The risk-free asset and other assets

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QUESTION

Question 1 (20 points)
The following graph presents the efficient frontier of all of the risky assets, the efficient frontier of all of the
risky assets and the risk-free asset and other assets:
a. What is the expected return of the market portfolio?
Answer: the expected return of the market portfolio is: _________%
b. What is the beta of asset A?
Answer: the beta of asset A is: _________
A
��!
�
0.02
��!! B
0.15
C
0.10
0.2 0.25
0.03
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c. Will a risk averse investor invest also in asset B?
Answer: a risk averse investor will / will not invest also in asset B (circle the right answer)
d. What is the specific risk (specific variance) of asset C?
Answer: the specific risk of asset C is: _________
e. Which asset, A or C, has higher correlation with the market portfolio?
Answer: asset A / asset C has higher correlation with the market portfolio (circle the right answer)
f. Assume that asset C is a stock and asset A is a portfolio. Is it possible that stock C will be included in
portfolio A?
Answer: it is possible / not possible that stock C will be included in portfolio A (circle the right answer)
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Question 2 (20 points)
“Stringer” and “Bell” are two similar construction companies, both operating in Baltimore, Maryland.
“Stringer” has 2 million outstanding shares, trading at $20 per share. “Stringer” has no debt and it’s
perpetualannualoperationalprofitis$8million.
“Bell” has 1 million outstanding shares trading at $25 per share and a perpetual debt worth $25 million.
Assumethatbell’sdebtisriskfreeandthat�! = 4%.Assumethatthecorporatetaxis40%.
a. WhatisthemarketvalueofStringer?
Answer: the market value of Stringer is: $
b. What is Stringer’s cost of capital?
Answer:Stringer’scostofcapital is:
c. What isBell’svalue?
Answer:Bell’svalueis:$
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d. What is Bell’s �!?
Answer:Bell’s �� is:
AssumethatBelldecidedtoraisemoredebtintheamountof$10millionandusetheproceeds to
repurchase its shares.
e. What isBell’snewvalue?
Answer: Bell’s new value is: $
f. What isBell’snew�! afterthesharerepurchase?
Answer: Bell’s new �� is:
g. What isBell’snewsharepriceafterthesharerepurchase?
Answer: Bell’s new share price is:
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Question 3 (20 points)
You are offered a lottery ticket which will give you the following outcomes two years from now:
Probability prize
0.8 0
0.1 2,100
0.1 10,000
The ticket price is $1,000.
Additionally, you know the following information:
1) The market portfolio’s expected return is 15%.
2) Your portfolio’s beta is 0.75.
3) The risk-free rate of return for a two-year investment is 5% per year.
Should you buy the ticket? Explain why or why not.
Answer: You should buy/not buy the ticket (circle one).
Calculation:
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Question4 (20 points):
Part A
Youobservedthreecompaniesfromtheperfumemanufacturingindustry.CompanyAandcompanyBhave
each operating profit of $50,000. Company C has operating profit of $100,000.
CompanyAandcompanyBarebothallequitycompaniesandthevalueofeachcompanyis$500,000witha
costofequityofr! = 10%. CompanyChasdebtwithamarketvalueof$400,000andwithacostofdebtof
�! = 3% andacostofequityofr! = 12.6%.TheequityvalueofcompanyCis$700,000.Thepriceper
shareforeachofthethreecompaniesis P=$1.
You have $1,000 to invest in one of the following two alternatives and you plan to invest the whole $1,000:
a. Invest in company A and company B (you can choose any combination of A and B).
b. Invest all of the money in company C.
Assume that under both alternatives you will be well diversified.
Assumetherearenotaxes.
Which option will you choose?
Answer: invest all of the money in company A and company B / in company C
Part B
Inordertofinanceanewproject,companyXissuedatwoyear bondcarriesafacevalueof$1000million
and an annual coupon of 10%.
According to your analysis, you expect that:
Withprobabilityof100%,thecompanywillbeabletopayitspaymentsattheendoftheyear(thefirst
paymentofthebond).However,thereisaprobabilityofonly30%thatattheendofthesecondyearthe
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companywillgointodefault.Inthatcase,thecompanywillbeabletopayonly50%ofitspayments(its
second payment) to the bond holders.
Assumethattherequiredreturnbythebondholdersofthecompanyis4%andthatthecompany’sdebt
does not carry any systematic risks.
a. What is the value of the debt of company X?
Answer: the value of the debt of company X is _____________
b. What is the YTM’s of company X’s debt?
Answer: the YTM of the debt of company X is _____________
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Page 9 of 11
Question 5 (20%)
Below you will find a WACC calculation performed by a big accounting firm:
Step 1: calculate the unlevered beta from comparable firms:
Company Debt Equity Tax rate
Equity
Beta D/E
Unlevered
beta
ReLevered
beta
A 5,866 14,816 12.5% 1.477 40% 1.097 1.805
B 11,666 23,251 17.9% 1.273 50% 0.902 1.484
C 244,429 186,933 30.0% 1.208 131% 0.631 1.038
D 8,152 11,051 29.6% 1.091 74% 0.718 1.181
E 11,410 16,696 34.4% 1.305 68% 0.901 1.483
F 2,802 1,706 31.4% 1.247 164% 0.586 0.965
Average 1.267 88% 0.806 1.326
Source: Bloomberg, December 2014.
Note: the unlevered beta was based on the average D/E ratio of 88%.
Step 2: calculate the cost of equity and debt
Cost of equity (Re)
Rf βe MRP (Rm–Rf) Re
3.1% 1.326 6.8% 12.1%
Cost of debt (Rd)
Liabilities to fund the activities:
Loan Loan value YTM
Bonds 435 6.88%
Loan from institutional 187 6.06%
Loan from Banks 400 6.30%
Weighted average 6.5%
Step 3: calculate WACC
WACC:
D/(D + E) E/(D + E) Tax WACC
44% 56% 26.5% 8.89%
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Required:
A. TracetheformulausedthecalculatetheUnleveredbetaandtherelevered betaofcompanyA(showthe
formula and substitute the data to show that it holds).
B. What is the inconsistency in the WACC calculation?
C. Correct mistake and update the WACC calculation.
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