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