Chapter 3, Problem 11PS

a.

Summary Introduction

To calculate: Percentage increase in the net worth of the brokerage account.

Introduction: A brokerage account refers to an investment account that allows the account holder to deposit money and execute the trade in the place of the customer.

Answer to Problem 11PS

Percentage change in net worth if price changes to $22 is 13.33%

Percentage change in net worth if price changes to $20 is 0%

Percentage change in net worth if price changes to $18 is -13.33%

Explanation of Solution

Given Information:

Selling price per share: $20

Number of shares: 1,000

Initial investment: $15,000

If share price of X changes to $22

  $\begin{array}{c}\text{Percentage change in net worth}=\frac{({\text{New Net Worth}}^1-\text{Old Net Worth)}}{\text{Old Net Worth}}\\ \text{= }\frac{\text{(\$17,000}-\$15,000)}{\$15,000}\\ =13.33\%\end{array}$

If share price of X changes to $20

  $\begin{array}{c}\text{Percentage change in net worth}=\frac{({\text{New Net Worth}}^2-\text{Old Net Worth)}}{\text{Old Net Worth}}\\ =\frac{(\$15,000-\$15,000)}{\$15,000}\\ =0\%\end{array}$

If share price of X changes to $18

  $\begin{array}{c}\text{Percentage change in net worth}=\frac{({\text{New Net Worth}}^3-\text{Old Net Worth)}}{\text{Old Net Worth}}\\ \text{= }\frac{\text{(\$13,000}-\$15,000)}{\$15,000}\\ =-13.33\%\end{array}$

Working Notes:

Calculation of current net worth:

  $\begin{array}{c}\text{Current Net worth}=\text{No}\text{. of Shares}\times \text{Current Market Price }-\text{Borrowed Funds}\\ \text{=}1,000\times \$20-\$5,000\\ =\$15,000\end{array}$

  $\begin{array}{c}\text{New Net worth= 1,000}\times \$\text{22}-\text{5,000}\\ \text{=\$17,000}\end{array}$

  $\begin{array}{c}\text{New Net worth= 1,000}\times \$\text{20}-\text{5,000}\\ \text{=\$15,000}\end{array}$

  $\begin{array}{c}\text{New Net worth= 1,000}\times \$18-\$\text{5,000}\\ \text{=\$13,000}\end{array}$

b.

Summary Introduction

To calculate: The price at which the margin call will be generated.

Introduction: A margin call occurs when an investor’s account has fallen below the maintenance margin requirement, and then the margin call occurs.

Answer to Problem 11PS

Margin call will be generated when the price is $13.33 or lower.

Explanation of Solution

Given Information:

Maintenance margin: 25%

Computing the price at which margin call will be generated:

Price is denoted by P

The total value of shares is 1000P

  $\begin{array}{c}\text{Price}=\frac{(\text{No}\text{. of Shares }\times \text{ Price)}-\text{Borrowed Funds}}{\text{No}\text{. of Shares }\times \text{ Price}}\\ =\frac{\left(1,000P-\$5,000\right)}{1,000P}\\ =0.25\\ \text{When P= \$13}\text{.33 or lower}\end{array}$

The chances of getting a margin call increases when the equity of business gets decreased.

c.

Summary Introduction

To calculate: The price at which margin call will be generated.

Introduction: When an investor’s account has reduced to a certain amount which is equal to or less than the account’s maintenance margin, then the margin call occurs.

Answer to Problem 11PS

Margin call will be generated when price is $13.33 or lower.

Explanation of Solution

Given,

Initial investment: $10,000

The total value of shares is 1,000P, (Here P denotes the price)

Now, the money of your own is reduced to $10,000 which means the borrowed amount is increased to $10,000.

  $\begin{array}{c}\text{Price}=\frac{(\text{No}\text{. of Shares }\times \text{ Price)}-\text{Borrowed Funds}}{\text{No}\text{. of Shares }\times \text{ Price}}\\ \text{=}\frac{\left(1,000P-\$10,000\right)}{1,000P}\\ =0.25\\ \text{When P}\text{= \$26}\text{.67 or lower}\end{array}$

d.

Summary Introduction

To calculate: The rate of return on the margined position and the relationship between percentage change and percentage return in the price of X

Introduction: The return on investment is the total profit or loss of the initial investment using a margined position, which is calculated as a percentage change for analyzing the relationship between change in the price and return over the price.

Answer to Problem 11PS

Return over the price if a price change to $22 is 10.67%

Return over the price if price changes to $20 is -2.67%

Return over the price if price changes to $18 is -16%

Explanation of Solution

Given Information:

Number of shares: 1,000

Initial investment: $15,000

Return over the price if Price of X changes to $22

  $\begin{array}{c}\mathrm{Return}\text{ Over Price}=\frac{\text{Purchasing Price}-\text{ Borrowed fund}-\text{ Intial investment}}{\text{Initial Investment}}\\ =\frac{1,000(\$22)-(\$1.08)5,000-\$15,000}{\$15,000}\\ =\frac{1,000(\$22)-\$20,400}{\$15000}\\ =10.67\%\end{array}$

Return over the price would be 10.67%

Return over the price if Price of X changes to $20

  $\begin{array}{c}\mathrm{Return}\text{ Over Price}=\frac{\text{Purchasing Price}-\text{ Borrowed fund}-\text{ Intial investment}}{\text{Initial Investment}}\\ =\frac{1,000(\$20)-(1.08)5,000-\$15,000}{\$15,000}\\ =\frac{1,000(\$20)-\$20,400}{\$15,000}\\ =-2.67\%\end{array}$

Return over the price would be -2.67%

Return over the price if Price of X changes to $18

  $\begin{array}{c}\mathrm{Return}\text{ Over Price}=\frac{\text{Purchasing Price}-\text{ Borrowed Fund}-\text{ Intial Investment}}{\text{Initial Investment}}\\ =\frac{1,000(\$18)-(1.08)\$5,000-\$15,000}{\$15,000}\\ =\frac{1,000(\$18)-\$20,400}{\$15,000}\\ =-16\%\end{array}$

Return over the price would be -16%

e.

Summary Introduction

To calculate:The price at which margin call occurs after year passed.

Introduction: When an investor’s account arrives at a point where the initial margin deposit is equal to or less than the loss, which reduces the initial margin then the margin call occurs.

Answer to Problem 11PS

Lowest Price fall before margin call is $7.2

Explanation of Solution

Calculating margin ratio:

  $\begin{array}{c}\text{Margin ratio= }\frac{\text{Value of shares }-\text{Margin amount}}{\text{Value of Shares}}\\ \text{= }\frac{\text{1,000}p-5,400}{1,000p}=0.25\\ =1,000p-5,400=250p\\ p=\frac{5,400}{750}=\$7.2\end{array}$