Question

Suppose that Intel is currently selling at $40 per share. You buy 250 shares by using $7,500 of your own money and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 10% per annum.

1. What is the percentage increase in the net worth (or return on equity) of your brokerage account if the price of Intel immediately changes to (a) $46; (b) $34?

2. If the maintenance margin is 25%, how low can Intel stock price fall before you get a margin call?

3. How would your answer to (#2) change if you had financed the initial purchase with only $5,000 of your own money?

4. What is the rate of return on your margined position (assuming again that you invest $7,500 of your own money) if Intel is selling after one year at (a) $46; (b) $34?

5. What is the relationship between your percentage return and the percentage change in the price of Intel in (#4), assuming that Intel pays no dividends?

Answer 1

Price of 1 Intel share = $ 40

Price of 250 Intel share = No. of Shares * Price per share

= 250 * 40

= $10,000

Own money = $ 7,500

Borrowed Money = 10,000 - 7,500

= $ 2,500

Formulas used in the excel sheet are:

B)  Margin call is the call that occurs when the price of the equity position falls below the maintenance margin

When maintenance margin is 25%, margin call occurs at share price (P) :

((Value of Shares) - Borrowed Funds) / Value of Shares  = Maintenance margin of Funds Invested

(250*P - 2500) / 250P = 25%

250*P - 2500 = 250P * 0.25

250P - 2500 = 62.5P

187.5P = 2500

P = 2500 / 187.5

Price = $ 13.33

So Margin call will occur when the price is $ 13.33 or lower

C)  Initial Purchases = $ 10,000

Borrowed Funds = $ 5,000

Margin call will occur when:

(250*P - 5000) / 250P = 25%

250*P - 12,500 = 250P * 0.25

250P - 5000 = 62.5P

187.5P = 5,000

P = 5,000 / 187.5

Price = $ 26.67

Margin call will occur when the price is $ 26.67 or lower

D) We can calculate the rate of return on margined position after 1 year as follows:

Formulas used in the excel sheet are:

As there are multiple questions asked, I have solved the first 4 sub parts. Please post the question separately for rest parts to be answered. Hope it helps you.