QCU and Exercise for Part 3 :
30 QCU (only one answer is right) and 1 Exercise
Risk and return
Cost of equity
From the cost of equity to the cost of capital
Corporate Finance
Master 1
2012-2013
All campuses
1
30 QCU
1) Which of the following statements is false?
A) The variance increases with the magnitude of the deviations from the mean.
B) The variance is the expected squared deviation from the mean.
C) Two common measures of the risk of a probability distribution are its variance and standard
deviation.
D) If the return is riskless and never deviates from its mean, the variance is equal to one.
2) Which of the following equations is incorrect?
A) Var ( R ) = SD ( R ) 2
∑ P × ( R − E [ R]) C) Var ( R ) = ∑ P × ( R − E [ R ])
D) E [ R] = ∑ P × R
B SD ( R ) =
R
R
R
R
2
R
R
3) Which of the following investments offered the lowest overall return over the past eighty years?
A) Small stocks
B) Treasury Bills
C) S&P 500
D) Corporate bonds
4) Suppose an investment is equally likely to have a 35% return or a - 20% return. The expected
return for this investment is closest to:
A) 7.5%
B) 15%
C) 5%
D) 10%
2
Use the table for the question(s) below.
Consider the following Price and Dividend data for General Electric Company:
Date
December 31, 2008
January 26, 2009
April 28, 2009
July 29, 2009
October 28, 2009
December 30, 2009
Price ($)
$14.64
$13.35
$9.14
$10.74
$8.02
$7.72
Dividend ($)
$0.10
$0.10
$0.10
$0.10
5) Assume that you purchased General Electric Company stock at the closing price on December 31,
2008 and sold it after the dividend had been paid at the closing price on January 26, 2009. Your
dividend yield for this period is closest to:
A) -8.15%
B) 0.75%
C) 0.70%
D) -8.80%
6) Assume that you purchased General Electric Company stock at the closing price on December 31,
2008 and sold it after the dividend had been paid at the closing price on January 26, 2009. Your
capital gains rate (yield) for this period is closest to:
A) 0.75%
B) 0.70%
C) -8.80%
D) -8.15%
Use the table for the question(s) below.
Consider the following realized annual returns:
Year End
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Index Realized Return
23.6%
24.7%
30.5%
9.0%
-2.0%
-17.3%
-24.3%
32.2%
4.4%
7.4%
Stock A Realized Return
46.3%
26.7%
86.9%
23.1%
0.2%
-3.2%
-27.0%
27.9%
-5.1%
-11.3%
7) The average annual return on the Index from 2000 to 2009 is closest to:
A) 7.10%
B) 4.00%
C) 9.75%
D) 8.75%
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8) The variance of the returns on the Index from 2000 to 2009 is closest to:
A) .0450
B) .3400
C) .1935
D) .0375
9) Which of the following is not a systematic risk?
A) The risk that oil prices rise, increasing production costs
B) The risk that the Federal Reserve raises interest rates
C) The risk that the economy slows, reducing demand for your firm's products
D) The risk that your new product will not receive regulatory approval
10) Which of the following is not a diversifiable risk?
A) The risk that oil prices rise, increasing production costs
B) The risk of a product liability lawsuit
C) The risk that the CEO is killed in a plane crash
D) The risk of a key employee being hired away by a competitor
Use the following information to answer the problems below.
Consider two banks. Bank A has 1000 loans outstanding each for $100,000, that it expects to be fully
repaid today. Each of Bank A's loans have a 6% probability of default, in which case the bank will
receive $0 for each of the defaulting loans. Bank B has 100 loans of $1 million outstanding, which it
also expects to be fully repaid today. Each of Bank B's loans have a 5% probability of default, in
which case the bank will receive $0 for each of the defaulting loans. The chance of default is
independent across all the loans.
11) The expected overall payoff to Bank A is:
A) $5,000,000
B) $6,000,000
C) $94,000,000
D) $95,000,000
12) The expected overall payoff to Bank B is:
A) $5,000,000
B) $6,000,000
C) $94,000,000
D) $95,000,000
13) The standard deviation of the overall payoff to Bank A is closest to:
A) $689,000
B) $751,000
C) $2,179,000
D) $2,375,000
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14) The standard deviation of the overall payoff to Bank B is closest to:
A) $751,000
B) $2,179,000
C) $2,375,000
D) $21,794,000
15) Consider a portfolio that consists of an equal investment in 20 firms. For each of these firms, there
is a 70% probability that the firms will have a 16% return and a 30% that they will have a - 8% return.
Each of these firms returns are independent of each other. The standard deviation of this portfolio is
closest to:
A) 2.5%
B) 4.2%
C) 8.8%
D) 11.0%
Use the following information to answer the question(s) below.
Company
Ticker
Ford Motor Company
F
International
Business
Machines
IBM
Merck
MRK
Beta
2.77
0.73
0.90
16) If the market risk premium is 6% and the risk-free rate is 4%, then the expected return of investing
in Ford Motor Company is closest to:
A) 10.0%
B) 16.2%
C) 17.1%
D) 20.6%
17) If the market risk premium is 6% and the risk-free rate is 4%, then the expected return of investing
in Merck is closest to:
A) 5.4%
B) 9.4%
C) 10.0%
D) 10.4%
18) If the expected return on the market is 11% and the expected return of investing in Merck is
10.35%, then the risk-free rate must be:
A) 3.0%
B) 4.0%
C) 4.5%
D) 5.0%
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19) If the risk-free rate is 5% and the expected return of investing in Merck is 11.3%, then the
expected return on the market must be:
A) 8.0%
B) 10.0%
C) 10.4%
D) 12.0%
Use the information for the question(s) below.
Suppose that in the coming year, you expect Exxon-Mobil stick to have a volatility of 42% and a beta
of 0.9, and Merck's stock to have a volatility of 24% and a beta of 1.1. The risk free interest rate is
4% and the markets expected return is 12%.
20) Which stock has the highest total risk?
A) Merck since it has a lower volatility
B) Merck since it has a higher Beta
C) Exxon-Mobil since it has a higher volatility
D) Exxon-Mobil since it has a lower beta
21) Which stock has the highest systematic risk?
A) Merck since it has a higher Beta
B) Exxon-Mobil since it has a lower beta
C) Exxon-Mobil since it has a higher volatility
D) Merck since it has a lower volatility
22) The beta for the market portfolio is closest to:
A) 1
B) 0
C) Unable to answer this question without knowing the markets expected return
D) Unable to answer this question without knowing the markets volatility
23) The beta for the risk free investment is closest to:
A) 1
B) 0
C) Unable to answer this question without knowing the risk free rate
D) Unable to answer this question without knowing the markets volatility
6
Use the figure for the question(s) below.
Consider the following graph of the security market line:
24) Stock "A"
A) has a relatively lower expected return than predicted.
B) is underpriced.
C) falls below the SML.
D) is overpriced.
25) Stock "D"
A) is less risky than the market portfolio.
B) is overpriced.
C) has a beta equal to 1.
D) falls above the SML.
26) The market portfolio
A) is underpriced.
B) has a beta equal to 2.
C) is overpriced.
D) falls on the SML.
27) Which of the following statements is false?
A) The tax deductibility of interest lowers the effective cost of debt financing for the firm.
B) When a firm uses debt financing, the cost of the interest it must pay is offset to some extent by the
tax savings from the interest tax shield.
C) With tax-deductible interest, the effective after-tax borrowing rate is r(τC).
D) The WACC represents the cost of capital for the free cash flow generated by the firm’s assets.
7
Use the information for the question(s) below.
Flagstaff Enterprises expected to have free cash flow in the coming year of $8 million, and this free
cash flow is expected to grow at a rate of 3% per year thereafter. Flagstaff has an equity cost of
capital of 13%, a debt cost of capital of 7%, and it is in the 35% corporate tax bracket.
28) If Flagstaff currently maintains a .5 debt to equity ratio, then Flagstaff's WACC is closest to:
A) 10.00%
B) 10.25%
C) 9.50%
D) 8.75%
29) If Flagstaff currently maintains a .5 debt to equity ratio, then the value of Flagstaff is closest to:
A) $114 million
B) $100 million
C) $111 million
D) $140 million
30) Consider the following equation:
E
D
rwacc =
rE +
rD (1 − τ c ) E+D
E+D
the term E in this equation is
A) the amount of equity.
B) the amount of debt.
C) the required rate of return on debt.
D) the required rate of return on equity.
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Exercise
Exercise 1
Suppose the risk-free interest rate is 5%, and the stock market will return either 40% or −20% each
year, with each outcome equally likely. Compare the following two investment strategies: (1) invest
for one year in the risk-free investment, and one year in the market, or (2) invest for both years in the
market.
a.
b.
c.
Which strategy has the highest expected final payoff?
Which strategy has the highest standard deviation for the final payoff?
Does holding stocks for a longer period decrease your risk?
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30 QCU :Answer
1) Answer: D
Explanation: D) If the return is riskless and never deviates from its mean, the variance is equal to
zero.
2) Answer: A
Explanation: A) SD ( R ) = Var ( R ) 3) Answer: B
4) Answer: A
Explanation: A) E [ R] = ∑ R PR × R = .50 (35%) + .50 ( −20% ) = 7.5%
5) Answer: C
Explanation: C) = div / P0 = .10 / 14.64 = .0068
6) Answer: C
Explanation: C) = (P1 - P0) / P0 = (13.35 - 14.64) / 14.64 = -.088115
7) Answer: D
Explanation: D) Rannual =
R1 + R2 + .... + RN R1 + R2 + .... + R10 0.878
=
=
= 8.82% N
10
10
8) Answer: D
Explanation: D) Rannual =
Year
End
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Index
Realized
Return
23.6%
24.7%
30.5%
9.0%
-2.0%
-17.3%
-24.3%
32.2%
4.4%
7.4%
R1 + R2 + .... + RN R1 + R2 + .... + R10 0.878
=
=
= 8.82%
N
10
10
(R - R ) ( R − R )
14.78%
15.88%
21.68%
0.18%
-10.82%
-26.12%
-33.12%
23.38%
-4.42%
-1.42%
2
0.0218448
0.0252174
0.0470022
3.24E-06
0.0117072
0.0682254
0.1096934
0.0546624
0.0019536
0.0002016
2
Variance = SUM of ( R − R ) / T - 1 = 0.3405116 / 9 = 0.0378346
9) Answer: D
10) Answer: A
10
11) Answer: C
Explanation: C) E[payoff] = (.06)(1000)($0) + (1 - .06)(1000)($100,000) = $94,000,000
12) Answer: D
Explanation: D) E[payoff] = (.05)(100)($0) + (1 - .05)(100)($1,000,000,000) = $95,000,000
13) Answer: B
Explanation: B) E[payoff] = (.06)(1000)($0) + (1 - .06)(1000)($100,000) = $94,000,000
2
2
SD ( Payoff ) = .06 × ($0 − $94 ) + .94 × ($100 − $94 ) = 23.748684 million SD ( Overall Payoff ) =
23, 748, 684
= $750,999.33 1000
14) Answer: B
Explanation: B) E[payoff] = (.05)(100)($0) + (1 - .05)(100)($1,000,000) = $95,000,000
2
2
SD ( Payoff ) = .05 × ($0 − $95 ) + .95 × ($100 − $95 ) = 21.794495 million
SD ( Overall Payoff ) =
21,794, 495
= $2,179, 450
100
15) Answer: A
Explanation: A) E[return] = (.70)(16%) + (.30)(-8%) = 8.8%
2
2
SD ( R t ) = .70 × (16% − 8.8% ) + .30 × ( −8% − 8.8% ) = 10.9982% 10.9982%
= 2.459268% 20
16) Answer: D
Explanation: D) Return = .04 + 2.77(.06) = .2062
SD ( R portfolio ) =
17) Answer: B
Explanation: B) Return = .04 + 0.9(.06) = .094
18) Answer: C
Explanation: C) Return => .1035 = × + 0.9(.11 - X) => .1X = .1035 - .9(.11) => × = .045
19) Answer: D
Explanation: D) Return => .113 = .05 + 0.9(X - .05) => .9X = .113 - .05 + .045 => × = .12
20) Answer: C
21) Answer: A
22) Answer: A
Explanation: A)
Beta of the Market Portfolio =
(
) = SD ( R ) Corr ( R
SD ( R )
SD ( R )
Cov Rmkt , Rmkt
mkt
mkt
mkt
mkt
The market is perfectly correlated with itself.
11
, Rmkt
)
= Corr(Rmkt,Rmkt) = 1
23) Answer: B
Explanation: B)
Since the risk free investment has zero volatility, the Beta must equal zero.
24) Answer: B
25) Answer: B
26) Answer: D
27) Answer: C
Explanation: C) With tax-deductible interest, the effective after-tax borrowing rate is r(1 - τC).
28) Answer: B
Explanation: B) rWACC =
rWACC =
E
D
rE +
rD (1 − τ c )
E+D
E+D
1
.5
.13 +
.07 (1 − .35) = .101833
1 + .5
1 + .5
29) Answer: C
Explanation: C) rWACC =
E
D
rE +
rD (1 − τ c ) E+D
E+D
1
.5
.13 +
.07 (1 − .35) = .101833 1 + .5
1 + .5
FCF
$8
ValueFlagstaff =
=
= $111.37 million Wacc − g .101833−.03
rWACC =
30) Answer: A
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Exercise : Answer
Exercise 1
R(i) : (1.05)(1.40)-1 = 47% or (1.05)(0.80) –1 = –16%
R(ii) : 1.42 -1 = 96%, 1.4 × 0.8 – 1 = 12%, 0.8 × 1.4 – 1=12%, .8 × .8 – 1 = –36%
a.
ER(i) = (47% – 16%)/2 = 15.5%
ER(ii) = (96% + 12% + 12% – 36%)/4 = 21%
b.
Vol(i) =sqrt(1/2 (47% – 15.5%)2 + 1/2(–16% – 15.5%)2) = 31.5%
Vol(ii)=sqrt(1/4 (96%-21%)2 + ½(12% – 21%)2 + 1/4(–36% – 21%)2) = 47.5%
c.
No
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