Q1C.

Expert-verifiedFound in: Page 81

Book edition
9th

Author(s)
Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus

Pages
748 pages

ISBN
9780078034695

** 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**

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

**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%**

**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%**

**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**

**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.**

**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%**

**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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