Financial management spring 2014 assignment 4 the returns on a stock

Financial Management Spring 2014 Assignment 4 The returns on a stock for the last 5 years have been 25%, 6%, -11%, 2%, and -20%.

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Financial Management

 

Spring 2014

 

Assignment 4

 

90 points

 

1. The returns on a stock for the last 5 years have been 25%, 6%, -11%, 2%, and -20%.

 

a. Assuming that you purchased the stock for $31.50 five years ago and that all

 

returns have come in the form of either capital gains or losses (i.e., there have

 

been no dividends), what is the price of the stock today? (3 points)

 

b. Compute the average (arithmetic) return. (3 points)

 

c. Compute the geometric average return. (3 points)

 

d. What is the yearly return standard deviation? (3 points)

 

2. The following describes the probability distribution of future returns for 2 stocks:

 

State of the Economy

 

High growth

 

Low growth

 

No growth

 

Recession

 

 

 

Probability

 

.15

 

.20

 

.40

 

.25

 

 

 

Stock A return

 

30%

 

13%

 

6%

 

-5%

 

 

 

Stock B return

 

10%

 

8%

 

4%

 

-2%

 

 

 

The beta of stock A is 1.3 and the beta of stock B is 0.4.

 

a. Compute the expected return and standard deviation for both stocks. (3 points)

 

b. Compute the expected return, standard deviation, and beta of a portfolio

 

consisting of 50% in stock A and 50% in stock B. (6 points)

 

c. Which risk measure is more appropriate for determining a stock’s contribution to

 

the riskiness of a well-diversified portfolio, its return standard deviation, or its

 

beta? Clearly explain your reasoning (3 points)

 

To answer Question 3, you need to download the spreadsheet with stock price data from

 

the “assignment” section of lesson 7 in Angel. This file contains monthly stock prices,

 

dividends, and stock split information for Advanced Micro Devices, Green Mountain

 

Coffee Roasters, and UnitedHealth Group for the period spanning from December 2008

 

through December 2013. For each company, there are 61 monthly closing prices, from

 

which you will be able to calculate 60 months of stock returns.

 

3. Calculate the monthly returns for each of the stocks:

 

a. Calculate the arithmetic average monthly return for each stock. (3 points)

 

b. Calculate the geometric average monthly return for each stock. (3 points)

 

c. Calculate the monthly return standard deviation for each stock. (3 points)

 

d. Calculate the total percentage return (this would be what is referred to in the text

 

as the holding period return) for each stock based on purchasing a share at the end

 

of December 2008 and holding it through the end of December 2013. In your

 

calculations assume that any dividends are reinvested immediately in the stock

 

 

 

C540 – Spring 2014

 

 

 

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rather than being stuffed under a mattress where they would earn no further

 

returns. (3 points)

 

e. If you constructed a portfolio at the end of December 2008 consisting of 50 shares

 

of each of the stocks and held this portfolio through the end of December 2013

 

(once again, reinvesting all dividends), what would be the total percentage return

 

(holding period return) on the portfolio? What would the portfolio’s geometric

 

average monthly return be? (3 points)

 

 

 

To answer questions 4 through 6, you will to access the tab labeled “stock return data

 

for Q4-6” in the previously downloaded spreadsheet. The tab contains monthly stock

 

returns for Polaris Industries (PII), Emmis Communications (EMMS), and Johnson &

 

Johnson (JNJ), for the months from January 2009 through December 2013, along with

 

monthly stock returns for the S&P Composite Index over the same period.

 

4. a. Using the returns on the S&P 500 Composite Index as the proxy for the overall

 

stock market return, estimate a beta for each stock listed above in Excel. Report the

 

betas and comment on your level of confidence in each of the beta estimates given the

 

significance level (p-values) of the t-statistics for the beta estimates in the regression

 

models. Clearly demonstrate your understanding of beta calculations and statistical

 

estimates. (15 points)

 

b. What beta estimates do you find at Yahoo Finance (the links below)? Why might

 

the beta estimates from Yahoo Finance differ from the beta estimates that you

 

calculated? (3 points)

 

http://finance.yahoo.com/q/ks?s=PII

 

http://finance.yahoo.com/q/ks?s=EMMS

 

http://finance.yahoo.com/q/ks?s=JNJ

 

5. Which of the three stocks (PII, EMMS, and JNJ) has the most total risk if held in

 

isolation? Clearly convey what measure you used to identify the amount of risk of a

 

stock held in isolation. (3 points)

 

6. Which of the three stocks (PII, EMMS, and JNJ) has the most systematic risk?

 

Clearly convey what measure you used to identify the amount of systematic risk. (3

 

points)

 

 

 

C540 – Spring 2014

 

 

 

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7. a. Based on the following beta estimates, what would be the portfolio beta for a

 

portfolio invested as follows? (3 points)

 

 

 

2nd National Bank

 

Chesapeake Energy

 

Pentair

 

Pegasus

 

Sodastream

 

 

 

Portfolio

 

Weights

 

20%

 

15%

 

30%

 

15%

 

20%

 

100%

 

 

 

Beta

 

0.5

 

0.6

 

0.9

 

0.5

 

1.6

 

 

 

b. Based on the Beta estimates in part a, a Treasury bond rate of 2.97% and an

 

expected market risk premium of 7%, what would be the expected return on the

 

portfolio described in part a (assuming the stocks are fairly priced based on the

 

CAPM)? (3 points)

 

8. Vaughn Manufacturing (VM) has 720 bonds outstanding with a 5.75 percent coupon

 

rate (semi-annual coupon payments) and 15 years left to maturity. The bonds sell for

 

$927.50. VM’s common stock has a beta of 1.24. The 10-year Treasury-Bond rate is

 

currently 2.75 percent, and historically, the market has earned 7% more per year than

 

the 10-year Treasury rate. The firm has 147,000 shares of common stock outstanding

 

at a market price of $21.50 a share (book value of $9 per share). There are 40,000

 

shares of preferred stock outstanding at a market price of $30 a share (book value of

 

$40 per share). The preferred stock pays a $2.50 annual dividend. The company’s

 

marginal tax rate is 38 percent.

 

a.

 

b.

 

c.

 

d.

 

 

 

What is the after-tax cost of debt? (3 points)

 

What is the cost of preferred stock? (3 points)

 

What is the cost of common stock? (3 points)

 

What is the weighted average cost of capital for Vaughn Manufacturing? (3

 

points)

 

 

 

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9. SL Jones Corporation, an all equity-financed company, has traditionally employed a

 

firm wide discount rate for capital budgeting purposes. However, its two divisions –

 

publishing and entertainment, have different degrees of risk given by ßP = 1.0, ßE =

 

2.0, and the beta for the overall firm is 1.3. Use 6% as the risk-free rate and 12% as

 

the expected return on the market. The firm is considering the following capital

 

expenditures:

 

 

 

Publishing

 

 

 

Entertainment

 

 

 

Proposed Project

 

P1

 

P2

 

P3

 

 

 

Initial Investment

 

$1M

 

$3M

 

$2M

 

 

 

IRR

 

.130

 

.121

 

.090

 

 

 

E1

 

E2

 

E3

 

 

 

$4M

 

$6M

 

$5M

 

 

 

.160

 

.170

 

.140

 

 

 

a. Which projects would the firm accept if it uses the opportunity cost of capital for

 

the entire company? (3 points)

 

b. Which projects would it accept if it estimates cost of capital separately for each

 

division? (3 points)

 

c. If SL Jones Corporation only uses the cost of capital for the entire firm, what will

 

happen to the riskiness of the firm, compared to using the appropriate divisional

 

cost of capital? (3 points)

 

 

 

C540 – Spring 2014

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