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Valuation for special firms
Issues to be addressed in this
chapter

How if the base case scenario does not hold?
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Negative earnings
Insufficient financial information
No comparable firms to provide valuation
approximation
The remedies might sacrifice precision in
valuation
A Primer on Valuation
tN
Value of Asset 

t 0
E (Cash Flowt )
(1  r ) t
Free Cash Flow to the Firm = EBIT (1 - tax rate)
– (Capital Expenditures - Depreciation) – Change in Non-cash Working Capital
Cost of Capital = k equity (Equity/(Debt + Equity) ) + k debt (Debt/(Debt + Equity))
Expected Growth EBIT = Reinvestment Rate * Return on Capital
Capital Expenditure - Depreciation   Non - cash WC
Reinvestment Rate 
EBIT (1 - tax rate)
Return on Capital = EBIT (1-t) / Capital Invested
Terminal value n = FCFF n+1 / (Cost of Capital n+1 - g n )
Difficulties in Valuing New Firms
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Negative Earnings
Absence of historical data (financial
information, market trading data
needed for estimating market risk)
Absence of Comparable Firms
Negative Earnings
Earnings growth rates cannot be estimated or used in
valuation:
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Estimating historical growth when current earnings are
negative is difficult, and the numbers, even if estimated, often
are meaningless.
An alternative approach to estimating earnings growth is to
use analyst estimates of projected growth in earnings,
especially over the next 5 years.
Tax computation becomes more complicated:
The Going Concern Assumption
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If a firm has negative earnings as a normal situation; the best
thing, in theory, is to liquidate immediately.
Absence of historical data
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In estimating risk parameters
For estimating variables that vary significantly
from year to year
Absence of Comparable Firms
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Analysts use information of comparable firms
frequently in valuation.
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Beta
Return on asset or equity
Profit margin
Revenue growth
Revenue to capital ratio
How to resolve the problems:
Negative Earnings
Normalize Earnings
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Average the firm’s dollar earnings over prior periods
Average the firm’s return on capital or equity (or profit margins)
over prior periods
Use current return on capital or equity (or margin) of
comparable firms
Revenues and Margins
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Sustainable Margin
Adjustment Period
Adjust Leverage
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Optimal Debt Level
How to Adjust Leverage
Illustration 1: Normalizing Earnings
for a Cyclical Firm in a Recession

In 1992, towards the end of the last recession in the
United States, Ford Motor Company reported
earnings per share of -$0.73. To value the firm, we
first had to normalize earnings. We used Ford’s
average return on equity from 1988 to 1992 of
11.05% as a measure of the normal return on equity,
and applied it to Ford’s book value of equity in 1992
of $11.60 to estimate normalized earnings per share:

Normalized EPS in 1992 = $11.60 * .1105 = $1.28

To value the equity per share, we assumed that Ford was in
stable growth, a reasonable assumption given its size and
the competitive nature of the automobile industry.

In addition, we anticipated that net capital expenditures
would be about $0.20 per share in 1993. Using a stable
growth rate of 6% and a cost of equity of 12%, we estimated
the value of equity per share:

Expected FCFE in 1993 = $1.28 - $0.20 = $1.08

Value of Equity per share = $1.08/(.12-.06) = $18.00

The stock was trading at about $ 25 at the end of 1992.
Implicitly, we are assuming that Ford’s earnings will rebound
quickly to normalized levels and that the recession will end in
the very near future.
The Ford case

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Using normalized performance provided by itself
prevent the criticism of inappropriate benchmark.
This approach is suitable when the firm’s
negative earnings was resulted from cyclical
movement, not poor performance.
The 11.05% normalized ROE maybe too low,
since the cost of equity for the firm was
estimated to be 12%. This might result that the
estimated stock price ($18) to be lower than
current price ($25).
Illustration 2: Normalizing Earnings
for a Firm after a Poor Year

In 1995, Daimler Benz reported earnings before
interest and taxes of minus DM 2,016 million, and a
net loss of DM 5,674 million. Much of the loss could
be attributed to firm specific problems. To estimate
normalized earnings at Daimler Benz, we used the
average pre-tax return on capital at European
automobile firms in 1995, which was 18%. We
applied this return on capital to Daimler’s book value
of capital of 33,209 million DM.

Normalized EBIT = 33.209 (.18) = 5,978 Million DM
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To complete the valuation, we made the
following additional assumptions:
Revenues at Daimler had been growing 3-5%
a year prior to 1995, and we anticipated that
the long term growth rate would be 5%.
The capital expenditures in 1995 were 8.0
billion DM, while the depreciation in that year
was 7.4 billion DM.
Working capital was expected to remain at
5% of revenues (Total revenues were
106.747 Bil DM in 1995).
The firm’s tax rate is 30%.
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With these assumptions, we were able to compute
Daimler’ free cash flows in 1996:
EBIT (1-t)= 5,978 (1-.3)
= 4,184M
- (Capital Exp – Deprec’n) = (8000-7400)(1.05)
= 630 Mil
- Change in Working Capital =106,747 (.05)(.05)
= 267 Mil
Free Cash Flow to Firm
= 3,287Mil DM
To compute the cost of capital to apply to this cash flow,
we assumed that the beta for the stock would be 1.00.
The long term bond rate in Germany was 6%, whereas
Daimler Benz could borrow long term at 6.1%. The
market value of equity was 50,000 Mil DM, and there was
26,281 Mil DM in debt outstanding at the end of 1995.
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We also used a corporate tax rate of 30%.
Cost of Equity = 6%+1.00(.5.5%)= 11.5%
Cost of Debt = 6.1%(1-.3) = 4.27%
Debt Ratio = 26,281/(50,000+26,281) = 32.34%
Cost of Capital = 11.5%(.6766) + 4.27% (.3234) =
9.16%
The firm value can now be computed, if we
assume that earnings and cash flows will grow at
5% a year in perpetuity:
Firm Value = 3,287/(.0916-.05) = $ 78,982 million
Equity Value = $ 78,982 million - 26,281 million
= $52,701 million

If Daimler normalize earnings in the very first
period, that is, if the loss this year resulted from
non operating problem, and the firm will jump back
to normal right next year, then the equity value
would be $52,701 million

If Daimler is anticipated to take three years to
normalize earnings; then the firm value becomes
Firm Value = $78,982/1.0916**3 = $60,721 million
Equity Value = $60,721 million - 26,281 million =
$34,440 million
This is an approximation because it assumes cash
flows over the first three years, while Daimler
normalizes earnings, will be zero.
The Daimler Benz Case
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Used 18% (average pre-tax return on capital at
1995 European automobiles) to normalize 1996
earnings, is it appropriate? Or just convenient?
If by 1996, Banz can jump back to normal (18%
pre-tax return) performance, then the firm value is
$ 78,982 M.
If it takes several years before it gets back to
normal, then the firm value is $60,721M.
Illustration 3: The Boston Chicken case:
Valuing a Firm with Changing Margins
and Leverage:
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The firm is in big financial deficit, and the
deficit resulted from multiple forces.
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Underperform operationally
High leverage due to low stock price, which
resulted from the bad operating results. It in turn
raises the borrowing costs, and high financial risk.
The latter also raises the cost of equity.
When valuing the firm…
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Improve operating results
Change the leverage
The Boston Chicken case:

In 1998, Boston Chicken was a firm beset with
financial problems. After a highflying beginning,
the firm ran into problems controlling costs. In
1997, the firm had an operating loss of $ 34
million on revenues of $ 462 million. In the same
year, the firm had capital expenditures of $ 44
million and depreciation of $ 35 million. To value
Boston Chicken, we made the following
assumptions:
The firm would continue to lose money over the next 3
years, but its pre-tax (and pre-depreciation) operating
margins will converge on the industry average of 17%
for fast food restaurants, by the end of the fifth year. The
expected margins over the next 5 years are as follows:
Year
Pre-tax (Pre-depreciation) Margin
Current
1
2
3
4
5-∞
-5%
-2%
2%
7%
12%
17%
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The firm’s revenues will grow 10% a year for the
next five years and 5% a year thereafter.
Capital expenditures will grow 5% a year forever, but
depreciation (reflecting past capital expenditures) will
grow 10% a year for the next 4 years, and 5%
thereafter.
Working capital is expected to remain at 2% of
revenues, which reflect the average for the sector.
In the course of estimating after-tax cash flows,
note that we assume that there will be no taxes
paid in years 4 and 5, because the firm will have
accumulated operating losses to carry forward to
those years. In the terminal year, we assume that
the marginal tax rate will be 35%.
1
2
3
4
Revenues
$508.20
$559.02
$614.92
$676.41
$744.06
$781.26
- COGS
$518.36
$547.84
$571.88
$595.24
$617.57
$648.44
-Depreciation
$38.50
$42.35
$46.59
$51.24
$53.81
$56.50
($48.66)
($31.17)
($3.54)
$29.93
$72.68
$76.32
EBIT
Terminal Terminal
Year
Year +1
- EBIT*t
EBIT (1-t)
$26.71
($48.66)
($31.17)
($3.54)
$29.93
$72.68
$49.61
+ Depreciation
$38.50
$42.35
$46.59
$51.24
$53.81
$56.50
- Capital
Spending
$46.20
$48.51
$50.94
$53.48
$56.16
$62.15
-△Working
Capital
$0.92
$1.02
$1.12
$1.23
$1.35
$0.74
Free CF to
Firm
($57.29)
($38.35)
($9.01)
$26.46
$68.98
$43.21
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The drop in its stock price has pushed the market debt to
capital ratio to 83.18%.
Concurrently, the beta of the stock, estimated using the
unlevered beta of 0.82 for the restaurant industry and the
current market debt to equity ratio has risen to 3.46.
The high default risk in the firm has caused the cost of
borrowing to increase to 11%; the absence of a tax
benefit has the secondary impact of keeping the after-tax
cost of debt at the same level.
As we project earnings and cash flow improvements over
the next 5 years, the consistent assumption to make is
that all of these parameters will adjust over time; the debt
ratio will move towards 50%, the beta towards one and
the borrowing rate towards 7% in the terminal year +1.
1
2
3
4
5
3.46
2.97
2.47
1.98
1.49
1.00
Cost of Equity
24.01% 21.31% 18.61% 15.90%
13.20%
10.50%
Debt Ratio
83.18% 76.55% 69.91% 63.27%
56.64%
50%
Cost of Debt
11.00% 10.20%
9.40%
8.60%
7.80%
7.00%
After-tax Cost
of Debt
11.00% 10.20%
9.40%
8.60%
7.80%
4.55%
Cost of Capital 13.19% 12.81% 12.17% 11.28%
10.14%
7.53%
Beta
Terminal
Year
Terminal Value 5 = FCFF 6 / (WACC 6 – gstable)
= 43.21 / (0.0753 - 0.05) = $1711 million
Free CF to
Firm
1
2
3
4
5
($57.29)
($38.35)
($9.01)
$26.46
$68.98
Terminal
Value
Discount
Factor
Present
Value
$1711.41
1.1319
1.2768
1.4322
1.5938
1.7554
($50.61)
($30.03)
($6.29)
$16.60
$1014.20
The cumulated present value of the cash flows is $943.87.
Netting out the debt of $763 million yields a value for the equity
of $ 180.87 million. Dividing by the number of shares
outstanding provides an estimate of value of $2.34 per share.
Valuing a tech stock -The case with No-Earnings, NoHistory, No-Comparables Firms
Illustration 4: Amazon.com:
Updated Information
Last Financial Trailing 12 months
Year (1998)
(Last quarter of 1998 and
first 3 quarters of 1999)
Revenues
Operating Income
(Loss)
$610 million
$ 1,117 million
- $125 million
- $ 410 million
Expected Revenue Growth

It is hard for Amazon to estimate its own
growth rate, since its business does not involve
with store outlets. The possible solutions:

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Past growth rate in revenues at the firm itself
Growth rate in the overall market that the firm
serves
Also consider the Barriers to Entry and Competitive
Advantages possessed by the firm
Illustration 5: Estimating Revenue Growth
Year
Current
1
2
Expected Growth
150.00%
100.00%
Revenues
$1,117
$2,793
$5,585
Change in Rev.
3
4
5
75.00%
50.00%
30.00%
$9,774
$14,661
$19,059
$4,189
$4,887
$4,398
6
7
8
9
25.20%
20.40%
15.60%
10.80%
$23,862
$28,729
$33,211
$36,798
$4,803
$4,868
$4,482
$3,587
10
11-∞
6.00%
6.00%
$39,006
$2,208
$1,676
$2,793
Illustration 6: Estimating Sustainable
Margin and Path to Margin:
Year
Operating Margin
Current
-36.71%
1
-13.35%
2
-1.68%
3
4.16%
4
7.08%
5
8.54%
6
9.27%
7
9.64%
8
9.82%
9
9.91%
10
9.95%
After year 10
10.00%
Illustration 7: Estimating Reinvestment:
How you estimate reinvestment when
growth rate is 150%

There are three alternatives to using this formulation:
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We can assume that the firm’s existing reinvestments (in
the form on net capital expenditures and non-cash working
capital) will grow at the same rate as revenues.
We can assume that the firm’s reinvestment rate will
approach that of the industry. For instance, we can
measure the reinvestments as a percent of revenues.
While the return on capital and reinvestment rate will be
negative for firms with negative earnings, we can compute
the typical payoff in revenues that we get for a given dollar
reinvestment in the form of a sales-to-capital ratio:
Estimating Reinvestment:
Constant sales-to-capital ratio
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Sales to Capital Ratio = Revenues/ Capital Invested
Sales to Cap Ratio = △ revenue 1998 to 1999 / (Cap
ex – Depreciation)= (1117-474)/(243-31) = 3.03
The average sales to capital ratio, in January 2000,
for specialty retailers was 3.46 and the average for
retail stores was 2.99. We will use a sales to capital
ratio of 3.00 for the next decade.
Reinvestment stable growth = Expected Growth stable /
ROC stable
Illustration 7: Estimating Reinvestment Needs:
Year
Change in Revenue
Sales/Capital
Reinvestment
1
$1,676
3.00
$559
2
$2,793
3.00
$931
3
$4,189
3.00
$1,396
4
$4,887
3.00
$1,629
5
$4,398
3.00
$1,466
6
$4,803
3.00
$1,601
7
$4,868
3.00
$1,623
8
$4,482
3.00
$1,494
9
$3,587
3.00
$1,196
10
$2,208
3.00
$736
The calculation of Return on Capital:
Year
Revenues
Operating
Margin
EBIT
EBIT(1-t)
Capital
Invested
ROC
1
$2,793
-13.35%
-$373
-$373
$487
-76.62%
2
$5,585
-1.68%
-$94
-$94
$1,045
-8.96%
3
$9,774
4.16%
$407
$407
$1,976
20.59%
4
$14,661
7.08%
$1,038
$871
$3,372
25.82%
5
$19,059
8.54%
$1,628
$1,058
$5,001
21.16%
6
$23,862
9.27%
$2,212
$1,438
$6,467
22.23%
7
$28,729
9.64%
$2,768
$1,799
$8,068
22.30%
8
$33,211
9.82%
$3,261
$2,119
$9,691
21.87%
9
$36,798
9.91%
$3,646
$2,370
$11,185
21.19%
10
$39,006
9.95%
$3,883
$2,524
$12,380
20.39%
The calculation of Return on Capital:

The return on capital of 20.39% is lower than
the average return on capital for the specialty
retail sector (28.49%) and retail stores
(23.76%), but it is higher than Amazon’s cost
of capital. Consequently, the sales to capital
ratio of 3.00 seems to be a reasonable one.
Illustration 8: Estimating Risk Parameters
and Discount Rates:
Amazon’s beta can be first close to 1.6 (internet companies)
and gradually decreases to 1.0 (book stores)
Year
1-5
6
7
8
9
10
Beta
1.60
1.48
1.36
1.24
1.12
1.00
Illustration 8: Estimating Risk Parameters
and Discount Rates:
Amazon’s debt ratio is maintained 1.2％ from years 1 to 5;
and gradually increases to 15％from years 6 to 10.
Year Beta Cost of
Equity
Pre-tax
Cost of
Debt
Tax Rate
After-tax
Cost of
Debt
Debt
Ratio
Cost of
Capital
1-3
1.60 12.90%
8.00%
0.00%
8.00%
1.20%
12.84%
4
1.60 12.90%
8.00%
16.13%
6.71%
1.20%
12.83%
5
1.60 12.90%
8.00%
35.00%
5.20%
1.20%
12.81%
6
1.48 12.42%
7.80%
35.00%
5.07%
3.96%
12.13%
7
1.36
11.94%
7.75%
35.00%
5.04%
4.65%
11.62%
8
1.24
11.46%
7.67%
35.00%
4.98%
5.80%
11.08%
9
1.12 10.98%
7.50%
35.00%
4.88%
8.10%
10.49%
10
1.00 10.50%
7.00%
35.00%
4.55%
15.00%
9.61%
After 1.00 10.50%
7.00%
35.00%
4.55%
15.00%
9.61%
Illustration 9: Estimating Firm and
Equity Value
Terminal Value





The perpetual ROC is set to be 20％, and stable growth is
6％, and we can calculate reinvestment rate in stable
period as follows:
Stable Reinvestment Rate = Stable Growth Rate/ Return
on Capital = 6%/20% = 30%
FCFF 11 = EBIT 11 (1- tax rate) – Reinvestments = $ 2,688
million – 0.3 ($2,688) = $ 1,881 million
Terminal value can be calculated by applying WACC in
stable period as 9.61%
Terminal Value 10 = FCFF 11 /(Cost of Capital – Stable
Growth Rate) = 1881/(.0961 - .06) = $ 52,148 million
Year
FCFF
Terminal
Value
Cost of
Capital
Compounded Cost
of Capital a
Present
Value
1
-$931
12.84%
112.84%
-$825
2
-$1,024
12.84%
127.33%
-$805
3
-$989
12.84%
143.68%
-$689
4
-$758
12.83%
162.11%
-$468
5
-$408
12.81%
182.87%
-$223
6
-$163
12.13%
205.05%
-$80
7
$177
11.62%
228.88%
$77
8
$625
11.08%
254.25%
$246
9
$1,174
10.49%
280.90%
$418
10
$1,788
9.61%
307.89%
$17,518
$52,148
Value of Operating Assets of the firm =
Value of Cash and Non-operating assets =
Value of Firm =
- Value of Outstanding Debt =
Value of Equity =
$ 15,170
$ 26
$ 15,196
$ 349
$14,847
Valuation of Equity Per Share
Value of Firm
- Value of Debt
= Value of Equity
-Value of Options granted to Employees
= Value of Equity in Common Stock
/ Number of Shares outstanding
= Value per Share
Illustration 10: Valuing Equity per
Share: Amazon.com
Having estimated the equity value of Amazon.com to be $14,847 million, we
can estimate the value per share. As of December 1998, the firm had
options outstanding on 38 million shares, with a weighted average life of 8.4
years and a weighted exercise price of $ 13.375. Using a standard deviation
in the stock price of 50% and the current stock price19 of $ 84, we estimated
the value of these options, allowing for dilution to be $ 2,892 million.
Value of Equity =
$ 14,847 million
－Value of Equity in Options Outstanding =
- $ 2,892 million
= Value of Equity in Common Stock
$ 11,955 million
Value of Equity in Common Stock $ 11,955 million
/ Number of Shares outstanding
340.79 million
= Value of Equity per Share
$ 35.08
Value of Equity per share
(Treasury stock approach)

Value of Equity per share (Treasury stock
approach)

= (Value of Equity from DCF Valuation +
Exercise Price * Number of Options)/(Number
of Shares + Number of Options)

= (14,847 + 13.375*38)/(340.79+38) = $ 40.54
Illustration 11: Value Drivers for
Amazon.com



Expected compounded growth rate in revenues:
Sustainable operating margin:
Reinvestment requirements:
Sensitivity Analysis
Pre-tax Operating Margin
Revenue
growth
30%
35%
40%
45%
50%
55%
60%
6%
8%
$ (1.94)
$ 1.41
$ 6.10
$ 12.59
$ 21.47
$ 33.47
$ 49.53
$ 2.95
$ 8.37
$ 15.93
$ 26.34
$ 40.50
$ 59.60
$ 85.10
10%
12%
14%
$ 7.84
$ 12.71 $ 17.57
$ 15.33 $ 22.27 $ 29.21
$ 25.74 $ 35.54 $ 45.34
$ 40.05 $ 53.77 $ 67.48
$ 59.52 $ 78.53 $ 97.54
$ 85.72 $ 111.84 $ 137.95
$ 120.66 $ 156.22 $ 191.77