Question

1. Assume you purchased 1,000 shares of Motorola on January 2, 2001 (a Tuesday) at $100 per share. Your broker charged a commission of 1% of the value of the trade.

a. How much will you owe, and when will you owe it?

b. Assume you purchased the stock on margin. Your broker required a 50% initial margin and maintenance margin of 25%. How much cash would you have to come up with initially?

c. At what price would you face a margin call?

d. Using the information provided in the prior questions, assume the price of Motorola rises from 100 to 125, compute the return assuming you purchased the stock for cash and assuming you purchased the stock on margin. What have you not considered when computing these returns?

Answer 1

(a) Purchase Volume = 1000 shares and Price per Share = $ 100

Broker Commission = 1 % of Purchase Value = 0.01 x 1000 x 100 = $ 1000

The buyer will owe the broker his/her commission once the trade is settled at t+2 with trade date being t.

(b) Maintence Margin = 25% and Inital Margin = 50 %

Initial Cash Required = Initial Margin x Trade Value = 0.5 x 100000 = $ 50000

(c) The buyer would face a margin call when the buyer's equity value of margin account (initial cash required from part (b)) goes below 25% of the total margin account value. Let the margin call price be $ K

Therefore, Margin Account Value = 1000 x K

Hence, 100K - Value of Debt = 25 % of 1000K

1000K - 50000 = 0.25 x 1000K

750K = 50000

K = 50000 / 750 = $ 66.67

(d) Return if Stock is Purchased in Cash = [125 x 1000 - (100000 + 1000)] / 100000 = 24000 / 100000 = 0.24 or 24 %

Return if Stock is Purchased on Margin = [125 x 1000 - 50000 - 50000] / 50000 = 25000 / 50000 = 0.5 or 50 %

The entity that is ignored in computing returns for stock purchased on margin is the broker commission.