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CHAPTER 13
B249
27.
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 risk premiums of the assets equal to each other and solving for
the riskfree rate, we find:
(.132 – R
f
)/1.35 = (.101 – R
f
)/.80
.80(.132 – R
f
) = 1.35(.101 – R
f
)
.1056 – .8R
f
= .13635 – 1.35R
f
.55R
f
= .03075
R
f
= .0559 or 5.59%
Now using CAPM to find the expected return on the market with both stocks, we find:
.132 = .0559 + 1.35(R
M
– .0559)
.101 = .0559 + .80(R
M
– .0559)
R
M
= .1123 or 11.23%
R
M
= .1123 or 11.23%
28.
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(R
A
) = .15(–.08) + .70(.13) + .15(.48) = .1510 or 15.10%
E(R
B
) = .15(–.05) + .70(.14) + .15(.29) = .1340 or 13.40%
b.
We can use the expected returns we calculated to find the slope of the Security Market Line. We
know that the beta of Stock A
is .25 greater than the beta of Stock B. Therefore, as beta increases
by .25, the expected return on a security increases by .017 (= .1510 – .1340). The slope of the
security market line (SML) equals:
Slope
SML
= Rise / Run
Slope
SML
= Increase in expected return / Increase in beta
Slope
SML
= (.1510 – .1340) / .25
Slope
SML
= .0680 or 6.80%
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SOLUTIONS
Since the market’s beta is 1 and the riskfree rate has a beta of zero, the slope of the Security
Market Line equals the expected market risk premium. So, the expected market risk premium must
be 6.8 percent.
We could also solve this problem using CAPM. The equations for the expected returns of the two
stocks are:
E(R
A
) = .151 = R
f
+ (
B
+ .25)(MRP)
E(R
B
) = .134 = R
f
+
B
(MRP)
We can rewrite the CAPM equation for Stock A as:
.151 = R
f
+
B
(MRP) + .25(MRP)
Subtracting the CAPM equation for Stock B from this equation yields:
.017 = .25MRP
MRP = .068 or 6.8%
which is the same answer as our previous result.
CHAPTER 14
COST OF CAPITAL
Answers to Concepts Review and Critical Thinking Questions
1.
It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than
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This document was uploaded on 10/31/2011 for the course FIN 3403 at University of Florida.
 Spring '06
 Tapley
 Finance

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