Question

You are bullish on Telecom stock. The current market price is $30 per share, and you have $3,000 of your own to invest. You borrow an additional $3,000 from your broker at an interest rate of 6.5% per year and invest $6,000 in the stock.

a. What will be your rate of return if the price of Telecom stock goes up by 8% during the next year? (Ignore the expected dividend.) (Round your answer to 2 decimal places.)

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.)

Answer 1

a.

We are bullish on Telecom stock, so we will take long position in stock.

Amount of Position or long position = amount borrowed + margin or own investment

=3000+3000

=6000

number of shares long = total positon vlaue/per share price

=6000/30

=200

Price of closing or sale price = 30*(1+8%) = 32.4

sale price of 200 shares = 32.4*200 =6480

interest paid on borrowed amount = borrowed amount * interest rate * number of year

=3000*6.5%*1

=195

Rate of return = (sale price - buying price or position - interest paid/investment amount

=(6480-6000-195)/3000

=0.095 or 9.5%

So rate of return is 9.5%

b.

intial margin = 3000

maintenance margin = 30% of value of position

=6000*30% = 1800

Price to make margin call for long = long price - ( (initial margin - maintenance margin)/number of shares)

=30 - ((3000-1800)/200)

=24

So Price of telecom stock can ball upto $24 to get a margin call afterwards.