Chapter 12, Problem 6PA

Summary Introduction

(a)

To determine:

Change in value of stocks when S&P 500 increases by 15%.

Introduction:

S&P 500 is the market index of Standard and Poor’s 500, an American stock exchange, based on the current market capitalization of 500 large cap and mega cap stocks which are listed in the New York Stock Exchange (NYSE) or National Association of Securities Dealers Automated Quotations (NASDAQ).

Explanation of Solution

Given,

Change in S&P 500 index is 15 percent.

Beta of stock of S. Corp. is 0.70.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 0.70 for beta and 15 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{0}\text{.70}\times 15}{100}\\ =\frac{10.5}{100}\\ =0.105\end{array}$

Percentage change in stock price of S. Corp. is 0.105 percentages.

Given,

Change in S&P 500 index is 15 percent.

Beta of stock of H. Industries is 1.35

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 1.35 for beta and 15 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{1.35\times 15}{100}\\ =\frac{20.25}{100}\\ =0.2025\end{array}$

Percentage change in stock price of H. Industries is 0.2025 percentages.

Given,

Change in S&P 500 index is 15 percent.

Beta of stock of A Records is 2.05.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 2.05 for beta and 15 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{2.05\times 15}{100}\\ =\frac{30.75}{100}\\ =0.3075\end{array}$

Percentage change in stock price of A Records is 0.3075 percentages.

Given,

Change in S&P 500 index is 15 percent.

Beta of stock of E. Enterprises is 0.45.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 0.45 for beta and 15 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{0}\text{.45}\times 15}{100}\\ =\frac{6.75}{100}\\ =0.0675\end{array}$

Percentage change in stock price of E. Enterprises is 0.0675 percentages.

Conclusion

Thus, it shows that there will be 0.105, 0.2025, 0.3075, 0.0675 percentage change in stock price of S. Corp., H. Industries, A. Records, and E. Enterprises respectively.

Summary Introduction

(b)

To determine:

Change in value of stocks when S&P 500 decreases by 10%. and the stock that will outperform in this case.

Introduction:

Outperform is a situation where a stock is expected to perform better than the promised return over the other stocks listed in the market.

Explanation of Solution

Given,

Change in S&P 500 index is 10 percent.

Beta of stock of S Corp. is 0.70.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 0.70 for beta and 10 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{0}\text{.70}\times 10}{100}\\ =\frac{7}{100}\\ =0.07\end{array}$

Percentage change in stock price of S. Corp. is 0.07 percentages.

Given,

Change in S&P 500 index is 10 percent.

Beta of stock of H Industries is 1.35.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 1.35 for beta and 10 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{1.35\times 10}{100}\\ =\frac{13.5}{100}\\ =0.135\end{array}$

Percentage change in stock price of H. Industries is 0.135 percentages.

Given,

Change in S&P 500 index is 10 percent.

Beta of stock of A Records is 2.05.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 2.05 for beta and 10 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{2.05\times 10}{100}\\ =\frac{20.5}{100}\\ =0.205\end{array}$

Percentage change in stock price of A Records is 0.205 percentages.

Given,

Change in S&P 500 index is 10 percent.

Beta of stock of E Enterprises is 0.45.

Formula to calculate change in value of stock is,

$\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{Beta}\times \text{Change}\text{in}\text{market}}{100}$

Substitute 0.45 for beta and 10 for change in market in the above equation.

$\begin{array}{c}\text{Percentage}\text{change}\text{in}\text{stock}\text{price}=\frac{\text{0}\text{.45}\times 10}{100}\\ =\frac{4.5}{100}\\ =0.045\end{array}$

Percentage change in stock price of E. Enterprises is 0.045 percentages.

Conclusion

Thus, the stocks of S Corp. and E Enterprise will outperform others in case the market decreases by 10 percent.