You execute a margin purchase of $200$ shares of a stock at $$46$ per share. The initial margin

requirement is $50\%$ 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 $$48$ 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 $$52$

per share. During the year the stock paid a dividend of fifty cents. The interest rate on your loan

was $8\%$ 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$.$