Question

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 so that no interest needs to be paid. (Round your answer to 2 decimal places.)

Answer 1

Sol:

Stock current market price = $50

Own investment = $5,000

Borrowed fund = $5,000

Interest rate = 8% per year

Total investment = $10,000

a) To determine rate of return if the price of Telecom stock goes up by 10% during the next year:

Total number of shares = Total investment / Stock current market price

Total number of shares = 10,000 / 50 = 200 shares

Profit on shares = Total investment * rate of return

Profit on shares = 10,000 * 10% = $1,000

Interest cost = Borrowed fund * Interest rate

Interest cost = 5000 * 8% = $400

Rate of return = (Profit on shares - Interest cost) / 5,000

Rate of return = (1,000 - 400) / 5,000

​​​​​​​Rate of return = 600 / 5,000 = 0.12 or 12%

Therefore rate of return if the price of Telecom stock goes up by 10% during the next year = 12%

b)

To determine the fall in stock price to get a margin call:

Maintenance margin = 30%

Number of shares = 10,000 / 50 = 200 shares

Maintenance margin = [(Number of shares * Price) - Borrowed fund] / Number of shares * Price

30% = [(200 x Price) - 5,000] / 200 * Price

30% x 200 x Price = 200 x P - 5,000

200Price - 60Price = 5,000

Price = 5,000 / 140 = $35.71

Therefore you will get a margin call if the stock price will fall to $35.71 or below.