You have $30,000 in your margin account, and you want to invest in BMO stock. Th

Question

You have $30,000 in your margin account, and you want to invest in BMO stock. The minimum margin requirement for BMO is 30%. You just got a quote on BMO as follows:

Bid: 55.25

Ask: 55.26

The interest rate on the margin loan is 6% per annum.

If you want to buy BMO in margin, what is the maximum number of shares can you buy?

Suppose you want to buy 1200 shares of BMO in margin. Answer the following questions:

What is the initial margin ratio?

Suppose you are going to hold the shares for one year. At what price at the end of next year will your investment break even? (assuming no margin calls in the year)

How far could the stock price fall before getting a margin call?

If the stock price falls to $40, you would get a margin call. If this happens, how much new fund would you need to add to your account to respond the margin call?

Explanation / Answer

The shares will be bought at the ask price, as it is higher than the bid price. So, cost of buying 1 share is 55.26

Amount for 1200 shares = no. of shares*price per share = 1200*55.26 = 66,312

Amount in margin account = 30,000. Thus amount required on margin = Total purchase price - amount in margin account.

= 66,312 - 30,000 = 36,312

Initial margin ratio = amount in margin account/investment purchased on margin

= 30,000/36,312 = 0.83

Interest rate = 6%. Interest amount for 1 year = interest rate*amount of loan

= 6% of 36,312 = 2,179

Total investment on 1,200 shares = amount paid for purchase+loan interest = 66,312+2,179 = 68,491

Break even price = total investment/no. of shares = 68,491/1,200 = 57.08 (break even price)

Let the price be (after falling) "x". Total price = 1,200x

30% of margin is required. Balance after margin = 70%

70% of 1,200 x = 840x

So 840x = 30,000 (amount of initial margin)

or x = 35.71. If the stck price falls to 35.71 or lower amount, you will get a margin call.

at $40, value of investment = 40*1200 = 48,000

70% of 48,000 = 33,600

So new fund needed = Current margin value - amount in margin account

= 33,600 - 30,000 = 3,600

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