Question

11. Suppose that Intel currently is selling at $40 per share. You buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on n/bkm 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) $44; (ii) $40; (iii) $362 What is the relationship between your percentage return and the percentage change in the price of Intel? call? S10,000 of your own money? b. If the maintenance margin is 25%, how low can Intel's price fall before you get a margin c. How would your answer to (b) change if you had financed the initial purchase with only 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 I year at: () $44 ii) $40; iii) $36? What is the relationship between your percentage return and the percentage change in the price of Intel? Assume that Intel pays no dividends. e. Continue to assume that a year has passed. How low can Intel's price fall before you get a margin call?

Answer 1

Price of 1 Intel share = $40

Price of 500 Intel share = 500*40 = $20,000

Own money = $15,000

Borrowed Money = $5000

Rate on margin loan = 8%

a. (i) When price changes to $44,

Net worth of brokerage account = 44*500 = $22,000

(ii) When price changes to $40,

Net worth of brokerage account = 40*500 = $20,000

ii) When price changes to $36,

Net worth of brokerage account = 36*500 = $18,000

The percentage return is directly proportional to the percentage change in the price of intel shares

b. Margin call occurs when the price of the equity position falls below the maintenance margin

When maintenance margin is 25%, margin call occurs at share price (S) which is obtained as follows:

500*S - 5000 = 25% of 15000

500*S = 3750+5000

S= $17.5

c. When initial purchase is financed with just $10,000, margin call is activated at

500*S - 10000 = 25% of 10000

S = $25

d. (i) When Intel shares sell at $44 after 1 year

Portfolio value = 500*(44) - 8% of 5000 - 5000 (paid back to broker) = 22000 - 400-5000 = $16,600

Initial investment = $15,000

Profit = $16,600 - $15,000 = $1,600

Rate of return = Profit / Initial investment = 1600 / 15000 = 10.66%

(ii) When Intel shares sell at $40 after 1 year

Portfolio value = 500*(40) - 8% of 5000 - 5000 (paid back to broker) = 20000 - 400-5000 = $14,600

Initial investment = $15,000

Profit = $14,600 - $15,000 = -$400

Rate of return = Profit / Initial investment = -400 / 15000 = -2.66%

(iii) When Intel shares sell at $36 after 1 year

Portfolio value = 500*(36) - 8% of 5000 - 5000 (paid back to broker) = 18000 - 400-5000 = $12,600

Initial investment = $15,000

Profit = $12,600 - $15,000 = $2,400

Rate of return = Profit / Initial investment = -2400 / 15000 = -16.0%

e. After Year 1, Let margin call be called at share price S

Now, equity position = $15000 - 8% of 5000 (interest paid to broker for borrowing $5000) = $14,600

500*S - 5000 = 25% of 14,600

S= $17.3