You are bullish on Telecom stock. The current market price is $90 per share, and you have $13,500 of your own to invest. You borrow an additional $13,500 from your broker at an interest rate of 7.8% per year and invest $27,000 in the stock.
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.) (Round your answer to 2 decimal places.)
Rate of return %
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. (Round your answer to 2 decimal places.)
Stock price falls below $
The Correct Answer and Explanation is :
Part a. Rate of Return
Let’s break down the components needed to calculate the rate of return. The initial investment is $27,000, which consists of your own $13,500 and the borrowed amount of $13,500. The price per share is $90, so the number of shares you are purchasing is:
[
\text{Number of shares} = \frac{\text{Total Investment}}{\text{Price per Share}} = \frac{27,000}{90} = 300 \text{ shares}
]
If the price of the stock increases by 10%, the new stock price will be:
[
\text{New price} = 90 \times (1 + 0.10) = 99
]
Now, the total value of your investment at the new price will be:
[
\text{New value of investment} = 300 \times 99 = 29,700
]
Your total profit or loss is the new value of the investment minus the total amount you borrowed and your own contribution:
[
\text{Profit} = \text{New value of investment} – \text{Total borrowed} – \text{Your investment}
]
[
\text{Profit} = 29,700 – 13,500 – 13,500 = 2,700
]
The rate of return is:
[
\text{Rate of return} = \frac{\text{Profit}}{\text{Your investment}} \times 100 = \frac{2,700}{13,500} \times 100 = 20\%
]
So, the rate of return is 20%.
Part b. Margin Call Price
A margin call occurs when the equity in your account falls below the maintenance margin requirement. To find the price at which a margin call occurs, we first calculate your equity.
- The maintenance margin is 30%, so your equity should be at least 30% of the total value of your investment. This means:
[
\text{Equity} = \text{Total value of investment} – \text{Amount borrowed}
]
The total equity required is 30% of the total value of the investment. So,
[
\text{Equity} = 0.30 \times \text{Total value of investment}
]
Now, we set up the equation for the total value of the investment (new stock price multiplied by the number of shares):
[
\text{Equity} = (\text{New stock price} \times 300) – 13,500
]
And set it equal to 30% of the total value of the investment:
[
(\text{New stock price} \times 300) – 13,500 = 0.30 \times (\text{New stock price} \times 300)
]
Simplifying the equation:
[
(\text{New stock price} \times 300) – 13,500 = 0.30 \times \text{New stock price} \times 300
]
[
(\text{New stock price} \times 300) – 0.30 \times \text{New stock price} \times 300 = 13,500
]
[
0.70 \times \text{New stock price} \times 300 = 13,500
]
[
\text{New stock price} = \frac{13,500}{0.70 \times 300} = \frac{13,500}{210} = 64.29
]
Thus, the price at which you would receive a margin call is $64.29 per share.
Explanation:
- Part a (Rate of Return): The rate of return is calculated by finding the profit (difference between the new value of the investment and the initial investment) and dividing it by the amount of your own money invested. A 10% increase in the stock price results in a 20% return on your initial investment.
- Part b (Margin Call Price): The margin call occurs when the equity in your account falls below the maintenance margin, which is 30%. By setting up an equation for the maintenance margin requirement, we solve for the stock price at which the margin call would occur, which turns out to be around $64.29. This price represents the threshold below which the value of your investment would no longer be sufficient to cover the borrowed amount, triggering the margin call.