Chapter 3, Problem 24C

Summary Introduction

(A)

Introduction:

Margin in stock purchasing means the portion of the purchase price is contributed by investor, the remaining is borrowed from the broker. Thus it describes stock purchased with money borrowed in part from broker.

Requirement 1:

To calculate percentage change in net worth if price of each share changes to $44

Explanation of Solution

Adequate Information:

Market price of each share- $40

Number of shares purchased- 500

Money in hand - $15000

Loan rate - 8%

Calculate:

Calculation of percentage increase in net worth if selling price changes to $44

$\begin{array}{l}\begin{array}{l}\text{Market value of shares = market price of each share × number of shares purchased}\hfill \\ \text{ = \$40×500shares}\hfill \\ \text{ = \$20000}\hfill \\ \text{Loan amount = market value of shares-Money in hand}\hfill \\ \text{ = \$20000-\$15000}\hfill \\ \text{ = \$5000}\hfill \\ \text{Net worth before price change = market value of shares-loan amount}\hfill \\ \text{ = \$20000-\$5000}\hfill \\ \text{ = \$15000}\hfill \\ \text{If price of each share is \$44, the value= market price of each share×number of shares purchased}\hfill \\ \text{ = \$44×500shares}\hfill \\ \text{ = \$22000}\hfill \\ \begin{array}{l}\text{Percentage change in price =}\frac{\text{\$22000-\$20000}}{\text{\$20000}}\text{×100}\\ \text{=10\%}\end{array}\hfill \\ \text{Net worth if price of each share changes to \$44 = (\$44×500 shares)-\$5000}\hfill \\ \text{ = \$17000}\hfill \end{array}\\ \text{Percentage Gain=}\frac{\text{Net worth after price change}}{\text{Net worth before price change}}\text{-1×100}\\ \text{=}\frac{\text{\$17000}}{\text{\$15000}}\text{-1×100}\\ \text{=13}\text{.33\%}\\ \text{Ratio of percentage change in price and percentage return}\\ \text{=}\frac{\text{0}\text{.10}}{\text{0}\text{.133}}\\ \text{=0}\text{.75}\end{array}$

Conclusion

Thus the percentage gain is 13.33% if the price of each share changes to $44 and the ratio of percentage change in return with percentage change in price is 0.75

Summary Introduction

(B)

Introduction:

Margin in stock purchasing describes stock purchased with money borrowed in part from broker. It is calculated as:

$\text{Margin=}\frac{\text{Equity in account}}{\text{Value of Stock}}$

Where equity in account = Value in stock − Loan from broker.

Explanation of Solution

Adequate information:

Margin- 25%

Number of shares purchased- 500

Loan amount = $5000

To calculate Xtel's share price if the Margin is 25 %

Calculation of price of each share if Margin is 25%$\begin{array}{l}Equityinaccount=Value\text{ of }stock–Loanfrombroker\\ \text{ = }500\times P-\$5000\\ \text{Margin=}\frac{\text{Equity in account}}{Value\text{ of stock}}\\ \text{ 0}\text{.25 = }\frac{500\times P-\$5000}{500\times P}\\ \text{ P = \$13}\text{.33}\\ \end{array}$

Conclusion

Thus the price of share will be $13.33 when the margin is 25%.

Summary Introduction

(C)

Introduction:

Margin in stock purchasing describes stock purchased with money borrowed in part from broker. It is calculated as:

$\text{Margin=}\frac{\text{Equity in account}}{\text{Value of Stock}}$

Where equity in account = Value in stock − Loan from broker.

Also, Loan from broker = Market value of shares − Money in hand.

Explanation of Solution

Adequate information:

Margin- 25%

Number of shares purchased- 500

Money in hand -$10000

To calculate Xtel's share price if the Margin is 25 %

Calculation of price of each share if margin is 25% and money in hand is $10000

$\begin{array}{l}\text{Loan from broker = Market value of shares – Money in hand}\text{.}\\ \text{ = \$20000-\$10000}\\ \text{ = \$10000}\\ \text{Equity in account = Value in stock – Loan from broker}\\ \text{ = 500×P - \$10000}\\ \text{ Margin = }\frac{\text{Equity in account}}{\text{Value of stock}}\\ \text{ 0}\text{.25 = }\frac{\text{500×P-\$10000}}{\text{500×P}}\\ \text{ P = \$26}\text{.67}\end{array}$

Conclusion

Thus the price of share will be $26.67 when the margin is 25% and money in hand is $10000.

Summary Introduction

(D)

Introduction:

Margin in stock purchasing describes stock purchased with money borrowed in part from broker. The loan from broker is:

Loan from broker = Market value of shares − Money in hand.

Requirement 1:

To calculate rate of return if price of each share is changed after one year to $44

Explanation of Solution

Adequate Information:

Money in hand -$15000

Number of shares- 500

Loan rate- 8%

Market price of each share- $40

Conclusion

Thus the percentage return if price of each share changes to $ 44 is 10.67% and the ratio of percentage change in price and return is 0.93.

Summary Introduction

(E)

Introduction:

Margin in stock purchasing describes stock purchased with money borrowed in part from broker. It is calculated as:

$\text{Margin=}\frac{\text{Equity in account}}{\text{Value of Stock}}$

Where equity in account = Value in stock − Loan from broker.

Explanation of Solution

Adequate Information:

Money in hand -$15000

Number of shares- 500

Loan rate- 8%

Market price of each share- $40

To calculate Xtel's share price after one year if the Margin is 25 %

Calculation of price of each share after one year if Margin is 25%$\begin{array}{l}After\text{ one year loan payment = loan amount +loan rate}\times \text{loan amount}\\ \text{ =\$5000 + (0}\text{.08}\times \$5000)\\ \text{ = \$5400}\\ \text{For 500 shares and margin at 25\%, now the price of each share will be calculated as:}\\ \text{ Margin=}\frac{\text{Equity in account}}{Value\text{ of stock}}\\ \text{ 0}\text{.25 = }\frac{500\times P-\$5400}{500\times P}\\ \text{ P = \$14}\text{.40}\end{array}$

Conclusion

Thus the price of share will be $14.40 when the margin is 25% after one year.