Question

1. You opened a margin account with borrowing $50,000 from your broker a year ago. Your account started at the initial margin requirement of 50%. With the margin account you bought ABC stock at $50 per share. The maintenance margin is 35%. Today, the stock price falls to $45 per share. Assume interest rate is 10%. What is the margin (your equity) in your account when you first purchase the stock? b. Will you receive a margin call? (Please consider interest expenses and Show percentage margin after price falls) C. How low can the price of ABC shares fall before you receive a margin call? Please show both with and without interest expenses. d. What is your rate of return (Consider Interest Expenses)?

Answer 1

Given,

Initial Margin (IM) = 50%

Maintenance Margin (MM) = 35%

Amount borrowed a year ago = $ 50,000

Buying price of the stock = $ 50 a share

Current Price = $ 45 a share

a. Initial Margin per share when the equity was purchased = 50% of $50 = $ 25 per share

Since, $ 50,000 is borrowed initially, the rest amount should be the initial margin. As the initial margin is 50% of total value, the borrowed money must also be 50% of the same.

So number of share purchased = (50,000*2)/50 = 2,000 shares

Net IM = 2,000 * 25 = $ 50,000

Maintenance margin = 100,000 * 0.35 = $ 35,000

b. The value of stock is $ 45 a share now.

Net value of the account = 45 * 2000 = $ 90,000

Loss = 100,000 - 90,000 = $ 10,000

Interest = 10 % of 50,000 = $ 5,000

So opening margin = $ 50,000

Final Margin = 50,000 - (10,000 + 5,000) = $ 35,000

Since, the Margin = maintennace margin, he will not get a margin call.

c.

With interest expense:

As we saw in the previous question that when the price is $ 45 a share, the margin becomes equal to the maintenance margin. If it falls further, there will be a margin call. So it can fall upto $ 45 a share only to avoid a call.

Without interest expense:

We need a loss of 50,000 - 35,000 = 15,000 to get a margin call.

Let the current price is 'x'

So (50 - x) * 2000 = 15000

Or, x = $ 42.50 a share

d.

Rate of return = (final value - Initial value) * 100 / invested value = (90,000 - 100,000) * 100/50,000 = -20%