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Chapter 3 – Answer Key:
Problem Sets: 11, 12, & 16
Problem Sets:
11.
The total cost of the purchase is: $40
×
500 = $20,000
You borrow $5,000 from your broker, and invest $15,000 of your own funds.
Your margin account starts out with equity of $15,000.
a.
(i)
Equity increases to: ($44
×
500) – $5,000 = $17,000
Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%
(ii)
With price unchanged, equity is unchanged.
Percentage gain = zero
(iii)
Equity falls to ($36
×
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
×
equity
initial
s
Investor'
investment
Total
= % change in price
×
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%
×
000
,
15
$
000
,
20
$
= 13.33%
b.
The value of the 500 shares is 500P. Equity is (500P – $5,000). You will
receive a margin call when:
P
500
000
,
5
$
P
500
−
= 0.25
⇒
when P = $13.33 or lower
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The value of the 500 shares is 500P. But now you have borrowed $10,000
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 Spring '11
 Chen

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