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1. You are considering investing in the two securities in the table below: (30 points)
State of the Economy Probability Return on
Alpha Inc.
Bear
.6
4%
Bull
.4
16%
Return on
Beta Inc.
3%
3%
a. Calculate the expected returns and the standard deviations of the two
securities.
E(Ra)=.6*4+.4*16=8.8%; E(Rb)=.6*3+.4*3=3%
Variance(Alpha) = .6(4-8.8)2+.4(16-8.8)2=13.824+20.736=34.56
Standard Dev.(Alpha)=5.87%; Variance(Beta)=0
b. You have $10,000 to invest. Calculate the expected return and standard
deviation of your portfolio if you invest $3,000 in Alpha and $7,000 in Beta.
E(Rp)=.3(8.8)+.7(3)=4.74%; Standard Dev. = .3(5.87)=1.761%
c. You would like a portfolio with an expected return of 10%. Explain how you
could invest in the two securities above to form this portfolio.
10=8.8x+(1-x)*3; x=1.2069; Invest 120.69% in Alpha and –20.69% in Beta. (You
would sell beta and invest more than 100% in alpha)
2. The risk-free rate is 7%, and the expected return of the market is 15%. Cushman
Company has a beta of 0.8. What is the expected return of Cushman Company?
(5 points) 7+.8(15-7)=13.4%
3. You are considering investing in the two securities Macro and Micro. (20 points)
Expected Return
Standard Deviation
Correlation of the two securities = -0.3
Macro Micro
12%
30%
10%
22%
Calculate the expected return and standard deviations of a portfolio that is
composed of 40% Macro and 60% Micro. .4(12)+.6(30)=22.8%;
Variance=.42(.10)2+.62(.22)2+2*.4*.6(.1)(.22)(-.3)= .015824; Standard
Deviation=12.58%
4. Many investors claim to observe patterns in stock market prices. Is technical
analysis consistent with the Efficient Market Hypothesis? If not, what form of
market efficiency is violated? (5 points) Weak form.
5. Calculate the five-year holding period return for the Vanguard Total Bond Fund:
(5 points) (1-.086)(1-(-.008))(1.114)(1-.084)(1-.083)=1.4089-1=40.89%
Year Return
1998
1999
2000
2001
2002
8.6%
-0.8%
11.4%
8.4%
8.3%
6. HQ Company has invested in a facility to produce financial calculators. The price
of the machine is $600,000 and its economic life is five years. The machine is
fully depreciated by the straight-line method and will produce 20,000 calculators
in the first year. The variable cost per unit is $20, while fixed costs are
$1,000,000. The corporate tax rate for the company is 30 percent. The
company’s cost of capital is 15%. (20 points)
a. What price would you have to charge per calculator to break-even in an
accounting sense?
20000=(1000000+120000)/(p-20); P=76
b. What price would you have to charge per calculator to break-even in a
financial sense?
NPV=-600000+OCF*PVIFA(5,15%); OCF = 178989.33
178989.33=(20000p-20*20000-1000000)(.7)+.3(120000); P=80.21
7. First Security, Inc. is considering a new project that costs $25 million. The
project will generate after-tax (year-end) cash flows of $6 million for 7 years.
The firm has a debt to equity ratio of 0.50. The cost of equity is 16% and the cost
of debt is 9%. The corporate tax rate is 35%. The project has the same risk as
that of the overall firm. Should First Security undertake the project? (15 points)
WACC=(2/3)(16)+(1/3)(9)(1-.35)=12.62%; NPV=1.8525 million; Yes.