b.
The aftertax cost of debt is:
RD = .0633(1 .35) = .0412 or 4.12%
c.
6.
The aftertax rate is more relevant because that is the actual cost to the company.
The book value of debt is the total par value of all outstanding debt, so:
BVD = $60,000,000 + 80,
b.
The unsystematic return is the return that occurs because of a firm specific factor such as the
bad news about the company. So, the unsystematic return of the stock is 2.6 percent. The total
return is the expected return, plus the two components of une
Intermediate
5.
We can express the multifactor model for each portfolio as:
E(RP ) = RF + 1F1 + 2F2
where F1 and F2 are the respective risk premiums for each factor. Expressing the return equation for
each portfolio, we get:
16% = 4% + 0.85F1 + 1.15F2
12%
CHAPTER 12
AN ALTERNATIVE VIEW OF RISK AND
RETURN: THE ARBITRAGE PRICING
THEORY
Answers to Concept Questions
1.
Systematic risk is risk that cannot be diversified away through formation of a portfolio. Generally,
systematic risk factors are those factors
E(RP) = 0.1014 or 10.14%
c.
Using the derivative from part a, with the new covariance, the weight of each stock in the
minimum variance portfolio is:
wA = [ 2 + Cov(A,B)] / [ 2 + 2 2Cov(A,B)]
B
A
B
wA = (.452 + .05) / [.222 + .452 2(.05)]
wA = .7196
This
To find the standard deviation of the portfolio, we first need to calculate the variance. The variance
of the portfolio is:
2 = w 2 2 + w 2 2 + 2wAwBABA,B
P
A A
B B
2 = (.70)2(.141)2 + (.30)2(.34)2 + 2(.70)(.30)(.141)(.34)(.48)
P
2 = .02981
P
And the s
The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of the stock is:
E(RA) = .20(.160) + .60(.107) + .20(.280) = .0880 or 8.80%
And the variance of
37. a.
The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of each stock is:
E(RA) = .15(.08) + .70(.13) + .15(.48) = .1510 or 15.10%
E(RB) = .15(.0
P = .0411 or 4.11%
d.
The expected return of the portfolio is the sum of the weight of each asset times the expected
return of each asset, so, for a portfolio of Asset 1 and Asset 3:
E(RP) = w1E(R1) + w3E(R3)
E(RP) = .50(.1750) + .50(.1750)
E(RP) = .1750
b.
To find the covariance, we multiply each possible state times the product of each assets
deviation from the mean in that state. The sum of these products is the covariance. The
correlation is the covariance divided by the product of the two standard de
g.
The competitors announcement is also unexpected, but it is not a welcome surprise. This
announcement will lower the returns on Lewis-Striden.
The systematic factors in the list are real GNP, inflation, and interest rates. The unsystematic risk
factors
b.
Since we don't have the actual market return or unsystematic risk, we will get a formula with
those values as unknowns:
RP = .30RA + .45RB + .25RC
RP = .30[10.5% + 1.2(RM 14.2%) + A] + .45[13.0% + 0.98(RM 14.2%) + B]
+ .25[15.7% + 1.37(RM 14.2%) + C]
R
b.
Consider the expected return equation of a portfolio of five assets we calculated in part a. Since
we now have a very large number of stocks in the portfolio, as:
N ,
1
0
N
But, the js are infinite, so:
(1/N)(1 + 2 + 3 + 4 +.+ N) 0
Thus:
R P = 11% + 0.
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rou
CHAPTER 13
RISK, COST OF CAPITAL, AND CAPITAL
BUDGETING
Answers to Concepts Review and Critical Thinking Questions
1.
No. The cost of capital depends on the risk of the project, not the source of the money.
2.
Interest expense is tax-deductible. There is
7.
RSup = .12 + .75(.08) = .1800 or 18.00%
Both should proceed. The appropriate discount rate does not depend on which company is investing;
it depends on the risk of the project. Since Superior is in the business, it is closer to a pure play.
Therefore,
b.
Following the same logic as in part a, we have
P2 = 0 = X331 + (1 X3)41
P2 = 0 = X3(1) + (1 X3)(1.5)
and
X3 = 3
X4 = 2
Thus, sell short Security 4 and buy Security 3. Then,
E(RP2) = 3(10%) + (2)(10%)
E(RP2) = 10%
P2 = 3(0.5) 2(0.75)
P2 = 0
Note that si
d.
10. a.
If short selling is allowed, rational investors will sell short asset C, causing the price of asset C
to decrease until no arbitrage opportunity exists. In other words, the price of asset C should
decrease until the return becomes 14.25 percent.
Realize that Ri,t, RM, and i,t are random variables, and i and i are constants. Then, applying
the above properties to this model, we get:
Var(Ri) = i2 Var(RM) + Var(i)
and now we can find the standard deviation for each asset:
2 = 0.72(0.0121) + 0.01 =
c.
If we assume (1i,1j) = 0, and (2i,2j) = .5, the variance of each portfolio is:
Var(R1P) = 0.0225 + 0.04(1i,1j)
Var(R1P) = 0.0225 + 0.04(0)
Var(R1P) = 0.0225
Var(R2P) = 0.0025 + 0.04(2i,2j)
Var(R2P) = 0.0025 + 0.04(0.5)
Var(R2P) = 0.0225
Since Var(R1P)
Finally, since we can have as many stocks in each market as we want, in the limit, as N ,
1
0, so we get:
N
Var(RP) = 22 + Cov(i,j)
and, since:
Cov(i,j) = ij(i,j)
and the problem states that 1 = 2 = 0.10, so:
Var(RP) = 22 + 12(i,j)
Var(RP) = 2(0.01) + 0.
Note however, to use this, first we must find RP and E(RP). So, using the assumption about equal
weights and then substituting in the known equation for Ri:
1
N
1
RP =
N
RP =
R
i
(0.10 + F + i)
RP = 0.10 + F +
1
N
i
Also, recall from Statistics a property
35. Here we have the expected return and beta for two assets. We can express the returns of the two
assets using CAPM. If the CAPM is true, then the security market line holds as well, which means
all assets have the same risk premium. Setting the reward-
Challenge
34. The amount of systematic risk is measured by the of an asset. Since we know the market risk
premium and the risk-free rate, if we know the expected return of the asset we can use the CAPM to
solve for the of the asset. The expected return of
According to the Capital Market Line:
E(RI) = Rf + SlopeCML(I)
Since we know the expected return on the market portfolio, the risk-free rate, and the slope of the
Capital Market Line, we can solve for the standard deviation of the market portfolio which i
8.
If we assume that the market has not stayed constant during the past three years, then the lack in
movement of Southern Co.s stock price only indicates that the stock either has a standard deviation
or a beta that is very near to zero. The large amount
6.
The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of each stock asset is:
E(RA) = .15(.06) + .65(.07) + .20(.11) = .0765 or 7.65%
E(RB) = .15(.
2.
The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. The total value of the portfolio is:
Total value = $1,900 + 2,300 = $4,200
So, the expected return of this portfolio is:
E(Rp) = ($1,900/
CASE: E308
DATE: 02/14/08
ENDEAVOR
Endeavor was formed for the purpose of promoting entrepreneurs in emerging markets, beginning
in Latin America. Its basic model is to link up small and midsize businesses with seasoned
entrepreneurs so that little guys a