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.

Answer 1

Answer:

a. Rate of return is 12%

Explanation:

a.  What will be your rate of return if the price of Telecom stock goes up by 10% during the next year?

Initial investment = Personal fund + Borrowed fund

                             = $5,000 + $5,000 = $10,000

Number of shares purchased = Initial investment ÷ Share price

                                                 = $10,000 ÷ $50 = 200 shares

Amount of increase in stock value = $10,000 × 10% = $1,000

Interest paid on borrowed fund = $5,000 × 8% = $400

Rate of return =  (Amount of increase in stock value - Interest paid on borrowed fund) ÷ Borrowed fund

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

                       = $600 ÷ $5,000

                       = 0.12 or 12%

Therefore, the rate of return is 12%

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%?

Total share value = 200P

Where P denotes the price per share

Equity = Total share value - Borrowed fund = 200P - $5,000

Required/maintenance margin = Equity ÷ Total share value

30% = (200P - $5,000) ÷ 200P

Since 30% = 0.30, we can now solve for P as follows:

0.30 × 200P = 200P - $5,000

60P = 200P - $5,000

200P - 60P = $5,000

140P = $5,000

P = $5,000 ÷ 140

P = $35.71

Therefore, the price of Telecom stock have to fall to $35.71 to receive a margin call if the maintenance margin is 30%.