Solutions to Chapters 7

1
Solutions to Chapters 7 8 Problem Sets
2
7-11. ABC Incorporated shares are currently
trading for 32 per share. The firm has 1.13
billion shares outstanding. In addition, the
market value of the firms outstanding debt is 2
billion. The 10-year Treasury bond rate is 6.25.
ABC has an outstanding credit record and has
earned an AAA rating from the major credit rating
agencies. The current interest rate on AAA
corporate bonds is 6.45. The historical risk
premium for stocks over the risk-free rate of
return is 5.5 percentage points. The firms beta
is estimated to be 1.1 and its marginal tax rate,
including federal, state, and local taxes is
40. What is the cost of equity (COE)? What is
the after-tax cost of debt? What is the weighted
average cost of capital (WACC)? COE .0625
1.1 (.055) .123 i(after-tax cost of debt)
.0645 x (1-.4) .039 WACC (32x1.13)/38.16 x
.1230 2.0/38.16 x .039 .1166 .002 .119
3
7-12. HiFlyer Corporation does not currently have
any debt. Its tax rate is .4 and its unlevered
beta is estimated by examining comparable
companies to be 2.0. The 10-year Treasury bond
rate is 6.25 and the historical risk premium
over the risk free rate is 5.5. Next year,
HiFlyer expects to borrow up to 75 of its equity
value to fund future growth. Calculate the firms
current cost of equity. Estimate the firms cost
of equity after it increases its leverage to 75
of equity? COE .0625 2.0 (5.5)
.1725 COE (with leverage) .0625 Bl
(5.5), where Bl Bu(1(D/E)(1-t))
2.0(1(.75)(.6)) 2.9
.0625 2.9(.055)
.222
4
7-13. Abbreviated financial statements are given
for Fletcher Corporation in the following table
2001 2002
Revenues 600.0 690.0
Operating expenses 520.0 600.0
Depreciation 16.0 18.0
Earnings before interest and taxes 64.0 72.0
Less Interest Expense 5.0 5.0
Less Taxes 23.6 26.8
Equals Net income 35.4 40.2
Addendum Addendum Addendum
Yearend working capital 150 200
Principal repayment 25.0 25.0
Capital expenditures 20 10

• Yearend working capital in 2000 was 160 million
  and the firms marginal tax rate is 40 in both
  2001 and 2002. Estimate the following for 2001
  and 2002
• Free cash flow to equity.
• Free cash flow to the firm.
• Answers
• 16.4 million in 2001 and (26.8) million in 2002
  
• 44.4 million in 2001 and 1.2 million in 2002
• FCFE2001 NI Dep Capex Chg WC Principal
  Repayments
• 35.4 16 20 (150-160) 25 16.4
• FCFE2002 40.2 18 10 (200 150) 25
  -26.8
• FCFF2001 EBIT (1-t) Dep Capex Chg. WC 64
  (1-.4) 16 20 (150-160) 44.4
• FCFF2002 72 (1-.4) 18 10 (200-150) 1.2

5
7-14. No Growth Incorporated had operating income
before interest and taxes in 2002 of 220
million. The firm was expected to generate this
level of operating income indefinitely. The firm
had depreciation expense of 10 million that same
year. Capital spending totaled 20 million
during 2002. At the end of 2001 and 2002,
working capital totaled 70 and 80 million,
respectively. The firms combined marginal
state, local, and federal tax rate was 40 and
its debt outstanding had a market value of 1.2
billion. The 10-year Treasury bond rate is 5
and the borrowing rate for companies exhibiting
levels of creditworthiness similar to No Growth
is 7. The historical risk premium for stocks
over the risk free rate of return is 5.5. No
Growths beta was estimated to be 1.0. The firm
had 2,500,000 common shares outstanding at the
end of 2002. No Growths target debt-to-total
capital ratio is 30. a. Estimate free cash
flow to the firm in 2002. b.
Estimate the firms cost of capital. c.
Estimate the value of the firm (i.e., includes
the value of equity and debt) at the end of 2002,
assuming that it will generate
the value of free cash flow estimated in (a)
indefinitely. d. Estimate the value
of the equity of the firm at the end of 2002.
e. Estimate the value per share at the
end of 2002. a FCFF2002
220x(1-.4) 10 20 (80-70) 132 10 20 10
112 million b. COE .05
1.0(.055) 10.5 c. WACC .70 x .105
.07 x (1-.4) x .3 .0735 .0126 .0861
d. PV 112,000,000/.0861 1,300,813,008
e. Equity Value 1,300.8 - 1,200.0
100.8 million Equity value per
share 100.8/2.5 40.33
6
7-15. Carlisle Enterprises, a specialty
pharmaceutical manufacturer, has been losing
market share for three years since several key
patents have expired. The free cash flow to the
firm in 2002 was 10 million. This figure is
expected to decline rapidly as more competitive
generic drugs enter the market. Projected cash
flows for the next five years are 8.5 million,
7.0 million, 5 million, 2.0 million, and .5
million. Cash flow after the fifth year is
expected to be negligible. The firms board has
decided to sell the firm to a larger
pharmaceutical company interested in using
Carlisles product offering to fill gaps in its
own product offering until it can develop similar
drugs. Carlisles cost of capital is 15. What
purchase price must Carlisle obtain to earn its
cost of capital? PV 8.5/1.15 7.0/1.152
5/1.153 2/1.154 .5/1.155 7.39 5.29
3.29 1.14 .25 17.4
7
7-16. Ergo Unlimiteds current years free cash
flow is 10 million. It is projected to grow at
20 per year for the next five years. It is
expected to grow at a more modest 5 beyond the
fifth year. The firm estimates that its cost of
capital is 12 during the next five years and
then will drop to 10 beyond the fifth year as
the business matures. Estimate the firms
current market value. PV1-5 10(1.2)/1.12
10(1.2)2/1.122 10(1.2)3/1.123
10(1.2)4/1.124 10(1.2)5/1.125
10.71 11.48 12.30 13.18 14.12
61.79 PVtv 10(1.20)5x1.05/(.10-.05)
522.55 296.51 1.125
1.125 Total PV 61.79
296.51 358.30
8

• 7-17. In the year in which it intends to go
  public, a firm has revenues of 20 million and
  net income after taxes of 2 million. The firm
  has no debt, and revenue is expected to grow at
  20 annually for the next five years and 5
  annually thereafter. Net profit margins are
  expected to remain constant throughout. Capital
  expenditures are expected to grow in line with
  depreciation and working capital requirements are
  minimal. The average beta of a publicly traded
  company in this industry is 1.50 and the average
  debt/equity ratio is 20. The firm is managed
  very conservatively and does not intend to borrow
  through the foreseeable future. The Treasury bond
  rate is 6 and the marginal tax rate is 40. The
  normal spread between the return on stocks and
  the risk free rate of return is believed to be
  5.5. Reflecting the slower growth rate in the
  sixth year and beyond, the discount rate is
  expected to decline by 3 percentage points.
  Estimtate the value of the firms equity.
• ?u (unlevered beta) for comparable firms
  ____?l_____ ___1.5___ 1.5 1.34
• 
  (1 D/E (1-t)) (1 .2 x
  .6) 1.12
• COE1-5 Rf ?u (Rm Rf) .06 1.34 (.055)
  13.4
• Projected free cash flows (FCFE) to the firm
  during the next five years and for the terminal
  year are as follows

Year 1 2 3 4 5 Terminal Year
Net Income 2.40 2.88 3.46 4.15 4.98 5.23
P0,1-5 2.4/1.134 2.88/(1.134)2
3.46/(1.134)3 4.15/(1.134)4 4.98/(1.134)5
2.40/1.134 2.88/1.29
3.46/1.46 4.15/1.65 4.98/1.88
2.12 2.23 2.37 2.52 2.65
11.89 PTV Terminal Value 5.23 / (.104 -
.05)/1.13455 5.23 / .054/1.88 96.85/1.88
51.52 Total PV0 11.89 51.52 63.41
9
7-18. The following information is available for
two different common stocks company A and
Company B.
Company A Company B
Free cash flow per share at the end of year 1 1.00 5.00
Growth rate in cash flow per share 8 4
Beta 1.3 .8
Risk-free return 7 7
Expected return on all stocks 13.5 13.5

• Estimate the cost of equity for each firm.
• Assume that the companies growth rates will
  continue at the same rate indefinitely. Estimate
  the per share value of each companies common
  stock.
• Answer
• a. Company A 7 1.3 (13.5-7) 78.4515.45
• Company B 7 .8 (13.5-7.) 7 5.2
  12.2
• b. Company A P 1.00 / (.154-.08) 13.50
• Company B P5.00 / (.122-.04)
  5.00/.082 61

10
7-19. You have been asked to estimate the beta of
a high-technology firm, which has three divisions
with the following characteristics.
Division Beta Market Value
Personal Computers 1.6 100 million
Software 2.00 150 million
Computer Mainframes 1.2 250 million

• What is the beta of the equity of the firm?
• If the risk free return is 5 and the spread
  between the return on all stocks is 5.5,
• estimate the cost of equity for the
  software division?
• c. What is the cost of equity for the
  entire firm?
• Free cash flow to equity investors in the
  current year (FCFE) for the entire firm is 7.4
• million and for the software division
  is 3.1 million. If the total firm and the
  software
• division are expected to grow at the
  same 8 rate into the foreseeable future,
  estimate
• the market value of the firm and of
  the software division.
• Answer
• Beta 1.6 x 100/500 2.00 x 150/500 1.2 x
  250/500 1.52
• b. COE (software division) .05 2.0
  (.055) 16
• c. COE (entire firm) .05 1.52 (.055)
  13.4
• d, PV (total firm) 7.4 (1.08) / (.134 -
  .08) 7.99/.054 148
• PV (software division) 3.1 (1.08) /
  (.16 - .08) 3.35 / .08 41.85

11
7-20. Financial Corporation wants to acquire
Great Western Inc. Financial has estimated the
enterprise value of Great Western at 104
million. The market value of Great Westerns
long-term debt is 15 million, and cash balances
in excess of the firms normal working capital
requirements are 3 million. Financial estimates
the present value of certain licenses that Great
Western is not currently using to be 4 million.
Great Western is the defendant in several
outstanding lawsuits. Financial Corporations
legal department estimates the potential future
cost of this litigation to be 3 million, with an
estimated present value of 2.5 million. Great
Western has 2 million common shares outstanding.
What is the value of Great Western per common
share? Answer (104 3 4 - 15 - 2.5) / 2
46.75
12
8-11. BigCos Chief Financial Officer is trying
to determine a fair value for PrivCo, a
non-publicly traded firm that BigCos is
considering acquiring. Several of PrivCos
competitors, Ion International, and Zenon are
publicly traded. Ion and Zenon have
price-to-earnings ratios of 20 and 15,
respectively. Moreover, Ion and Zenons shares
are trading at a multiple of earnings before
interest, taxes, depreciation, and amortization
(EBITDA) of 10 and 8, respectively. BigCo
estimates that next year PrivCo will achieve net
income and EBITDA of 4 million and 8 million,
respectively. To gain a controlling interest in
the firm, BigCo expects to have to pay at least a
30 premium to the firms market value. What
should BigCo expect to pay for PrivCo? Based on
price-to-earnings ratios? Based on EBITDA?
Answers (20 15) / 2 17.5
PV (based on P/E and incl. 30 premium) 17.5 x
4 x 1.3 91 (10 8)/2 9 PV
(based on EBITDA incl. 30 premium) 9 x 8 x
1.3 93.6
13
8-12. LAFCO Industries believes that its two
primary product lines, automotive and commercial
aircraft valves, are rapidly becoming obsolete.
Its free cash flow is rapidly diminishing as it
loses market share to new firms entering its
industry. LAFCO has 200 million in debt
outstanding. Senior management expects the
automotive and commercial aircraft valve product
lines to generate 25 million and 15 million,
respectively, in earnings before interest, taxes,
depreciation, and amortization next year. Senior
management also believes that they will not be
able to upgrade these product lines due to
declining cash flow and excessive current
leverage. A competitor to its automotive valve
business last year sold for 10 times EBITDA.
Moreover, a company that is similar to its
commercial aircraft valve product line sold last
month for 12 times EBITDA. Estimate LAFCOs
breakup value before taxes. Answer PV
(automotive valves) 25 x 10 250 PV
(aircraft valves) 15 x 12
180 Less outstanding debt
200 Break-up
value
230
14

• 8-13. Siebel Incorporated, a non-publicly traded
  company, has 2002 earnings before interest and
  taxes (EBIT) of 33.3 million, which is expected
  to grow at 5 annually into the foreseeable
  future. The firms combined federal, state, and
  local tax rate is 40 capital spending will
  equal the firms rate of depreciation and the
  annual change in working capital is expected to
  be minimal. The firms beta is estimated to be
  2.0, the 10-year Treasury bond is 5, and the
  historical risk premium of stocks over the
  risk-free rate is 5.5.Rand Technology, a direct
  competitor of Siebels, recently was sold at a
  purchase price of 11 times 2002 EBIT, which
  included a 20 premium. Siebels equity owners
  would like to determine what it might be worth if
  they were to attempt to sell the firm in the near
  future. They have chosen to value the firm using
  the discounted cash flow and comparable recent
  transactions methods. They believe that either
  method would provide an equally valid estimate of
  the firms value.
• What is the value of Siebel using the DCF method?
• What is the value using the comparable recent
  transactions method?
• c. What would be the value of the firm if we
  combine the results of both methods?
• Answers
• a. COE .05 2.0 (.055) .16
• PV (33.3(1-.4) x 1.05 / (.16-.05)) x 1.2
  228.9
• b. PV 11 x 20 220
• c. (220 228.9) / 2 224.5

15
8-14. Titanic Corporation has reached agreement
with its creditors to liquidate voluntarily its
assets and to use the proceeds to pay off as much
of its liabilities as possible. The firm
anticipates that it will be able to sell off its
assets in an orderly fashion, realizing as much
as 70 of the book value of its receivables, 40
of its inventory, and 25 of its net fixed assets
(excluding land). However, the firm believes
that the land on which it is located can be sold
for 120 of book value. The firm has legal and
professional expenses associated with the
liquidation process of 2,900,000. The firm has
only common stock outstanding. Estimate the
amount of cash that would remain for the firms
common shareholders once all assets have been
liquidated.
Balance Sheet Item Book Value of Assets Liquidation Value
Cash 10 10
Accounts Receivable 20 14
Inventory 15 6
Net Fixed Assets, Excluding Land 8 2.0
Land 6 7.2
Total Assets 59 39.2
Total Liabilities 35 35
Shareholders Equity 24 4.2
Liquidation Related Expenses .9 2.9
Cash Available for Common Shareholders 1.3
16
8-15. Bests Foods is seeking to acquire the
Heinz Baking Company, whose shareholders equity
and goodwill are 41 million and 7 million,
respectively. A comparable bakery was recently
acquired for 400 million, 30 percent more than
its tangible book value (TBV). What was the
tangible book value of the recently acquired
bakery? How much should Bests Foods expect to
have to pay for the Heinz Baking Company? Show
your work. Answer 1.3 x TBV 400 million and
TBV 307.7 million Likely
purchase price of Heinz Baking Company

1.3 x (41-7)

44.2 million
17
8-16. Delhi Automotive Inc. is the leading
supplier of specialty fasteners for passenger
cars in the U.S. market, with an estimated 25
percent share of this 5 billion market. Delhis
rapid growth in recent years has been fueled by
high levels of reinvestment in the firm. While
this has resulted in the firm having state of
the art plants, it has also resulted in the firm
showing limited profitability and positive cash
flow. Delhi is privately owned and has announced
that it is going to undertake an initial public
offering in the near future. Investors know that
economies of scale are important in this high
fixed cost industry and understand that market
share is an important determinant of future
profitability. Thornton Auto Inc., a publicly
traded firm and the leader in this market, has an
estimated market share of 38 percent and an 800
million market value. How should investors value
the Delhi IPO? Answer If the market leader has
a market value and market share of 800 million
and 38, respectively, the market is valuing each
percentage point of market share at 21.05
million (i.e., 800 million/38). If Delhi has a
market share of 25 percent, the IPO could have a
potential value of 526.3 million (i.e., 25
points of market share times 21.05 million).
18
8-17. Photon Inc. is considering acquiring one of
its competitors. Photons management wants to
buy a firm it believes is most undervalued. The
firms three major competitors, AJAX, BABO, and
COMET, have current market values of 375
million, 310 million, and 265 million,
respectively. AJAXs FCFE is expected to grow at
10 percent annually, while BABOs and COMETs
FCFE are projected to grow by 12 and 14 percent
per year, respectively. AJAX, BABO, and COMETs
current year FCFE are 24, 22, and 17 million,
respectively. The current industry average
price-to-FCFE ratio and growth rate are 10 and
8, respectively. Estimate the market value of
each of the three potential acquisition targets
based on the information provided? Which firm is
the most undervalued? Which firm is most
overvalued? Answer Ajax is most overvalued
and Comet is most undervalued. Industry average
PEG ratio10/8 .1.25 Market Value of AJAX
1.25 x 10 x 24 300 million Market Value of
BABO .1.25 x 12 x 22 330 million Market
Value of COMET 1.25 x 14 x 17 298 million
Current Market Value Estimated
Market Value Difference AJAX
375 300 75
BABO 310
330
(20) COMET 265
298 (33)
19
8-18. Acquirer Incorporateds management believes
that the most reliable way to value a potential
target firm is by averaging multiple valuation
methods, since all methods have their
shortcomings. Consequently, Acquirers Chief
Financial Officer estimates that the value of
Target Inc. could range, before an acquisition
premium is added, from a high of 650 million
using discounted cash flow analysis to a low of
500 million using the comparable companies
relative valuation method. A valuation based on a
recent comparable transaction is 672 million.
The CFO anticipates that Target Inc.s management
and shareholders would be willing to sell for a
20 percent acquisition premium. The CEO asks the
CFO to provide a single estimate of the value of
Target Inc. based on the three estimates. In
calculating a weighted average of the three
estimates, she gives a value of .5 to the recent
transactions method, 3 to the DCF estimate, and
.2 to the comparable companies estimate. What it
weighted average estimate she gives to the CEO?
Answer 690 million Answer 690 million Answer 690 million
Estimated Value ( Millions) Relative Weight (As Determined by Analyst) Weighted Average ( Millions)
672 .50 336.0
650 x 1.2 780 .30 234.0
500 x 1.2 600 .20 120.0
1.00 690.0
20
8-19. An investor group has the opportunity to
purchase a firm whose primary asset is ownership
of the exclusive rights to develop a parcel of
undeveloped land sometime during the next 5
years. Without considering the value of the
option to develop the property, the investor
group believes the net present value of the firm
is (10) million. However, to convert the
property to commercial use (i.e., exercise the
option), the investors will have to invest 60
million immediately in infrastructure
improvements. The primary uncertainty associated
with the property is how rapidly the surrounding
area will grow. Based on their experience with
similar properties, the investors estimated that
the variance of the projected cash flows is 5 of
the NPV, which is 55 million, of developing the
property. Assume the risk-free rate of return is
4 percent. What is the value of the call option
the investor group would obtain by buying the
firm? Is it sufficient to justify the
acquisition of the firm? Answer The value of
the option is 13.54 million. The investor group
should buy the firm since the value of the
option more than offsets the (10) million NPV
of the firm if the call option were not
exercised. Value of the underlying asset
(Expected value of the property) (S) 55
million Exercise price (Upfront investment to
commercialize the property) (E) 60 million
Variance in underlying assets value (Measure of
cash flow risk) (s2) .05 Time to expiration (t)
5 Risk free interest rate (R) 4
Where C Theoretical call option value SN(d1)
Ee-RtN(d2) 55 x N(.6844) - 60 x
2.7183.04x5x N(.4920) 37.64
24.1 13.54 million. d1 ln(S/E) ?R
(1/2)?2?t ln(55/60) .04 (1/2).055
-.0870 .3250 .2380 .4780
??t
?.05 ?5 2236 x
2.2361 .50 d2 d1 -
??t .4760 - .5 -.0240 S Stock price or
underlying asset price E Exercise price R
Risk free interest rate corresponding to the life
of the option ?2 Variance of the stocks or
underlying assets returns t Time to
expiration of the option N(d1) and N(d2)
Cumulative normal probability values of d1 and
d2 e 2.7183
21
8-20. Acquirer Companys management believes that
there is a 60 percent chance that Target
Companys free cash flow to the firm will grow at
20 percent per year during the next five years
from this years level of 5 million. Sustainable
growth beyond the fifth year is estimated at 4
percent per year. However, they also believe that
there is a 40 percent chance that cash flow will
grow at half that annual rate during the next
five years and then at a 4 percent rate
thereafter. The discount rate is estimated to be
15 percent during the high growth period and 12
percent during the sustainable growth period for
each scenario. What is the expected value (EV)
of Target Company? Answer 94.93 million PV20
5(1.20) 5(1.2)2 5(1.2)3 5(1.2)4
5(1.2)5 5(1.2)5(1.04)/(.12-.04)
(1.15) (1.15)2 (1.15)3 (1.15)4
(1.15)5 (1.15)5 5.22
5.44 5.68 5.93
6.19 80.41 108.87 PV10 5(1.10)
5(1.1)2 5(1.1)3 5 (1.1)4 5(1.1)5
5(1.1)5(1.04)/(.12-.04) (1.15)
(1.15)2 (1.15)3 (1.15)4 (1.15)5
(1.15)5 4.78 4.57
4.38 4.19 4.01 52.1
74.03 EV .6 x 108.87 .4 x 74.03 94.93