## The risk-free asset and other assets

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

Page 2 of 11

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)

Page 3 of 11

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

perpetual annual operational profit is $8 million.

“Bell” has 1 million outstanding shares trading at $25 per share and a perpetual debt worth $25 million.

Assume that bell’s debt is risk free and that �! = 4%. Assume that the corporate tax is 40%.

a. What is the market value of Stringer?

Answer: the market value of Stringer is: $

b. What is Stringer’s cost of capital?

Answer: Stringer’s cost of capital is:

c. What is Bell’s value?

Answer: Bell’s value is: $

Page 4 of 11

d. What is Bell’s �!?

Answer: Bell’s �� is:

Assume that Bell decided to raise more debt in the amount of $10 million and use the proceeds to

repurchase its shares.

e. What is Bell’s new value?

Answer: Bell’s new value is: $

f. What is Bell’s new �! after the share repurchase?

Answer: Bell’s new �� is:

g. What is Bell’s new share price after the share repurchase?

Answer: Bell’s new share price is:

Page 5 of 11

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:

Page 6 of 11

Question 4 (20 points):

Part A

You observed three companies from the perfume manufacturing industry. Company A and company B have

each operating profit of $50,000. Company C has operating profit of $100,000.

Company A and company B are both all equity companies and the value of each company is $500,000 with a

cost of equity of r! = 10%. Company C has debt with a market value of $400,000 and with a cost of debt of

�! = 3% and a cost of equity of r! = 12.6%. The equity value of company C is $700,000. The price per

share for each of the three companies is 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.

Assume there are no taxes.

Which option will you choose?

Answer: invest all of the money in company A and company B / in company C

Part B

In order to finance a new project, company X issued a two year bond carries a face value of $1000 million

and an annual coupon of 10%.

According to your analysis, you expect that:

With probability of 100%, the company will be able to pay its payments at the end of the year (the first

payment of the bond). However, there is a probability of only 30% that at the end of the second year the

Page 7 of 11

company will go into default. In that case, the company will be able to pay only 50% of its payments (its

second payment) to the bond holders.

Assume that the required return by the bondholders of the company is 4% and that the company’s debt

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 ise. 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)

Page 3 of 11

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

perpetual annual operational profit is $8 million.

“Bell” has 1 million outstanding shares trading at $25 per share and a perpetual debt worth $25 million.

Assume that bell’s debt is risk free and that �! = 4%. Assume that the corporate tax is 40%.

a. What is the market value of Stringer?

Answer: the market value of Stringer is: $

b. What is Stringer’s cost of capital?

Answer: Stringer’s cost of capital is:

c. What is Bell’s value?

Answer: Bell’s value is: $

Page 4 of 11

d. What is Bell’s �!?

Answer: Bell’s �� is:

Assume that Bell decided to raise more debt in the amount of $10 million and use the proceeds to

repurchase its shares.

e. What is Bell’s new value?

Answer: Bell’s new value is: $

f. What is Bell’s new �! after the share repurchase?

Answer: Bell’s new �� is:

g. What is Bell’s new share price after the share repurchase?

Answer: Bell’s new share price is:

Page 5 of 11

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:

Page 6 of 11

Question 4 (20 points):

Part A

You observed three companies from the perfume manufacturing industry. Company A and company B have

each operating profit of $50,000. Company C has operating profit of $100,000.

Company A and company B are both all equity companies and the value of each company is $500,000 with a

cost of equity of r! = 10%. Company C has debt with a market value of $400,000 and with a cost of debt of

�! = 3% and a cost of equity of r! = 12.6%. The equity value of company C is $700,000. The price per

share for each of the three companies is 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.

Assume there are no taxes.

Which option will you choose?

Answer: invest all of the money in company A and company B / in company C

Part B

In order to finance a new project, company X issued a two year bond carries a face value of $1000 million

and an annual coupon of 10%.

According to your analysis, you expect that:

With probability of 100%, the company will be able to pay its payments at the end of the year (the first

payment of the bond). However, there is a probability of only 30% that at the end of the second year the

Page 7 of 11

company will go into default. In that case, the company will be able to pay only 50% of its payments (its

second payment) to the bond holders.

Assume that the required return by the bondholders of the company is 4% and that the company’s debt

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

*_*Page 8 of 11

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%

Page 10 of 11

Required:

A. Trace the formula used the calculate the Unlevered beta and the relevered beta of company A (show the

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.

Page 11 of 11