Investment Analysis 2023 Board Question Paper

True/False Analysis: Commercial Paper

False. Commercial paper is an unsecured short-term promissory note issued by large, creditworthy corporations (not Nepal Rastra Bank) to raise working capital funds from the money market. Nepal Rastra Bank (NRB) issues Treasury Bills and NRB Bonds, not commercial paper.

Treasury Bill Bank Discount Yield

$$\text{Given: } \text{Face Value } (F) = \text{Rs } 10,000, \quad \text{Purchase Price } (P) = \text{Rs } 9,600, \quad \text{Discount } (D) = F - P = \text{Rs } 400$$

Assuming standard 91-day maturity ($t = 91$):

$$\text{Bank Discount Yield } (r_{bd}) = \frac{D}{F} \times \frac{360}{t} = \frac{400}{10,000} \times \frac{360}{91} = 0.04 \times 3.956 = 15.82\%$$

$$\text{Investment Yield / Money Market Yield } (r_{mm}) = \frac{D}{P} \times \frac{365}{t} = \frac{400}{9,600} \times \frac{365}{91} = 16.71\%$$

True/False Analysis: Maintenance Margin

False. The maintenance margin is the minimum (not maximum) percentage of equity that an investor must maintain in a margin account at all times after the purchase. If equity falls below this threshold, a margin call is triggered.

True/False Analysis: Value-Weighted Index

True. A value-weighted (capitalization-weighted) index—such as the NEPSE Index or S&P 500—weights each stock by its total market capitalization ($P_i \times Q_i$), taking into account both the market price per share and the number of shares outstanding.

True/False Analysis: Blue Chip Stocks

True. Blue-chip stocks represent shares of large, nationally recognized, financially sound, and well-established corporations with a consistent track record of dividend payments and earnings stability through economic downturns (e.g., Nabil Bank in Nepal).

True/False Analysis: Back-End Load

False. A back-end load is a redemption fee incurred when an investor sells/redeems mutual fund shares (an exit load), not when purchasing them. Fees charged at the time of purchase are known as front-end loads.

True/False Analysis: Optimal Risky Portfolio

False. The optimal risky portfolio is the combination of risky assets that maximizes the Sharpe ratio (the tangency point on the efficient frontier). The combination of the optimal risky portfolio with the risk-free asset forms the complete portfolio along the Capital Allocation Line (CAL).

True/False Analysis: Bond Indenture

True. A bond indenture is the legal, binding contract between the bond issuer and bondholders (represented by a trustee) specifying the coupon rate, maturity date, collateral, and protective covenants.

True/False Analysis: Price Earnings Ratio

False. The Price-Earnings (P/E) ratio measures market valuation (how much investors are willing to pay per rupee of current earnings), not liquidity. Liquidity is measured by ratios such as the Current Ratio and Quick Ratio.

True/False Analysis: Municipal Bonds in Nepal

False. In fiscal practice, municipal bonds are debt obligations issued by local urban/municipal governments, not the federal government. The federal government issues Treasury Bills, Development Bonds (Bikas Rinpatra), and Citizen Savings Bonds.

Solution: Margin Trading Calculations

$$\text{Given: } P_0 = \text{Rs } 80, \quad \text{Initial Margin } (IM) = 50\%, \quad \text{Interest Rate } (r) = 9\%, \quad \text{Maintenance Margin } (MM) = 30\%$$

a. Long Position Without Margin

• Purchase Price = Rs 80; Selling Price ($P_1$) = Rs 100
  $$\text{Rate of Return } = \frac{P_1 - P_0}{P_0} = \frac{100 - 80}{80} = \frac{20}{80} = 25.00\%$$

b. Long Position Using Margin

• Own Equity Invested per share = $80 \times 0.50 = \text{Rs } 40$
• Borrowed from Broker (Loan) = $80 \times 0.50 = \text{Rs } 40$

i. Stock Price that Triggers a Margin Call ($P^*$)

$$\text{Margin Call Price } P^* = \frac{\text{Loan Amount}}{1 - MM} = \frac{40}{1 - 0.30} = \frac{40}{0.70} = \mathbf{\text{Rs } 57.14}$$

A margin call will be triggered if the market price drops to or below Rs 57.14 per share.

ii. Rate of Return at $P_1 = \text{Rs } 100$ After 1 Year

• Interest Paid on Loan = $40 \times 0.09 = \text{Rs } 3.60$
• Capital Gain per share = $100 - 80 = \text{Rs } 20.00$
• Net Dollar Return = $\text{Capital Gain} - \text{Interest} = 20 - 3.60 = \text{Rs } 16.40$$\text{Rate of Return on Equity} = \frac{\text{Net Dollar Return}}{\text{Initial Equity Invested}} = \frac{16.40}{40} = \mathbf{41.00\%}$$

Solution: Evaluation of Mutual Fund Investment Options

$$\text{Total Investment Capital} = \text{Rs } 10,000, \quad \text{NAV per share for all funds} = \text{Rs } 10.00$$

a. Number of Shares Ended Up in Each Case

1. Closed-End Fund A:

   • Market Price = NAV = Rs 10.00. Broker commission = 2% on market price = $10 \times 0.02 = \text{Rs } 0.20$.
   • Total Cost per share = $10.00 + 0.20 = \text{Rs } 10.20$.
   • Shares Purchased = $\frac{10,000}{10.20} = \mathbf{980.39 \text{ shares}}$.

2. Closed-End Fund B:

   • Selling at 20% discount to NAV: Market Price = $10 \times (1 - 0.20) = \text{Rs } 8.00$.
   • Broker commission = 2% on market price = $8.00 \times 0.02 = \text{Rs } 0.16$.
   • Total Cost per share = $8.00 + 0.16 = \text{Rs } 8.16$.
   • Shares Purchased = $\frac{10,000}{8.16} = \mathbf{1,225.49 \text{ shares}}$.

3. Mutual Fund D (Net 8.54% Load):

   • Offering Price = $\frac{\text{NAV}}{1 - \text{Load}} = \frac{10}{1 - 0.0854} = \frac{10}{0.9146} = \text{Rs } 10.9337$.
   • Shares Purchased = $\frac{10,000}{10.9337} = \mathbf{914.60 \text{ shares}}$.

b. Recommendation

• The investor should purchase Closed-End Fund B.
• Rationale: Purchasing Fund B allows the investor to acquire 1,225.49 shares (the highest number of shares), effectively gaining Rs 12,254.90 worth of underlying NAV assets for only Rs 10,000, creating immediate discount arbitrage advantage.

Solution: Actual Realized 5-Year Return for Kamal

$$\text{Initial Investment } (t = 0): \quad \text{Purchase Price } = \text{Rs } 1,000, \quad \text{Coupon Rate } = 10\% \implies C_1 = C_2 = \text{Rs } 100$$

Cash Flows During Years 1 and 2:

• Year 1: Receives coupon of Rs 100.
• Year 2: Receives coupon of Rs 100, plus bond called for Rs 1,160. Total Year 2 proceeds = Rs 1,260.

Reinvestment at Year 2:

• Kamal reinvests Rs 1,000 in a new 3-year bond at par (Rs 1,000) paying 7% annual coupon ($C = \text{Rs } 70$).
• Surplus cash of $1,260 - 1,000 = \text{Rs } 260$ remains.

Cash Flows Over 5 Years:

• $t = 0: -1,000$
• $t = 1: +100$
• $t = 2: +260$ (surplus cash kept)
• $t = 3: +70$
• $t = 4: +70$
• $t = 5: +1,070$ (Rs 70 coupon + Rs 1,000 principal redemption)

Solving for internal rate of return ($r$):

$$1,000 = \frac{100}{(1+r)^1} + \frac{260}{(1+r)^2} + \frac{70}{(1+r)^3} + \frac{70}{(1+r)^4} + \frac{1,070}{(1+r)^5}$$

At $r = 10.2\%$, the discounted cash flows equate to Rs 1,000.

$$\mathbf{\text{Kamal's actual realized return is approximately } 10.20\% \text{ per annum.}}$$

Solution: Alpha Bank vs. Beta Bank Expected Return and Risk

$$\begin{array}{lccccc} \hline \text{Probability } (P_i) & 0.10 & 0.20 & 0.40 & 0.20 & 0.10 \\ \text{Alpha Return } (R_A) & -10\% & 5\% & 10\% & 25\% & 35\% \\ \text{Beta Return } (R_B) & -20\% & 0\% & 15\% & 30\% & 40\% \\ \hline \end{array}$$

a. Expected Rate of Return

$$E(R_A) = (0.10)(-10) + (0.20)(5) + (0.40)(10) + (0.20)(25) + (0.10)(35) = -1 + 1 + 4 + 5 + 3.5 = \mathbf{12.50\%}$$

$$E(R_B) = (0.10)(-20) + (0.20)(0) + (0.40)(15) + (0.20)(30) + (0.10)(40) = -2 + 0 + 6 + 6 + 4 = \mathbf{14.00\%}$$

b. Standard Deviation of Returns

$$\sigma_A^2 = 0.1(-10-12.5)^2 + 0.2(5-12.5)^2 + 0.4(10-12.5)^2 + 0.2(25-12.5)^2 + 0.1(35-12.5)^2$$

$$\sigma_A^2 = 0.1(506.25) + 0.2(56.25) + 0.4(6.25) + 0.2(156.25) + 0.1(506.25) = 50.625 + 11.25 + 2.5 + 31.25 + 50.625 = 146.25$$

$$\sigma_A = \sqrt{146.25} = \mathbf{12.09\%}$$

$$\sigma_B^2 = 0.1(-20-14)^2 + 0.2(0-14)^2 + 0.4(15-14)^2 + 0.2(30-14)^2 + 0.1(40-14)^2$$

$$\sigma_B^2 = 0.1(1156) + 0.2(196) + 0.4(1) + 0.2(256) + 0.1(676) = 115.6 + 39.2 + 0.4 + 51.2 + 67.6 = 274.00$$

$$\sigma_B = \sqrt{274.00} = \mathbf{16.55\%}$$

c. Coefficient of Variation (CV) & Preference

$$CV_A = \frac{\sigma_A}{E(R_A)} = \frac{12.09}{12.50} = \mathbf{0.967}$$

$$CV_B = \frac{\sigma_B}{E(R_B)} = \frac{16.55}{14.00} = \mathbf{1.182}$$

• Recommendation: Prefer Alpha Bank’s stock because its Coefficient of Variation (0.967) is lower than Beta Bank (1.182), indicating lower relative risk per unit of return.

Solution: Electronic Corporation Stock Valuation and PVGO

$$\text{Given: } ROE = 9\%, \quad \beta = 1.25, \quad b = \frac{2}{3}, \quad EPS_0 = \text{Rs } 3.00, \quad R_f = 6\%, \quad R_m = 14\%$$

Required Rate of Return (CAPM):

$$k = R_f + \beta(R_m - R_f) = 6\% + 1.25(14\% - 6\%) = 6\% + 10\% = 16.00\%$$

Sustainable Growth Rate:

$$g = b \times ROE = \frac{2}{3} \times 9\% = 6.00\%$$

Dividend Payout Ratio and $D_1$:

$$\text{Payout Ratio } (1 - b) = 1 - \frac{2}{3} = \frac{1}{3}$$

$$D_0 = EPS_0 \times (1 - b) = 3 \times \frac{1}{3} = \text{Rs } 1.00$$

$$D_1 = D_0(1 + g) = 1.00(1 + 0.06) = \text{Rs } 1.06$$

a. Price at Which Electronic Stock Should Sell ($P_0$):

$$P_0 = \frac{D_1}{k - g} = \frac{1.06}{0.16 - 0.06} = \frac{1.06}{0.10} = \mathbf{\text{Rs } 10.60}$$

b. Price to Earnings (P/E) Ratio:

$$\text{Forward P/E} = \frac{P_0}{EPS_1} = \frac{10.60}{3(1.06)} = \frac{10.60}{3.18} = \mathbf{3.33 \times}$$

c. Present Value of Growth Opportunities (PVGO):

$$\text{No-growth value per share } = \frac{EPS_1}{k} = \frac{3.18}{0.16} = \text{Rs } 19.875$$

$$PVGO = P_0 - \frac{EPS_1}{k} = 10.60 - 19.875 = \mathbf{-\text{Rs } 9.275}$$

PVGO is negative because the company’s ROE (9%) is lower than the investors’ required rate of return (16%), destroying value by reinvesting earnings.

Role of Stock Market and Current Status of Nepalese Stock Market

1. Fundamental Roles of the Stock Market

• Capital Mobilization: Channels idle household savings into productive corporate investments (hydropower, commercial banking, manufacturing).
• Liquidity Provision: Enables investors to convert long-term financial securities into immediate cash seamlessly.
• Price Discovery and Valuation: Continuously establishes fair market clearing prices reflecting company performance and macroeconomic conditions.
• Corporate Governance Discipline: Mandates quarterly audited financial disclosures, protecting public minority shareholders.

2. Current Status of the Nepalese Stock Market (NEPSE)

• Institutional Architecture: The Nepal Stock Exchange (NEPSE), regulated by SEBON, operates a fully automated electronic trading system (NOTS) integrated with Central Depository Services (CDSC / MeroShare).
• Structural Dominance: The market was historically heavily skewed toward the Financial Sector (Commercial Banks, Microfinance, Insurance), but Hydropower companies now comprise the largest numerical listing segment.
• Challenges: High retail speculation, lack of diverse derivative instruments (futures/options), shallow corporate bond trading, and reliance on bank margin lending policies regulated by NRB loan caps.

Solution: Minimum Variance Portfolio Calculations

$$\text{Given: } E(R_A) = 8\%, \quad \sigma_A = 12\%, \quad \sigma_A^2 = 144$$

$$E(R_B) = 13\%, \quad \sigma_B = 20\%, \quad \sigma_B^2 = 400$$

$$Cov(A, B) = 72, \quad \rho_{AB} = 0.30$$

a. Minimum Variance Portfolio Weights ($w_A$ and $w_B$)

$$w_A = \frac{\sigma_B^2 - Cov(A, B)}{\sigma_A^2 + \sigma_B^2 - 2 \cdot Cov(A, B)} = \frac{400 - 72}{144 + 400 - 2(72)} = \frac{328}{544 - 144} = \frac{328}{400} = \mathbf{0.82 \text{ (or } 82\%\text{)}}$$

$$w_B = 1 - w_A = 1 - 0.82 = \mathbf{0.18 \text{ (or } 18\%\text{)}}$$

b. Expected Return of Minimum Variance Portfolio ($E(R_p)$)

$$E(R_p) = w_A E(R_A) + w_B E(R_B) = (0.82)(8\%) + (0.18)(13\%) = 6.56\% + 2.34\% = \mathbf{8.90\%}$$

c. Standard Deviation of Minimum Variance Portfolio ($\sigma_p$)

$$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B Cov(A, B)$$

$$\sigma_p^2 = (0.82)^2(144) + (0.18)^2(400) + 2(0.82)(0.18)(72)$$

$$\sigma_p^2 = (0.6724)(144) + (0.0324)(400) + (0.2952)(72) = 96.8256 + 12.96 + 21.2544 = 131.04$$

$$\sigma_p = \sqrt{131.04} = \mathbf{11.45\%}$$

d. Conclusion

• By combining Fund A and Fund B, the portfolio standard deviation ($\sigma_p = 11.45\%$) is lower than the individual risk of both Fund A (12%) and Fund B (20%), while generating a return ($8.90\%$) superior to Fund A.
• This proves Markowitz diversification: when asset correlation is less than +1.0, combining assets significantly eliminates unsystematic risk without sacrificing proportional return.

Solution: Calculation of Market Indices and Uses

a. Index Values on July 16, 2021 (Base Date = July 16, 2020 = 100)

$$\begin{array}{lcccc} \hline \text{Stock} & \text{Shares } (Q) & P_0 \text{ (2020)} & P_1 \text{ (2021)} & \text{Price Ratio } (P_1/P_0) \\ \hline A & 60,000 & 1,000 & 600 & 0.60 \\ B & 50,000 & 1,000 & 2,000 & 2.00 \\ C & 100,000 & 200 & 300 & 1.50 \\ D & 50,000 & 100 & 40 & 0.40 \\ \hline \end{array}$$

(i) Value-Weighted Index:

$$\text{Base Mkt Cap } (V_0) = (60k \times 1000) + (50k \times 1000) + (100k \times 200) + (50k \times 100) = 60M + 50M + 20M + 5M = \text{Rs } 135 \text{ Million}$$

$$\text{Current Mkt Cap } (V_1) = (60k \times 600) + (50k \times 2000) + (100k \times 300) + (50k \times 40) = 36M + 100M + 30M + 2M = \text{Rs } 168 \text{ Million}$$

$$\text{Value-Weighted Index } I_1 = \frac{V_1}{V_0} \times 100 = \frac{168}{135} \times 100 = \mathbf{124.44}$$

(A 24.44% increase in overall aggregate market wealth).

(ii) Price-Weighted Index:

$$\text{Sum of Prices } t=0 = 1000 + 1000 + 200 + 100 = \text{Rs } 2,300 \implies \text{Divisor } d = 4 \implies I_0 = 575$$

$$\text{Sum of Prices } t=1 = 600 + 2000 + 300 + 40 = \text{Rs } 2,940 \implies I_1 = \frac{2940}{4} = 735$$

$$\text{Normalized to Base 100: } \frac{735}{575} \times 100 = \mathbf{127.83}$$

(iii) Equally-Weighted Index:

$$\text{Average Return Ratio} = \frac{0.60 + 2.00 + 1.50 + 0.40}{4} = \frac{4.50}{4} = 1.125$$

$$\text{Equally-Weighted Index } I_1 = 100 \times 1.125 = \mathbf{112.50}$$

b. Uses of Market Indices

1. Benchmark for Portfolio Performance: Evaluating whether active mutual fund managers outperform the broader market.
2. Economic Barometer: Signaling future macroeconomic business cycles and investor confidence.
3. Underlying Asset for Derivatives: Serving as underlying instruments for index futures, options, and Exchange-Traded Funds (ETFs).