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

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An investor purchases 200 shares of Merxx on margin. The shares are trading at $40. Initial and maintenance margins are 50% and 25%.

If the investor sells the stock when the price rises to $50 at year-end, the return on the investment would be closest to:

A) 25.00%.

B) 50.00%.

C) 18.75%.

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Profit = 10,000 – 8,000 = 2,000
Return = 2,000 / 4,000 = 50%

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If the company pays a dividend of $0.75, the return on the investment would be closest to:

A) 39.55%.

B) 15.75%.

C) 53.75%.

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Dividends income = (0.75) × (200) = $150
Profit = 10,000 – 8,000 + 150 = 2,150
Return = 2,150 / 4,000 = 53.75%

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An investor buys 200 shares of ABC at the market price of $100 on full margin. The initial margin requirement is 40% and the maintenance margin requirement is 25%.

If the shares of stock later sold for $200 per share, what is the rate of return on the margin transaction?

A) 250%.

B) 400%.

C) 100%.

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One quick (and less than intensive) way to calculate the answer to this on the examination (and it is very important to save time on the examination) is to first calculate the return if all cash, then calculate the margin leverage factor and then finally, multiply the leverage factor times the all cash return to obtain the margin return.

Calculations:

Step 1: Calculate All Cash Return:

Cash Return % = [(Ending Value / Beginning Equity Position) – 1] × 100

= [(($200 × 200) / ($100 × 200)) – 1] × 100 = 100%

Step 2: Calculate Leverage Factor:

Leverage Factor = 1 / Initial Margin % = 1 / 0.40 = 2.50

Step 3: Calculate Margin Return:

Margin Transaction Return = All cash return × Leverage Factor = 100% × 2.50 = 250%

Note: You can verify the margin return as follows:

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

= [(([$200 × 200] – [$100 × 200 × 0.60]) / ($100 × 0.40 × 200)) – 1] × 100

= [ ((40,000 ? 12,000) / 8,000) ? 1] × 100 = 250%

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An investor buys 400 shares of a stock for $25 a share. The initial margin requirement is 50%, and the maintenance margin requirement is 25%. At what price would an investor receive a margin call?

A) $21.88.

B) $30.00.

C) $16.67.

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Margin call trigger price = [25(1 - 0.5)] / (1 - 0.25) = 16.67.

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An investor buys 200 shares of ABC at the market price of $100 on full margin. The initial margin requirement is 40% and the maintenance margin requirement is 25%.

At what price will the investor get a margin call?

A) $112.

B) $48.

C) $80.

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In a long stock position, the equation to use to determine a margin call is:

long = [(original price)(1 ? initial margin %)] / [1 ? maintenance margin %]
       = $100(1 ? 0.4) / (1 ? 0.25) = $80

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When using margin to invest in equities, which of the following defines initial margin and what level will the margin be brought back to in the event of a margin call?

Initial Margin

Margin Call Action

A) amount of borrowed funds in the transactions a deposit must be made to bring the margin back to the maintenance margin

B) minimum amount of equity required of the investor a deposit must be made to bring the margin back to the initial margin

C) minimum amount of equity required of the investor a deposit must be made to bring the margin back to the maintenance margin

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The initial margin requirement refers to the minimum amount of equity required of the investor.

With equities, if the margin falls below the maintenance margin, funds must be deposited to bring it back up to the maintenance margin level.

1215

Lynne Hampton purchased 100 shares of $75 stock on margin. The margin requirement set by the Federal Reserve Board was 40%, but Hampton’s brokerage firm requires a total margin of 50%. Currently the stock is selling at $62 per share. What is Hampton’s return on investment before commission and interest if she sells the stock now?

A) -40%.

B) -35%.

C) -17%.

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Hampton originally purchased 100 shares at $75 for a total value of $7500. Half of the value ($3750) was borrowed and Hampton paid cash for the other half. The current total market value of the stock is $6200. If Hampton sells her holdings she will have $2450 left after she pays off the loan. Hampton’s return on her original investment is:

$2450/3750 – 1 = 0.65 – 1 = -0.35 = -35%.

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Mark Ritchie purchased, on margin, 200 shares of TMX Corp. stock at a price of $35 per share. The margin requirement was 50%. The stock price has increased to $42 per share. What is Ritchie’s return on investment before commissions and interest if he decides to sell his TMX holdings now?

A) 40%.

B) 20%.

C) 10%.

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200 shares × $35 = $7000 Initial Market Value

$7000 × .50 = $3500 cash payment and $3500 borrowed.

The new market value of the stock after price increase is (200 × $42) = $8400. If Ritchie sold his holdings he would have $4900 ($8400 × $3500) left after the loan was paid. So Ritchie’s return on his original $3500 investment is:

$4900/3500 – 1 = 1.4 – 1.0 = 0.40 = 40%.

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If an investor buys 100 shares of a $50 stock on margin when the initial margin requirement is 40%, how much money must she borrow from her broker?

A) $2,000.

B) $4,000.

C) $3,000.

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An initial margin requirement of 40% would mean that the investor must put up 40% of the funds and brokerage firm may lend the 60% balance. Therefore, for this example (100 shares) * ($50) = $5,000 total cost. $5,000 * 0.60 = $3,000.

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Becky Kirk contacted her broker and placed an order to purchase 1,000 shares of Bricko Corp. stock at a price of $60 per share. Kirk wishes to buy on margin. Assuming the margin requirement is 40%, how much money does Kirk have to pay up front to make the purchase?

A) $24,000.

B) $60,000.

C) $36,000.

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The margin requirement represents the amount of money an investor must put down on the purchase. So Kirk must put $24,000 down ($60,000 x .40 = $24,000) and can borrow the balance