(A) Initial Margin: Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan. Short sale: In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock. Maintenance margin: It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin. Margin call: If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account. To compute: The rate of return for the given stock after one year of short sale, assuming no dividends paid, when The stock price is $44. The stock price is $40. The stock price is $36.

Question

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Answer 1

Question

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

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Answer 2

Question

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

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Answer 3

Question

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

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Answer 4

Question

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

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Answer 5

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

Answer 6

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Answer 7

Chapter 3, Problem 25C

Summary Introduction

(A)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The rate of return for the given stock after one year of short sale, assuming no dividends paid, when

The stock price is $44.

The stock price is $40.

The stock price is $36.

Answer 8

Expert Solution

Answer to Problem 25C

The rate of return on short position is -13.33%.
The rate of return on short position is 0%.
The rate of return on short position is 13.33%.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed. Here no dividends are paid.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$0×500$15,000×100%=−13.33%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$0×500$15,000×100%=0%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$0

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$0×500$15,000×100%=13.33%

Answer 13

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Answer 14

Summary Introduction

(B)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

To compute:

The price of stock below of which the investor would get a margin call

Answer 15

Expert Solution

Answer to Problem 25C

If the stock price falls below $40 per share, the investor would get a margin call.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Here maintenance margin is 25%. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000 . Here the percentage margin is 500P−$15,000500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,000500P=0.25500P−500×0.25P=$15,000P=$40

So, if the stock price falls below $40 per share, the investor would get a margin call.

Answer 20

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.

500P−$15,500500P=0.25500P−500×0.25P=$15,500P=$41.33

So, if the stock price falls below $41.33 per share, the investor would get a margin call.

Answer 21

Summary Introduction

(C)

Initial Margin:

Sometimes, securities are bought with initial margin. It is the percentage of purchase price of stock that the investor has to pay with his own cash. 50% of initial margin means, the investor has to pay 50% or more of the stock price up front and remaining amounts can be taken as a loan.

Short sale:

In case of short sale, the investor borrows the shares of a stock and first sells them. Later on, the investor has to buy the shares of the same stock to replace to what was borrowed initially. Short sale happens when the investor predicts that stock price decreases in future. So, they earn money by the difference of buying and selling price of the stock. Here, investor has to give dividends (if any dividends distributed) to the broker with whom he has borrowed the shares of a stock.

Maintenance margin:

It is the minimum equity amount that must be maintained in a margin account. If the stock value falls below the equity value, then the value of stock provides no longer the enough collateral to cover the loan from the broker. In order to protect it, the broker asks to set the maintenance margin.

Margin call:

If the percentage of the margin falls below the maintenance level, the broker will issue a call margin. When a call margin is issued it is required by the investor has to add new cash to margin account.

Redo work of part a.

To compute:

The rate of return for the given stock after one year of short sale, assuming $1 dividends paid, when

The stock price is $44.

The stock price is $40

The stock price is $36

Redo work of part b.

To compute:

The price of stock below of which the investor would get a margin call

Answer 22

Expert Solution

Answer to Problem 25C

Part a

The rate of return on short position is -16.67%.
The rate of return on short position is -3.33%.
The rate of return on short position is 10%.

Part b

If the stock price falls below $41.33 per share, the investor would get a margin call.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Part a

Total stock price is $20,000=$40×500 where per stock price is $40 and 500 shares of stock have to be purchased. Initial margin requirement is $15,000, which should be given to broker to establish the margin account. So, $15,000 is the equity value.

Rate of return should be found on the equity value. In case of short sale, profit is the initial price less ending price less dividends, if any distributed.

i.

Given:

Initial price= $40

Ending price = $44

Number of shares=500

Equity value=$15,000

Dividends=$1per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$44−$1×500$15,000×100%=−16.67%

ii.

Given:

Initial price= $40

Ending price = $40

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$40−$1×500$15,000×100%=−3.33%

iii.

Given:

Initial price= $40

Ending price = $36

Number of shares=500

Equity value=$15,000

Dividends=$1 per share

Calculation:

Rate of return on short position=Initial price−Ending price−Dividends×No. of sharesEquity value×100%=$40−$36−$1×500$15,000×100%=10%

Part b

Calculation:

Here maintenance margin is 25% and dividend is $1 per share. Let P be the stock price. The value of stock at P price for 500 shares will be 500P. And the equity in the margin account will be 500P−$15,000−$500 . Here the percentage margin is 500P−$15,500500P . The price at which percentage margin equals to the maintenance margin of 25% is determined by solving the following equation for P.