- You are bullish on Telecom stock. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5.000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. (LO 3-4)
a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? (Ignore the expected dividend.)
b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately. - You are bearish on Telecom and decide to sell short 100 shares at the current market
price of $50 per share. (LO 3-4)
a. How much in cash or securities must you put into your brokerage account if the bro-ker’s initial margin requirement is 50% of the value of the short position?
b. How high can the price of the stock go before you get a margin call if the mainte-nance margin is 30% of the value of the short position?
The Correct Answer and Explanation is :
18. Bullish on Telecom Stock
a. Rate of return if Telecom stock price goes up by 10%
You invest a total of $10,000 in Telecom stock. Of this, $5,000 is your own money and $5,000 is borrowed from the broker.
- Initial Investment: $10,000 (where $5,000 is your own money and $5,000 is borrowed).
- If the stock price increases by 10%, the new stock price per share would be:
[
\text{New Stock Price} = 50 \times (1 + 0.10) = 55
]
- Number of shares you bought:
[
\text{Number of Shares} = \frac{10,000}{50} = 200 \, \text{shares}
]
- The value of the stock after a 10% increase:
[
\text{Value of Shares} = 200 \times 55 = 11,000
]
- You now sell the shares for $11,000, but you still owe your broker the $5,000 you borrowed, plus interest at 8%. For simplicity, assume the interest applies for one year:
[
\text{Interest} = 5,000 \times 0.08 = 400
]
- Total repayment to the broker is $5,400 ($5,000 principal + $400 interest).
Your net profit:
[
\text{Net Profit} = 11,000 – 5,400 – 5,000 = 600
]
Rate of Return (RoR) on your $5,000 investment:
[
\text{Rate of Return} = \frac{600}{5,000} = 0.12 \, \text{or} \, 12\%
]
So, your rate of return is 12% if the price of Telecom stock goes up by 10%.
b. Price fall for margin call with a maintenance margin of 30%
A margin call happens when the equity in the account falls below the maintenance margin requirement. You borrowed $5,000 from the broker to purchase 200 shares, which means the value of your loan is $5,000.
- Maintenance margin = 30%, meaning your equity must remain at least 30% of the total value of the stock.
Let ( P ) be the price at which you get a margin call. Your equity is the difference between the total value of the shares and the amount you owe the broker, which is:
[
\text{Equity} = (\text{Number of Shares} \times P) – 5,400
]
The total value of the shares is ( 200 \times P ), and your total equity should be at least 30% of that value:
[
\text{Equity} = 0.30 \times (200 \times P)
]
Set these two expressions for equity equal to each other:
[
(200 \times P) – 5,400 = 0.30 \times (200 \times P)
]
Solving for ( P ):
[
200P – 5,400 = 60P
]
[
140P = 5,400
]
[
P = \frac{5,400}{140} = 38.57
]
Therefore, the price must fall to $38.57 per share for you to get a margin call.
19. Bearish on Telecom Stock
a. Cash or securities required for the short sale
When you sell short 100 shares at $50 per share, the total value of the short position is:
[
\text{Value of Short Position} = 100 \times 50 = 5,000
]
The broker requires an initial margin of 50% of the value of the short position:
[
\text{Initial Margin Requirement} = 0.50 \times 5,000 = 2,500
]
Thus, you must deposit $2,500 in your brokerage account to meet the initial margin requirement.
b. Price rise for margin call with a maintenance margin of 30%
For a short position, you need to maintain a margin that is 30% of the value of the position. If the price of the stock rises, the value of the short position increases, and you may get a margin call if the equity in the account falls below the maintenance margin.
Let ( P ) be the price at which you will receive a margin call. The total value of the short position is ( 100 \times P ), and the maintenance margin requirement is 30% of that value:
[
\text{Equity} = \text{Initial Margin} – (\text{New Value of Short Position} – \text{Proceeds from Short Sale})
]
[
\text{Equity} = 2,500 – (100 \times P – 5,000)
]
You must maintain at least 30% of the total value of the short position as equity:
[
\text{Equity} = 0.30 \times (100 \times P)
]
Setting these equal:
[
2,500 – (100P – 5,000) = 0.30 \times (100 \times P)
]
Simplifying:
[
2,500 – 100P + 5,000 = 30P
]
[
7,500 = 130P
]
[
P = \frac{7,500}{130} = 57.69
]
Thus, the price can rise to $57.69 before you get a margin call.
Summary
- For the bullish position, your rate of return is 12% if the stock price increases by 10%.
- For the margin call on the bullish position, the stock price must fall to $38.57 for you to get a margin call.
- For the bearish position, you must deposit $2,500 in your brokerage account.
- For the margin call on the bearish position, the price can rise to $57.69 before you get a margin call.