Fundamentals of corporate finance brealey chapter 11 risk return and capital budgeting

Solutions to Chapter 11
Risk, Return, and Capital Budgeting
1.

a.

False. Investors require higher expected rates of return on investments with
high market risk, not high total risk. Variability of returns is a measure of
total risk. Stocks with high total risk (highly variable returns) can have low
market risk. That is, their returns have low correlation with the market.

b.

False. If beta = 0, the asset’s expected return should equal the risk-free rate,
not zero.

c.

False. The portfolio is one-third invested in Treasury bills and two-thirds in
the market. Its beta will be
1/3  0 + 2/3  1.0 = 2/3.

d.

True. High exposure to macroeconomic changes cannot be diversified away
in a portfolio. Thus stocks with higher sensitivity to macroeconomic risks
have higher market risk and higher expected returns when compared to
stocks with lower sensitivity to macroeconomic changes.

e.

True. For similar reasons as in (d). Sensitivity to fluctuations in the stock
market cannot be diversified away. Such stocks have higher systematic risk
and higher expected rates of return.

2.

The risks of deaths of individual policyholders are largely independent, and
therefore are diversifiable. Therefore, the insurance company is satisfied to charge
a premium that reflects actuarial probabilities of death, without an additional risk
premium. In contrast, flood damage is not independent across policyholders. If my
coastal home floods in a storm, there is a greater chance that my neighbor's will
too. Because flood risk is not diversifiable, the insurance company may not be
satisfied to charge a premium that reflects only the expected value of payouts.

3.

The actual returns on the Snake Oil fund exhibit considerable variation around the
regression line. This indicates that the fund is subject to diversifiable risk: it is not
well diversified. The variation in the fund's returns is influenced by more than just
market-wide events.

4.

Investors would buy shares of firms with high degrees of diversifiable risk, and
earn high risk premiums. But by holding these shares in diversified portfolios, they
would not necessarily bear a high degree of portfolio risk. This would represent a
profit opportunity, however. As investors seek these shares, we would expect their
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prices to rise, and the expected rate of return to investors buying at these higher
prices to fall. This process would continue until the reward for bearing
diversifiable risk dissipated.
5.

a.

Required return = rf + (rm – rf) = 4% + .6 (11% – 4%) = 8.2%
With an IRR of 14%, the project is attractive.

b.

If beta = 1.6, required return increases to:
4% + 1.6 (11% – 4%) = 15.2%
which is greater than the project IRR. You should now reject the project.

6.

c.

Given its IRR, the project is attractive when its risk and therefore its required
return are low. At a higher risk level, the IRR is no longer higher than the
expected return on comparable risk assets available elsewhere in the capital
market.

a.

The expected cash flows from the firm are in the form of a perpetuity. The

discount rate is:
rf + (rm – rf) = 5% + .4×7% = 7.8%.
Therefore, the value of the firm would be:
P0 = = = $128,205

b.

If the true beta is actually .6, the discount rate should be:
rf + (rm – rf) = 5% + .6×7% = 9.2%
Therefore, the value of the firm is:
P0 = = = $108,696
By underestimating beta, you would overvalue the firm by
$128,205 – 108,696 =$19,509

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Copyright © 2006 McGraw-Hill Ryerson Limited


7.

Required return = rf + (rm – rf) = 4% + 1.25(11% – 4%) = 12.75%
Expected return = 11%
The stock’s expected return is less than the required return given its risk. Thus the
stock is overpriced. Why? Given the stock’s future cash flows and its current
price, investors can expect to earn only 11%. Comparable risk investments earn
12.75%. At the current price, investors are better off investing in these other
investments. This lack of demand will cause the stock price to fall until its
expected return increases to the required return of 12.75%.

8.

Required return = riskfree rate + beta × [expected return on market – riskfree rate]
= rf + (rm – rf)
For the stock, we know that 12% = rf + .8 ( 14% - rf )
Using the CAPM, solve for the riskfree rate of interest:
rf = (Required return -  rm) / ( 1 - ) = (12% - .8 × 14%) / (1 - .8) = 4%
We assume that the riskfree rate is not changed. Therefore, if the market return
turns out to be 10%, we expect that the stock’s return will be 4% + .8(10% - 4%) =
8.8%.

9.

a.

A diversified investor will find the highest-beta stock most risky. This is
Microsoft, which has a beta of 1.53.

b.

Ford has the highest total volatility; the standard deviation of its returns is
42.7%.

c.

 = (1.34 + .97 + 1.53)/3 = 1.28

d.

The portfolio will have the same beta as Microsoft, 1.53. The total risk of the
portfolio will be 1.53 times the total risk of the market portfolio because the

effect of firm-specific risk will be diversified away. The standard deviation
of the portfolio is therefore 1.53  20% = 30.6%.

e.

Using the CAPM, we compute the expected rate of return on each stock from
the equation r = rf +   (rm – rf). In this case, rf = 4% and (rm – rf) = 7%.
Ford:
r = 4% + 1.34(7%) = 13.38%
General Electric: r = 4% + .97(7%) = 10.79%
Microsoft:
r = 4% + 1.53(7%) = 14.71%
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10.

The following table shows the average return on Tumblehome for various values
of the market return. It is clear from the table that, when the market return
increases by 1%, Tumblehome’s return increases on average by 1.5%. Therefore, 
= 1.5. If you prepare a plot of the return on Tumblehome as a function of the
market return, you will find that the slope of the line through the points is 1.5.
Market return(%)
2
1
0
1
2

Average return on Tumblehome(%)
3.0
1.5
0.0
1.5
3.0

Note: If your calculator supports statistics then you can estimate this. Enter points
as X,Y values. In stats linear mode you see that b = 1.5 which is the slope of the
line. Using the SLOPE function in Excel will also calculate the slope of 1.5.
11.

a.

Beta is the responsiveness of each stock's return to changes in the market
return. Then:
A = = = = 1.2
D = = = = .75
D is considered to be a more defensive stock than A because its return is less
sensitive to the return of the overall market. In a recession, D will usually
outperform both stock A and the market portfolio.

b.

We take an average of returns in each scenario to obtain the expected return.
rm = (32% – 8%)/2 = 12%
rA = (38%– 10%)/2 = 14%
rD = (24% – 6%)/2 = 9%

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c.

According to the CAPM, the expected returns that investors will demand of
each stock, given the stock betas and given the expected return on the
market, are:
r = rf + (rm – rf)
rA = 4% + 1.2(12% – 4%) = 13.6%
rD = 4% + .75(12% – 4%) = 10.0%

d.

12.

The return you actually expect for stock A, 14%, is above the fair return,
13.6%. The return you expect for stock D, 9%, is below the fair return, 10%.
Therefore stock A is the better buy.

Figure follows below.
Cost of capital = risk-free rate + beta × market risk premium
Since the risk-free rate is 4% and the market risk premium is 7%, we can write the
cost of capital as:
Cost of capital = 4% + beta × 7%
Cost of capital (from CAPM)
= 10% + beta × 8%
4% + .75  7% = 9.25%
4% + 1.75  7% = 16.25%

Beta
.75
1.75

r
SML

11%

7% = market risk
premium

4%
beta
0

1.0

The cost of capital of each project is calculated using the above CAPM formula.
Thus, for Project P, its cost of capital is: 4% + 1.0 × 7% = 11%.
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If the cost of capital is greater than IRR, then the NPV is negative. If the cost of
capital equals the IRR, then the NPV is zero. Otherwise, if the cost of capital is
less than the IRR, the NPV is positive.
Project
P

Q
R
S
T
13.

Beta
1.0
0.0
2.0
0.4
1.6

Cost of capital
11.0%
4.0
18.0
6.8
15.2

IRR
11%
6
17
7
16

NPV
0
+


+
+

The appropriate discount rate for the project is:
r = rf + (rm – rf) = 4% + 1.4(11% – 4%) = 13.8%
Therefore:
NPV = –100 + 15  annuity factor(13.8%, 10 years) = –100 + 78.8563 = -$21.14
You should reject the project.

14.

We need to find the discount rate for which:
15  annuity factor(r, 10 years) = 100.
Solving this equation on the calculator, we find that the project IRR is 8.14%. The
IRR is less than the opportunity cost of capital, 13.8%. Therefore you should
reject the project, just as you found from the NPV rule.

15.

From the CAPM, the appropriate discount rate is:
r = rf + (rm – rf) = 4% +.75(7%) = 9.25%
r = .0925 = =
P1 = $52.625

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Copyright © 2006 McGraw-Hill Ryerson Limited


16.

If investors believe the year-end stock price will be $54, then the expected return
on the stock is:
= .12 = 12%,
which is greater than the opportunity cost of capital. Alternatively, the “fair” price
of the stock (that is, the present value of the investor's expected cash flows) is
(2 + 54)/1.0925 = $51.26, which is greater than the current price. Investors will
want to buy the stock, in the process bidding up its price until it reaches $51.26.
At that point, the expected return is a “fair” 9.25%:
= .0925 = 9.25%.

17.

a.

The expected return of the portfolio is the weighted average of the returns on
the TSX and T-bills. Similarly, the beta of the portfolio is a weighted average
of the beta of the TSX (which is 1.0) and the beta of T-bills (which is zero).
(i)
(ii)
(iii)
(iv)
(v)

18.

E(r) = 0  13% + 1.0  5% = 5%
E(r) = .25  13% + .75  5% = 7%
E(r) = .50  13% + .50  5% = 9%
E(r) = .75  13% + .25  5% = 11%

E(r) = 1.00  13% + 0  5% = 13%

= 01 + 10 = 0
 = .25  1 + .75  0 = .25
 = .50  1 + .50  0 = .50
 = .75  1 + .25  0 = .75
 = 1.0  1 + 0  0 = 1.0

b.

For every increase of .25 in the  of the portfolio, the expected return
increases by 2%. The slope of the relationship (additional return per unit of
additional risk) is therefore 2%/.25 = 8%.

c.

The slope of the return per unit of risk relationship is the market risk
premium:
rM – rf = 13% – 5% = 8%, which is exactly what the SML predicts. The SML
says that the risk premium equals beta times the market risk premium.

a.

Call the weight in the TSX w and the weight in T-bills (1 – w). Then w must
satisfy the equation:
w  10% + (1 – w)  5% = 8%
which implies that w = .6. The portfolio would be 60% in the TSX and 40%
in T-bills. The beta of the portfolio would be the weighted average of the
betas of the TSX and T-Bills. Since T-Bills are risk-free, their beta is zero.
The beta of the portfolio is: .6×1 + .4×0 = .6

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Copyright © 2006 McGraw-Hill Ryerson Limited


b.

To form a portfolio with a beta of .4, use a weight of .40 in the TSX and a
weight of .60 in T-bills. Then, the portfolio beta would be:
 = .40  1 + .60  0 = .40
The expected return on this portfolio is .4 × 10% + .6 × 5% = 7%

c.

Both portfolios have the same ratio of risk premium to beta:
= = 5%.
Notice that the ratio of risk premium to risk (i.e., beta) equals the market risk
premium (5%) for both stocks.

19.

If the systematic risk were comparable to that of the market, the discount rate
would be 12.0%. The property would be worth $50,000/.120 = $416,667.

20.

The CAPM states that r = rf + (rm – rf). If  < 0, then r < rf. Investors would
invest in a security with an expected return below the risk-free rate because of the
hedging value such a security provides for the rest of the portfolio. Investors get
their “reward” in terms of risk reduction rather than in the form of high expected

return.

21.

The historical risk premium on the market portfolio has been about 7%. Therefore,
using this value and the assumed risk-free rate of 3%, we can use the CAPM to
derive the cost of capital for these firms as 3% +   7%.
Beta
CHC Helicopter
Open Text
Loblaw
Companies
Tim Hortons

Return
1.34
12.38%
1.52
13.64%
0.71
0.9

7.97%
9.30%

22.
CHC Helicopter : (TSX: FLY-A.TO) CHC is a world leader in search and rescue
(SAR), helicopter training, and repair and overhaul (R&O), operating the world's only
facility for the repair and overhaul of Super Pumas – the No. 1 aircraft for the offshore
industry – in Stavanger, Norway. Approximately 69 per cent of CHC's total revenue

involves providing helicopter support to the oil and gas industry, primarily providing
service to offshore platforms operated by the world's major oil and gas companies . The
stock beta is 1.34, indicating that returns on CHC’s stock are quite sensitive to
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changes in the market. In a booming economy, the demand for helicopter services in
the oil and gas industry will be quite high but in a recession, the demand will be low.
It is not surprise that the stock beta is well above 1.
Open Text: (Nasdaq: OTEX) (TSX: OTC) is the market leader in providing
Collaboration, Enterprise Content Management software solutions. The stock beta is
1.52, indicating an even higher sensitivity to variations in the market than CHC
Helicopters. Like CHC, the customers of Open Text are other businesses. The demand
for Open Text’s solutions will be higher when the economy is growing and businesses
are investing in new technologies. Likewise, the demand will be low when the
economy is down. It makes sense that a high tech company such as Open Text will
have a stock beta of 1.52.
Loblaw Companies: (TSX:L-PA.TO) is Canada’s largest food distributor, with grocery
stores across the country. Since food is an essential for survival, it is expected that a
grocery chain’s earnings won’t vary much with the business cycle. It is not surprising
the beta of the Loblaw is the lowest of these four and is less than 1. The sensitivity of
the return on Loblaw stock to changes in market is low. We say that the market risk
of a grocery chain is low.
Tim Hortons: (TSX:THI.TO) Offers coffee and doughnuts in locations across Canada
and the United States. The beta of Tim Hortons is a bit less than 1, indicating that the
sensitivity of the return on Tim Hortons stock to changes in the market is less than
average. This makes sense. The demand for coffee and doughnuts is not hugely
variable with market conditions.

23.

r = rf + (rm – rf)
5 = rf + .5(rm – rf)

(stock A)

13 = rf + 1.5(rm – rf)

(stock B)

Solve these simultaneous equations to find that r f = 1% and rm = 9%. Thus the
market risk premium is 9% - 1%, or 8%.

24.

r = rf + (rm – rf)
Stock:
13.6 = 3 +  ×7
 = (13.6 – 3)/7 = 1.51
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Bond:
5.5 = 3 +  ×7
 = (5.5 – 3)/7 = 0.36
25.

3 month Treasury Bills yield 2.22% as of Oct 2008. 7% market premium.
TD Bank:
Beta = 1.13, r = 2.22%+1.13×7% = 10.13%
The Toronto-Dominion Bank and its subsidiaries provides financial services in
North America. It operates through four segments: Canadian Personal and
Commercial Banking, Wealth Management, U.S. Personal and Commercial
Banking, and Wholesale Banking. The Canadian Personal and Commercial
Banking segment provides personal and business banking services. It offers
various financial products and services to approximately 11 million personal and
small business customers. This segment also provides financing, investment, cash
management, international trade, and day-today banking services; and insurance
products, including home and automobile coverage, life and health insurance, and
credit protection coverage. As of October 31, 2007, it offered banking solutions
through telephone and Internet banking, approximately 2,500 automated banking
machines, and a network of 1,070 branches. The Wealth Management segment
provides various investment products and services, including advisory,
distribution, and asset management; trader program and long-term investor
solutions; and discount brokerage, financial planning, and private client services to
retail and institutional customers. The U.S. Personal and Commercial Banking
segment provides personal and commercial banking products and services,
insurance agency, wealth management, mortgage banking, and other financial
services to approximately 1.5 million households. As of the above date, it offered
products and services through a network of 617 branches and 761 automated
banking machines. The Wholesale Banking segment provides various capital
markets and investment banking products and services, which include
underwriting and distribution of new debt and equity issues, providing advice on
strategic acquisitions and divestitures, and executing daily trading and investment
needs primarily to corporate, government, and institutional customers. The
company was founded in 1855 and is headquartered in Toronto, Canada.
Find 4 other Canadian firms the same way as it is done to TD.

26.
IMAX: (TSX: IMX.TO) large-format film company.
Research in Motion: (TSX:RIM.TO) RIM is a leader in wireless communications.
Products include the BlackBerry™ wireless email solution, wireless handhelds and
wireless modems.
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Biovail (TSX: BVF.TO) Manufactures, sells and promotes products utilizing
advanced oral controlled- release and FlashDose technologies
Cameco(TSX: CCO.TO) is the world's largest publicly traded uranium company.
Gildan Activewear: (TSX: GIL.TO) is a vertically-integrated marketer and
manufacturer of quality branded basic apparel. The Company is the leading
supplier of activewear for the wholesale imprinted sportswear market in the U.S.
and Canada, and also a leading supplier to this market in Europe. The Company
sells T-shirts, sport shirts and fleece in large quantities to wholesale distributors as
undecorated “blanks”, which are subsequently decorated by screenprinters with
designs and logos.
EnCana: (TSX: ECA.TO) a leading North American energy company,
headquartered in Calgary, Alberta.
Barrick Gold: (TSX: ABX.TO) Barrick is the world’s pre-eminent gold producer,
with a portfolio of 27 operating mines, many advanced exploration and
development projects located across five continents, and large land positions on
the most prolific and prospective mineral trends. The Company also has the largest
reserves in the industry, with 124.6 million ounces of proven and probable gold
reserves, 6.2 billion pounds of copper reserves and 1.03 billion ounces of
contained silver within gold reserves as at December 31, 2007.
Shaw Communications :( TSX: SJR-B.TO) is a diversified Canadian

communications company whose core business is providing broadband cable
television, High-Speed Internet, Digital Phone, telecommunications services
(through Shaw Business Solutions) and satellite direct-to-home services (through
Star Choice Communications Inc.) to 3.2-million customers.
Canadian Pacific Railway: (TSX: HCH.TO) connects the Atlantic and the Pacific
coasts with the heart of North America.
Royal Bank : (TSX: RY-PR-L.TO) RBC provides personal and commercial
banking, wealth management services, insurance, corporate, investment banking
and transaction processing services on a global basis. RBC employs more than
70,000 full and part-time employees who serve more than 15 million personal,
business, public sector and institutional clients through offices in Canada, the
U.S. and 46 other countries.
TransCanada Corp :( TSX: TRP.TO) TransCanada is a leader in the responsible
development and reliable operation of North American energy infrastructure.
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27.

Cara Operations should use the beta of Tim Horton’s (which is 0.9) to find that the
required rate of return is 9.3%. The project is an investment in a chain of coffee
shops and the beta of Tim Horton’s reflects the risk of a firm in the coffee shop
business. The beta of Cara Operations reflects the risk of a coffee shop business.

28.

a.

False. The stock’s risk premium, not its expected rate of return, is twice as

high as the market’s.

b.

True. The stock’s unique risk does not affect its contribution to portfolio risk
but its market risk does.

c.

False. A stock plotting below the SML offers too low an expected return
relative to the expected return indicated by the CAPM. The stock is
overpriced. Investors will not want to pay that price to receive the stock’s
cash flows. The price must fall to increase the stock’s rate of return.

d.

True. If the portfolio is diversified to such an extent that it has negligible
unique risk, then the only source of volatility is its market exposure. A beta
of 2 then implies twice the volatility of the market portfolio.

e.

False. An undiversified portfolio has more than twice the volatility of the
market. In addition to the fact that it has double the sensitivity to market risk,
it also has volatility due to unique risk.

29.

The CAPM implies that the expected rate of return that investors will demand of
the portfolio is:

r = rf + (rm – rf) = 4% + .8(11% – 4%) = 9.6%
If the portfolio is expected to provide only a 9% rate of return, it’s an unattractive
investment. The portfolio does not provide an expected return that is sufficiently
high relative to its risk.

30.

A portfolio invested 80% in a stock market index fund (with a beta of 1.0) and
20% in a money market fund (with a beta of zero) would have the same beta as
this manager's portfolio:
 = .80  1.0 + .20  0 = .80
However, it would provide an expected return of
.80  11% + .20  4% = 9.6%

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which is better than the portfolio manager's expected return.
31.

The security market line provides a benchmark expected return that an investor
can earn by mixing index funds with money market funds. Before you place your
funds with a professional manager, you will need to be convinced that he or she
can earn an expected return (net of fees) in excess of the expected return available
on an equally risky index fund strategy.

32.

a.

r = rf + (rm  rf) = 5% + [–.2  (12% – 5%)] = 3.6%

b.Portfolio beta = .90  market + .10  law firm
= .90  1.0 + .10  (.2) = .88

33.

Expected income on stock fund: $2 million  .12
Interest paid on borrowed funds: $1 million  .04
Net expected earnings:

= .24 million
= .04 million
$0.20 million

Expected rate of return on the $1 million you invest is:
= .20 = 20%
Risk premium = 20% – 4% = 16%
This is double the risk premium of the market index fund (which is 8%, = 12% - 4%)
The risk is also double that of holding a market index fund. You have $2 million at
risk, but the net value of your portfolio is only $1 million. A 1% change in the rate
of return on the market index will change your profits by .01  $2 million = $20,000.
But this changes the rate of return on your portfolio by $20,000/$1,000,000 = 2%,
double that of the market. So your risk is in fact double that of the market index.
34.

a.

Expected rate of return = rf + (rm  rf)

= .04 + .9 × (.11 - .04) = .103 = 10.3%

b.

The appropriate discount rate to evaluate ChemCo is one that reflects the
riskiness of ChemCo’s cash flows. Since we know that ChemCo's current
beta is 1.4, it is reasonable to use this in the calculation of the appropriate
discount rate. Note that the discount rate of BigCo is irrelevant because
BigCo has three different divisions, of which only one is in the same business
of ChemCo.
Discount rate = rf + (rm  rf) = .04 + 1.4 × (.11 - .04) = .138 = 13.8%

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c.

Assuming that these are after-tax cash flows and using the constant dividend
growth model, the value of ChemCo is
Value of ChemCo = = $91.837 million

d.

Think of BigCo as a portfolio consisting of the original three divisions plus
the new ChemCo division. Thus, the new beta of BigCo will equal the
weighted average of its old beta and the beta ChemCo, with the weights
based on the market values of three original divisions, ChemCo and the new
combined BigCo. The value of BigCo is its original $1,000 million plus the
value of ChemCo, for a total of $1,091.837 million.

Weight for ChemCo division = =
= .084 = 8.4%
Weight for original BigCo = =
= .916 = 91.6%
New beta of BigCo = .084 × 1.4 + .916 × .9 = .942
As expected, adding ChemCo, with its higher beta, causes the beta of BigCo
to increase.

35.

a.

We take advantage of the formula for the present value of a growing
annuity, found in Chapter 4: × [1 - () T] for valuing the Year 2 to 5 cash
flows and recognize that starting in Year 6, each stock has a constant
perpetual growth rate and can be valued using the constant dividend
growth model, DIV/(r – g).
Food Express (FE)
Required rate of return = rf + (rm  rf) = .04 + .85 × (.07) = .10
Value of FE today:
= + × × [1 - ()4] + ×
= $100.00 million
Note: Since FE has the same growth rate for Years 2 and onward, the
constant growth formula can be used to value the stock:
Value of FE today:
= = $100.00 million
Computer Power (CP)
Required rate of return = rf + (rm  rf) = .04 + .95 × (.07) = .107
Value of CP today:

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= + × × [1 - ()4]
+×
= $34.00 million
Bridge Steel (BS)
Required rate of return = rf + (rm  rf) = .04 + 1.3 × (.07) = .131
Value of BS today:
= + × × [1 - ()4]
+×
= $96.00 million
b.

Total portfolio value = $100.00 + 34.00 + 96.00 = 230.00 million
Company
FE

Weight in Portfolio
= .4348


.85

CP

= .1478

.95

.1404

BS

= .4174

1.3

.5426

Total

Weight × 
.3696

1.0526

The portfolio beta is the weighted average of the individual stocks’ betas and
is about 1.05.
36.

a.

This question is most easily handled with a spreadsheet but can be done
using the formulas.

State of the
Economy
Recession

Normal
Boom
Expected return
Standard
deviation

Probability Division Division Division Division
A
B
C
D
0.2
8%
-10%
-1%
-4%
0.6
8%
15%
7%
15%
0.2
9%
30%
10%
20%

Firm

Market

-1.75%
11.25%
17.25%

-3%
11%
22%

8.2%

13.0%

6.0%

12.2%

9.9%

10.4%

0.40%

12.88%

3.69%

8.33%

6.25%

7.94%

11­15
Copyright © 2006 McGraw-Hill Ryerson Limited


b. Using the formula j = , where corrjm is the correlation between stock j’s return
and the market return, σj is the standard deviation of stock j’s return and σ m is
the standard deviation of the market return:
market = = = 1
A = = = .0368
B = = = 1.61
C = = = .451
D = = = .991
Since each of the four divisions is worth about ¼ of the firm’s market value,
the beta of the firm is the equal-weighted average of the four divisions’ betas:
Firm = = (.0368 + 1.61 + .451 + .991)/4 = .77
c. According to the CAPM, the required rate of return is
rj = rf + j (rm  rf)
Assuming the riskfree rate is 4 percent, and using the expected return on the
market calculated in (a), the required rate of return to each division is:
rA = .04 + .0368 × (.104 - .04) = .0424 = 4.24%
rB = .04 + 1.61 × (.104 - .04) = .143 = 14.3%
rC = .04 + .451 × (.104 - .04) = .0689 = 6.89%
rD = .04 + .991 × (.104 - .04) = .103 = 10.3%
d. Compare each division’s expected return, calculated in (a), with its required
return, calculated according to the CAPM and reported in (c). Divisions with
expected return at least equal to or greater than the required return are
generating positive NPV. Those whose expected return is less than the required

return are underperforming and provide negative NPV. Conglomerate should a
buyer who can improve the performance of these negative NPV divisions.
Hopefully, Conglomerate will sell these poorly performing divisions for more
than they are worth under its control, capturing some of gains from the
improved performance (See Chapter 23 for more on how companies share
gains from mergers).
Both Divisions A and D have expected returns greater than the CAPM required
rate of return. However, Division B, with a required rate of return of 14.3%,
has an expected return of 13%. Likewise, Division C has a required rate of
return of 6.89% but its expected rate of return is 6%. This means Divisions B
and C are likely candidates for sale. However, Conglomerate may want to
11­16
Copyright © 2006 McGraw-Hill Ryerson Limited


consider whether improvements in performance can be made to increase the
expected rates of return, without resorting to selling the divisions.
37.

Standard & Poor's
Expected results: This will give students hands-on experience with beta
estimations.
Alliance Atlantis Communications was acquired by CanWest MediaWork.
The problem was done with Ford stock returns instead.
1
2
3
4
5
6

7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

37
38
39
40
41
42
43
44
45

A
Date
Oct08
Sep08
Aug08
Jul08
Jun08
May08
Apr08
Mar08
Feb08
Jan08
Dec07
Nov07
Oct07
Sep07
Aug07
Jul07
Jun07
May07

Apr07
Mar07
Feb07
Jan07
Dec06
Nov06
Oct06
Sep06
Aug06
Jul06
Jun06
May06
Apr06
Mar06
Feb06
Jan06
Dec05
Nov05
Oct05
Sep05
Aug05
Jul05
Jun05
May05
Apr05

B
Ford Stock
Price
2.19

5.20
4.46
4.80
4.81
6.80
8.26
5.72
6.53
6.64
6.73
7.51
8.87
8.49
7.81
8.51
9.42
8.34
8.04
7.89
7.91
8.13
7.51
8.13
8.28
8.09
8.37
6.67
6.93
7.16
6.95

7.96
7.97
8.58
7.72
8.13
8.32
9.86
9.97
10.74
10.24
9.98
9.11

C
S&P 500 Index
Value
968.75
1,166.36
1,282.83
1,267.38
1,280.00
1,400.38
1,385.59
1,322.70
1,330.63
1,378.55
1,468.36
1,481.14
1,549.38
1,526.75

1,473.99
1,455.27
1,503.35
1,530.62
1,482.37
1,420.86
1,406.82
1,438.24
1,418.30
1,400.63
1,377.94
1,335.85
1,303.82
1,276.66
1,270.20
1,270.09
1,310.61
1,294.83
1,280.66
1,280.08
1,248.29
1,249.48
1,207.01
1,228.81
1,220.33
1,234.18
1,191.33
1,191.50
1,156.85

11­17
Copyright © 2006 McGraw-Hill Ryerson Limited

D
Rate of Return
Ford
-0.5788
0.1659
-0.0708
-0.0021
-0.2926
-0.1768
0.4441
-0.1240
-0.0166
-0.0134
-0.1039
-0.1533
0.0448
0.0871
-0.0823
-0.0966
0.1295
0.0373
0.0190
-0.0025
-0.0271
0.0826
-0.0763
-0.0181

0.0235
-0.0335
0.2549
-0.0375
-0.0321
0.0302
-0.1269
-0.0013
-0.0711
0.1114
-0.0504
-0.0228
-0.1562
-0.0110
-0.0717
0.0488
0.0261
0.0955
-0.1959

E
Rate of Return
S&P 500
-0.1694
-0.0908
0.0122
-0.0099
-0.0860
0.0107
0.0475

-0.0060
-0.0348
-0.0612
-0.0086
-0.0440
0.0148
0.0358
0.0129
-0.0320
-0.0178
0.0325
0.0433
0.0100
-0.0218
0.0141
0.0126
0.0165
0.0315
0.0246
0.0213
0.0051
0.0001
-0.0309
0.0122
0.0111
0.0005
0.0255
-0.0010
0.0352
-0.0177

0.0069
-0.0112
0.0360
-0.0001
0.0300
-0.0201


46
47
48
49
50
51

Mar05
Feb05
Jan05
Dec04
Nov04
Oct04

11.33
12.65
13.17
14.64
14.18
13.03

1,180.59

1,203.60
1,181.27
1,211.92
1,173.82
1,130.20



-0.1043
-0.0395
-0.1004
0.0324
0.0883



-0.0191
0.0189
-0.0253
0.0325
0.0386

Estimated beta = Slope(D3:D50,E3:E50) =2.25
38.

Standard & Poor's
Expected results: Use Market Insight to provide beta estimates. Student
hopefully will be able to see patterns in the betas that relate business activities of
the
companies. Encourage the students to learn more about each company's main

businesses and think about how market-wide factors affect their revenues and
costs.

Betas

MGA
F
MSFT
GOOG
BAC

Oct08
1.634
2.240
0.934
1.553
0.938

Sep08
1.488
1.647
0.806
2.045
0.390

Aug08
1.611
2.362
0.898
2.104

0.743

Jul08
1.643
2.384
0.885
2.128
0.739

Jun08
1.679
2.393
0.872
2.095
0.877

May08
1.627
2.216
1.000
2.258
0.348

Apr08
1.713
2.146
0.901
2.270
0.341

If the company’s business is riskier than average market, its beta will be greater than 1,
otherwise smaller than 1. Ford (F) is in an industry that has been struggling to survive
for the past a few years, therefore its risk is much higher than market average, so its
beta is much greater than 1. Blue chip MSFT (Microsoft) is about or below market
average. Financial industry usually has lower risk than market average, that’s why BAC
(Bank of America) has lower than 1 beta all along, the recent jump from 0.39 in Sep 08
to 0.938 Oct 08 is probably related to the recent financial crisis in the United States.

11­18
Copyright © 2006 McGraw-Hill Ryerson Limited