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QUESTION-1
Assume that you recently graduated and landed a job as a financial planner with Cicero Services,
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
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%.
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
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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