Financial management spring 2014 assignment 4 the returns on a stock

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

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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

1

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

2

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)

C540 – Spring 2014

3

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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