1. Valuation for special firms

2. Issues to be addressed in this chapter
How if the base case scenario does not hold?
Negative earnings
Insufficient financial information
No comparable firms to provide valuation approximation
The remedies might sacrifice precision in valuation

4. A Primer on Valuation
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
Return on Capital = EBIT (1-t) / Capital Invested
Terminal value n = FCFF n+1 / (Cost of Capital n+1 - g n )

5. Difficulties in Valuing New Firms
Negative Earnings
Absence of historical data (financial information, market trading data needed for estimating market risk)
Absence of Comparable Firms

6. Negative Earnings
Earnings growth rates cannot be estimated or used in valuation:
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
If a firm has negative earnings as a normal situation; the best thing, in theory, is to liquidate immediately.

7. Absence of historical data
In estimating risk parameters
For estimating variables that vary significantly from year to year

8. Absence of Comparable Firms
Analysts use information of comparable firms frequently in valuation.
Beta
Return on asset or equity
Profit margin
Revenue growth
Revenue to capital ratio

9. How to resolve the problems: Negative Earnings
Normalize Earnings
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
Sustainable Margin
Adjustment Period
Adjust Leverage
Optimal Debt Level
How to Adjust Leverage

10. 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 * = $1.28

11. 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 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 = $ $0.20 = $1.08
Value of Equity per share = $1.08/( ) = $18.00
The stock was trading at about $ 25 at the end of 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.

12. The Ford case
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).

13. 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 = (.18) = 5,978 Million DM

14. 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 Bil DM in 1995).
The firm’s tax rate is 30%.

15. 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) = ( )(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 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.

16. = $52,701 million 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) % (.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/( ) = $ 78,982 million
Equity Value = $ 78,982 million - 26,281 million
= $52,701 million

17. 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.

18. The Daimler Benz Case
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.

19. Illustration 3: The Boston Chicken case: Valuing a Firm with Changing Margins and Leverage:
The firm is in big financial deficit, and the deficit resulted from multiple forces.
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…
Improve operating results
Change the leverage

20. 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:

21. Pre-tax (Pre-depreciation) Margin Current -5% 1 -2% 2 2% 3 7% 4 12%
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
-5% 1
-2% 2 2% 3 7% 4
12%
5-∞
17%

22. 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%.

23. 1 2 3 4
Terminal Year
Terminal Year +1
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
EBIT
($48.66)
($31.17)
($3.54)
$29.93
$72.68
$76.32
- EBIT*t
$26.71
EBIT (1-t)
$49.61
+ Depreciation
- 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

24. 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.

25. 1 2 3 4 5
Terminal Year
Beta
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
4.55%
Cost of Capital
13.19%
12.81%
12.17%
11.28%
10.14%
7.53%

26. Terminal Value 5 = FCFF 6 / (WACC 6 – gstable) = 43. 21 / (0. 0753 - 0
Terminal Value 5 = FCFF 6 / (WACC 6 – gstable) = / ( ) = $1711 million 1 2 3 4 5
Free CF to Firm
($57.29)
($38.35)
($9.01)
$26.46
$68.98
Terminal Value $
Discount Factor
1.1319
1.2768
1.4322
1.5938
1.7554
Present Value
($50.61)
($30.03)
($6.29)
$16.60 $
The cumulated present value of the cash flows is $ Netting out the debt of $763 million yields a value for the equity of $ million. Dividing by the number of shares outstanding provides an estimate of value of $2.34 per share.

28. Illustration 4: Amazon.com:
Valuing a tech stock -- The case with No-Earnings, No-History, No-Comparables Firms
Illustration 4: Amazon.com:

29. Updated Information Last Financial Year (1998) Trailing 12 months
(Last quarter of 1998 and first 3 quarters of 1999)
Revenues
$610 million
$ 1,117 million
Operating Income (Loss)
- $125 million
- $ 410 million

30. 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:
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

31. Illustration 5: Estimating Revenue Growth
Year
Expected Growth
Revenues
Change in Rev.
Current
$1,117 1
150.00%
$2,793
$1,676 2
100.00%
$5,585 3
75.00%
$9,774
$4,189 4
50.00%
$14,661
$4,887 5
30.00%
$19,059
$4,398 6
25.20%
$23,862
$4,803 7
20.40%
$28,729
$4,868 8
15.60%
$33,211
$4,482 9
10.80%
$36,798
$3,587 10
6.00%
$39,006
$2,208
11-∞

32. 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%

33. Illustration 7: Estimating Reinvestment: How you estimate reinvestment when growth rate is 150%
There are three alternatives to using this formulation:
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:

34. Estimating Reinvestment: Constant sales-to-capital ratio
Sales to Capital Ratio = Revenues/ Capital Invested
Sales to Cap Ratio = △ revenue 1998 to 1999 / (Cap ex – Depreciation)= ( )/(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 We will use a sales to capital ratio of 3.00 for the next decade.
Reinvestment stable growth = Expected Growth stable / ROC stable

35. Illustration 7: Estimating Reinvestment Needs:
Year
Change in Revenue
Sales/Capital
Reinvestment 1
$1,676
3.00
$559 2
$2,793
$931 3
$4,189
$1,396 4
$4,887
$1,629 5
$4,398
$1,466 6
$4,803
$1,601 7
$4,868
$1,623 8
$4,482
$1,494 9
$3,587
$1,196 10
$2,208
$736

36. The calculation of Return on Capital:
Year
Revenues
Operating Margin
EBIT
EBIT(1-t)
Capital Invested
ROC 1
$2,793
-13.35%
-$373
$487
-76.62% 2
$5,585
-1.68%
-$94
$1,045
-8.96% 3
$9,774
4.16%
$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%

37. 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.

38. 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
Beta
1-5
1.60 6
1.48 7
1.36 8
1.24 9
1.12 10
1.00

39. 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
Capital
1-3
1.60
12.90%
8.00%
0.00%
1.20%
12.84% 4
16.13%
6.71%
12.83% 5
35.00%
5.20%
12.81% 6
1.48
12.42%
7.80%
5.07%
3.96%
12.13% 7
1.36
11.94%
7.75%
5.04%
4.65%
11.62% 8
1.24
11.46%
7.67%
4.98%
5.80%
11.08% 9
1.12
10.98%
7.50%
4.88%
8.10%
10.49% 10
1.00
10.50%
7.00%
4.55%
15.00%
9.61%
After

40. 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/( ) = $ 52,148 million

41. Year
FCFF
Terminal Value
Cost of Capital
Compounded Cost of Capital a
Present Value 1
-$931
12.84%
112.84%
-$825 2
-$1,024
127.33%
-$805 3
-$989
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
$52,148
9.61%
307.89%
$17,518
Value of Operating Assets of the firm =
$ 15,170
Value of Cash and Non-operating assets =
$ 26
Value of Firm =
$ 15,196
- Value of Outstanding Debt =
$ 349
Value of Equity =
$14,847

42. 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

43. 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 $ 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 million
= Value of Equity per Share $ 35.08

44. 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, *38)/( ) = $ 40.54

45. Illustration 11: Value Drivers for Amazon.com
Expected compounded growth rate in revenues:
Sustainable operating margin:
Reinvestment requirements:

46. Sensitivity Analysis Pre-tax Operating Margin Revenue growth 6% 8% 10%
12%
14%
30%
$ (1.94)
$ 2.95
$ 7.84
$ 12.71
$ 17.57
35%
$ 1.41
$ 8.37
$ 15.33
$ 22.27
$ 29.21
40%
$ 6.10
$ 15.93
$ 25.74
$ 35.54
$ 45.34
45%
$ 12.59
$ 26.34
$ 40.05
$ 53.77
$ 67.48
50%
$ 21.47
$ 40.50
$ 59.52
$ 78.53
$ 97.54
55%
$ 33.47
$ 59.60
$ 85.72 $ $
60%
$ 49.53
$ 85.10 $ $ $