Problem Set #3

The management of Ark Industries wants to analyze the performance of the companys 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. Please make sure to show all work.

Year	Ark Industries		Apex Incorporated	Market Index
Capital gain/loss	Dividend	Purchased Price	Capital gain/loss	Dividend	Purchased price	Rate of Return
2020	$6.79	$2.23	$23.53	$5.80	$3.52	$79.32	51.8%
2019	-$5.08	$2.65	$28.61	$5.00	$3.65	$74.32	1.30%
2018	$13.40	$2.73	$15.21	-$12.80	$3.45	$87.12	11.90%
2017	$2.58	$2.57	$12.63	-$8.00	$3.47	$95.12	13.90%
2016	-$0.58	$2.23	$13.21	$10.88	$3.55	$84.25	15.80%

*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.

1. Calculate the historical average returns for Ark Industries, Apex Inc., and the market index during the 5-year period.
2. Calculate the standard deviation of the returns for Ark Industries.
3. An individual investor, James Bond needs an extra return of 6.0% before he will take on the stock markets risk to invest in Ark Industries. If the risk-free rate on long-term Treasury bonds is 5.0%. what would be the required return on the market?
4. 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 = 11.0%; Risk free rate =5.0%; Beta for stock A= 0.77; Beta for stock B = 0.99. 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	0.70	30%	9.20%
Renfro Inc.	0.79	20%	9.74%
Heath Inc.	1.10	30%	11.60%
Lincoln Inc.	1.44	20%	13.64%

1. 1. Calculate the portfolio beta.
   2. Calculate the portfolios required returnGoodman Industries is expected to pay a $4.50 per share dividend at the end of this year (i.e., D1 = $4.50). 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 9.2%. 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 9.0%. 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:

1. 1. total intrinsic value for Heath Inc.
2. 1. intrinsic value of equity for Heath Inc.
3. 1. 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.)