Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. You have been asked to value LoraLee enterprises, a privately held restaurant chain
that is expected to make an initial public offering in five years. You have been
provided with the following information:
• The firm generated after-tax operating income of $ 10 million on revenues of $
100 million in the most recent year.
• The firm is all equity funded, with all equity held by venture capitalists, and the
book value of equity at the start of the most recent year was $ 50 million.
• The unlevered beta for publicly traded firms in the sector is 1.00; the correlation
of restaurants with the market is 40% but the correlation of the venture capitalists’
portfolios with the market is 80%.
• The riskfree rate is 3% and the equity risk premium is 5%.
a. If you expect that after-tax operating income will grow 10% a year for the next 5
years and that the firm will maintain its current return on capital, estimate the
expected cash flows each year for the next 5 years. (2 points)
b. At the end of year 5, the firm plans to go public. It plans to remain all equity funded
and the return on capital will be 12% in perpetuity, after year 5. If the firm will be in
stable growth, growing 3% a year after year 5, estimate the value at the end of year 5.
(2 points)
c. If there is a 20% chance that the firm will not survive to go public, estimate the value
of equity today, given the plan to go public in 5 years. (You can assume equity will be
worth nothing if the firm does not make it. Remember also that the firm is held entirely
by venture capitalists) (2 points)
2. You are evaluating Trader Jack’s, a publicly traded grocery store that sells organic
food. The firm is expected to report after-tax operating income of $18 million on
revenues of $300 million and generate an after-tax return on capital of 12% next year.
a. The typical grocery store is in stable growth, growing 3% a year. It has half the aftertax operating margin, and 1.5 times the sales to capital ratio of Trader Jack’s. If the
median EV/Sales ratio for grocery stores is 0.40 and the market is fairly pricing these
companies, estimate the EV/Sales ratio for Trader Jack’s. (Assume that Trader Jack’s has
the same cost of capital and growth rate as the other grocery stores) (3 points)
b. You have run a regression of EV/Sales ratios against after-tax operating margins for
the entire market and arrived at the following regression
EV/Sales = 0.35 + 15.0 (Growth Rate for next 5 years) + 7.50 After-tax operating margin
(Both growth rate and margins are entered as decimals: 5% is entered as 0.05)
Based on this regression, estimate the EV/Sales ratio for Trader Jack’s today, using the
growth rates and margins from part (a). (1 point)
c. Trader Jack’s is considering cutting prices, with the intent of increasing both revenues
and the growth rate. Assuming that the price cut will reduce the after-tax margin by 25%Fall 2010 Name:
2
and increase revenues by 10%, how much will the new growth rate over the next 5 years
have to be for this policy to be value increasing for the company? (You can use the
regression in part (b) to make this judgment). ( 2 points)
3. Keiko Inc., an entertainment company, is considering an acquisition of Matterhorn
Inc., a maker of animated movies. The information on the two companies is provided
below ($ values are in millions):
Keiko Matterhorn
EBIT (1-t) expected next year $100 $ 80
Revenues $1000 $1250
Book Capital invested $1000 $1000
Expected growth 3% 3%
Cost of capital 9% 9%
a. Estimate the value of the combined company, assuming no synergy in the merger.
(2 points)
b. Now assume that Keiko Inc. believes that the combined company will be much
stronger, relative to the competition, and will therefore be able to find more new
investments in the next 4 years (doubling the reinvestment rate over that period for the
combined firm) and earn a return on capital of 12% on new investments in perpetuity.
(Existing investments at both firms will continue to generate their existing returns on
capital) After year 4, the growth rate will drop back to 3% but the return on capital will
stay at 12%. Estimate the value of synergy in this merger. (4 points)
4. You are trying to assess the value of control in Aamco, a troubled automobile parts
supplies company. You have collected the following information:
• The company is expected to generate $48 million in after-tax operating income
next year, on a book value capital invested of $ 800 million.
• The firm currently is currently extremely over levered with a debt to capital ratio
of 80%. The levered beta for the stock is 2.72 and the pre-tax cost of debt is 12%.
The marginal tax rate is 40%, the riskfree rate is 4% and the market risk premium
is 6%.
• You believe that new management can turn the firm around by
o Restructuring the firm’s financing mix, to make it 50% debt and 50%
equity. That will reduce the pre-tax cost of debt to 8%.
o Improving the after-tax return on capital on both existing and new
investments to 9%.
a. Assuming that the firm is in stable growth, growing 3% a year in perpetuity, estimate
the value of the firm today. (2 points)
b. Estimate the cost of capital, if new management is able to restructure the debt in the
firm (lowering the debt to capital ratio to 50% and the pre-tax cost of debt to 8%). (2
points)Fall 2010 Name:
3
c. Assuming that the firm will stay in stable growth, growing at 3% a year, even with new
management, estimate the new value for the firm. (2 points)
d. Now assume that the probability of management changing is 40%, that the market
value of debt today is $400 million and there is no cash balance. Estimate the value of
equity today. ( 1 point)
5. You are helping a vulture investor decide whether he should be investing in the equity
of Grappa Steel. You have collected the following information on the firm:
• The firm reported earnings before interest and taxes of $10 million and had
depreciation charges of $ 15 million.
• Mature steel companies trade at an EV/EBITDA multiple of 6. The standard
deviation in enterprise value at these companies is approximately 30% and the
standard deviation in equity value is 40%.
• Given the state of the market, you estimate that you will face an illiquidity discount of
approximately 20% on the value of the assets liquidated.
• The firm has substantial debt outstanding. The firm has two zero coupon bonds
outstanding, $ 120 million (face value) in five-year bonds and 80 million (face value)
in ten-year bonds.
• The treasury bill rate is 2% and the long term treasury bond rate (for both 5-year and
10-year bonds) is 4%.
a. If you consider equity as an option (to liquidate), value the equity in the firm. (2
points for the inputs; 2 points for the correct solution)
S =
K =
r =
t =
σ =Fall 2010 Name:
4
b. Now assume that you are interested in buying the bonds issued by the
company. Given your analysis in part (a), estimate the probability that these bonds
will default and what you would charge as a default spread (over the riskfree rate)
to buy these bonds. (2 point)Fall 2010 Name:
5
Cumulative Normal DistributionFall 2011 Name:
1
Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. BigDiscount inc. is a retail firm with a hundred stores, many of which are not
very profitable. The company reported $15 million in after-tax operating income
on revenues of $ 500 million and total capital invested of $ 200 million in the
most recent year. You can assume that both revenues and capital are spread
equally across the hundred stores; each store accounts for $ 5 million in revenues
and has $2 million in capital invested. The company currently has a high debt
ratio (70% of capital, in market value terms) and a cost of capital of 10%.
a. Assume that the firm plans to shut down ten unprofitable stores each year and
fully recover the capital invested in these stores. Also assume that the unprofitable
stores generate an after-tax operating margin of only 1.2%. Estimate the free cash
flows to the firm each year for the next 5 years, assuming that revenues per store
and the current margin at each store that remains open does not change. (2 points)
b. At the end of year 5, BigDiscount Inc, expects to be a mature company,
growing 3% a year in perpetuity and to maintain the margin and after-tax return
on capital from year 5 (part a). It also hopes to bring its debt ratio down to 40%
and have a cost of capital of 8% in perpetuity, after year 5. Estimate the terminal
value for the operating assets. (2 points)
c. Given the high debt ratio, if there is a 30% probability that the firm will default
sometime over the next five years. If is does default, you can expect to get only
half of your invested capital back as divestiture proceeds. Assuming that the cost
of capital will stay at 10% for the next five years, estimate the value of the
operating assets today. (2 points)
2. United Holdings Inc. is a company in four different businesses and you have been
asked to do a relative valuation of the company. You have collected the following
information on United’s performance in each business for the most recent year.
Business Revenues EBITDA Net Interest Expense Net Income
Steel $ 2 billion $ 100 million $ 20 million $ 30 million
Technology $ 1 billion $ 100 million $ 10 million $ 60 million
Chemicals $ 1 billion $ 50 million $ 20 million $ 5 million
Financial Svcs $ 1 billion NA $ 50 million $ 50 million
The company has $ 1.2 billion in debt outstanding and a cash balance of $ 200
million. The net interest expense is allocated to each of the divisions, based upon
the estimated net debt of that division. There are 100 million shares outstanding.
a. You find comparable firms within each business and estimate the median
values for different multiples for each business:
Business Multiple used Median value
Steel EV/EBITDA 6.00
Technology EV/Revenues 1.25
Chemicals EV/EBITDA 5.00
Financial Services PE 12Fall 2011 Name:
2
Assuming that each business of United should trade at the median value for
other companies in that business, estimate the value of equity per share in
United Holdings. (3 points)
b. Now assume that you were told that the United Holdings is trading at
$25/share and that you believe that this is because the steel business at United
Holdings has a much higher return on capital than the rest of the peer group.
You have run a regression of EV/EBITDA for the peer group and arrived at
the following:
Steel: EV/EBITDA = 3.0+ 30 (Return on capital)
(The regression is run with decimals; a 10% growth rate is input as 0.10)
Estimate what the return on capital at United Holdings’ steel business will
have to be to justify the price of $25/share. (You can assume that the other
businesses at United Holdings should continue to trade at peer group
medians). (3 points)
3. Celio Inc., a music production company, is considering acquiring Dellwood Inc, a
manufacturer of musical instruments. Dellwood reported $ 15 million in after-tax
operating income on revenues of $ 200 million in the most recent year and had
invested capital of $150 million at the end of the prior year. Dellwood is all equity
funded and has a cost of equity of 9% (Risk free rate is 4%, the equity risk
premium is 5% and the marginal tax rate is 40%.). The firm is in stable growth,
expected to grow 3% a year in perpetuity.
a. Value Dellwood as a stand alone firm, run by its existing management. (2
points)
b. Now assume that Celio is planning to fund half the acquisition with debt
and that Celio’s pre-tax cost of debt is 4%. Dellwood’s optimal debt ratio
is 20% and the firm’s pre-tax cost of debt at that level will be 5%. If this is
only change you see yourself making in Dellwood’s operations, estimate
the value of control in this acquisition. (3 points)
c. You expect to be able to write up the book value of Dellwood’s assets
from $125 million to $ 150 million, after the acquisition. Assuming that
you have ten years of depreciable life left in these assets, that you use
straight line depreciation and that the marginal tax rate for all corporations
is 40%, estimate the value of synergy from this asset write up. (2 points)
4. Sonicare is a manufacturer of electric toothbrushes and other dental appliances. In
the most recent year, the firm reported after-tax operating income of $ 20 million
on total capital invested of $250 million; the firm had capital expenditures of $ 25
million, depreciation of $ 15 million and non-cash working capital increased by $
5 million during the year. The firm is expected to maintain its existing
reinvestment rate and return on capital, at least for the next five years after which
the expected growth rate is expected to drop to 2% in perpetuity (with return on
capital staying unchanged). The cost of capital in perpetuity for the company is
10%, it is all equity funded, and there are 10 million shares outstanding. There is
no cash balance.
a. Estimate the status quo value per share for the firm. (3 points)Fall 2011 Name:
3
b. Now assume that if you ran the firm, you would dial down growth
expectations immediately, and settle for stable growth in perpetuity
starting now, while lowering the reinvestment rate to 20% and increasing
the return on capital to 12%. You also plan to borrow $ 120 million and
buy back shares, lowering your cost of capital in perpetuity to 9%.
Estimate the value of equity per share with you in charge. (3 points)
5. Please pick only one answer to the multiple choice questions (and provide a very,
very short explanation, if needed) (Each is worth one point)
a. You are valuing drug patents as options in two pharmaceutical companies.
The patents both have 12 years left to expiration and roughly the same
characteristics (similar present values if developed today, similar initial
development costs and similar standard deviations). However, one of the
companies is in a competitive environment and the other is a monopoly. In
which company would you expect the patent be valued more highly (as an
option) and why?
i. The company in the competitive environment
ii. The monopolist
iii. It will be valued the same at both companies
Explanation:
b. A gold mining company has substantial undeveloped reserves. Under
which of the following scenarios would you expect the company to most
quickly exploit these reserves.
i. If gold prices go up and gold price volatility increases
ii. If gold prices go down and gold price volatility increases
iii. If gold prices go up and gold price volatility decreases
iv. If gold prices go down and gold price volatility decreases
Explanation:
c. Companies hold back on using debt capacity because they value financial
flexibility, i.e., the ability to use the debt capacity to take advantage of
unexpected investment opportunities. In which of the following companies
does this action make the most sense?
i. Companies that earn low excess returns in businesses with
predictable reinvestment needs
ii. Companies that earn high excess returns in businesses with
predictable reinvestment needs.
iii. Companies that earn low excess returns in businesses with
unpredictable reinvestment needs
iv. Companies that earn high excess returns in businesses with
unpredictable reinvestment needs.
Explanation:Fall 2011 Name:
4
d. You are interested in investing in the securities of Ajax Airlines, a money
losing company with significant debt obligations. You estimate that the
firm generated $8 million in EBITDA last year and that airlines typically
trade at 5 times EBITDA. The average duration of the debt is 5 years and
the total payments (interest and principal) on the debt (corporate bonds)
are expected to amount to $ 60 million over that period. If the risk free rate
is 2% and the standard deviation in firm value for airlines is 30%, would
you buy bonds in Ajax Airlines, if the market interest rate on the bonds is
11%? (3 points)Fall 2012 Name:
1
Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. TriCity Inc. is a publicly traded company with the following characteristics:
– It generated $60 million in after-tax operating income in the most recent year,
on revenues of $ 500 million.
– The company has 100 million shares trading at $ 4/share; the book value of
equity at the start of the most recent year was $ 300 million.
– The company has $ 200 million in debt outstanding currently (book value, as
well as market value) and that number did not change over the course of the
most recent year.
– The company had a cash balance of $ 100 million at the start of the most
recent year, unchanged again over the course of the year.
– The cost of capital for the firm is expected to be 12% next year, 11% the year
after and 10% thereafter (in perpetuity).
a. You expect TriCity’s after-tax operating income to grow 20% a year, each
year for the next 3 years, and TriCity to maintain its current return on
invested capital in perpetuity. Estimate the free cash flows to the firm each
year for the next 3 years. (2 points)
b. At the end of year 3, you expect TriCity to be in stable growth, growing
3% a year in perpetuity, while maintaining its current return on invested
capital. Estimate the terminal value at the end of year 3. (2 points)
c. Assume now that TriCity has 20 million options outstanding, with an
average exercise price of $ 5/share. Using the treasury stock approach,
estimate the value per share for the company today. (2 points)
2. Zeller Inc. is a publicly traded retail firm with a financial arm. You have been
provided with the following information on the firm’s operations (in millions):
Zeller Retail Zeller Financial
BV of equity $300 $100
BV of debt (= market value) $20 $200
PV – leases $85 $0
Revenues $500 NA
EBITDA $65 NA
EBIT (adjusted for leases) $50 NA
Net Income $30 $20
a. You have looked at publicly traded companies in the retail and the financial
services businesses and arrived at the following regressions:
Retail: EV/Sales = 0.60 + 2.50 (Pre-tax operating margin)
Finance: P/BV = 0.80 + 4.00 (Return on Equity)Fall 2012 Name:
2
(Example: With a 5% pre-tax margin, EV/Sales = 0.60+2.50(.05) = 0.725)
Assuming that Zeller Inc. has no cash balance and 50 million shares
outstanding, estimate the value of equity per share. (You capitalized leases for
all retail firms in the regression) (3 points)
b. Assuming that the value of equity that you compute in part (a) is a “fair’
value (i.e., equal to intrinsic value), estimate the cost of equity that the market
is using to value the company. (You can assume that the firm is in stable
growth, growing 3% a year in perpetuity).
(3 points)
1. Smartcell Inc. is a large market-cap smartphone manufacturer that is considering
acquiring Litcell Inc. a much smaller company that develops smartphone
software. Both companies are in stable growth (growing 3% a year) currently,
with the following characteristics (in millions):
SmartCell LitCell
After-tax Operating Income next year $100.00 $15.00
Book value of equity $400.00 $100.00
Book value of debt (= market value) $150.00 $0.00
Cash $50.00 $0.00
Number of shares 100 5
Cost of capital 9% 10%
a. Assuming that there are no synergies in the merger and that each company’s
shares are priced at intrinsic value, what exchange ratio (of SmartCell shares
for LitCell shares) would make this a fair value acquisition? (2 points)
b. Now assume that if Smartcell acquires Litcell, the after-tax return on capital
and cost of capital of the combined company will converge on SmartCell’s
current return on capital (with operating income rising for the combined firm)
and cost of capital. If SmartCell wants to retain 40% of the value of synergy
for its stockholders, what exchange ratio should it offer? (You can assume that
the stable growth rate will remain unchanged at 3%.) (4 points)
2. Dry Goods Inc. is a consumer product company that has seen its earnings
plummet and is indebtedness increase over the last five years. It operates in two
business, packaged goods and toiletries, with the following results (in millions):
Packaged Goods Toiletries Combined firm
Invested Capital $600.00 $900.00 $1,500.00
After-tax Operating Income next year= $66.00 $54.00 $120.00
Expected growth rate in perpetuity = 2% 2% 2%
The company currently has 100 million shares trading at $3 a share and $ 1,200
million in market value of debt (with an 9% pre-tax interest rate on the debt) and a
cost of equity of 20%; the corporate tax rate is 40%, riskfree rate is 2% and the
equity risk premium is 6%. (You can assume that both businesses are equally
risky)Fall 2012 Name:
3
a. Estimate the intrinsic value per share for Dry Goods, assuming that it continues
to be run as is, with its current return on capital and cost of capital remaining
unchanged in perpetuity. (2 points)
b. Now assume that there is the possibility that Dry Goods will be offered $ 600
million for its toiletries business and if it is, it will use the proceeds to retire $ 300
million in debt (which will lower the pre-tax cost of debt to 7% for the remaining
debt) and to invest $300 million in its packaged goods business (where it will earn
the same return on capital as the existing investment in that business). Estimate
the intrinsic value per share, assuming that the packaged goods business will
remain a stable growth business, growing 2% a year in perpetuity. (3 points)
c. Now assume that the current market price is correct and reflects an expectation
that the restructuring in part (b) may happen. Assuming that your intrinsic value
per share estimates in (a) and (b) are right, what is the probability of the
restructuring happening? (1 point)
6. You are interested in investing an eight-story rental building in Manhattan. The
building has 80,000 square feet of rental space and the rental income (pre-tax)
next year is expected to be $60/square foot. You can assume that the building will
be fully rented out next year and that the rental income will grow 2% a year in
perpetuity; the cost of capital for real estate is 8%.
a. Allowing for a 40% tax rate, estimate how much you would be willing to pay
for the building, based just on the rental income. (You can assume no
reinvestment is needed) (2 points)
b. Now assume that owning the building will give you the right to add twelve
more floors, with a cumulative 100,000 square feet in rentable space, any time
over the next 20 years (at which point the rights lapse). The cost of adding these
additional floors today is $ 50 million and given the state of the rental market, you
believe that you will be able to get only $40/square foot (pre-tax) as rental income
for this new space, growing at 2% a year in perpetuity. However, the standard
deviation in rental income (per square foot) in Manhattan over the last twenty
years has been 30% and the risk free rate is 3%. Estimate how much you would
be willing to pay for the rental building, with the option to add the additional
floors. (2 points for inputs, 2 points for right option value)
S =
K =
t =
σ =
r =Final Spring 2013 Name:
1
Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. Callaway Copper is a mature copper mining company. While the company is
expected to be in stable growth, with revenues growing at 2.5% a year in perpetuity,
its earnings are unstable and are a function of copper prices. The company has a book
value of invested capital of $1,200 million. The table below reports revenues and
after-tax operating income over the last 5 years.
Last
year
2 years
ago
3 years
ago
4 years
ago
5 years
ago
Revenues $1,000 $980 $950 $920 $900
After-tax Operating
Income -$120 $325 $330 -$80 $250
a. Assume that the average after-tax operating margin over the last 5 years is a
good estimate of the normalized margin and that operating margins will revert
back immediately to normalized levels. The cost of capital for the firm is
7.5%. Based on these assumptions, estimate the value of the operating assets
in the firm today. (3 points)
b. Now assume that the company has a cash balance of $150 million, debt
outstanding of $ 500 million and a 10% holding in another mining company.
That holding has a book value of $75 million and an estimated market value
of $290 million. Estimate the value of equity in the firm today. (1 point)
c. Finally, assume that there is a 20% chance that the company will get
nationalized in the near future and that if it is nationalized, you will receive
the book value of the invested capital as your compensation. Estimate the
value of equity per share today, given this danger. (2 points)
2. You are analyzing the apparel business and have separated the firms in the business
broadly into brand name and generic companies. While you believe that both groups
are in stable growth, growing 3% a year and have the same cost of capital and sales to
invested capital ratio, the generic companies are trading at an EV/Sales ratio of 0.60
whereas the brand name companies are trading at an EV/Sales ratio of 1.40.
a. If the generic companies are fairly priced and expect to have an after-tax
operating margin of 4% next year and have a sales to capital ratio of 3.0,
estimate the cost of capital for these companies. (2 points)
b. Now assume that brand name companies have the same cost of capital and
sales to capital ratio as the generic companies and are also fairly priced.
Estimate the after-tax operating margin for brand name companies. (2 points)
c. Finally, assume that brand name companies are considering cutting prices by
10. If this will result in an operating margin of 8%, but increase sales by 15%
(holding capital constant), what effect will this have on the EV/Sales ratio of
brand name companies? (2 points)Final Spring 2013 Name:
2
3. Zuma Inc., a small US-based consumer product company, is looking at acquiring Alta
Inc., a Brazilian consumer product company. The information on the two companies
is provided below:
Zuma Alta
After-tax Operating Income
next year $100.00 R$ 50.00
Invested Capital $800.00 R$ 250.00
Cost of equity 9% 16%
After-tax cost of debt 3% 6%
Debt ratio 40% 20%
Expected growth 2.5% 6%
Note that Alta’s cost of equity, debt and expected growth rates are all specified in $R
terms. The current exchange rate is US$ = 2 $R.
a. Estimate the value of the combined firm in US$ right after the acquisition,
assuming that there is no synergy. (3 points)
b. Now assume that as a result of the acquisition, you expect the following
changes in the combined company:
• The company will be able to cut costs and save $10 million, while
also shedding $25 million in invested capital. The resulting return on
capital can be maintained in perpetuity.
• The company will continue to be in stable growth but the expected
growth rate will be 3% in perpetuity.
• The company’s new cost of equity will be 9.5%, its after-tax cost of
debt will be 3.5% and it will have a 40% debt ratio.
Estimate the value of synergy in this merger. (3 points)
4. Manza Inc. is a publicly traded company in three businesses. The details of the three
businesses are provided below (in millions):
Next year’s
EBIT (1-t) Book equity Book debt Cost of capital Growth rate (in perpetuity)
Steel 100 600 200 8% 2.50%
Chemicals 50 400 100 10% 2.00%
Real Estate 60 600 600 8% 3.00%
The company has no cash balance.
a. Estimate the value of the operating assets of the company assuming it stays
with its existing business mix (and management). (3 points)Final Spring 2013 Name:
3
b. Now assume that you have been brought in as a CEO and are thinking about
restructuring the company. You believe that you can divest the real estate
business for 75% of book value of invested capital and reinvest half the
divestiture proceeds in the steel business and the other half in the chemical
business. If you can maintain the current returns on capital in each of these
businesses, estimate the new value for the business. (3 points)
5. A venture capitalist is interested in investing in a young, high growth start up. You
have estimated the cash flows in your business as follows:
1 2 3 4 5 Beyond
FCFF -$100.00 -$50.00 $50.00 $75.00 $100.00 Grows 3% forever
Cost of capital 15% 15% 15% 15% 15% 10%
The firm currently has no debt or cash.
a. Assume that the VC will invest $150 million in the firm (with the cash being held
by it to meet future reinvestment needs), what percentage of the company should
the VC get in return (given your intrinsic valuation)? (2 points)
b. If you do invest, you will be given the option to either (1) invest an extra $150
million at the end of year 4 and double your ownership stake in the firm or (2) sell
your current stake back to the other owners and receive half of your initial
investment back at the end of year 4. If the standard deviation in firm value of
publicly traded firms in this business is 30% and the risk free rate is 3%, what is
the value of the option(s)? (Show the inputs to the option pricing model and then
value the option(s))Final Fall 2013 Name:
1
Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. Vista Inc. is a chemical firm that generated $15 million in after-tax operating
income on $1 billion in revenues in the most recent year. At the start of that year,
it has book value of equity of $90 million, debt outstanding of $45 million and a
cash balance of $15 million. The company has 10 million shares outstanding
today and is expected to generate its current return on capital in perpetuity. The
company’s cost of capital is expected to be 9% for the next 5 years.
a. Vista is expected to grow 15% a year for the next 5 years, while
maintaining its current return on capital. Estimate the expected free cash
flows to the firm each year for the next 5 years. (2 points)
b. Now assume that Vista’s stock is trading at $26.85/share and that the
market has correctly priced the stock today and shares your views on cash
flows (in part a). Estimate the terminal value for Vista (at the end of year
5) that the market is forecasting. (2 points)
c. Given the terminal value that you have estimated in part b, estimate the
cost on capital that the market expects for Vista in perpetuity, if the
growth rate forever, after year 5, is 2.5%. (2 points)
2. You are trying to assess whether the S&P 500 is correctly priced today and have
collected the following information:
Current Average: 1981-2013
Forward PE 20 12
Return on equity 15% 12%
Expected nominal growth (in perpetuity) 3% 4%
T.Bond rate = 3% 5%
a. Given the average values for the S&P 500 from 1981-2013, estimate the
implied equity risk premium over that period. (2 points)
b. If the average implied equity risk premium that you estimated (in part a) is
the correct equity risk premium today, how under or over valued are
stocks today? (2 points)
c. Now assume that you believe that the Fed can keep the T.Bond rate at 3%,
even as the economy improves. How high would the nominal growth rate
have to be in perpetuity for stocks to be fairly valued? (2 points)
3. Gallaway Inc. is a company that is in two businesses: it produces alcoholic
beverages and runs restaurants. The table below summarizes key operating
metrics ($ values in millions) for both businesses:
Business Expected EBIT
(1-t) next year
Invested
Capital
Cost of
capital
Expected Growth
(in perpetuity)
Alcoholic $10 $200 7% 2%Final Fall 2013 Name:
2
Beverages
Restaurants $60 $300 8% 2%
The firm is expected to have $9 million in unallocated after-tax corporate
expenses next year, growing 1.5% a year in perpetuity and the cost of capital for
the entire company is 7.5%.
a. Assuming that both businesses continue to earn their current return on
invested capital in perpetuity, estimate the intrinsic value of Gallaway Inc. as
a company. (3 points)
b. Now assume that you can have been hired as the new CEO. While you cannot
do much about improving returns on existing investments in the alcoholic
beverage business, you plan to stop reinvesting in that business and redirect
that money into the restaurant business (while maintaining the current return
on capital in the restaurant business). You also believe that you can cut
corporate expenses by 50%. Estimate the value of Gallaway after the
restructuring. (3 points)
4. Delta Appliances, a publicly traded appliance manufacturer, is considering an
acquisition of CafeCoz, a privately owned appliance manufacturer. You have
been provided with the following information:
Delta Appliances CafeCoz
After-tax operating
income next year
$10 million $ 5 million
Debt/Capital ratio 20.00% 0.00%
Invested Capital $100 million $25 million
Both companies are in stable growth, growing 3% a year. The risk free rate is 3%
and the equity risk premium is 5%. The appliance sector has an unlevered beta of
0.80 and a correlation of 0.40 with the market. The marginal tax rate for all firms
is 40%.
a. Value Delta Appliances as a stand alone company. (2 points)
b. Value CafeCoz as a stand alone company to its existing owner, who is
undiversified. (2 points)
c. Delta plans to acquire CafeCoz, paying twice the owner’s estimated value
(from part b) for the company, using a 20% debt to capital ratio (with the after-tax
cost of debt remaining at 3%). Estimate the value of Delta Appliances after the
transaction. (2 points)
5. SpiceAir Inc. is a publicly traded airline that is burdened with $1 billion in debt
(face value), with a weighted-average duration of approximately 4 years. The
company is losing money but has substantial assets that you have valued as
following:
Assets Estimated Going concern
(DCF) value
Liquidity Discount
Aircraft $250 million 20%
Airline routes $400 million 0%
Other assets $150 million 25%Final Fall 2013 Name:
3
The standard deviation in asset value for airlines is 50% and the risk free rate is
3%.
a. If the debt trades at a discount of 40% on face value, and the company has no
cash balance, estimate the going concern (DCF) value of equity in the company.
(1 point)
b. Given the market value of the debt, estimate the probability of default that the
bond market is attaching to the company. (1 point)
c. Estimate the value of equity in SpiceAir as a liquidation option. (2 points for
inputs, 2 points for correct option value)
S = Value of the underlying asset =
K = Strike price =
t = Life of the option =
Standard deviation =
r = Riskless rate =Final Fall 2014 Name:
1
Valuation: Final Exam
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. You are valuing Trent Oil, a small, publicly traded oil company. The company
reported $250 million in after-tax operating income in the most recent year on
revenues of $ 5 billion. The company also reported having $500 million in book
equity, $1 billion in debt (book and market) and a cash balance of $250 million.
a. During the most recent year, oil prices averaged $110/barrel, but the current
oil price is $60/barrel. Regressing after-tax operating income (in millions) at
Trent Oil against oil prices ($/barrel) over the last 25 years, you have arrived
at the following:
After-tax Operating Income = 30 + 2.00 (Price/Barrel of Oil) R2 = 90%
Assuming that you want to value Trent Oil at the current oil price (which you
feel is the new normal), and that Trent Oil is a mature company, growing at
1.5% a year, estimate the value of Trent Oil’s operating assets. (You can
assume that the cost of capital for a small oil company is 7.5%) (3 points)
b. Now assume that you are given the following additional information:
– Trent Oil owns 20% of RigWorks, an oil services company, and the holding
is classified as a minority, active investment and this equity holding is
recorded on Trent Oil’s balance sheet as having a value of $50 million (in
book value terms). RigWorks is a mature company growing at 2% a year, with
a ROE of 14% and a cost of equity of 8% in perpetuity.
– Trent Oil has100 million shares outstanding as well as 10 million employee
options. While you don’t have the information to value the options, they have
a strike price of $10/share and five years to maturity.
Estimate the value per share in Trent Oil. (3 points)
2. You are examining Retail ETFs (exchange traded funds) and have compiled the
following information on three of the ETFs.
All Retail
ETF
Luxury Retail
ETF
Online Retail
ETF
EV/Sales 0.90 2.25 7.50
After-tax operating margin (next year) 6.00% 16.00% NA
Sales/Capital Ratio 2.00 1.25 6.00
Expected growth rate in operating
income
3.00% 3.00%
NA
Life Cycle Mature Mature High Growth
a. If you assume that the All Retail ETF is priced fairly, estimate the cost of
capital for a typical retail firm. (2 points)
b. Now assume that you believe that luxury retailers have a 10% cost of capital.
How under or over valued is the luxury retail ETF? (2 points)Final Fall 2014 Name:
2
c. Finally, consider online ETFs, which are showing high revenue growth, while
losing money today. While you unable to estimate an intrinsic EV/Sales ratio,
a regression of all retail firms yields the following:
EV/Sales = 1.80 + 25.0 (Annual Revenue growth rate) – 15.0 (Cost of
Capital)
(Enter percentages as decimals in the regression, 15% is entered as .15)
If the cost of capital for online retailers is 12%, estimate the annual growth
rate you would need in revenues to justify today’s EV/Sales ratio. (2 points)Final Fall 2014 Name:
3
3. You have been just hired as CEO of Mirra Inc., a conglomerate that operates in three
businesses. The details of the businesses are provided below:
Entertainment
Movie
Theaters
Travel
Services Company
Revenues (millions) $400 $300 $300 $1,000
Operating Income (next year in millions) $100 $30 $50 $180
Effective tax rate 36% 20% 36% 33.33%
After-tax Operating Income (next year in
millions) $64 $24 $32 $120
Invested Capital ( in millions) $500 $400 $100 $1,000
Expected Growth Rate 3.00% 3.00% 3.00% 3.00%
Cost of capital 10.00% 8.00% 7.00% 9.00%
a. What is the value of the consolidated company, using the combined
company’s cash flows and cost of capital? (2 points)
b. What is the value of Mirra as the sum of its parts, using the divisional cash
flows and the industry average cost of capital for each division? (3 points)
c. If you are getting a different value for Mirra in part b, where is the difference
coming from? ( 1 point)
i. A conglomerate discount is being applied by the market.
ii. The broken-up businesses will be run more efficiently as stand alone
units
iii. The combined company has a less optimized capital structure than
that the individual units could have.
iv. The broken-up businesses will pay less in taxes than the combined
company
v. The broken-up businesses will have higher growth than the
combined company
vi. All of the above
4. You have been asked to assess the value of synergy in a merger of two entertainment
companies, StreamTV, a company that streams only horror movies and DigiMovies, a
maker of zombie/cult movies. The details of each company are provided below:
StreamTV DigiMovies
Business Streaming Content
Revenues (in millions) $1000 $800
Pre-tax operating income (this year in millions) $100 $60
Effective tax rate 40.00% 20.00%
Invested capital (in millions) $800.00 $400.00
Expected growth rate 2% 2%
Cost of capital 10% 10%
a. Estimate the value of the Stream TV as a standalone firm. (1 point)Final Fall 2014 Name:
4
b. Estimate the value of DigiMovies as a standalone firm. (1 point)
c. Now assume that the combined company is planning to do the following:
• Hire more movie production staff, increasing operating expenses (pre-tax)
by $10 million immediately.
• The resulting pre-tax operating income will grow at 5% a year for the next
five years. However, the combined company will reinvest the same amount
(in dollar terms) that the standalone companies would have invested
collectively over the next five years.
• Move operations to Singapore (which is DigiMovies base) and lower the
effective tax rate to 20% for all of the company’s income. The company
will face an upfront cost (legal and other) of $150 million to make this
move.
After year 5, the growth rate is expected to drop back to 2% and the return on
invested capital will be whatever the company is expected to generate based on
operating income and invested capital in year 5. Estimate the value of synergy in
this merger. (4 points)
5. The following three questions are all related to real options.
a. We used the option to delay framework to value patents. Assume that you
have a 20-year patent on a diabetes drug, with 12 years left to expiration. You
have already spent $250 million on R&D and believe that you will need to
spend an additional $ 500 million to make it commercially viable. The net
present value of this investment, if developed today, is -$50 million. If the
standard deviation in stock prices is 40% and the standard deviation in firm
values is 30% for drug companies, estimate the values that you would use for
the following in an option price model. (1 point)
i. S (Value of underlying asset) =
ii. K (Strike price) =
iii. t =
iv. Standard deviation =
v. Cost of delay (if any) =
b. Redix Inc. is a company that has no debt and a cost of equity of 10%. You
have computed an optimal debt ratio of 40% for the company and a cost of
capital of 9% at that optimal ratio. Redix argues that it should stay under
levered because of the value of financial flexibility. In which of the following
scenarios would this argument make the most sense? (1 point)
i. Redix has wide access to capital, predictable reinvestment needs and
earns a return on capital greater than its cost of capital.
ii. Redix has limited access to capital, predictable reinvestment needs
and earns a return on capital greater than its cost of capital.
iii. Redix has limited access to capital, unpredictable reinvestment needs
and earns a return on capital greater than its cost of capital.
iv. Redix has wide access to capital, predictable reinvestment needs and
earns a return on capital less than its cost of capital.Final Fall 2014 Name:
5
v. Redix has limited access to capital, predictable reinvestment needs
and earns a return on capital less than its cost of capital.
vi. Redix has limited access to capital, unpredictable reinvestment needs
and earns a return on capital less than its cost of capital.
c. Best Buy (a US electronics retailer) is considering buying Zee TV, an Indian
electronics company with exclusive rights to sell Apple products in India, for
$2.25 billion. Zee TV is a mature company, with an expected after-tax cash
flow of $150 million, next year, growing 3% (in US dollar terms) a year in
perpetuity, with a cost of capital of 13%. As part of the acquisition, Best Buy
can also get the exclusive right to double the number of Zee TV stores and its
expected after-tax cash flows (in perpetuity) by investing an extra $ 1 billion
any time over the next five years. If the standard deviation in firm value in
electronic stores is 40% and the five-year risk free rate is 3%, should Best Buy
go through with this acquisition? (4 points)Spring 2015 Name:
1
Final Exam: Valuation
Answer all questions and show necessary work. Please be brief. This is an open books,
open notes exam.
1. You have been asked to value Dexia Financials, a small, high growth bank, and are
told that Dexia generated $150 million in net income in the most recent year on a
book value of equity of $ 750 million; you can assume that the book value of equity is
equal to the regulatory capital of the bank and that it has risk-adjusted assets of $ 5
billion right now.
a. Dexia expects its risk adjusted assets and net income to grow 10% a year for
the next five years and plans to increase its regulatory capital ratio to 20% of
risk-adjusted assets by the end of year 5 (with the ratio changing in equal
annual increments over the five years). Estimate the FCFE of Dexia each year
for the next 5 years. (2 points)
b. After year 5, Dexia expects to be a mature bank, growing 3% a year in
perpetuity, while continuing to earn the return on equity that it had at the end
of year 5. If the cost of equity for mature banks is 9%, estimate the value of
equity at the end of year 5. (2 points)
c. If Dexia expects to have a cost of equity of 12% for the next 5 years, estimate
the value per share, assuming that Dexia has 50 million shares and 10 million
options outstanding (with a strike price of $20 each) today. (2 points)
2. PeopleMeet is a social media company that currently has 10 million users but
reported an operating loss of $5 million on $10 million in revenues in the most recent
year, mostly from advertising. The company expects revenues to grow 80% a year for
the next 5 years and its pre-tax operating margin to improve to 20% of revenues by
year 5. After year 5, you expect revenue growth to drop to 10% a year for the
following 5 years and margins to stay stable. (The company has no debt and no cash
balance.)
a. You have run a regression across more established advertising companies to
arrived at the following regression (with all percentage numbers entered as decimals,
i.e., 20% will be entered as 0.20):
EV/Sales = 0.80 + 45.0 (Expected annual revenue growth in the next 5
years) + 25.0 (Pre-tax Operating Margin) – 1.5 (Earnings Loss Dummy)
where the earnings loss dummy is set equal to one if the company is reporting an
operating loss and zero if it is not. Using this regression and current numbers,
estimate the value of PeopleMeet today. (2 points)
b. Using the same regression, estimate the enterprise value of People Meet at the end
of year 5, based upon your expectations for what the company will look like then. (2
points)
c. Now assume that the cost of equity for PeopleMeet is 15% for the next 5 years and
10% beyond. If there is no chance that the company will fail over the next 5 years and
your estimates from parts a and b are both correct, estimate how much new equity (in
PV terms) the company will have to issue over the next 5 years. (You can assume that
the company will have a 20% debt to capital ratio at the end of year 5).(2 points)Spring 2015 Name:
2
3. You have been asked to look at a merger of two pharmaceutical companies, Griffin
and Leblow Inc.,, and have been provided the following information on them (with all
dollar values in millions of dollars):
Griffin Leblow
Revenues $2,000 $1,000
Expected EBIT next year $200 $150
Tax rate 40% 40%
Beta (Levered) 1.2 1.2
Debt to capital ratio 20% 20%
Cost of equity 9.20% 9.20%
Pre-tax cost of debt 4.00% 4.00%
Expected growth rate (& Risk free
rate) 2% 2%
Invested capital $1,200.00 $900.00
a. Estimate the value of Griffin as a stand-alone company. (1.5 points)
b. Estimate the value of Leblow as a stand-alone company. (1.5 points)
c. Now assume that the combined company will be able to cut S,G&A expenses
by $70 million next year, while keeping expected growth intact. In addition, the
combined company will be able to use its larger size (and stability) to increase its
debt to capital ratio to 30%, without affecting its pre-tax cost of debt. Estimate the
value of synergy in this merger. (2 points)
4. You have been asked to assess a potential buyout of Dryden Inc., a manufacturer of
condiments. The company currently is managed very conservatively, with no debt
and $400 million in invested capital, all in the United States. It also expects to
generate $60 million in pre-tax operating income on $500 million in revenues, all in
the United States, next year. The risk free rate is 2.5%, the marginal and effective tax
rates for US income is 40% and the equity risk premium for the US is 6%. The beta
for the stock is 1.00.
a. If the firm expects operating income to grow at 2.5% forever, estimate the
value of the company’s operating assets. (2 points)
b. GeoFund, a Brazil-based private equity fund is considering buying out Dryden and
making significant changes to the company:
• The company plans to move its headquarters to Brazil, lowering the effective
tax rate on earnings for the entire company to 30%.
• GeoFund expects to invest $100 million immediately to expand into the
Brazilian market. The expansion is expected to generate $250 million in
additional revenues in Brazil next year and these revenues are expected to
grow 2.5% a year in perpetuity thereafter. The pre-tax operating margin on
Brazilian sales is expected to be only 8%.
• The company plans to increase its debt to capital ratio to 20%, though it will
keep all of its debt in the US (where the marginal tax rate is 40%). The pre-tax
cost of debt is 4.5% and the country risk premium for Brazil is 3%.
What is the most that GeoFund can afford to pay for Dryden? (4 points)Spring 2015 Name:
3
5. IOL is an internet service provider that has hit a plateau in terms of users and revenues.
In the most recent year, it had 10 million users, each of whom paid $200/year for the
service. The company’s income statement and balance sheet are below (in millions).
Most recent year Start of most recent year
Revenues $2,000 Net Fixed Assets $1,300
EBITDA $500 Cash $100
EBIT $400 Non-cash Current Assets $200
Interest expenses $50 Total Assets $1,600
Taxable Income $350 Non-debt Current Liabilities $100
Taxes $105 Debt $500
Net Income $245 Equity $1,000
Total Liabilities $1,600
The tax rate paid in 2014 is the effective tax rate. The risk free rate is 2%, the cost of
capital for IOL is 8%
a. If IOL expects to generate a 2% growth rate in perpetuity (from increasing user fees),
while maintaining its existing return on capital, estimate the value of its operating assets.
(2 points)
b. Now assume that if IOL has the rights (for the next 10 years) to a proprietary
technology that it can use to provide streaming media services (a mini Netflix) to its
current users. The initial investment needed in infrastructure and media content is $4
billion, depreciable straight line over 10 years, and while the service will not attract any
new users to IOL, it will allow IOL to charge more for its service. A market testing
survey suggests that users will be willing to pay an additional $50 a year for the service,
but there is substantial uncertainty in this estimate (standard deviation is 30%). Estimate
the value of the proprietary technology to IOL. (You can assume that there you will be
able to generate ten years of revenues from the service, once initiated, and that there is no
cost to delaying initiation.) How much would you willing to pay as a premium for IOL
because it owns these rights? (4 points)Final Fall 2014 Name:
6
Cumulative Normal Distribution table
d N(d) d N(d) d N(d)
-3.00 0.0013 -1.00 0.1587 1.05 0.8531
-2.95 0.0016 -0.95 0.1711 1.10 0.8643
-2.90 0.0019 -0.90 0.1841 1.15 0.8749
-2.85 0.0022 -0.85 0.1977 1.20 0.8849
-2.80 0.0026 -0.80 0.2119 1.25 0.8944
-2.75 0.0030 -0.75 0.2266 1.30 0.9032
-2.70 0.0035 -0.70 0.2420 1.35 0.9115
-2.65 0.0040 -0.65 0.2578 1.40 0.9192
-2.60 0.0047 -0.60 0.2743 1.45 0.9265
-2.55 0.0054 -0.55 0.2912 1.50 0.9332
-2.50 0.0062 -0.50 0.3085 1.55 0.9394
-2.45 0.0071 -0.45 0.3264 1.60 0.9452
-2.40 0.0082 -0.40 0.3446 1.65 0.9505
-2.35 0.0094 -0.35 0.3632 1.70 0.9554
-2.30 0.0107 -0.30 0.3821 1.75 0.9599
-2.25 0.0122 -0.25 0.4013 1.80 0.9641
-2.20 0.0139 -0.20 0.4207 1.85 0.9678
-2.15 0.0158 -0.15 0.4404 1.90 0.9713
-2.10 0.0179 -0.10 0.4602 1.95 0.9744
-2.05 0.0202 -0.05 0.4801 2.00 0.9772
-2.00 0.0228 0.00 0.5000 2.05 0.9798
-1.95 0.0256 0.05 0.5199 2.10 0.9821
-1.90 0.0287 0.10 0.5398 2.15 0.9842
-1.85 0.0322 0.15 0.5596 2.20 0.9861
-1.80 0.0359 0.20 0.5793 2.25 0.9878
-1.75 0.0401 0.25 0.5987 2.30 0.9893
-1.70 0.0446 0.30 0.6179 2.35 0.9906
-1.65 0.0495 0.35 0.6368 2.40 0.9918
-1.60 0.0548 0.40 0.6554 2.45 0.9929
-1.55 0.0606 0.45 0.6736 2.50 0.9938
-1.50 0.0668 0.50 0.6915 2.55 0.9946
-1.45 0.0735 0.55 0.7088 2.60 0.9953
-1.40 0.0808 0.60 0.7257 2.65 0.9960
-1.35 0.0885 0.65 0.7422 2.70 0.9965
-1.30 0.0968 0.70 0.7580 2.75 0.9970
-1.25 0.1056 0.75 0.7734 2.80 0.9974
-1.20 0.1151 0.80 0.7881 2.85 0.9978
-1.15 0.1251 0.85 0.8023 2.90 0.9981
-1.10 0.1357 0.90 0.8159 2.95 0.9984
-1.05 0.1469 0.95 0.8289 3.00 0.9987
-1.00 0.1587 1.00 0.8413
