Open end mutual fund A has 100 shares of KBL equity value at Rs. 160 each and 50 shares of NMB valued at Rs. 200 each. Closed end fund B has 75 shares at KBL and 100 shares of NBM. Each fund has…

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a. Calculation of NAVs for Funds A and B

Fund A (Open-end Mutual Fund)

• KBL Shares: 100 shares × Rs. 160 = Rs. 16,000
• NMB Shares: 50 shares × Rs. 200 = Rs. 5,000
• Total Market Value: Rs. 16,000 + Rs. 5,000 = Rs. 21,000
• Shares Outstanding: 2,000
• NAV per Share: $${\text{NAV}}_A=\frac{\text{Total Market Value}}{\text{Shares Outstanding}}=\frac{21,000}{2,000}=\text{Rs. 10.50}$$

Fund B (Closed-end Mutual Fund)

• KBL Shares: 75 shares × Rs. 160 = Rs. 12,000
• NMB Shares: 100 shares × Rs. 200 = Rs. 20,000
• Total Market Value: Rs. 12,000 + Rs. 20,000 = Rs. 29,000
• Shares Outstanding: 2,000
• NAV per Share: $${\text{NAV}}_B=\frac{\text{Total Market Value}}{\text{Shares Outstanding}}=\frac{29,000}{2,000}=\text{Rs. 14.50}$$

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b. Decision to Buy or Sell Fund Shares at Rs. 14 per Share

Explanation:

• Fund A is trading at Rs. 14, which is higher than its NAV of Rs. 10.50. This indicates that the fund is overvalued in the market, so investors should sell to realize capital gains.
• Fund B is trading at Rs. 14, which is lower than its NAV of Rs. 14.50. This suggests the fund is undervalued, making it a good buying opportunity.

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c. Impact of Price Changes on NAVs and Realized Returns

New Stock Prices After One Month

• KBL: Rs. 165 (↑ from Rs. 160)
• NMB: Rs. 195 (↓ from Rs. 200)

New NAV Calculations

Fund A (Open-end)

• KBL: 100 × Rs. 165 = Rs. 16,500
• NMB: 50 × Rs. 195 = Rs. 9,750
• Total Market Value: Rs. 16,500 + Rs. 9,750 = Rs. 26,250
• New NAV: $${\text{NAV}}_A=\frac{26,250}{2,000}=\text{Rs. 13.125}$$

Fund B (Closed-end)

• KBL: 75 × Rs. 165 = Rs. 12,375
• NMB: 100 × Rs. 195 = Rs. 19,500
• Total Market Value: Rs. 12,375 + Rs. 19,500 = Rs. 31,875
• New NAV: $${\text{NAV}}_B=\frac{31,875}{2,000}=\text{Rs. 15.9375}$$

Realized Returns (Assuming Purchase at Original NAV and Sale at New NAV)

Calculations:

• Fund A: $${\text{Return}}_A=\left(\frac{13.125-10.50}{10.50}\right)\times 100=25.0\%$$
• Fund B: $${\text{Return}}_B=\left(\frac{15.9375-14.50}{14.50}\right)\times 100=9.9\%$$

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d. Effect of Adding 100 More KBL Shares to Fund A

New Portfolio Composition of Fund A

• KBL Shares: 100 (original) + 100 (new) = 200 shares
• NMB Shares: 50 shares (unchanged)
• Stock Prices (unchanged): KBL = Rs. 160, NMB = Rs. 200

New Total Market Value

• KBL: 200 × Rs. 160 = Rs. 32,000
• NMB: 50 × Rs. 200 = Rs. 5,000
• Total Market Value: Rs. 32,000 + Rs. 5,000 = Rs. 37,000

New NAV Calculation

• Shares Outstanding: 2,000 (unchanged)
• New NAV: $${\text{NAV}}_A=\frac{37,000}{2,000}=\text{Rs. 18.50}$$

Impact:

• The NAV increases from Rs. 10.50 to Rs. 18.50 because the total market value of the fund’s assets rose due to the addition of more KBL shares.
• However, the number of shares outstanding remains the same (2,000), so the per-share value increases.

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e. Why Closed-end Fund Shares Trade at a Price Different from NAV

Closed-end mutual funds often trade at prices that differ from their Net Asset Value (NAV) due to the following key reasons:

Example of Premium/Discount Trading

• If Fund B (from part a) is trading at Rs. 14 while its NAV is Rs. 14.50, it is trading at a 5% discount.
• If another closed-end fund has a strong track record, it may trade at a 10-20% premium to NAV.

Conclusion: The price-NAV discrepancy in closed-end funds is a result of market dynamics, investor behavior, and structural differences compared to open-end funds. Arbitrage opportunities may exist, but they are not always perfectly exploited.

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# Python code to calculate NAV dynamically (for educational purposes)
def calculate_nav(shares_kbl, price_kbl, shares_nmb, price_nmb, total_shares):
    total_value = (shares_kbl * price_kbl) + (shares_nmb * price_nmb)
    nav = total_value / total_shares
    return nav

# Example usage for Fund A (initial case)
nav_A = calculate_nav(100, 160, 50, 200, 2000)
print(f"NAV of Fund A: Rs. {nav_A:.2f}")  # Output: Rs. 10.50

How it works:

• The function takes shares and prices of KBL/NMB and total outstanding shares as inputs.
• It computes the total market value and divides by shares outstanding to get NAV.
• Useful for sensitivity analysis (e.g., changing stock prices or share counts).