Question

Calculate your pre-tax rate of return (profit divided by investment) in each of these scenarios (SHOW YOUR WORK):

1. buy 1,000 shares of ABC common stock at $50 and sell at $60 one year later.
2. buy 1,000 shares of ABC common stock at $50, borrowing 50% of the amount necessary to buy it, at a 2% interest rate, sell the stock at $60 one year later, paying back the loan at the same time.
3. buy listed options at $400 for 1,000 shares of ABC, giving you the right but not the obligation to buy the shares at $50 one year later, you exercise the option one year later when the stock price is $60. Also, use the Long Call chart (from the CBOE material in this PDF) to explain what is going on
   Profit + 1 Profit = Unlimited / Loss = Limited Increasing Underlying Stock- Price Loss - Long Call
   

Answer 1

a)

• Selling Price per share = $60
• Cost price per share = $50
• Profit = $10
• Profit% = Profit/Cost price x 100 = 10/50 x 100 = 20%

b)

• Total share bought = 1000
• Cost price per share = $50
• Total amount spent on purchase = 50 x 1000 = 50000
• Loan amount = 50% x 50000 = 25000
• Interest = 2% x 25000 = 500
• Selling Price per share = $60
• Total Amount available at sale = 60 x 1000 = 60000
• Amount paid off as loan repayment & interest = 25000+500 = 25500
• Amount remaining = 60000-25500 = 34500
• Original amount invested = 50% x 50000 = 25000
• So profit = 34500-25000 = 9500
• Profit % = 9500/25000 x 100 = 38%

c)

Lets first discuss what's happening in the below chart:

Profit + 1 Profit = Unlimited / Loss = Limited Increasing Underlying Stock- Price Loss - Long Call

Till the time the selling price per share is below $50 the option holder doesn't exercise it and therefore the $400 spent on purchasing the option is the only loss he has to bear. This is depicted in the above chart for all the time the graph is below the x axis and parallel to it

The graph intersects the x axis when the (SP-CP) x number of shares = 400. This happens when (SP-50) x 1000 = 400, Sp = 50.40

For all other Selling price higher than 50.40, the option holder earns a profit. So at SP = 60, the profit = 10 x 1000 - 400 = 9600

As the profit has no upper limit, because the selling price can go up to any amount, the graph is upward sloping without any upper bound