6. Suppose that Intel currently is selling at $20 per share.You buy 1,000 shares

Question

6. Suppose that Intel currently is selling at $20 per share.You buy 1,000 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker.The rate on the margin loan is 8%.

A. What is the percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to (i) $22? (ii) $20? (iii) $18?What is the relationship between your percentage return and the percentage change in the price of Intel?

B. If the maintenance margin is 25%, how low can Intel’s price fall before you receive a margin call?

C. How would your answer to b (above) change if you had financed the initial purchase with only $10,000 of your own money?

D. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if Intel is selling after 1 year at: (i) $22? (ii) $20? (iii) $18?

E. What is the relationship between your percentage return and the percentage change in the price of Intel?Assume that Intel pays no dividends.

a. Depends on the gravitational constant of the Sun

b. return depends on the bid-ask spread in OTC future contracts

c. return depends on interest and principal amount of loan on margin

d. return depends on the price of moon rocks on the internet

F. Continue to assume that 1 year has passed.How low can Intel’s price fall before you receive a margin call?

a. 0

b. 10.05

c. 7.20

d. 3.17

Explanation / Answer

Assumption: No transaction costs

A.

(i) ((22-20)/20) = 10%

(ii) ((20-20)/20) = 0%

(iii) ((18-20)/20) = -10%

The relationship between the percentage return and price is positive i.e. as price increases, return increases too.

B.

Margin Call Price = ($ 20 * (.25)) / (1-.25) = $ 6.67

Thus, if the price falls below $ 6.67, you will receive a margin call.

C.

In B. above the margin requirement was 75% ($15000/ $20000). When the initial purchase is financed with $ 10000 of your own funds, the margin requirement changes to 50% ($10000/ $20000).

Therefore, the margin call price will be as calculated below:

($20*(.50)) / (1-.50) = $ 20

Thus, a margin call will be made when the price falls below $20.

D. Profit = Sale amount - Total cost - Interest paid to broker (@ 8%)

Rate of return = Profit / Own funds invested

Assumption: Margin Requirement is 75%

(i) Profit = $ (22000 - 20000 - 400) = $ 1600

Rate of Return = $ (1600/15000) = 10.67%

(ii) Profit = $ (20000 - 20000 - 400) = - $ 400

Rate of Return = $ (-400/15000) = - 2.67%

(iii) Profit = $ (18000 - 20000 - 400) = - $ 2400

Rate of Return = $ (-2400/15000) = - 16%

E.

Option (c) return depends on interest and principal amount of loan on margin is correct.

F.

None of the options are correct. Refer to the margin call calculation under part B for the answer and calculation.

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