Valuation for special firms

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

A Primer on Valuation

Nt

0t )1(

) ( Asset of Value

tt

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FlowCashE

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

rate) tax - (1 EBIT

cash WC-Non on Depreciati - eExpenditur Capital Ratent Reinvestme

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

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:

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.

Absence of historical data

In estimating risk parameters For estimating variables that vary significantly

from year to year

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

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

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 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

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%.

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.

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 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:

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

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 -5%

1 -2%

2 2%

3 7%

4 12%

5-∞ 17%

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 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) ($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

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 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 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%

Terminal Value 5 = FCFF 6 / (WACC 6 – gstable) = 43.21 / (0.0753 - 0.05) = $1711 million

1 2 3 4 5

Free CF to Firm

($57.29) ($38.35) ($9.01) $26.46 $68.98

Terminal Value

$1711.41

Discount Factor

1.1319 1.2768 1.4322 1.5938 1.7554

Present Value

($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, No-History, No-Comparables Firms

Illustration 4: Amazon.com:

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

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

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 $2,793

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-∞ 6.00%

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: 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

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 Beta

1-5 1.60

6 1.48

7 1.36

8 1.24

9 1.12

10 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 ofEquity

Pre-tax Cost of Debt

Tax Rate After-tax Cost of Debt

Debt Ratio

Cost ofCapital

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 $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

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

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 $ 111.84 $ 137.95

60% $ 49.53 $ 85.10 $ 120.66 $ 156.22 $ 191.77