Question

You execute a margin purchase of 200 shares of a stock at $52 per share. The initial margin requirement is 60% and the maintenance margin is 35%.

     a.    On a per share basis, what is the minimum amount you must you put up and how much can you borrow from the brokerage house?

     b.    If the price of the stock increases to $64 per share, what is the actual margin in your account? Assume you borrowed the maximum amount possible when taking the position initially.

     c.    How far can the stock price fall prior to your receiving a margin call? (Note, ignore any interest expense when calculating actual margins.)

     d.    Suppose you hold your initial position for one year, at which time the stock is selling for $68 per share. During the year the stock paid a dividend of fifty cents. The interest rate on your loan was 7% annually. Calculate the percentage return on your investment. Then calculate the percentage return on your investment if you had made a cash purchase originally instead of a margin purchase. Explain the difference in the returns.

     e.    Repeat part d leaving everything as before except now assume an ending stock price of $40 per share. Explain why the two returns differ as they do.

Answer 1

No of shares purchased = 200

Initial Stock price = $52

Initial margin requirement = 60%

Maintenance margin = 35%

a)

Minimum funds required upfront = No of shares purchased * Initial Stock price * Initial margin requirement

Minimum funds required upfront = 200 * $52 * 60%

Minimum funds required upfront = $6240

Amount borrowed = No of shares purchased * Initial Stock price * (1 - Initial margin requirement)

Amount borrowed = 200 * $52 * (1 - 60%)

Amount borrowed = $4160

b)

If the price of the stock increases to $64 per share

Margin change = No of shares purchased * Change in Market price

Margin change = 200 * ($64 - $52)

Margin change = $2400

Current value of Margin Account = Minimum funds required upfront + Margin change

Current value of Margin Account = $6240 + $2400

Current value of Margin Account = $8640

c)

Margin call price = Initial Stock price * (1 - Initial margin requirement) / (1 - Maintenance margin)

Margin call price = $52 * (1 - 60%) / (1 - 35%)

Margin call price = $32

d)

After 1 year, the stock is selling for $68 per share

Initial Investment value = No of shares purchased * Initial Stock price

Initial Investment value = 200 * $52

Initial Investment value = $10,400

Investment value after 1 year = No of shares purchased * Stock price after 1 year

Investment value after 1 year = 200 * $68

Investment value after 1 year = $13,600

Total Dividend payment = No of shares purchased * Dividend per share

Total Dividend payment = 200 * $0.5

Total Dividend payment = $100

Interest payment on loan = Interest rate * Amount borrowed

Interest payment on loan = 7% * $4160

Interest payment on loan = $291.2

Holding period return on margin = (Investment value after 1 year - Initial Investment value + Total Dividend payment - Interest payment on loan) / Minimum funds required upfront

Holding period return on margin = ($13,600 - $10,400 + $100 - $291.2) / $6,240

Holding period return on margin = 48.22%

Holding period return on cash purchase = (Investment value after 1 year - Initial Investment value + Total Dividend payment) / Initial Investment value

Holding period return on cash purchase = ($13,600 - $10,400 + $100) / $10,400

Holding period return on cash purchase = 31.73%

e)

After 1 year, the stock is selling for $40 per share

Initial Investment value = No of shares purchased * Initial Stock price

Initial Investment value = 200 * $52

Initial Investment value = $10,400

Investment value after 1 year = No of shares purchased * Stock price after 1 year

Investment value after 1 year = 200 * $40

Investment value after 1 year = $8,000

Total Dividend payment = No of shares purchased * Dividend per share

Total Dividend payment = 200 * $0.5

Total Dividend payment = $100

Interest payment on loan = Interest rate * Amount borrowed

Interest payment on loan = 7% * $4160

Interest payment on loan = $291.2

Holding period return on margin = (Investment value after 1 year - Initial Investment value + Total Dividend payment - Interest payment on loan) / Minimum funds required upfront

Holding period return on margin = ($8,000 - $10,400 + $100 - $291.2) / $6,240

Holding period return on margin = - 41.53%

Holding period return on cash purchase = (Investment value after 1 year - Initial Investment value + Total Dividend payment) / Initial Investment value

Holding period return on cash purchase = ($8,000 - $10,400 + $100) / $10,400

Holding period return on cash purchase = - 22.12%