Table 11-5: Summary of Effects of Valuation Errors

Table 11-5 summarizes the effects of the valuation errors. Each cell in the

table contains three items:

Part 4 Putting It All Together

400

T A B L E 11-4A

Percent Valuation Error for 10% Relative Error in Growth

A B C D E F G

4 Description Huge Firm Small Firm

5 r 11% 27%

6 g 9% 9%

7 Gordon model 50.0000 5.5556

8 Cash Flow 300,000,000 100,000

9 V1 15,000,000,000 555,556

10 (1 PctError)*g 8.10% 8.10%

11 Gordon model 2 34.4828 5.2910

12 V2 10,344,827,586 529,101

13 V2/ V1 0.6897 0.9524

14 (V2/ V1) 1 31.03% 4.76%

16 Sensitivity Analysis: Valuation Error for Combinations of r and g

18 Growth rate g

19 Discount Rate r 5% 6% 7% 8% 9% 10%

20 11% 7.69% 10.71% 14.89% 21.05% 31.03% NA

21 12% 6.67% 9.09% 12.28% 16.67% 23.08% 33.33%

22 13% 5.88% 7.89% 10.45% 13.79% 18.37% 25.00%

23 14% 5.26% 6.98% 9.09% 11.76% 15.25% 20.00%

24 15% 4.76% 6.25% 8.05% 10.26% 13.04% 16.67%

25 16% 4.35% 5.66% 7.22% 9.09% 11.39% 14.29%

26 17% 4.00% 5.17% 6.54% 8.16% 10.11% 12.50%

27 18% 3.70% 4.76% 5.98% 7.41% 9.09% 11.11%

28 19% 3.45% 4.41% 5.51% 6.78% 8.26% 10.00%

29 20% 3.23% 4.11% 5.11% 6.25% 7.56% 9.09%

30 21% 3.03% 3.85% 4.76% 5.80% 6.98% 8.33%

31 22% 2.86% 3.61% 4.46% 5.41% 6.47% 7.69%

32 23% 2.70% 3.41% 4.19% 5.06% 6.04% 7.14%

33 24% 2.56% 3.23% 3.95% 4.76% 5.66% 6.67%

34 25% 2.44% 3.06% 3.74% 4.49% 5.33% 6.25%

35 26% 2.33% 2.91% 3.55% 4.26% 5.03% 5.88%

36 27% 2.22% 2.78% 3.38% 4.04% 4.76% 5.56%

38 Relative Error in g 10.0%

Formula in B20: (which copies to the other cells in the sensitivity analysis) (($A20 B$19)/($A20 ((1 $PctError)*B$19))) 1

1. The formula for the valuation error.

2. The equation number containing the error formula.

3. Whether the error is larger for large ¬rms, small ¬rms, or there

is no difference.

The upper half of the table shows the valuation effects of absolute

errors in forecasting the variables (cash ¬‚ow, discount rate, and growth

rate), and the lower half of the table shows the valuation effects of relative

errors in forecasting the variables.

In 10 of the 12 cells in the table that contain error formulas, the

valuation errors are greater for large ¬rms than for small ¬rms. Only

equation (11-5), which is the relative valuation error resulting from a dol-

lar error in forecasting cash ¬‚ows, affects small ¬rms more than large

¬rms. Equation (11-8), the relative valuation error resulting from a relative

error in forecasting cash ¬‚ows, affects both small and large ¬rms alike. It

CHAPTER 11 Measuring Valuation Uncertainty and Error 401

T A B L E 11-4B

Percent Valuation Error for 10% Relative Error in Discount Rate

A B C D E F G

4 Description Huge Firm Small Firm

5 r 11% 27%

6 g 9% 9%

7 Gordon model 50.0000 5.5556

8 Cash Flow 300,000,000 100,000

9 V1 15,000,000,000 555,556

10 (1 PctError)*g 12.10% 29.70%

11 Gordon model 2 32.2581 4.8309

12 V2 9,677,419,355 483,092

13 V2/ V1 0.6452 0.8696

14 (V2/ V1) 1 35.48% 13.04%

16 Sensitivity Analysis: Valuation Error for Combinations of r and g

18 Growth rate g

19 Discount Rate r 5% 6% 7% 8% 9% 10%

20 11% 15.49% 18.03% 21.57% 26.83% 35.48% 52.38%

21 12% 14.63% 16.67% 19.35% 23.08% 28.57% 37.50%

22 13% 13.98% 15.66% 17.81% 20.63% 24.53% 30.23%

23 14% 13.46% 14.89% 16.67% 18.92% 21.88% 25.93%

24 15% 13.04% 14.29% 15.79% 17.65% 20.00% 23.08%

25 16% 12.70% 13.79% 15.09% 16.67% 18.60% 21.05%

26 17% 12.41% 13.39% 14.53% 15.89% 17.53% 19.54%

27 18% 12.16% 13.04% 14.06% 15.25% 16.67% 18.37%

28 19% 11.95% 12.75% 13.67% 14.73% 15.97% 17.43%

29 20% 11.76% 12.50% 13.33% 14.29% 15.38% 16.67%

30 21% 11.60% 12.28% 13.04% 13.91% 14.89% 16.03%

31 22% 11.46% 12.09% 12.79% 13.58% 14.47% 15.49%

32 23% 11.33% 11.92% 12.57% 13.29% 14.11% 15.03%

33 24% 11.21% 11.76% 12.37% 13.04% 13.79% 14.63%

34 25% 11.11% 11.63% 12.20% 12.82% 13.51% 14.29%

35 26% 11.02% 11.50% 12.04% 12.62% 13.27% 13.98%

36 27% 10.93% 11.39% 11.89% 12.44% 13.04% 13.71%

38 Relative Error in g 10%

Formula in B20: (which copies to the other cells in the sensitivity analysis) (($A20 B$19)/($A20 ((1 $PctError)*B$19))) 1

is not surprising that the only two exceptions to the greater impact of

valuation errors being on large ¬rms comes from cash ¬‚ows, as value is

linear in cash ¬‚ows. The nonlinear relationship of value to discount rate

and growth rate causes errors in those two variables to impact the val-

uation of large ¬rms far more than small ¬rms and to impact the value

of both more than errors in cash ¬‚ow.

Errors in forecasting growth have the greatest impact on value. Value

is positively related to forecast growth. Errors in forecasting discount

rates are a close second in effect,17 though opposite in sign. Value is neg-

atively related to discount rate. Errors in forecasting the ¬rst year™s cash

¬‚ow by far have the least impact on value.

17. Again, this result comes from using the midyear Gordon model, not the end-of-year formula.

Part 4 Putting It All Together

402

T A B L E 11-5

Summary of Effects of Valuation Errors

Valuation Effects of Absolute Errors in the Variables [1]

Valuation Error Cash Flow Discount Rate r Growth Rate g

Absolute ($) 1 r g r g

V CF V CF V CF

(r g) (r1 g1)(r2 g2) (r1 g1)(r2 g2)

(11-3) (11-15) (11-15)

Large ¬rms Large ¬rms Large ¬rms

Relative (%) V CF r g r g

V V

V CF V (r2 g2) V (r2 g2)

(11-5) (11-17) Note [3] (11-17) Note [3]

Small ¬rms Large ¬rms Large ¬rms

Valuation Effects of Relative Errors in the Variables [1]

Valuation Error Cash Flow Discount Rate r Growth Rate g

Absolute ($) V kV1 Note [4] Note [4]

Note [2] NA NA

Large ¬rms Large ¬rms Large ¬rms

Relative (%) V2 r g r g

1 k %Error 1 %Error 1

V1 r (1 k)g

(1 k)r g

(11-8) (11-21) (11-20)

No difference Large ¬rms Large ¬rms

[1] Each cell shows the formula for the valuation error, the equation number in the chapter for the formula, and whether the valuation error is larger for large ¬rms, small ¬rms, or there is

no difference.

[2] This formula is not explicitly calculated in the chapter. We can calculate it as: V2 V1 [(1 k)V1 V1] kV1.

[3] While there is no difference in the magnitude of valuation errors arising from an error in r or g when we measure value by the end-of-year Gordon model, when we use the midyear

Gordon model, errors in g have slightly more impact than errors in r (and much more impact than errors in cash ¬‚ow).

[4] Omitted because these expressions are complex and add little to understanding the topic.

Another issue in valuation error in using the log size model is that

while an initial error in calculating the discount rate is self-correcting

using an iterative method, an error in calculating cash ¬‚ows or the growth

rate not only causes its own error, but also will distort the calculation of

the discount rate. For example, overestimating growth, g, will cause an

overvaluation, which will lower the discount rate beyond its proper level,

which will in turn cause a second order overvaluation. We did not see

this in our comparative static analysis, because for simplicity we were

working with the Gordon model multiple in the form of equation (11-1).

We allowed r to be an apparently independent variable instead of using

its more proper, but complicated log size form of r a b ln V. Thus,

the proper Gordon model using a log size discount rate is: .

1

V CF

a b ln V g

The secondary valuation error caused by a faulty forecast of cash

¬‚ows or growth rate will be minimal because the discount rate, as cal-

culated using the log size model, is fairly insensitive to the error in the

estimate of value. As mentioned earlier, on the surface, this would not be

a source of error using CAPM, as the discount rate in CAPM does not

CHAPTER 11 Measuring Valuation Uncertainty and Error 403

depend on the magnitude of the subject company™s cash ¬‚ows. However,

that is not really true, as CAPM betas are correlated to size.

SUMMARY AND CONCLUSIONS

We discussed valuation uncertainty in the ¬rst part of this chapter and

valuation error in the second part. Using the past 60 years of NYSE data,

the actual 95% con¬dence intervals around the valuation estimate for our

statistical uncertainty in calculating the discount rate range from 5%

for huge ¬rms down to 2“3% for ¬rms of other sizes, as calculated in

Tables 11-1 and 11-2. Using all 72 years of NYSE data leads to much larger

con¬dence intervals, and using CAPM leads to even much larger con¬-

dence intervals. Additionally, we could calculate the 95% con¬dence in-

tervals around the sales and expense forecast.

Errors in forecasting the growth rate and calculating the discount rate

cause much larger valuation errors than errors in forecasting the ¬rst

year™s cash ¬‚ow. Thus, the bottom line conclusion from our analysis is

that we need to be most careful in forecasting growth and discount rates

because they have the most profound effect on the valuation. Usually we

spend the majority of our efforts forecasting cash ¬‚ows, and it might be

tempting to some appraisers to accord insuf¬cient analytic effort to the

growth forecast and/or the discount rate calculation. Hopefully, the re-

sults in this chapter show that that is a bad idea.

In this chapter we have not speci¬cally addressed uncertainty and

errors in calculating valuation discounts, but one must obviously realize

that they, too, add to the overall uncertainty that we have in rendering

an opinion of value. There is material in Chapter 7 relating to uncertainty

in calculating restricted stock discounts, which forms part of our overall

uncertainty in calculating the discount for lack of marketability.

After analysis of just the uncertainty alone in the valuation”

not even considering the possibility that somewhere we have made an

actual error”a healthy humility about our ¬nal valuation conclusions is

appropriate.

BIBLIOGRAPHY

Ibbotson and Associates. 1998. Stocks, Bonds, Bills and In¬‚ation: 1998 Yearbook. Chicago: The

Associates.

Part 4 Putting It All Together

404

PART FIVE

Special Topics

INTRODUCTION

Part 5, which consists of Chapters 12, 13, and 14, deals with topics that

do not ¬t into any other part of the book. All three are practical ˜˜how-

to™™ chapters.

Chapter 12 concerns valuing startups. The chapter discusses three

topics. The ¬rst is the ˜˜First Chicago™™ approach, which is a weighted

average, multiscenario approach to valuing startups. It has the bene¬t of

breaking down the vast range of possibilities into discrete scenarios that

are more credible than attempting to model all possibilities in a single

scenario. Whereas almost all of this book is my own original work, the

First Chicago Approach and the related section on the venture capital

approach are based on a series of articles by Brad Fowler. It is important

to understand the multiscenario approach, not only for its own sake in

valuing simple start-ups but also as a preparation to understand the de-

cision tree approach in the debt restructuring study.

Chapter 12 also provides an example”again based on Fowler™s

work”of using a venture capital valuation approach. While this is tech-

nically a different valuation approach, we will consider it as essentially

the same topic as the First Chicago approach.

The second topic in Chapter 12 is the presentation of the essential

parts of an actual debt restructuring study I did for a client. It is an

example of using an original adaptation of decision tree logic for incor-

porating the effects of probabilistic milestones into a spreadsheet for the

valuation. In this study the viability of the subject company, the proba-

bility of obtaining venture capital ¬nancing, its ability to survive on its

own without venture capital ¬nancing, and its value depend on the out-

come of four different sales milestones. The logic and structure of this

analysis work well for other types of milestones, such as technological

(e.g., successful development) and administrative (e.g., obtaining Food

and Drug Administration approval).

The third topic in Chapter 12 is presenting an exponentially declining

sales growth model1 to semiautomate the process of modeling different

1

I thank R. K. Hiatt for developing this.

405

Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

sales growth patterns. This is a great time saver in valuing startups using

a top-down approach.2 Typically, sales grow rapidly in the early years,

then more slowly, eventually coming to an expected constant growth rate.

Rather than manually insert every year™s sales growth, the appraiser can

instantly change the entire sales growth pattern over n years by changing

the contents of four spreadsheet cells. Furthermore, it makes extensive

sensitivity analysis, normally a cumbersome procedure, trivial.

ESOP valuation has generated a number of lawsuits. One of the sore

points of ESOP valuation that has led to litigation is the dilution in value

that the ESOP experiences after the sale. Selling stock to an ESOP that

does not have the cash to pay for the stock always causes a dilution in

value to the shareholders the instant the transaction takes place. Of

course, it takes time for the bad news to become known, as usually the

next valuation takes place one year later. Employees may be angry, feeling

that they (through the ESOP) paid too much for the owner™s stock. They

may feel someone has pulled a fast one. This can endanger the life and

health of the business.

In Chapter 13 we develop formulas to calculate the post-transaction

fair market value (FMV) before doing the transaction. This enables the

appraiser to provide accurate information to the ESOP trustee that will

enable both sides to enter the transaction with both eyes open. It also

demysti¬es the dilution in value and provides an accurate benchmark

with which to measure future performance. The chapter also provides

precise formulas with which the appraiser can perform the ¬nancial en-

gineering necessary to enable the owner to reduce his or her transaction

price in order to share some or all of the ESOP™s dilution. While this is

not common, sometimes there are benevolent owners who are suf¬ciently

well off and concerned about their employees to do that.

In general, this is a very mathematical chapter. For those readers who

prefer to minimize the amount of mathematics they must read, we have

included Appendix 13-B, a shortcut chapter.

Chapter 14 is a short, simple chapter that makes use of results in

Chapter 13. When partners or shareholders buy out one another, as a ¬rst

approximation there is no impact to the fair market value per share. This

is certainly true when the buyer has the cash to pay to the seller.

However, when the buyer does not have the cash and the company

itself takes out a loan to ¬nance the purchase, secondary effects occur that

can be signi¬cant. Post-transaction, the ¬rm will be more highly lever-

aged, which increases the discount rate. We use the dilution formulas

from Chapter 13 to provide a benchmark lower limit of fair market value

per share. The appraiser can then employ traditional discounted cash ¬‚ow

analysis to value the ¬rm. The result is likely to be a post-transaction fair

market value per share that is lower than the pre-transaction per share

value.

2

This is in contrast to the bottom-up approach, where the appraiser inserts a series of assumptions

to enable one to forecast sales. This might include line items such as market size, market

share for the subject company, etc.

PART 5 Special Topics

406

CHAPTER 12

Valuing Startups

ISSUES UNIQUE TO STARTUPS

ORGANIZATION OF THE CHAPTER

FIRST CHICAGO APPROACH

Discounting Cash Flow Is Preferable to Net Income

Capital Structure Changes

Venture Capital Rates of Return

Table 12-1: Example of the First Chicago Approach

Advantages of the First Chicago Approach

Discounts for Lack of Marketability and Control

VENTURE CAPITAL VALUATION APPROACH

Venture Capital Rates of Return

Summary of the VC Approach

DEBT RESTRUCTURING STUDY

Backgound

Key Events

Decision Trees and Spreadsheet Calculations

Table 12-3: Statistical Calculation of FMV

Organization

Section 1A: Venture Capital Scenario

Probability of VC Financing after Sale #1

Probability of VC Financing after Sale #2

Generalizing to Probability of VC Financing after Sale #k

Explanation of Table 12-3, Section 1A

Section 1B: The Bootstrap Scenario Assuming Debt Restructuring

with Parent

Section 2: No-Restructure Scenario

Section 3: FMVs per Share under Various Restructure Scenarios

Venture Capital Scenario

No-Restructure Scenario

407

Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

Conclusion

Section 4: Year 2000 Investor Percentage Taken

EXPONENTIALLY DECLINING SALES GROWTH MODEL

PART 5 Special Topics

408

ISSUES UNIQUE TO STARTUPS

A number of issues fairly unique to valuing startups arise chie¬‚y from

the uncertainty associated with new ventures. This uncertainty usually

necessitates a more complex, multiple scenario analysis known as the

First Chicago approach and requires more creativity on the part of the

appraiser than other, more routine assignments.3 In this chapter we also

present a much shorter, easier valuation method for startups, known as

the venture capital pricing approach.

Many new ventures have sequential events (milestones) that may or

may not occur, and the valuation depends upon the probabilities of the

occurrence of these milestones. Often, in order for event n to occur, event

(n 1) must occur”but it may or may not. When valuing such ¬rms,

we often combine the First Chicago approach with decision tree analysis

to arrive at a credible fair market value. This is a much more complex

task than the First Chicago approach by itself. The most common types

of milestones are sales, ¬nancing, technical, and regulatory, the latter two

being universal in the valuation of pharmaceutical and biotechnology

¬rms.

Another issue is that startups typically have a pattern of rapid sales

growth followed by declining sales growth rates, ¬nally reaching some

steady state growth rate. Performing sensitivity analysis can be cumber-

some when the appraiser manually enters sales growth rates under a

number of different scenarios.

ORGANIZATION OF THE CHAPTER

This chapter addresses these issues in three parts. Part 1 consists of the

First Chicago approach of forecasting multiple scenarios, each with its

own discounted cash ¬‚ow analysis. We produce a conditional FMV for

each scenario and then calculate a weighted average FMV based on VC

industry research that speci¬es the probabilities of each scenario coming

to fruition. We also include the venture capital pricing approach in Part

1, as it is short and simple.

Part 2 consists of using a very sophisticated decision tree analysis to

value an early stage ¬rm for the purpose of deciding whether or not to

restructure its debt (the ˜˜debt restructuring study™™). The success or failure

of the ¬rm depends on the outcome of a sequence of four events which

will impact the decision. This came from an actual valuation assignment.

Part 3 consists of a mathematical technique to streamline the process

of forecasting sales for a startup. We call the technique the exponentially

declining sales growth model. This model enables the user to generate a

realistic, exponentially declining sales pattern over the life of the product/

service with ease and greatly simpli¬es and facilitates sensitivity analysis,

as it eliminates or at least greatly reduces the need to manually insert

sales growth percentages in spreadsheets.

3

Two more sophisticated approaches are using Monte Carlo simulation and real options, which

are excellent solutions but beyond the scope of this chapter.

CHAPTER 12 Valuing Startups 409

FIRST CHICAGO APPROACH

Startups are much riskier ventures than mature businesses. Because of a

lack of sales history and often a lack of market information, a number of

widely varying scenarios are plausible, and the range of outcomes is

much wider and more unpredictable than that of mature businesses.

In a DCF analysis the forecast cash ¬‚ows are supposed to be the

weighted average cash ¬‚ows, with the appraiser having considered the

full range of possible outcomes. However, it is dif¬cult to do this with

such a wide range of possible outcomes. Instead, typically the appraiser,

investment banker, or venture capitalist uses the usually optimistic fore-

cast of the client”perhaps downplayed somewhat”and discounts that

to present value at a very high rate, around 50“75%.

Thus, a more traditional single-scenario DCF analysis to calculate fair

market value is not only more dif¬cult to perform, but it is also far more

subject to criticism by parties with different interests. Short of using

Monte Carlo simulation”a complex approach requiring specialized soft-

ware that is warranted only in a limited number of assignments with

very sophisticated clients”it is virtually impossible to portray the cash

¬‚ows accurately in a single scenario. Instead, the best solution is to use

a multi-scenario approach known as the First Chicago approach. I name

the typical scenarios: very optimistic (the grand slam home run), opti-

mistic (the home run), conservative (the single), and pessimistic (the

strikeout).

According to James Plummer (Plummer 1987), Stanley C. Golder

(Golder 1986) was the originator of the First Chicago approach, named

after First Chicago Ventures, a spinoff of First Chicago Bank™s Equity

Group. In 1980 he founded the venture ¬rm Golder, Thoma, and Cressey.

James Plummer actually gave the name to the First Chicago approach.

Bradley Fowler wrote the original literature on the First Chicago approach

(Fowler 1989, 1990, 1996).

Discounting Cash Flow Is Preferable to Net Income

While discounting forecast cash ¬‚ow is always preferable to discounting

forecast net income, it is even more important to use cash ¬‚ow in valuing

startups than it is in mature ¬rms. This is because cash is far more likely

to run out in a startup than in a mature ¬rm. When that happens, the

¬rm is forced either to take on new investment, which dilutes existing

shareholders™ ownership in the company, or go out of business. In both

cases, using a discounted future net income approach will lead to a se-

rious overvaluation.

When budget is a consideration, it is possible to discount forecast

net income instead of cash ¬‚ow. However, it is critical that the appraiser

at least do some due diligence to ascertain that the subject company will

not run out of cash.

Capital Structure Changes

Startups tend to have somewhat frequent changes in capital structure.

Investment often occurs in several traunches. These changes can involve

PART 5 Special Topics

410

replacing debt with common or preferred equity and new investment in

equity. This complicates the value calculations because one must be very

careful about whose equity he or she is measuring. Each round of in-

vestment dilutes existing equity, and it is easy to measure the wrong

equity portion if one is not careful.

Venture Capital Rates of Return

Venture capitalists price companies by determining the present value of

cash ¬‚ow or future earnings. One method of valuation is to discount an

optimistic forecast of FMV at the required rate of return. Required rates

of return for VC vary directly with the stage of the company, with star-

tups being the riskiest, hence requiring rates of return of 50“75% (Plum-

mer 1987).

Fowler cites (Fowler 1990) a survey published by Venture Economics

covering 200 companies which indicated that 40% of VC investments lost

money, 30% proceeded sideways or were classi¬ed as ˜˜the living dead,™™

20% returned 2“5 times invested capital, 8% returned 5“10 times, and 2%

returned greater than 10 times the investment. In a follow-up article

(Fowler 1996) he refers to comments made by Professor Stewart Myers

of MIT in his November 1995 address to the American Society of Ap-

praisers con¬rming that 70“80% of VC investments are failures, whereas

20“30% are big winners. In addition, Professor Myers observed that the

overall IRR for successful VC partnerships was approximately 25%.4

The 25% rate of return is consistent with a more recent Wall Street

Journal article (Pacelle 1999) which cites Venture Economics as a source

that venture capital ¬rms returned an average 27.4% over the past 5 years,

although they returned only 15.1% over the past 20 years. From this, we

can calculate the ¬rst 15 years™ (roughly 1979“1993) compound average

return as 11.27%.5 That is a very low return for VC ¬rms. It is comparable

to NYSE decile #1 ¬rm long-run returns. I would attribute that low return

to two factors. That period:

1. Was the infancy of the VC industry, and the early entrants faced

a steep learning curve.

2. Included two severe recessions.

It is not reasonable to expect VC investors to be happy with a 15% return

long run. The ¬ve-year average of 27.4% is more in line with the risk

undertaken.

As to batting averages, a reasonable synthesis of this information is

that 2% of VC investments are grand slams, 8% are home runs, 20% are

moderately successful, and 70% are worthless or close to it.

4

He also mentioned that the average VC project return was 1%. He said the difference in returns

is due to the skewness in the distribution that comes from the venture capitalists quickly

identifying and pulling the plug on the losers, i.e., they do not continue to fund the bad

projects. Thus, the bad projects have the least investment.

5

r15)(1.274)5 1.15120, which solves to r15

The equation is: (1 11.27%.

CHAPTER 12 Valuing Startups 411

Table 12-1: Example of the First Chicago Approach

In Table 12-1 we use these percentages for weighting the four different

scenarios, very optimistic, optimistic, conservative, and pessimistic, re-

spectively.

Initially we perform discounted cash ¬‚ow calculations to determine

the conditional FMV of the subject company under the different scenarios.

Typical venture capital rates of return include the discount for lack of

marketability (DLOM) and discount for lack of control (DLOC). This

tends to obscure the discount rate, DLOM, and DLOC. The appropriate

discount rate using the First Chicago approach begins with the average

success rate of approximately 25% reported by Professor Myers.

The 25%, however, is a geometric average rate of return. We should

estimate an increment to add in order to estimate the arithmetic rate of

return.6 In Table 5-4 we show arithmetic and geometric mean rates of

return from log size model regressions of the 1938“1997 New York Stock

Exchange data for different size ¬rms.

For a ¬rm of $1 million FMV, the regression forecast arithmetic and

geometric returns, rounded to the nearest percent, are 25% and 18%, re-

spectively, for a differential of 7%. For a ¬rm of $25 million FMV, the

regression forecast arithmetic and geometric returns, rounded to the near-

est percent, are 21% and 16%, respectively, for a differential of 5%. We

can add the size-based differential to estimate the arithmetic average rate

of return to use for our discount rate. For most size ranges the result

comes to approximately 30%.7

Column B of Table 12-1 lists the conditional FMVs obtained from

discounted cash ¬‚ow analyses using different sets of assumptions. In the

very optimistic scenario we forecast outstanding performance of the com-

pany, with a resulting FMV of $130,000,000 (B6). Cells B7 and B8 display

the FMVs arising from optimistic and conservative forecasts, respectively.

In the pessimistic scenario we assume the company fails completely, re-

sulting in zero value. When valuing a general partnership interest, which

T A B L E 12-1

First Chicago Method

A B C D

5 Conditional FMV [1] Probability [2] Wtd FMV

6 Very optimistic scenario $130,000,000 2% $2,600,000

7 Optimistic scenario 50,000,000 8% 4,000,000

8 Conservative scenario 10,000,000 20% 2,000,000

9 Pessimistic scenario [1] 0 70% ”

10 Weighted average FMV 100% $8,600,000

Notes:

[1] Individual discounted cash ¬‚ow analyses are the source for the numbers in this column

[2] Based on the VC rates discussed in the chapter

6

I con¬rmed this in a telephone conversation with Professor Myers.

7

Fowler™s article did not address this adjustment.

PART 5 Special Topics

412

has unlimited liability, the appraiser should consider the possibility of

negative value.

Column C lists the probability associated with each scenario. These

are derived directly from the empirical probabilities of VC success dis-

cussed above. We calculate the weighted FMV in column D by multiply-

ing the conditional FMV in column B by its associated probability in

column C and summing the results. Thus, in this example the weighted

average FMV is $8,600,000 (D10).

Advantages of the First Chicago Approach

The major advantages of the First Chicago approach are:

1. It reduces the uncertainty associated with a single FMV by

allowing for several scenarios representing differing levels of

success of the company.

2. It breaks down the huge range of potential outcomes into ˜˜bite-

size™™ chunks, i.e., the individual scenarios, that are credible and

plausible when performed carefully.

3. It makes the appraiser™s probability distribution of outcomes

explicit. In doing so, it has two additional advantages: (a) If the

client agrees with the conditional FMVs of each scenario but for

some reason feels the probabilities are not representative of the

subject company™s chances, it is an easy exercise for the client to

weight the probabilities differently and adjust the valuation him

or herself. This is particularly important when the assignment is

to provide existing shareholders with information to negotiate

with funding sources. If both sides accept the scenario

valuations, it is usually easy for them to come to terms by

agreeing on the probabilities of the outcomes, which they can

easily do without the appraiser; and (b) it protects the appraiser.

When the appraiser shows a ¬nal weighting of the conditional

FMVs multiplied by their probabilities to calculate the FMV and

the appraiser shows the probability of total failure as, say, 70%,

it can protect the appraiser from a disgruntled investor in the

event the company fails. The appraiser has clearly

communicated the high probability of investors losing all their

money, despite the fact that the FMV may be very high”and,

we hope, is”due to the large values in the upper 30% of

probable outcomes.

Therefore, the First Chicago approach is normally the preferred

method of valuation of startups. It is also useful in valuing existing ¬rms

that are facing radically different outcomes that are hard to forecast. For

example, I used it recently to assist warring shareholders who wanted

one side to buy out the other in a four-year-old company. The ¬rm was

pro¬table and had grown rapidly, but there were several major uncer-

tainties that were impossible to credibly consider with accuracy in a single

DCF scenario. The uncertainties were as follows:

1. There was much customer turnover in the prior year, despite

healthy growth.

CHAPTER 12 Valuing Startups 413

2. If one of the shareholders left, sales might suffer greatly for two

or three years and even endanger the company.

3. There were regulatory issues that could have had a dramatic

impact on the company.

4. Pro¬t margins were highly variable in the past four years and

could have been affected by regulation.

Collectively, these uncertainties made a single scenario forecast of

sales growth and pro¬tability very dif¬cult. Despite considerable parti-

sanship by the shareholders, who often actively lobbied for changes in

the DCF analyses, the First Chicago approach enabled us to credibly

model the different paths the Company could take and quantify the val-

uation implications of that. Ultimately, we presented them with the val-

uation of the different scenarios and our estimates of the probabilities,

and the weighted average of the product of the two constituted our es-

timate of FMV. We also explained that they could change their subjective

weighting of probabilities of outcomes, thus changing the FMV. Ulti-

mately, they worked out an arrangement without any further need for

our help.

Discounts for Lack of Marketability and Control

Finally, venture capitalists typically have more control and possibly mar-

ketability than most other investors. When valuing the interests of other

investors, the appraiser must add the incremental discounts for lack of

control and marketability that apply to the speci¬c interests, i.e., an arm™s-

length investor would typically require a higher rate of return on smaller

interests than the 30% that the VC expects.

VENTURE CAPITAL VALUATION APPROACH

In this approach the appraiser estimates net earnings at cash-out time,

often at Year 5 or 6. He or she then estimates a P/E multiple and mul-

tiplies the two to estimate the cash out.

In Table 12-2 we use Fowler™s (Fowler 1989) numbers, with minor

changes in the presentation. Fowler assumed Year 5 net income of

$1,936,167 and multiplied it by a P/E multiple of 12 to calculate the Year

5 cash out at $23.2 million (B5), rounded.

T A B L E 12-2

VC Pricing Approach [1]

A B

5 Assumed cash out-5 yrs @ 12 earnings $23,200,000

6 Present value factor-5 years @ 45% ROI 0.1560

7 Present value-rounded $ 3,619,000

[1] Source: Bradley Fowler, What Do Venture Capital ˜˜Pricing Methods Tell About Valuation of Closely Held Firms?™™ Business Valua-

tion Review, June 1989, page 77.

PART 5 Special Topics

414

He then used a 45% rate of return to discount cash ¬‚ows, based on

industry statistics he presented in the article, which we repeat below in

the next section. The present value factor at 45% for ¬ve years is 0.156,

and the present value of the Company is then $3,619,000 (B7, rounded).

Venture Capital Rates of Return

Fowler (1989) cited rates of return from two different studies. Plummer

(1990) found that the required rates of return (ROR), which included dis-

counts for lack of control (DLOC) and discounts for lack of marketability

(DLOM), were:

Stage of Development of Co. Required Rate of Return

Seed capital stage 50“75%

1st stage 40%“60%

2nd stage 35%“50%

3rd stage 30%“50%

4th stage 30%“40%

Morris (1988, p. 55) writes that VCs are looking for the following

rates of return:

Stage of Development of Co. Required Rate of Return

Seed capital stage 50%

2nd stage 30“40%

Summary of the VC Approach

The VC approach is a valid valuation approach, though certainly less

analytically precise than the First Chicago approach. Nevertheless, it is

used by venture capitalists, and it serves as a ˜˜quick-and-dirty™™ valuation

method, on the one hand, and as a useful alternative approach, on the

other.

This concludes Part 1 of this chapter. Part 2 is a complex decision

tree analysis combined with multiscenario valuation.

DEBT RESTRUCTURING STUDY

Early-stage technology-based companies often ¬nd themselves in ¬nan-

cial hot water. They incur large expenses for years during the develop-

ment of a new product. Consequently, they run short of funds and often

require the infusion of venture capital, which may or may not occur. In

the following example”which is based on an actual assignment, with

names and numbers changed”the Subject Company has several possible

events that can impact the probability of obtaining venture capital as well

as surviving as a ¬rm without venture capital, i.e., bootstrapping to

success.

CHAPTER 12 Valuing Startups 415

Background

The Company and its former parent (˜˜the parent™™) share a nearly iden-

tical set of shareholders”well over 100. The president is the major share-

holder of the ¬rm, with effective, but not absolute control. The parent had

lent the Company $1 million to get started as a spinoff, but the debt

would be coming due in four years, and the Company has no way of

paying it off.

The parent proposed the following restructuring of the debt:

1. The parent would convert the debt into $400,000 of convertible

preferred stock”and part of the valuation exercise was to

determine how many shares of preferred stock that would be.

There would be no preferred dividends, but the parent would

have a liquidation preference.

2. The president would have to relinquish a certain number of his

shares in the parent back to the parent, which had a ready

buyer for the shares.

In return for relinquishing his shares to the parent, the president

wants the Company to issue 1.3 million new shares to him. The board of

directors wants an independent appraisal to determine whether the trans-

action is favorable to the other shareholders. This example, however, is

typical of the types of decisions faced by startup ¬rms in their quest for

adequate funding. More importantly, the statistical approach we use in

this valuation is applicable to the valuation of many startups, regardless

of industry.

Key Events

The company president, Mr. Smith, has identi¬ed a sequence of four key

events that could occur, and each one of them increases the Company™s

ability to obtain venture capital ¬nancing as well as to successfully boot-

strap the ¬rm without VC ¬nancing. The events are sequentially depen-

dent, i.e., event #1 is necessary, but not suf¬cient for event #2 to occur.

Events #1, #2, and #3 must occur in order for #4 to occur. These events

are:

1. Event #1: The Company sells its product to company #1. The

conditional probability of this event occurring is 75% (Table

12-3, cell B11).

2. Event #2: The Company sells its product to company #2. The

conditional probability of this happening, assuming event #1

occurs, is 90% (B12).

3. Event #3: The Company sells its product to company #3, which

has a 60% (B13) conditional probability, i.e., assuming event #2

occurs.

4. Event #4: The Company sells its product to company #4. If the

Company sells its product to company #3, then it has an 80%

(B14) probability of selling it to company #4.

While these four events are all potential sales, the statistical process

involved in this analysis is generic. The four events could just as easily

PART 5 Special Topics

416

be a mixture of technology milestones, rounds of ¬nancing, regulatory,

sales, and other events.

Decision Trees and Spreadsheet Calculations

Our analysis begins as decision trees, which appear in Figures 12-1 and

12-2. However, careful analysis leads to our being able to generalize the

decision tree calculations mathematically and transform them into ex-

pressions that we can calculate in a spreadsheet. This has tremendous

computational advantage, which is not very apparent in a four-milestone

analysis. Increase the number of milestones to 20, and the decision tree

becomes very unwieldy to present, let alone to calculate, while the

spreadsheet is easy. The discussions over the next few pages ultimately

culminate in the development of equations (12-3) through (12-6). The

equations provide the blueprint for the structure of the calculations in

Table 12-3.

Table 12-3: Statistical Calculation of FMV

Table 12-3 is a statistical calculation of the FMV of the common shares of

the Company owned by the existing minority shareholders, based on the

probabilities of the different events occurring and the results of DCF anal-

yses of several different scenario outcomes.

Organization

The table is divided into three sections. In the ¬rst two sections, 1A and

1B, the Company does restructure its debt with the parent. Section 1A is

the calculation of the probability-weighted contribution to the FMV of the

current shareholders™ shares when the Company is successful in obtaining

venture capital. Several possible combinations of events can lead to this

outcome, and we identify the probabilities and payoffs of each combi-

nation in order to calculate the FMV of the common stock owned by the

existing minority shareholders. Section 1B is the probability-weighted

equivalent of section 1A when the Company is not successful in obtaining

venture capital and instead attempts to bootstrap its way to success. The

total of sections 1A and 1B is the FMV of current shareholders™ shares,

assuming the Company restructures the debt.

Section 2 is an analysis of the combination of events in which the

Company does not restructure its debt with the parent. Section 3 is a

summary of the FMVs under the different scenarios and contains calcu-

lations of the per share values. This is the bottom line of the valuation

assignment.

Section 1A: Venture Capital Scenario

In section 1A the primary task is to determine the probability of receiving

venture capital funding. Once we have accomplished that, it is simple to

determine the contribution to FMV from the VC scenario.

Figure 12-1 is a diagram of the decision tree for section 1A. We begin

by noting that there is a 75% probability of making sale #1 and a 25%

probability of not making sale #1, in which case the Company fails. We

denote the former as P(1) 75% and the latter as P( 1) 25%. We

CHAPTER 12 Valuing Startups 417

418

T A B L E 12-3

Statistical Calculation of Fair Market Value

A B C D E F G H I J K

4 Section 1A: Weighted Average Values Assuming Venture Capital Scenario & Debt Restructure With Parent

[C] [D] [G] B18

6 Cum. Product [B] [1 [D] Cumulative [Fn 1] 1 VC% [H] [1 Min] [I]

7 Product [E]

8 Event Conditional Cumulative Venture Prob No VC Current Current Current

9 Probability Joint Cap 1 VC Cond. Shareholders Shareholders Shareholders

10 of Sale Probability Conditional Probability Cum. no VC Prob of VC % Own FMV Control FMV Minor

of Sale Probability

11 #1: Company makes sale #1 75.000% 75.000% 50.000% 50.000% 50.000% 37.500% 50.000% $18,750,000 $14,062,500

12 #3: Company makes sale #2 90.000% 67.500% 60.000% 40.000% 20.000% 20.250% 60.000% $12,150,000 $9,112,500

13 #3: Company makes sale #3 60.000% 40.500% 70.000% 30.000% 6.000% 5.670% 70.000% $3,969,000 $2,976,750

14 #4: Company makes sale #4 80.000% 32.400% 100.000% 0.000% 0.000% 1.944% 85.000% $1,652,400 $1,239,300

15 Totals 63.364% $36,521,400 $27,391,050

Assumptions

18 FMV VC scenario $100,000,000

19 Minority interest discount 25%

(assumed)

21 Section 1B: Bootstrap Scenario Assuming Debt Restructuring With Parent

23 Cum. Product [B] 1 [D] Cum. Prod. P[Si i, [C] [F] Note [1] [H] [I] [1 Min] [J]

[E] (i 1)] {1 [Bt 1]}*[G]

Venture Wtd Avg

26 Cumulative Cap Prob No VC Bootstrap FMV Current

27 Conditional Joint Conditional 1 VC Cond. Conditional Prob of Survival/ Conditional FMV Shareholders

28 Event Probability Probability Probability Probability Cum. No VC Probability No VC FMV Control FMV Minor

29 #1: Company makes sale #1 75.000% 75.000% 50.000% 50.000% 50.000% 30.000% 1.125% 15,286,460 $171,973 $128,980

30 #3: Company makes sale #2 90.000% 67.500% 60.000% 40.000% 20.000% 35.000% 1.890% 15,464,845 292,286 219,214

31 #3: Company makes sale #3 60.000% 40.500% 70.000% 30.000% 6.000% 75.000% 0.365% 15,732,422 57,345 43,009

32 #4: Company makes sale #4 80.000% 32.400% 100.000% 0.000% 0.000% 90.000% 0.000% 16,000,000 0 0

33 Totals 3.380% $521,603 $391,202

35 Section 2: No Debt Restructure With Parent

37 #1: Company makes sale #1 75.000% 75.000% 0.000% 100.000% 100.000% 30.000% 2.250% 7,286,460 $163,945 $122,959

38 #3: Company makes sale #2 90.000% 67.500% 0.000% 100.000% 100.000% 35.000% 9.450% 7,464,845 705,428 529,071

39 #3: Company makes sale #3 60.000% 40.500% 0.000% 100.000% 100.000% 75.000% 6.075% 7,732,422 469,745 352,308

40 #4: Company makes sale #4 80.000% 32.400% 0.000% 100.000% 100.000% 90.000% 29.160% 8,000,000 2,332,800 1,749,600

41 Totals 46.935% $3,671,918 $2,753,938

43 No

Assumptions Restructure Restructure

44 Adjusted FMV $16,000,000 $8,000,000

bootstrap

45 Minority interest discount 25.0%

(assumed)

49 Section 3: Calculation of FMV per Share

50 Restructure No

51 Restructure:

Venture Investor %

52 Capital Bootstrap Total 33.33%

53 Sec 1: venture capital $27,391,050 $391,202 $27,782,252 $2,753,938

scenario

54 Calculation of fully diluted

shares:

55 Original shares 1,000,000 1,000,000 1,000,000

56 Options:

57 200,000 @ $0.50 per share 200,000 200,000 200,000

[2]

58 66,667shares @ $0.75 per 66,667 0 0

share

59 100,000 shares @ $1.00 per 100,000 0 0

share

60 Preferred stock conversion 9,624 0 0

[3]

61 Total option shares 376,290 200,000 200,000

62 Original shares plus options 1,376,290 1,200,000 1,200,000

63 Proposed issuance to 1,300,000 1,300,000 0

president

64 Shares to outside investors 0 0 600,000

[4]

65 Fully-diluted shares [5] 2,676,290 2,500,000 1,800,000

66 Fully-diluted FMV/share- $10.235 $0.156 $10.391 $1.530

post transaction

419

420

T A B L E 12-3 (continued)

Statistical Calculation of Fair Market Value

A B C D E F G H I J K

68 Section 4: 2000 Investor Percentage Taken

70 Control

FMVs

71 t2000 FMV-40% disc rate” $8,000,000

control basis

72 Less: minority interest 25.0%

discount-% (assumed)

73 Less: minority interest ($2,000,000)

discount-$

74 2000 FMV-40% discount $6,000,000

rate”minority basis

75 Percentage required for $2 33.3%

million investment

Notes:

[1] Column I Calculations: Beginning with FMV for Event #4, we subtract $750,000 for not reaching each of Events #4 and #3 and $500,000 for not reaching Event #2. All previous numbers are tax effected and present valued.

[2] Only the 200,000 shares are applicable in all scenarios. The remaining options apply only to the V.C. Scenario

[3] Assume 4 to 1 Preferred-to-Common conversion ratio, per CFO, as follows:

Preferred stock-stated value $400,000

FMV per share of common $10.391

Multiply by 4 $41.56

Convert to # common shares 9,624

[4] In the Bootstrap-No Restructure Scenario, the Company falls $1 million short of cash and owes $1 million to the parent. We assume it will have to take on $2M investment for 33% of the stock. See Section 4.

[5] Actually, fully-diluted shares will be more, as will FMV when VC shares are included. In Section 1A, Columns H and I, we calculated the FMV of the current shareholders™ shares, which is simpler than using actual FMV and wtd avg shares

F I G U R E 12-1

Decision Tree for Venture Capital Funding

VC Found

P(VC2)=0.2025

P(VC2|2)=0.6

VC Found Make Sale 3

Make Sale 2

P(VC1|1)=0.5 P(3|2)=0.6

P(VC1)=0.375 P(3)=0.081

P(2)=0.3375

P(2|1)=0.9

Make Sale 1

P(1)=0.75 No VC Found

P(-VC2|2)=0.4 P(-VC2)=0.135

START No VC Found

No Sale 3

P(-VC1|1)=0.5 P(-VC1)=0.375 No Sale 2

No Sale 1 P(-3|2)=0.4 P(-3)=0.054

P(-1)=0.25 P(-2|1)=0.1 P(-2)=0.0375

Company Fails

P(VC4|4)=1.0 VC Found

P(VC4)=0.01944

VC Found

P(VC3|3)=0.7

Make Sale 4

P(VC3)=0.0567

P(4)=0.01944

P(4|3)=0.8

No VC Found

Make Sale 3 P(-VC4)=0.0

P(-VC4|4)=0.0

P(3)=0.081

No VC Found

No Sale 4

P(-VC3)=0.0243

P(-4)=0.00486

P(-VC3|3)=0.3 P(-4|3)=0.2

Many of the probabilities in this figure appear in Table 12-3, Section 1A, Columns B, D, and G.

Also P(-VC1|1) is equivalent to [1-P(VC1|1)] in the text and P(-2|1)=[1-P(2|1)] etc.

denote the conditional probabilities of subsequent sales as P( j j 1),

where j is the sale number. For example, P(2 1) is the conditional proba-

bility of making sale #2, given that the Company already made sale #1.

The probability of making sale #2 is the probability of making sale #1

multiplied by the conditional probability of making sale #2, given that

the Company makes sale #1, or: P(2) P(1) P(2 1) 0.75 0.9

0.675. Also note that P(1) is the same as P(1 0) since there is no sale zero.

Probability of VC Financing After Sale #1. If the Company makes

sale #1, there is a 50% conditional probability of receiving VC funding at

that time. We denote that event as VC1, which means receiving VC fund-

ing after sale #1 but before sale #2 is attempted,8 and we denote its con-

ditional probability of occurrence as P(VC1 1), i.e., the probability of VC

funding after sale #1, given that sale #1 occurs. The probability of receiv-

ing VC funding after the ¬rst sale is the conditional probability of the

¬rst sale occurring times the conditional probability of VC funding, given

the sale.9 The statistical statement is: P(VC1) P(1) P(VC1 1), where

P(1) is the probability of making sale #1. Thus P(VC1) 0.75 0.5

0.375.

We denote the conditional probability of failure to obtain VC funding

after sale #1 as P( VC1 1) 1 P(VC1 1) 0.5. Thus the absolute prob-

8

From now on, when we say ˜˜after sale i,™™ we also mean ˜˜but before the Company attempts sale

i 1.™™

9

For the ¬rst sale, the conditional probability and the absolute probabilities are identical.

CHAPTER 12 Valuing Startups 421

ability of not receiving VC ¬nancing after sale #1 is P( VC1) P(1)

P( VC1 1) 0.75 0.5 0.375, which is the same result as P(VC1). This

occurs because the conditional probability of obtaining venture capital,

given that the Company makes the ¬rst sale, is 50%. At any other prob-

ability, P(VC1 1) P( VC1 1). These statements generalize for sale i, i

1, 2, 3, 4.

Probability of VC Financing after Sale #2. Let™s move on to the

next step in our analysis: sale #2 and the probability of VC funding after

it. If the Company receives VC after sale #1, we have already quanti¬ed

that above. Our task in this iteration is to quantify the probability of VC

funding if it did not come after sale #1 but does come after sale #2. Thus,

the chain of events we are quantifying in this round is: sale #1 ’ VC1

’ sale #2 ’ VC2, i.e., the Company makes sale #1, doesn™t receive venture

capital, makes sale #2, then receives venture capital.

The probability of obtaining VC funding after sale #2 is:

P(VC2) P(1) [1 P(VC1 1)] P(2 1) P(VC2 2)

0.75 (1 0.5) 0.9 0.6 0.2025 (12-1)

Note that the conditional probability of VC ¬nancing, given that the Com-

pany makes sale #2, P(VC2 2) 0.6, compared to 0.5 after sale #1. In

general, it makes sense that the conditional probability of receiving VC

¬nancing rises with each new key sale.

We can rearrange equation (12-1) as:

P(VC2) P(1) P(2 1) [1 P(VC1 1)] P(VC2 2) (12-2)

In other words, the probability of obtaining VC ¬nancing after sale #2 is

the cumulative joint probability of making both sale #1 and sale #2 times

the conditional probability of not obtaining VC funding after sale #1 times

the conditional probability of obtaining VC funding after sale #2.

Generalizing to Probability of VC Financing after Sale #k. We can

generalize the probability of obtaining VC funding after sale #k as:10

k k1

P(VCk) P(i i 1) [1 P(VCj j)] P(VCk k) (12-3)

i1 j0

Equation (12-3) states that the probability of obtaining venture capital

¬nancing after sale #k is the cumulative joint probability of sale #k oc-

curring times the cumulative joint probability of having been refused VC

¬nancing through sale #(k 1) times the conditional probability of re-

ceiving VC ¬nancing after sale #k.

Finally, the total probability of obtaining VC ¬nancing is the sum of

equation (12-3) across all n sales, where n 4 in this example:

10

Of course, P(1 0) P(1), as the former has no meaning. Also, in the ¬rst iteration of equation

(12-3), i.e., when j 0, the term P(VCj j ) is the cumulative probability of receiving VC

¬nancing from sale #0, which is a zero probability. Thus 1 P(VCj j ) goes to 1.0, as it

should.

PART 5 Special Topics

422

n k k1

P(VC) P(i i 1) [1 P(VCj j)] P(VCk k) (12-4)

k1 i1 j0

Explanation of Table 12-3, Section 1A. Column A lists the sales

events described above, and column B lists their associated conditional

probabilities in cells B11“B14, i.e., P(1) 75% (B11), P(2 1) 90% (B12),

etc. Column C is the cumulative joint probability, which is just the cu-

mulation of the conditional probabilities. For example, the cumulative

joint probability of making sale #4 is P(1) P(2 1) P(3 2) P(4 3)

75% 90% 60% 80% 32.4% (C14), where the conditional proba-

bilities we multiply by each other are in cells B11“B14. Cells C11“C14

n

represent the term P(i i 1) in equations (12-3) and (12-4).

i1

Column D is the president™s forecast of the conditional probability of

obtaining venture capital ¬nancing. Each conditional probability is

P(VCj j), i.e., the probability of obtaining VC ¬nancing after sale #j, given

that the Company makes sale #j, but before attempting sale #j 1. Every

subsequent sale increases the probability of obtaining venture capital be-

yond the level of the previous event. The conditional probability of VC

¬nancing rises from 50% (D11) after sale #1 to 60%, 70%, and 100% for

sales #2, #3, and #4, respectively (D12“D14).

Column E, the conditional probability of not receiving VC ¬nancing

after each sale, is one minus column D. Column F is the cumulative prod-

k1

uct of column E. It is the [1 P(VCj/j )] in equation (12-3) when we

j0

use the cumulation of the previous sale. For example, the probability of

obtaining VC ¬nancing after the sale to company #4 is the cumulative

joint probability of making sale #4, which is 32.4% (C14) the cumulative

joint probability of not having obtained VC ¬nancing after the ¬rst three

sales, which is 6% (F13) the conditional probability of making sale #4,

which is 100% (D14) 1.944% (G14).

Finally, the probability of obtaining VC ¬nancing, according to equa-

tion (12-4), is 65.364% (G15), the sum of column G. The FMV of the com-

pany, if it obtains VC ¬nancing, is $100 million (B18), which we deter-

mined with a DCF analysis.

Column H is one minus the percentage that Mr. Smith estimates the

venture capital ¬rm would take in the company™s stock. After sale #1, he

estimates the venture capitalist would take 50%, leaving 50% (H11) to the

existing shareholders after the conditional transaction. If the Company

makes the sale to company #2, it will be in a stronger bargaining position,

and Mr. Smith estimates the venture capitalist would take 40% of the

Company, leaving 60% (H12) to existing shareholders after the transac-

tion. If the Company makes the sale to company #3, then he estimates

the venture capitalist would take 30% of the Company, leaving 70% (H13)

to the existing shareholders after the transaction. Finally, if the Company

makes the sale to company #4, then he estimates the venture capitalist

would take 15% of the Company, leaving 85% (H14) to the existing share-

holders after the transaction.

Columns I and J are the FMVs of the current shareholders™ shares on

a control and minority basis resulting from obtaining venture capital ¬-

CHAPTER 12 Valuing Startups 423

nancing. Later on, we will add in the current shareholders™ FMV from

bootstrapping the Company to come to a total current shareholders™ FMV

for the debt restructure option. Column I is the control value FMV and

is obtained by multiplying the probability of obtaining VC ¬nancing in

column G times the $100 million FMV of the Company if it receives VC

¬nancing (B18) times column H, the current shareholder ownership per-

centages. Column J is the FMV on a minority interest basis, which is

column I times one minus the minority interest discount of 25.0% (B19),

the magnitude of which is an arbitrary assumption in this analysis. The

total FMVs of current shareholder shares are $36,521,400 (I15) and

$27,391,050 (J15) on a control and minority basis, respectively.

The ¬nal equation describing the FMV is:11

n k k1

FMV (VC) P(i i 1) [1 P(VCj/j)]

k1 i1 j0

P(VCk k) SH%k $100 million (12-5)

In words, the contribution to FMV from the VC scenario is the sum of

the probabilities of obtaining VC, which we quanti¬ed in equation

(12-4), times the $100 million FMV of the company, assuming it is VC

¬nanced.

Section 1B: The Bootstrap Scenario Assuming Debt

Restructuring with Parent

Bootstrapping occurs when the Company fails to attract venture capital

but still manages to stay in business. The bootstrap scenario includes both

success and failure at its attempts to bootstrap. Figure 12-2 shows the

decision tree for the bootstrap scenario.

The pattern of events is that in each iteration, the Company can make

the sale or not make the sale. After each sale, it might get VC ¬nancing

or it might not. In section 1B we are not interested in the nodes on the

decision tree where the Company receives VC ¬nancing, as we have al-

ready quanti¬ed that in section 1A. Thus, we do not show those nodes.

Nevertheless, it is important to account for the probabilities of obtaining

VC ¬nancing because if we don™t, we will be double-counting that portion

of the time that the Company could ¬nance through a VC or bootstrap

successfully. The Company can™t do both at the same time. Thus, we

remove the statistical probability of overlap. We accomplish that by mul-

tiplying all probabilities by [1 P(VCi i)] for all relevant i, where i is the

sale number (also the iteration number).

If the Company does not make the sale, then it has a probability of

survival and failure. We denote the survival after its last sale as Sj, where

j is the sale number. The conditional probability of survival after its last

sale is P[Sj j, ( j 1)]. For example, if the company makes sale #3, does

not make sale #4, and survives, we denote that as S3, and its conditional

11

The term SH% is the percentage ownership of the current shareholders after VC ¬nancing.

PART 5 Special Topics

424

F I G U R E 12-2

Decision Tree for Bootstrapping Assuming Debt Restructure and No Venture Capital

P(-VC4|4)(0.9)

Survive = S4

Make Sale 4

P(-VC3|3)(0.8)

No VC3

Fail

Sale 3 Sale 3

Make

P(-VC2|2)(0.6) 0.75

No Sale 4 Survive = S3

No VC2

No VC3

P(-VC3|3)(0.2)

Fail

0.25

P(-VC1|1)(0.9) Make Sale 2 0.35

No Sale 3 Survive = S2

No VC1

No VC2

P(-VC2|2)(0.4)

Fail

0.65

0.3

No Sale 2 Survive = S1

Make Sale 1

P(1)=0.75

No VC1

P(-VC1|1)(0.1)

START Fail

0.7

No Sale 1

Fail

P(-1)=0.25

Note: P(-VC1|1) is equivalent to [1-P(VC1|1)] in the text.

probability of occurrence is P(S3 3, 4), which reads, ˜˜the probability of

Company long-term survival, given that it made sale #3, but does not

make sale #4.™™ If the Company makes the next sale, then we repeat the

iteration, incrementing the sale number.

Without going through all of the step-by-step analysis we did for the

VC scenario, the FMV of the bootstrap scenario is:

j

n

FMV (Bootstrap) P(i i 1)[1 P(VCi i)]

(12-6)

j1 i1

(1 P( j 1 j)P[Sj j, (j 1)]FMV (Sj)

Let™s use the ¬rst iteration as an example. The probability of making

sale #1 is 0.75. There is a 0.5 probability of obtaining VC ¬nancing if the

company makes sale #1, so there is also a 0.5 probability of not obtaining

VC ¬nancing, i.e., [1 P(VCi i)] 0.5. In order to terminate at S1, the

company must make sale #1 and fail to make sale #2, which means we

multiply by [1 P(2 1)], which is equal to one minus the conditional

probability of making sale #2 1 0.9 (B30) 0.1. The probability of

survival if the Company makes sale #1 but stops there is 0.30 (G29). Thus,

P(S1) P(1) [1 P(VC1 1)] [1 P(2 1)] P(S1 1, 2) 0.75 (1

12

0.5) (1 0.9) 0.3 1.125% (H29).

Column I is the conditional FMV of the company at each respective

event level. This is different than in section 1, where the FMV is the same

12

Note that for the last milestone, 1 P(n 1 n) must be equal to 1, since the probability of

making the (n 1)st sale is zero.

CHAPTER 12 Valuing Startups 425

regardless of stage. The reason is that in section 1 the sole objective is

obtaining venture capital funding, which will enable the Company to sell

to the world. The lost pro¬ts on the key sales not made is immaterial

compared to the $100 million FMV. In contrast, in section 1B each sale is

signi¬cant relative to the total value and adds to the value of the com-

pany.13

In section 1B we begin with a conditional FMV of $16,000,000 (B44,

repeated in I32). That value contains an implicit assumption that the

Company makes it to event #4, the sale to Company #4. At each level

before that, we subtract the net present value of the after-tax pro¬ts14 from

the sale that does not occur, i.e., we work our way backwards up this

column. We assume pretax pro¬ts of $750,000 for the sales in events #3

and #4 and $500,000 for event #2. The numbers are then tax effected and

discounted to present value. If the Company does not make it to event

#1, this model assumes the Company fails entirely and has a zero value.

Column J is the contribution to the FMV of the Company on a control

basis coming from the bootstrap scenario and is simply column H times

column I, which totals $521,603 (J33).

Column K is the same value as column J, except that it is a minority

interest conditional FMV. The discount for minority interest is 25%, which

appears in B45. On a minority interest basis, the bootstrap scenario FMV

is $391,202 (K33).

Section 2: No Restructure Scenario

The ¬nal scenario is the no-restructure with parent scenario. Section 2 is

identical to section 1B, except:

1. Column F, the probability of not obtaining venture capital

¬nancing, is 100% by de¬nition for all four events in section 2,

since the president informs us that a VC will not ¬nance the

Company as long as it still has the parent™s debt on the books.

2. Column I is calculated identically to section 1B, except that the

baseline FMV as calculated by DCF analysis is $8 million (C44,

repeated in I40) for the no-restructure scenario instead of $16

million (B44, repeated in I32).

Columns J and K in section 2B are the same as in Section 2A, except

that there are no values originating from the venture capital scenario that

have to be removed.

Section 3: FMVs per Share under Various Restructure

Scenarios

In section 3 we calculate the fully diluted FMV per share post-transaction

under the various scenarios.

13

The sales actually do affect the values in section 1, but their impact is immaterial relative to the

much larger total value, which is not true in the bootstrap scenarios.

14

To be more precise, we would also include the related cash ¬‚ow effects.

PART 5 Special Topics

426

Venture Capital Scenario. The conditional FMV of the Company on

a minority interest basis from the venture capital scenario is $27,391,050

(B53, transferred from J15). The Company currently has 1,000,000 shares

of common stock outstanding, as appears in B55, C55, and F55. Rows 57“

59 show employee stock options. Row 57 shows outstanding options for

200,000 shares at $0.50 per share. These options are in the money, and we

assume they will be exercised. That would result in $100,000 being paid

to the Company, which is included in the DCF analysis and is therefore

already incorporated into the $27,391,050 value. These 200,000 additional

shares are taken into account in all of the valuation scenarios.

Rows 58 and 59, however, are for options that are granted but could

only be exercised if the Company does the restructure and obtains VC

¬nancing.15 Mr. Johnson says that if the Company does obtain VC ¬-

nancing, it will issue 66,667 options with a $0.75 exercise price this year

(B58) and 100,000 options (B59) at a $1.00 per share exercise price next

year. Again, the cash in¬‚ows from exercise of the options are already

included in the DCF analysis.

In the restructure scenario the parent receives $400,000 of preferred

stock, which can be converted to common if the Company goes public or

gets acquired. Otherwise, it only serves to increase the liquidation pref-

erence, as preferred dividends will never be paid. Therefore, the divi-

dends, which are not tax deductible, do not appear in any of the cash

¬‚ows. We presume in the venture capital scenario that the probability of

going public or being acquired is signi¬cant and that preferred will con-

vert. According to Mr. Johnson, a reasonable conversion ratio is 4 to 1. In

note 3 to section 3 the $400,000 is divided by four times the fully diluted

FMV of $10.391 per share (D66, repeated in footnote [3]) or $41.56 per

share, resulting in an estimated conversion to common shares of 9,624

(footnote [3], transferred to B60). This calculation is a simultaneous equa-

tion and requires the use of multiple iterations on the spreadsheet. The

number of converted shares depends on the fair market value per com-

mon share, but the FMV per common share depends on the number of

preferred shares.

The total option shares are 376,290 (B61), including the assumed con-

version of preferred in the venture capital scenario. In B63 we show the

proposed issuance of 1.3 million shares to the president. Adding the

1,000,000 original shares, 376,290 option granted shares, and the 1.3 mil-

lion new shares, we come to 2,676,290 (B65) fully diluted shares in the

venture capital scenario. Dividing the $27,391,050 FMV by 2,676,290

shares, we arrive at the FMV per share of $10.235 (B66) for the venture

capital scenario.

Next we consider the bootstrap portion of the restructure scenario.

We begin with the $391,202 (K33) FMV as calculated in section 1B and

repeat it in C53. Again, this is the portion of bootstrap value from which

venture capital is excluded.

In this scenario the fully diluted shares are the same as in the venture

capital scenario, except that the 66,667, 100,000 and 9,624 shares in rows