Assume that you sell short 500 shares of Nabil stock for Rs. 400 per share. The initial margin and maintenance margin requirements are 50 percent and 30 percent respectively. a. What is the initial…

Model Answer: Fundamentals of Investment (FIN253) – TU Board 2080

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Given:

• Short sale: 500 shares of Nabil stock
• Selling price per share: Rs. 400
• Initial margin requirement: 50%
• Maintenance margin requirement: 30%

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(a) Initial Value of Debt and Equity in Margin Account

When you sell short 500 shares at Rs. 400 per share, you receive Rs. 200,000 (500 × 400) from the buyer. This amount is credited to your margin account as equity, and you borrow the shares from a broker, creating a debt obligation equal to the market value of the shares sold short.

Step-by-Step Calculation:

1. Proceeds from short sale: $500\text{ shares}\times Rs.400=Rs.200,000$ This is the initial equity in the margin account.

2. Initial margin requirement (50%): The broker requires 50% of the short sale proceeds as margin. $50\%\times Rs.200,000=Rs.100,000$ This is the minimum equity required.

3. Debt (borrowed amount): Since you sold short, you must deposit the full market value of the shares as debt (but only 50% is required as margin). $\text{Debt}=500\times Rs.400=Rs.200,000$ However, the initial margin is Rs. 100,000 (50% of Rs. 200,000), which is the equity you must maintain.

   • Equity (initial margin deposit): Rs. 100,000
   • Debt (market value of short position): Rs. 200,000

   Final Answer:

   • Debt: Rs. 200,000
   • Equity: Rs. 100,000

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(b) Value of Debt and Equity if Stock Price Increases to Rs. 450

When the stock price rises to Rs. 450, the debt value (market value of the short position) increases, while the equity (your cash deposit) remains the same unless you add more funds.

Step-by-Step Calculation:

1. New debt value: $500\text{ shares}\times Rs.450=Rs.225,000$

2. Equity remains: Rs. 100,000 (initial margin deposit)

   Final Answer:

   • Debt: Rs. 225,000
   • Equity: Rs. 100,000

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(c) Margin Call if Stock Price Increases to Rs. 450?

A margin call occurs when the equity falls below the maintenance margin requirement.

Step-by-Step Calculation:

1. Maintenance margin requirement (30%): $30\%\times Rs.225,000=Rs.67,500$

2. Current equity: Rs. 100,000 Since Rs. 100,000 > Rs. 67,500, no margin call is triggered.

   Final Answer: No, you do not receive a margin call.

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(d) Rate of Return if Nabil Stock is Trading at Rs. 380

When the stock price decreases to Rs. 380, you buy back the shares to close the short position. Your return is calculated based on the difference between the selling price (Rs. 400) and the buying price (Rs. 380), adjusted for interest and margin.

Step-by-Step Calculation:

1. Cost to buy back shares: $500\times Rs.380=Rs.190,000$

2. Net profit/loss: $Rs.200,000\text{ (proceeds)}-Rs.190,000\text{ (buy-back)}=Rs.10,000\text{ profit}$

3. Rate of return (ignoring interest): $$\text{Return}=\left(\frac{\text{Profit}}{\text{Initial Margin}}\right)\times 100=\left(\frac{10,000}{100,000}\right)\times 100=10\%$$

   Assumption: No interest is charged on the margin account for simplicity.

   Final Answer: Your rate of return will be 10%.

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Summary of Key Concepts:

• Short selling involves borrowing shares, selling them, and repurchasing them later at a lower price.
• Margin account tracks debt (market value of short position) and equity (cash deposit).
• Margin call occurs when equity falls below the maintenance margin.
• Return on short selling is calculated based on the difference between selling and buying prices, adjusted for margin.