. NCBL was fully compliant with a comfortable lending headroom of Rs. 13.8 Billion ($230 \times 0.90 - 193.2$), creating surplus idle liquidity.

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Part (b): Operation of the Interest Rate Corridor (IRC) in Nepal (6 Marks)

The Interest Rate Corridor guides short-term interbank interest rates within a predictable bandwidth:

Corridor Ceiling: Bank Rate / Standing Liquidity Facility (SLF) Rate
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Corridor Target:  Policy Repo Rate (Mid-Point Benchmark)
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Corridor Floor:   Standing Deposit Facility (SDF) Rate / Reverse Repo

Central Bank Interventions During Liquidity Surplus:

When interbank rates crash below the lower floor (e.g., plunging to 2.75%):

1. Standing Deposit Facility (SDF): NRB allows commercial banks to deposit surplus uncollateralized funds overnight at the statutory floor rate, setting a hard bottom under market rates.
2. Deposit Collection Auctions: NRB conducts fixed-term deposit auctions (7 to 28 days) to absorb excess liquidity from the market against market-determined interest rates.
3. Outright Sale of Government Securities & NRB Bonds: Selling T-Bills and NRB bonds to mop up structural liquidity, tightening excess bank reserves.

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Part (c): Structural Drivers of Nepal’s Liquidity Cycles (4 Marks)

1. Remittance Inflow Volatility: Worker remittances (Rs. 1.4+ trillion) inject sudden, massive, unearned liquidity into commercial bank deposits without an immediate matching commercial demand for bank borrowing.
2. Fiscal Spending Seasonality (Asare Vikas): The Government of Nepal accumulates huge revenue surpluses in its NRB treasury account during Q1–Q3 while executing capital development projects in the final fiscal month (Asar). This drains liquidity all year and creates a sudden deluge in June/July.
3. Import-Driven Economy: Over 90% of trade is import-based. When imports surge, bank deposits are converted to foreign currency and remitted abroad to pay foreign suppliers, draining domestic bank reserves and triggering liquidity crunches.

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Part (d): Strategic Reforms for NRB and SEBON (4 Marks)

1. Infrastructure Debt Funds & Green Municipal Bonds: SEBON and NRB should enable commercial banks to invest idle liquidity into long-term infrastructure bonds (hydropower, transmission lines, toll highways) with tax-exempt interest yields.
2. Deepening Corporate Debt Market: Mandate corporate entities above a specific capital threshold to issue listed corporate debentures for long-term project debt rather than relying on short-term bank consortium loans.
3. Sovereign Wealth / Stabilization Fund: Establish an institutional sovereign fund that absorbs excess remittance liquidity during boom periods and deploys it into long-term productive domestic enterprise.
4. Counter-Cyclical Dynamic Provisioning & Fiscal Smoothing: Require the Ministry of Finance to implement milestone-based quarterly capital budget disbursements to eliminate seasonal fiscal treasury hoarding.