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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

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