The management of Ark Industries wants to analyze the performance of the company$$s stock in the stock market. They want to compare the stock performance with Apex Inc, a strong competitor in the industry, and the market index. The following data is available for managerial finance analysis.

Year

Ark Industries

Apex Incorporated

Market Index

Capital gain$/$loss

Dividend

Purchased

Price

Capital gain$/$loss

Dividend

Purchased

price

Rate of Return

$2020$

$$6\mathrm{.}79$

$$2\mathrm{.}23$

$$23\mathrm{.}53$

$$5\mathrm{.}80$

$$3\mathrm{.}52$

$$79\mathrm{.}32$

$51\mathrm{.}8\%$

$2019$

$-$$$5\mathrm{.}08$

$$2\mathrm{.}65$

$$28\mathrm{.}61$

$$5\mathrm{.}00$

$$3\mathrm{.}65$

$$74\mathrm{.}32$

$1\mathrm{.}30\%$

$2018$

$$13\mathrm{.}40$

$$2\mathrm{.}73$

$$15\mathrm{.}21$

$-$$$12\mathrm{.}80$

$$3\mathrm{.}45$

$$87\mathrm{.}12$

$11\mathrm{.}90\%$

$2017$

$$2\mathrm{.}58$

$$2\mathrm{.}57$

$$12\mathrm{.}63$

$-$$$8\mathrm{.}00$

$$3\mathrm{.}47$

$$95\mathrm{.}12$

$13\mathrm{.}90\%$

$2016$

$-$$$0\mathrm{.}58$

$$2\mathrm{.}23$

$$13\mathrm{.}21$

$$10\mathrm{.}88$

$$3\mathrm{.}55$

$$84\mathrm{.}25$

$15\mathrm{.}80\%$

$*$Capital gain $=$ difference between ending price and beginning price

A$)$ Use the data given to calculate the annual returns for Ark Industries, and Apex Inc during the $5-$year period.

Calculate the historical average returns for Ark Industries, Apex Inc., and the market index during the $5-$year period.

Calculate the standard deviation of the returns for Ark Industries.

An individual investor, James Bond needs an extra return of $6\mathrm{.}0\%$ before he will take on the stock market$$s risk to invest in Ark Industries. If the risk$-$free rate on long$-$term Treasury bonds is $5\mathrm{.}0\%.$ what would be the required return on the market?

James Bond wants to determine the required rate of return on two stocks $($stock A and stock B$)$ that he just added to his portfolio. The following information is available: Market rate of return $=11\mathrm{.}0\%$; Risk free rate $=5\mathrm{.}0\%$; Beta for stock A$=0\mathrm{.}77$; Beta for stock B $=0\mathrm{.}99.$ Use the Security Market Line $($SML$)$ equation to calculate the required rate of return for stock A and stock B$.$

B$)$ Richard Morgan, another individual investor wants to purchase four stocks for his portfolio. The expected return, portfolio weights, and the betas of the stocks are given below:

Stocks

Beta

Portfolio weight

Expected return

Goodman Industries

$0\mathrm{.}70$

$30\%$

$9\mathrm{.}20\%$

Renfro Inc.

$0\mathrm{.}79$

$20\%$

$9\mathrm{.}74\%$

Heath Inc.

$1\mathrm{.}10$

$30\%$

$11\mathrm{.}60\%$

Lincoln Inc.

$1\mathrm{.}44$

$20\%$

$13\mathrm{.}64\%$

Calculate the portfolio beta.

Calculate the portfolio$$s required returnGoodman Industries is expected to pay a $$4\mathrm{.}50$ per share dividend at the end of this year $($i$.$e$.,$ D$1=$ $$4\mathrm{.}50).$ The dividend is expected to grow at a constant rate of $5\%$ a year. The required rate of return on the stock is$,$ rs$,$ is $9\mathrm{.}2\%.$ What is the estimated value per share of Goodman stock?

C$)$ Renfro Inc. is expected to have free cash flow $($FCF$)$ of $$105$ million next year and an expected constant growth rate of $5\%$ thereafter. The weighted average cost of capital $($WACC$)$ for the company is $9\mathrm{.}0\%.$ Using the constant growth model, estimate the value of operations for Renfro Inc.

D$)$The most recent free cash flow $($FCF$)$ for Heath Inc. was $$200$ million, and the management expects the free cash flow to begin growing immediately at a $7\%$ constant rate. The cost of capital is $12\%.$ Using the constant growth model, determine the value of operations for Heath Inc.

E$)$ Heath Inc. balance sheet shows that it has $$10$ million short$-$term investments, $$15$ million in notes payable, $$60$ million in long$-$term bonds, and $$15$ million in preferred stock. Heath has $60$ million of shares outstanding. Calculate the following:

total intrinsic value for Heath Inc.

intrinsic value of equity for Heath Inc.

intrinsic stock price per share for Heath Inc.

F$)$ Distinguish between call option and put option.

G$)$ The current price of a stock is $$50.$ In $1$ year, the price will be either $$65$ or $$35.$ The annual risk$-$ free rate is $5\%.$ Find the price of a call option on the stock that has an exercise price of $$55$ and that expires in $1$ year. $($Hint: Use daily compounding.$)$