Question

You have deposited $30,000 in a brokerage account with an initial margin of 60%. The broker charges a spread of .5 percent and the call money rate is 5.5%. If IBM shares are currently traded at $50, how many shares of IBM can you purchase? A year later, IBM shares are being traded at $60 and you sell your IBM stocks. Calculate your rate of return. What would have been your rate of return if you had purchased IBM using a cash account instead? What would have been your rate of return if , a year later, IBM stock were being traded at $40 per share- with and without a margin loan? What would you conclude?

Answer 1

If 30000 is the amount deposited, it is the equity investment of the 60% of the total amount in the account. This implies that the account has

So if the price of per stock os 50 then the number of stocks you can buy is 1000

We are given the following information:

Purchase price of stock	$ 50.00
Sale price of stock	$ 60.00
Number of shares	1000
Time duration	1 Year
Equity = 60% x 50 =	$ 30.00
Debt= 40% x 50 =	$ 20.00

Cost of Buying 1 share = Equity + Commission

Cost of Buying 1 share = 30+ 0.5% x 50

Cost of Buying 1 share = $30.25

Total cost = Cost of Buying 1 share x number of shares

Total cost = 30.25x 1000

Total cost =30250

Receipts on sale= Sale price per share x number of shares

Receipts on sale= 60 x 1000

Receipts on sale= $60000

Interest on borrowed money = Call money rate x borrowed amount x number of shares

Interest on borrowed money = 0.06 x 20 x 1000

Interest on borrowed money = 1,100.00

Residual Receipts on sale = Receipts on sale – Borrowed money – Interest – commission on sale

Residual Receipts on sale = 60000-20000-1100-250

Residual Receipts on sale = 38,650.00

So the cost of shares was 30250 and the Residual receipts are only 38650 so the return on the stock is

b) If the shares were purchased using cash, then the cost would be 50250 and Sale receipts would be 99.5% x (60000) = 59700
So the return would be:

c)if the sale price is 40 (with margin)

Then the residual sale recipts would be

Residual Receipts on sale = Receipts on sale – Borrowed money – Interest – commission on sale

Residual Receipts on sale = 40000-20000-1100-250

Residual Receipts on sale = 18,650.00

And return would be

d)if the sale price is 40 (without margin)

If the shares were purchased using cash, then the cost would be 50250 and Sale receipts would be 99.5% x (40000) = 39800
So the return would be:

Conclusion:

Leverage is a double edged sword. It magnifies both the returns. When the price goes up, the return is higher with margin while when price goes down the negative return is higher with margin.