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QUESTION-1

Assume that you recently graduated and landed a job as a financial planner with Cicero Services,

an investment advisory company. Your first client recently inherited some assets and has asked

you to evaluate them. The client owns a bond portfolio with $1 million invested in zero coupon

Treasury bonds that mature in 10 years.47 The client also has $2 million invested in the stock of

Blandy, Inc., a company that produces meat-and-potatoes frozen dinners. Blandyâ??s slogan is â??Solid

food for shaky times.â? Unfortunately, Congress and the president are engaged in an acrimonious

dispute over the budget and the debt ceiling. The outcome of the dispute, which will not be resolved

until the end of the year, will have a big impact on interest rates 1 year from now. Your first task is

to determine the risk of the clientâ??s bond portfolio. After consulting with the economists at your

firm, you have specified five possible scenarios for the resolution of the dispute at the end of the

year. For each scenario, you have estimated the probability of the scenario occurring and the

impact on interest rates and bond prices if the scenario occurs. Given this information, you have

calculated the rate of return on 10-year zero coupon Treasury bonds for each scenario. The

probabilities and returns are shown here:

You have also gathered historical returns for the past 10 years for Blandy, Gourmange Corporation

(a producer of gourmet specialty foods), and the stock market.

The risk-free rate is 4% and the market risk premium is 5%.

a. What are investment returns? What is the return on an investment that costs $1,000 and is

sold after 1 year for $1,060?

b. Graph the probability distribution for the bond returns based on the 5 scenarios. What might

the graph of the probability distribution look like if there were an infinite number of

scenarios (i.e., if it were a continuous distribution and not a discrete distribution)?

c. Use the scenario data to calculate the expected rate of return for the 10-year zero coupon

Treasury bonds during the next year.

d. What is stand-alone risk? Use the scenario data to calculate the standard deviation of the

bondâ??s return for the next year.

e. Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave

it as it is. Now your client has asked you to use historical returns to estimate the standard

deviation of Blandyâ??s stock returns. (Note: Many analysts use 4â??5 years of monthly returns

to estimate risk and many use 52 weeks of weekly returns; some even use a year or less of

daily returns. For the sake of simplicity, use Blandyâ??s 10 annual returns.)

f. Your client is shocked at how much risk Blandy stock has and would like to reduce the level

of risk. You suggest that the client sell 25% of the Blandy stock and create a portfolio with

75% Blandy stock and 25% in the high-risk Gourmange stock. How do you suppose the

client will react to replacing some of the Blandy stock with high-risk stock? Show the client

what the proposed portfolio return would have been in each year of the sample. Then

calculate the average return and standard deviation using the portfolioâ??s annual returns.

g.

h.

i.

j.

k.

l.

m.

n.

How does the risk of this two-stock portfolio compare with the risk of the individual stocks

if they were held in isolation?

Explain correlation to your client. Calculate the estimated correlation between Blandy and

Gourmange. Does this explain why the portfolio standard deviation was less than Blandyâ??s

standard deviation?

Suppose an investor starts with a portfolio consisting of one randomly selected stock. As

more and more randomly selected stocks are added to the portfolio, what happens to the

portfolioâ??s risk?

(1) Should portfolio effects influence how investors think about the risk of individual

stocks? (2) If you decided to hold a one-stock portfolio and consequently were exposed to

more risk than diversified investors, could you expect to be compensated for all of your risk;

that is, could you earn a risk premium on that part of your risk that you could have

eliminated by diversifying?

According to the Capital Asset Pricing Model, what measures the amount of risk that an

individual stock contributes to a well-diversified portfolio? Define this measurement.

What is the Security Market Line (SML)? How is beta related to a stockâ??s required rate of

return?

Calculate the correlation coefficient between Blandy and the market. Use this and the

previously calculated (or given) standard deviations of Blandy and the market to estimate

Blandyâ??s beta. Does Blandy contribute more or less risk to a well-diversified portfolio than

does the average stock? Use the SML to estimate Blandyâ??s required return.

Show how to estimate beta using regression analysis.

(1) Suppose the risk-free rate goes up to 7%. What effect would higher interest rates have

on the SML and on the returns required on high-risk and low-risk securities?

(2) Suppose instead that investorsâ?? risk aversion increased enough to cause the market risk

premium to increase to 8%. (Assume the risk-free rate remains constant.) What effect

would this have on the SML and on returns of high- and low- risk securities?

o. Your client decides to invest $1.4 million in Blandy stock and $0.6 million in Gourmange stock.

What are the weights for this portfolio? What is the portfolioâ??s beta? What is the required return for

this portfolio?

p. Jordan Jones (JJ) and Casey Carter (CC) are portfolio managers at your firm. Each manages a

well-diversified portfolio. Your boss has asked for your opinion regarding their performance in the

past year. JJâ??s portfolio has a beta of 0.6 and had a return of 8.5%; CCâ??s portfolio has a beta of 1.4

and had a return of 9.5%. Which manager had better performance? Why?

q. What does market equilibrium mean? If equilibrium does not exist, how will it be established?

r. What is the Efficient Markets Hypothesis (EMH) and what are its three forms? What evidence

supports the EMH? What evidence casts doubt on the EMH?

QUESTION-2

Your employer, a mid-sized human resources management company, is considering expan- sion

into related fields, including the acquisition of Temp Force Company, an employment agency that

supplies word processor operators and computer programmers to businesses with temporary

heavy workloads. Your employer is also considering the purchase of Bigger- staff & McDonald

(B&M), a privately held company owned by two friends, each with 5 million shares of stock. B&M

currently has free cash flow of $24 million, which is expected to grow at a constant rate of 5%.

B&Mâ??s financial statements report short-term investments of $100 million, debt of $200 million,

and preferred stock of $50 million. B&Mâ??s weighted average cost of capital (WACC) is 11%.

Answer the following questions.

a. Describe briefly the legal rights and privileges of common stockholders.

b. What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash

flow valuation model?

c. Use a pie chart to illustrate the sources that comprise a hypothetical companyâ??s total value.

Using another pie chart, show the claims on a companyâ??s value. How is equity a residual claim?

d. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of gL forever. If gL

WACC, what is a formula for the present value of expected free cash flows when discounted at the

WACC? If the most recent free cash flow is expected to grow at a constant rate of gL forever (and

gL WACC), what is a formula for the present value of expected free cash flows when discounted at

the WACC?

e. Use B&Mâ??s data and the free cash flow valuation model to answer the following questions. (1)

What is its estimated value of operations? (2) What is its estimated total corporate value? (This is

the entity value.) (3) What is its estimated intrinsic value of equity? (4) What is its estimated

intrinsic stock price per share?

f. You have just learned that B&M has undertaken a major expansion that will change its expected

free cash flows to â??$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3

years, free cash flow will grow at a rate of 5%. No new debt or preferred stock was added; the

investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and

that there are still 10 million shares of stock outstanding.

(1) What is the companyâ??s horizon value (i.e., its value of operations at Year 3)? What is its current

value of operations (i.e., at Time 0)?

(2) What is its estimated intrinsic value of equity on a price-per-share basis

g. If B&M undertakes the expansion, what percent of B&Mâ??s value of operations at Year 0 is due to

cash flows from Years 4 and beyond? (Hint: Use the horizon value at t 3 to help answer this

question.)

h. Based on your answer to the previous question, what are two reasons why managers often

emphasize short-term earnings?

i. YouremployeralsoisconsideringtheacquisitionofHatfieldMedicalSupplies.Youhave gathered the

following data regarding Hatfield, with all dollars reported in millions:

(1) most recent sales of $2,000;

(2) most recent total net operating capital, OpCap $1,120;

(3) most recent operating profitability ratio,OP NOPAT Sales 45%;and

(4) most recent capital requirement ratio, CR OpCap Sales 56%. You estimate that the growth rate in

sales from Year 0 to Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will

be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate

beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not

change. Use this information to forecast Hatfieldâ??s sales, net operating profit after taxes (NOPAT),

OpCap, free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also estimate

the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital

(WACC) is 9%. How does the ROIC in Year 4 compare with the WACC?

j. What is the horizon value at Year 4? What is the total net operating capital at Year 0? How does

the value of operations compare with the current total net operating capital?

k. What are value drivers? What happens to the ROIC and current value of operations if expected

growth increases by 1 percentage point relative to the original growth rates (including the longterm growth rate)? What can explain this? (Hint: Use Scenario Manager.)

l. Assume growth rates are at their original levels. What happens to the ROIC and current value of

operations if the operating profitability ratio increases to 5.5%? Now assume growth rates and

operating profitability ratios are at their original levels. What happens to the ROIC and current value

of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their

original levels. What is the impact of simultaneous improvements in operating profitability and

capital requirements? What is the impact of simultaneous improvements in the growth rates,

operating profitability, and capital requirements? (Hint: Use Scenario Manager.)

m. What insight does the free cash flow valuation model provide regarding possible reasons for

market volatility? (Hint: Look at the value of operations for the combinations of ROIC and gL in the

previous questions

n. (1) Write out a formula that can be used to value any dividend-paying stock, regardless of its

dividend pattern.

(2) What is a constant growth stock? How are constant growth stocks valued?

(3) What happens if a company has a constant gL that exceeds its rs? Will many stocks have

expected growth greater than the required rate of return in the short run (i.e., for the next few

years)? In the long run (i.e., forever)?

o. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on Tbonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the

firmâ??s stock?

p. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid

yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate.

(1) What is the firmâ??s current estimated intrinsic stock price?

(2) What is the stockâ??s expected value 1 year from now?

(3) What are the expected dividend yield, the expected capital gains yield, and the expected total

return during the first year?

q. Now assume that the stock is currently selling at $30.29. What is its expected rate of return?

r. Now assume that Temp Forceâ??s dividend is expected to experience nonconstant growth of 30%

from Year 0 to Year 1, 25% from Year 1 to Year 2, and 15% from Year 2 to Year 3. After Year 3,

dividends will grow at a constant rate of 6%. What is the stockâ??s intrinsic value under these

conditions? What are the expected dividend yield and capital gains yield during the first year? What

are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year

4)?

s. What is the market multiple method of valuation? What are its strengths and weaknesses?

t. What are the advantages of the free cash flow valuation model relative to the dividend growth

model?

u. What is preferred stock? Suppose a share of preferred stock pays a dividend of $2.10 and

investors require a return of 7%. What is the estimated value of the preferred stock?

I HAVE ATTACHED EXCEL TOOL KITS TO ASSIST WITH THESE TWO QUESTION

A

1

2

Tool Kit

C

D

E

Chapter 6

F

10/27/2015

Risk and Return

3

4

5

6

7

8

9

10

11

B

6-1 Investment Returns and Risk

Amount invested

Amount received in one year

Dollar return (Profit)

Rate of return = Profit/Investment =

$1,000

$1,100

$100

10%

12

13

6-2 Measuring Risk for Discrete Distributions

14

15

16

17

18

19

20

21

The relationship between risk and return is a fundamental axiom in finance. Generally speaking, it

is totally logical to assume that investors are only willing to assume additional risk if they are

adequately compensated with additional return. This idea is rather fundamental, but the difficulty

in finance arises from interpreting the exact nature of this relationship (accepting that risk aversion

differs from investor to investor). Risk and return interact to determine security prices, hence it is

of paramount importance in finance.

22 A listing of possible outcomes and their probabilities is called a probability distribution, as shown

23 below.

24

25

Rate of

Scenario

Probability of

Return in

26

Scenario

Scenario

27 Best Case

0.30

37%

28 Most Likely

0.40

11%

0.30

â??15%

29 Worst Case

1.00

30

31

32

33 Figure 6-1

34 Discrete Probability Distribution for Three Scenarios

35

Probability of

36

Scenario

37

Most

0.5

Likely

38

39

0.4

Worst

40

0.4

Case

41

0.3

42

43

0.3

44

0.2

45

0.2

46

0.1

47

48

0.1

0.0

Best

Case

49

50

51

52

53

54

55

0.1 A

0.0

B

â??15%

C

D

E

F

11%

37%

Outcomes: Market Returns for 3 Scenarios

56 Given the probabilities and the outcomes for possible returns, it is possible to calculate the expected

57 return and standard deviation.

A

B

C

D

E

F

58

59 Figure 6-2

60 Calculating Expected Returns and Standard Deviations: Discrete Probabilities

Standard Deviation

61 INPUTS:

Expected Return

Product of

Squared

Probability of Market Rate Probability and Deviation from

Deviation

Scenario

of Return

Return

Expected Return

(1)

(2)

(3) = (1) Ã? (2)

(4) = (2) â?? D66

(5) = (4)2

62 Scenario

63 Best Case

64 Most Likely

65 Worst Case

66

0.30

0.40

0.30

37%

11%

â??15%

1.00

Exp. ret. =

11.1%

4.4%

â??4.5%

Sum = 11.0%

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Average =

Std. dev. =

0.0002

0.0011

0.0054

0.0205

0.0575

0.1201

0.1870

0.2167

0.1870

0.1201

0.0575

0.0205

0.0054

0.0011

0.0002

1.0000

0.0198

0.0307

0.0452

0.0625

0.0806

0.0969

0.1082

0.1123

0.1082

0.0969

0.0806

0.0625

0.0452

0.0307

0.0198

1.0000

11.0%

20.2%

11.0%

36.2%

Rate of Return in

Scenario

-66%

-55%

-44%

-33%

-22%

-11%

0%

11%

22%

33%

44%

55%

66%

77%

88%

Figure 6-3

Discrete Probability Distributions for 15 Scenarios

Panel A: Market Return for 15 Scenarios: Standard Devation = 20.2%

Probability

0.0676

0.0000

0.0676

Sum = Variance =

Std. Dev. = Square

root of variance =

67

68 Note: Calculations are not rounded in intermediate steps.

69

70

71 6-3 Risk in a Continuous Distribution

72

73 It is possible to add more scenarios.

74

Panel B:

Panel A:

Probability

Probability of

of Stock

Scenario

Market Return

Return

Scenario

Scenario

75

0.2600

0.0000

-0.2600

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

A

Probability

0.25

B

C

D

E

F

0.20

0.15

0.10

0.05

0.00

-66% -55% -44% -33% -22% -11%

0%

11%

22%

33%

44%

55%

66%

77%

88%

Outcomes: Market Returns

Panel B: Single Company’s Stock Return for 15 Scenarios: Standard Devation = 36.2%

Probability

0.25

0.20

0.15

0.10

0.05

0.00

â??66% â??55% â??44% â??33% â??22% â??11%

0%

11%

22%

33%

44%

55%

66%

77%

88%

Outcomes: Stock Returns

At some point, it becomes impractical to keep adding scenarios. Many analysts use the normal

distribution to estimate stock returns.

Here is an example of a normal distribution with a similar mean and standard deviation as the

discrete distribution shown above.

Normal Distribution

Probability

0.2500

A

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

Probability B

0.2500

C

D

E

F

0.2000

0.1500

0.1000

0.0500

0.0000

-100%

-50%

0%

50%

100%

Return

173 6-4 Using Historical Data to Estimate Risk

174

175 Investors often use historical data to estimate risk. This is quite easy in Excel by using the AVERAGE

176 and STDEV functions.

177

178

A

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

B

C

D

Standard Deviation Based On a Sample of Historical Data

Inputs:

Year

2014

2015

2016

Calculations:

=AVERAGE(E183:E185)

=STDEV(E183:E185)

E

F

Realized

return

15.0%

â??5.0%

20.0%

10.0%

13.2%

Measuring the Standard Deviation of MicroDrive

The monthly stock returns for MicroDrive and one of its competitors, SnailDrive, during the past 48

months are shown in the figure below. The actual data are below the figure.

Figure 6-5

Historical Monthly Stock Returns for MicroDrive and SnailDrive

Monthly Rate of

Return

50%

MicroDrive

40%

30%

SnailDrive

20%

10%

0%

-10%

-20%

-30%

0

6

12

Average Return (annualized)

225 Standard Deviation (annualized)

226

227

228

229

230

18

24

30

Month of Return

MicroDrive

14.6%

49.2%

36

42

48

SnailDrive

8.6%

25.8%

Portfolio weights

SnailDrive:

MicroDrive:

A

B

C

231

Period

232

1

233

2

234

3

235

4

236

5

237

6

238

7

239

8

240

9

241

10

242

11

243

12

244

13

245

14

246

15

247

16

248

17

249

18

250

19

251

20

252

21

253

22

254

23

255

24

256

25

257

26

258

27

259

28

260

29

261

30

262

31

263

32

264

33

265

34

266

35

267

36

268

37

269

38

270

39

271

40

272

41

273

42

274

43

275

44

276

45

277

46

278

47

279

48

280 Full 48 Months

281

Average monthly return:

282

Standard deviation of monthly returns:

283

Average return (annual):

284

Standard deviation (annual):

D

Market

2.37%

12.68%

-1.13%

10.93%

-0.02%

-3.31%

12.68%

-3.96%

-4.90%

7.10%

2.94%

-6.52%

3.72%

4.74%

-8.21%

-5.15%

3.92%

1.08%

-2.48%

3.92%

3.13%

0.17%

5.17%

2.56%

-5.41%

-2.09%

1.08%

10.47%

-3.74%

2.94%

-9.50%

5.17%

-0.75%

-9.04%

-9.50%

4.74%

-0.38%

4.32%

-1.89%

-3.96%

6.58%

-1.32%

4.74%

-3.10%

7.95%

10.93%

-1.70%

-3.96%

Market

0.9%

5.8%

11.0%

20.0%

E

MicroDrive

1.66%

23.52%

-4.76%

38.58%

-3.46%

-5.37%

22.52%

-8.58%

-13.02%

0.17%

24.40%

-18.05%

6.18%

12.24%

-18.22%

7.15%

9.69%

12.21%

-6.74%

-16.00%

-11.96%

-19.00%

13.91%

17.84%

14.67%

-16.88%

3.28%

28.86%

2.33%

12.48%

-7.21%

-9.79%

0.60%

0.88%

-8.94%

2.49%

-11 …

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