Reading 55: Market Organization and Structure-LOS f 习题精选 2011, following, interpret, receive

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Session 13: Market Organization, Market Indices, and Market Efficiency
Reading 55: Market Organization and Structure

LOS f: Calculate and interpret the leverage ratio, the rate of return on a margin transaction, and the security price at which the investor would receive a margin call.

 

 

Using the following assumptions, calculate the rate of return on a margin transaction for an investor who purchases the stock and the stock price at which the investor would have received a margin call.

• Market Price Per Share: $32
• Number of Shares Purchased: 1,000
• Holding Period: 1 year
• Ending Share Price: $34
• Initial Margin Requirement: 40%
• Maintenance margin: 25%
• Transaction and borrowing costs: $0
• The company pays no dividends

Margin Return

Margin Call Price

A) 6.3% $25.60

B) 15.6% $17.07

C) 15.6% $25.60

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Part 1: Calculate Margin Return:

Margin Return %

= [((Ending Value – Loan Payoff) / Beginning Equity Position) – 1] × 100
= [(([$34 × 1,000] – [$32 × 1,000 × 0.60]) / ($32 × 0.40 × 1,000)) – 1] × 100
= 15.6%

Alternative (Check): Calculate the all cash return and multiply by the margin leverage factor.
[(34,000 – 32,000) / 32,000] × [1 / 0.40] = 6.35% × 2.5 = 15.6%

Part 2: Calculate Margin Call Price:

The formula for the margin call price is:
Margin Call = (original price) × (1 - initial margin) / (1 - maintenance margin)
= $32 × (1 - 0.40) / (1 - 0.25) = approximately $25.60

1215

Byron Campbell purchased 300 shares of Crescent, Inc., stock at a price of $80 per share. The purchase was made on margin with an initial margin requirement of 50%. Assuming the maintenance margin is 25%, the stock price of Crescent, Inc. has to fall below what level for Campbell to receive a margin call?

A) $53.33.

B) $20.00.

C) $40.00.

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Trigger price (margin purchases) = P_o (1 ? initial margin) / (1 ? maintenance margin).

$80(1-.5)/(1-.25) = 40/.75 = $53.33.
P = $53.33

If Crescent, Inc. falls below $53.33 then Campbell will get a margin call.

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An investor purchases stock on 25% initial margin, posting $10 of the original stock price of $40 as equity. The position has a required maintenance margin of 20%. The investor later sells the stock for $45. Ignoring transaction costs and margin loan interest, which of the following statements is most accurate?

A) Leverage ratio is 3:1.

B) Return on investment is 50%.

C) Margin call price is $36.

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Return on invested equity is ($45 – $40) / $10 – 1 = 50%.
The leverage ratio is purchase price / equity = $40 / $10 = 4.
Margin call price is $40 × [(1 – 0.25) / (1 – 0.20)] = $37.50.

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An investor buys 1,000 shares of a non-dividend-paying stock for $18. The initial margin requirement is 40% and the maintenance margin is 30%. After one year the investor sells the stock for $24 per share. The investor's rate of return on this investment (ignoring borrowing and transactions costs and taxes), and the price at which the investor would receive a margin call, are closest to:

Rate of return

Margin call

A) 83%   $15.43

B) 83%   $21.00

C) 33%   $15.43

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To obtain the result:

Part 1: Calculate Margin Return:

Margin Return % = [((Ending Value  - Loan Payoff) / Beginning Equity Position) – 1] * 100 =

= [(([$24 × 1,000] – [$18 × 1,000 × 0.60]) /  ($18 × 0.40 × 1,000)) – 1] × 100 =

= 83.33%

Alternative (Check): Calculate the all cash return and multiply by the margin leverage factor.

                          = [(24,000 – 18,000)/18,000] × [1 / 0.40] = 33.33% × 2.5 = 83.33%

Part 2: Calculate Margin Call Price:

Since the investor is long (purchased the stock), the formula for the margin call price is:

          Margin Call = (original price) × (1 – initial margin) / (1 – maintenance margin)

   = $18 × (1 – 0.40) / (1 – 0.30) = $15.43

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An investor purchases 100 shares of Lloyd Computer at $26 a share. The initial margin requirement is 50%, and the maintenance margin requirement is 25%. The price below which the investor would receive a margin call is closest to:

A) 19.45.

B) 15.25.

C) 17.33.

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26 * (1 - 0.5)/(1 - 0.25) = $17.33.

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Which of the following statements about the maintenance margin requirement is least accurate?

A) The Federal Reserve sets the maximum maintenance margin.

B) The purpose of the maintenance margin requirement is to protect the broker in the event of a large stock decline.

C) Generally the maintenance margin requirement is lower than the initial margin requirement.

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The Federal Reserve sets the minimum maintenance margin and individual investment companies may set higher margins if they wish.

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Which of the following statements regarding margin accounts is most accurate?

A) The total equity in the margin account cannot fall below the initial margin requirement.

B) Maintenance margin refers to the amount of funds the investor can borrow.

C) Margin accounts can be used to purchase securities by borrowing part of the purchase price.

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Margin accounts are brokerage accounts that allow investors to borrow part of the purchase price from the broker.

1215

An investor bought a stock on margin. The margin requirement was 60%, the current price of the stock is $80, and the investor paid $50 for the stock 1 year ago. If margin interest is 5%, how much equity did the investor have in the investment at year-end?

A) 67.7%.

B) 60.6%.

C) 73.8%.

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Margin debt = 40% × $50 = $20; Interest = $20 × 0.05 = $1.

Equity % = [Value – (margin debt + interest)] / Value

$80 - $21 / $80 = 73.8%

1215

Assume 100 shares purchased at $75/share with an initial margin of 50%.

The initial cost to the investor is:

A) $3,750.

B) $7,500.

C) $0.

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$75/share × 100 shares = $7,500

50% margin means investor only pays ? of the $7,500

= $3,750.

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Now, assume that the stock rose to $112.50. The return on investment to the investor is:

A) 100%.

B) 50%.

C) 200%.

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(market value – initial own investment – margin loan repayment)/initial equity
=($11,250 – $3,750 – $3,750) / $3,750 = 100%. (Assuming no interest on the call loan and no transactions fees.)

1215

Sonia Fennell purchases 1,000 shares of Xpressoh Inc. for $35 per share. One year later, she sells the stock for $42 per share. Xpressoh Inc. pays no dividends. The initial margin requirement is 50%. Fennell's one-year return assuming an all-cash transaction, and if she buys on margin (assume she pays no transaction or borrowing costs and has not had to post additional margin), are closest to:

All-cash

50% margin

A) 20% 80%

B) 40% 80%

C) 20% 40%

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All-cash return = 42/35 ? 1 = 20%

Margin return = (42 ? 35)/[(35)(0.5)] = 40%