Question

Assume you want to buy 100 shares of stock at $50 per share because you feel it will rise to $60 within 3 months. The stock pays $4 per share in annual dividends. You are going to buy the stock with 70% margin and will pay 8.0% interest on the margin loan.

Calculate the return if the price go up to $55 in 3 months.

Answer #1

return = [(value of stock in 3 months + dividends for 3 months - loan amount - loan interest for 3 months)/investment amount] - 1

total cost of shares purchased = price per share*no. of shares purchased = $50*100 = $5,000

You are going to buy the stock with 70% margin means you will pay 70% of $5,000 from your own funds and 30% you will borrow from broker.

investment amount = $5,000*70% = $3,500

loan amount = $5,000*30% = $1,500

return = [($55*100 + $4/4 - $1,500 - $1,500*8%*3/12)/$3,500] - 1

there are 4 quarters in a year. so, dividend for 3 months will be: annual dividend/4. annual interest rate is 8%. so interest rate for 3 months will be: 8%*3/12. 12 is the no. of months in a year.

return = [($5,500 + $1 - $1,500 - $30)/$3,500] - 1 = ($3,971/$3,500) - 1 = 1.1346 - 1 = 0.1346 or 13.46%

the return if the price go up to $55 in 3 months is 13.46%.

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