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Essentials Of Investments
Found in: Page 81
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

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Short Answer

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 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) $36? 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 get a margin call?

c. How would your answer to ( b ) 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 one year at (i) $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?

a. (i) 13.33% (ii) Zero (iii) -13.33% and 13.33%

b. $13.33 or lower

c. More vulnerability to a margin calls

d. 10.67%

e. $14.40 or lower

See the step by step solution

Step by Step Solution

Step 1: Definition

Brokerage is a type of fee charged to execute transactions or provide services.

Step 2: Calculation of percentage increase in given scenarios

a. The total cost of the purchase is: $40 x 500 = $20,000

You borrow $5,000 from your broker, and invest $15,000 of your own funds. Your margin account starts out with net worth of $15,000.

(i) Net worth increases to: ($44 x 500) – $5,000 = $17,000

Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%

(ii) With price $ 40 that is price unchanged, net worth is unchanged.

Percentage gain = zero

(iii) Net worth falls to ($36 x 500) – $5,000 = $13,000

Percentage gain = (–$2,000/$15,000) = –0.1333 = –13.33%

Step 3:  Evaluation of relationship between percentage return and percentage increase

The relationship between the percentage return and the percentage change in the price of the stock is given by:

% return = % change in price x Investor's initial equity

Total investment = % change in price x 1.333

For example, when the stock price rises from $40 to $44, the percentage change

in price is 10%, while the percentage gain for the investor is:

% return = 10% x $20,000 / $15,000

= 13.33%

Step 4:  Calculation of low to receive margin call

b. Let’s assume the value of the 500 shares is 500P. Equity is (500P – $5,000).

You will receive a margin call when: 500P - $5000 / 500P

= 0.20 when

P = $13.33 or lower

Step 5: Evaluation of given scenario

c. The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is (500P – $10,000). You will receive a margin call when:

500P - $10,000/ 500P

=0.25 when P= $26.67

With less equity in the account, there is far more vulnerability to a margin calls.

Step 6:  Evaluation of relationship between percentage return and percentage change

d. By the end of the year, the amount of the loan owed to the broker grows to: Principal x (1 + Interest rate)= $5,000 x 1 + 08

$5,000 x 1.08 = $5,400

The equity in your account is (500P – $5,400).

Initial equity was $15,000.

Therefore, the rate of return after one year is as follows: Ending equity – Borrowed capital - Initial equity / Initial equity

(i) (500 x $44 - $ 5400 - $ 15000) /$15000 = 0.1067 = 10.67%

(ii) (500 x $40 - $ 5400 - $ 15000) /$15000 = - 0.0267 = -2.67%

(iii) (500 x $36 - $ 5400 - $ 15000) /$15000 = - 0.1600 = -16.00%

The relationship between the percentage return and the percentage change in the price of Intel =

% return = (% change in price x Total investment / Investor’s initial equity) – (8% x Funds borrowed/ Investor’s initial equity)

For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is:

(10% x $20,000/ $15000) – (8% x $5000/$15000)

= 10.67%

Step 7: Calculation of low to receive margin call

e. The value of the 500 shares is 500P. Equity is (500P – $5,400).

You will receive a margin call when: equity is divided by the value of shares

500P – 5400/ 500P = 0.25 when P = $14.40 or lower.

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