**1)     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.**
**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.**
**** 

Let’s break down each part of this problem and solve them step by step.

### Part a: Rate of return if the stock price increases by 10%

You are investing with leverage: 
- Your own investment: $5,000
- Amount borrowed: $5,000 at 8% interest rate per year
- Total investment in the stock: $10,000
- Initial stock price: $50 per share
- Number of shares purchased: $ \frac{10,000}{50} = 200 $ shares.

Now, if the stock price goes up by 10% in a year, the new price of the stock is:
\[
\text{New price} = 50 \times (1 + 0.10) = 50 \times 1.10 = 55
\]

The total value of your stock after the price increase:
\[
\text{New value of stock} = 200 \times 55 = 11,000
\]

Next, calculate the cost of borrowing. The interest on the $5,000 loan at 8% per year:
\[
\text{Interest} = 5,000 \times 0.08 = 400
\]

Now, calculate your profit:
\[
\text{Profit} = \text{New value of stock} - \text{Loan repayment} - \text{Original investment} = 11,000 - 5,400 - 5,000 = 600
\]

Finally, calculate your rate of return:
\[
\text{Rate of return} = \frac{\text{Profit}}{\text{Initial investment}} = \frac{600}{5,000} = 0.12 = 12\%
\]

### Part b: Price at which margin call occurs

A margin call happens when the value of your equity falls below the maintenance margin, which is 30%. Your equity is the difference between the value of the stock and the amount borrowed.

Let $ P $ be the stock price at which the margin call occurs. The value of the stock at this price is:
\[
\text{Value of stock} = 200 \times P
\]

The equity is:
\[
\text{Equity} = 200 \times P - 5,000
\]

The maintenance margin requirement is 30%, so we require that:
\[
\frac{\text{Equity}}{\text{Value of stock}} \geq 0.30
\]

Substituting the expressions for equity and stock value:
\[
\frac{200P - 5,000}{200P} \geq 0.30
\]

Simplifying:
\[
1 - \frac{5,000}{200P} \geq 0.30
\]

\[
\frac{5,000}{200P} \leq 0.70
\]

\[
P \geq \frac{5,000}{200 \times 0.70} = \frac{5,000}{140} = 35.71
\]

So, the stock price must not fall below **$35.71** for you to avoid a margin call.

### Summary:
- **a)** Your rate of return if the stock price increases by 10% is **12%**.
- **b)** The stock price must not fall below **$35.71** to avoid a margin call.

---

Would you like further details on any part of the solution?  
Here are some related questions to consider:

1. How would dividends affect your rate of return in part a?
2. What if you borrowed at a different interest rate—how would that impact your return?
3. How does increasing or decreasing the maintenance margin affect the price at which a margin call occurs?
4. How would your rate of return change if the stock price decreases by 10% instead of increasing?
5. What are the risks involved in using leverage when investing?

**Tip:** Always be cautious when using leverage for investments—while it can magnify your gains, it can also amplify your losses.

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. 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.

Learn how to calculate the rate of return when leveraging stock investments and determine the margin call threshold. This problem explores the concepts of leverage, stock price increases, and margin maintenance. Key formulas include rate of return and stock price at margin call, relevant for finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation