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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


15
The Company cannot obtain VC ¬nancing without restructuring its debt.




CHAPTER 12 Valuing Startups 427
58“60 are zero in this case. There are 1,200,000 shares (C62) in this sce-
nario before issuing the 1.3 million, and 2,500,000 (C65) shares after doing
so. Dividing $391,202 by 2,500,000 shares, we come to a FMV of this
scenario of $0.156 (C66) per share. Adding the per share values together,
we come to $10.235 $0.156 $10.391 (B66 C66 D66) as the
weighted average conditional FMV of the restructure scenario.

No-Restructure Scenario. The name of this scenario is somewhat of
a misnomer. It means that the Company does not restructure its debt with
the parent. At the onset of this assignment there was no way to know
this, but restructuring of debt would eventually be required. The dis-
counted cash ¬‚ow analysis leads to the conclusion that the Company is
unlikely to be able to generate enough cash to pay off the parent™s note
by its due date of December 31, 200016 ”even though the forecast shows
pro¬ts. Therefore, the Company has two choices: become insolvent and
undergo liquidation or restructure later, and undergo a distress sale of
equity approximately one year before the note becomes due.
The second choice obviously leads to a higher value for the share-
holders, as it preserves the cash ¬‚ows, even though some of them will
be diverted to the new investor. Accordingly, we ran a DCF analysis to
the ¬scal year ending closest to the due date of the note. That value is
$8,000,000 and appears in C44.
The subtotal number of shares is 1,200,000 (F62) before the new in-
vestor. Since there is no restructure with the parent in this scenario, the
shares issued to the president is zero here (F63). In section 4 we calculate
that the new investor will demand one-third of the Company post-
transaction (see description below). That implies the investor will demand
600,000 shares (F64), which will bring the total shares to 1,800,000 (F65).
Dividing $2,753,938 (K41, repeated in F53) by 1,800,000 shares leads to a
value of $1.530 (F66) per share for the no-restructure scenario (this should
more appropriately be called ˜˜restructure later™™).


Conclusion
Thus, the restructure is preferable by a FMV per share of $10.391 $1.530
$8.861 per share ( D66 F66).

Section 4: Year 2000 Investor Percentage
A future restructure would be a more distressed one than the current one.
The discounted cash ¬‚ow analysis indicates that the Company would be
short of cash to pay off the note. With two years gone by, the Company
is more likely to lose the possibility of becoming the market leader and
more likely to be an also ran. Also, it would be a far more highly lever-
aged ¬rm without the restructure. Therefore, it would be a higher-risk
¬rm in the year 2000, which dictates using a higher discount rate than
the other scenarios. The result is a value of $8,000,000 (C44, repeated as
B71) before the minority interest discount.


16
The analysis was done in 1996.




PART 5 Special Topics
428
Subtracting the $2 million (B73) minority interest discount leaves us
with an FMV of $6 million (B74). In the DCF we determined the Company
would need a $2 million investment by a new investor, who would re-
quire taking one-third (B75) of the Company. This percentage is used in
section 3, F52 in the no-restructure calculations, as discussed above.


EXPONENTIALLY DECLINING SALES GROWTH MODEL
When forecasting yearly sales for a startup, the appraiser ideally has a
bottom-up forecast based on a combination of market data and reasonable
assumptions. Sometimes those data are not available to us, and even
when they are available, it is often bene¬cial to use a top-down approach
based on reasonable assumptions of sales growth rates. In this section we
present a model for forecasting sales of a startup or early-stage company
that semiautomates the process of forecasting sales and can easily be ma-
nipulated for sensitivity analysis. The other choice is to insert sales
growth rates manually for, say, 10 years, print out the spreadsheet with
that scenario, change all 10 growth rates, and repeat the process for val-
uation of multiple scenarios. Life is too short.
One such sales model that has intuitive appeal is the exponentially
declining sales growth rate model, presented in Table 12-4. In the model
we have a peak growth rate (P), which decays with a decay rate constant
(k) to a ¬nal growth rate (G). The mathematics may look a little dif¬cult,
but it is not necessary to understand the math in order to bene¬t from
using the model.
The top of Table 12-4 is a list of the parameters of the model. In the
example the ¬nal sales growth rate (G) is set at 6% (E6), and the addi-
tional growth rate (A) is calculated to be 294% (E7). The additional growth
rate (A) is the difference between the peak growth rate (P), which is set
at 300% (E8), and the ¬nal sales growth rate of 6%. Next we have the
decay rate constant (k), which is set at 0.50 (E9). The larger the decay rate
constant, the faster the sales growth rate will decline to the ¬nal growth
rate. Finally, we have Year 1 forecast sales of 100 (E10). All the variables
are speci¬ed by the model user with the exception of the additional
growth rate (A), which depends on P and G.
Example #1 shows the forecast sales growth rates (row 17) and sales
(row 18) using the previously speci¬ed variables for a case where the
sales growth rate declines after Year 2. We have no sales growth rate in
Year 1 because we assume there are no prior year sales. The expression
Ae k(t 2), for all t greater than or equal
for the sales growth rate G
to 2, where t is expressed in years. For Year 2 the sales growth rate is G
Ae k(2 2) G A 6% 294% 300% (C17), which is our speci¬ed
Ae k(3 2)
peak growth rate P. Year 3 growth is G 6% (294%
0.5 1 k(4 2)
e ) 184% (D17). Year 4 growth is G Ae 6% 294%
0.5 2
e 114% (E17), etc. To calculate yearly sales, we simply multiply
the previous year sales by one plus the forecast growth rate.
Example #1A is identical to example #1, except that we have changed
the decay rate constant (k) from 0.50 to 0.30. Notice how reducing k slows
the decay in the sales growth rate. In example #2 we present a case of
the peak growth rate (P) occurring in a general future year f, where we



CHAPTER 12 Valuing Startups 429
T A B L E 12-4

Sales Model with Exponentially Declining Growth Rate Assumption


A B C D E F G H I J K

5 Variable Name Symbol Value Speci¬ed/Calculated

6 Final growth rate G 6% Speci¬ed
7 Additional growth rate A 294% Calculated
8 Peak growth rate P 300% Speci¬ed
9 Decay rate k 0.50 Speci¬ed
10 First year™s sales Sales1 100 Speci¬ed

13 Example # 1 - Sales growth rate declines after year 2
k(t 2)
14 Yearly growth G Ae for all t greater than or equal to 2

16 Year 1 2 3 4 5 6 7 8 9 10

17 Growth N/A 300% 184% 114% 72% 46% 30% 21% 15% 11%
18 Sales 100 400 1,137 2,436 4,179 6,093 7,929 9,566 10,989 12,240

21 Example # 1A - Changing the decay rate (k) from 0.50 to 0.30 slows the decline in the sales growth rate

23 Year 1 2 3 4 5 6 7 8 9 10

24 Growth N/A 300% 224% 167% 126% 95% 72% 55% 42% 33%
25 Sales 100 400 1,295 3,463 7,810 15,194 26,072 40,307 57,237 75,937

28 Example # 2 - Sales growth rate declines after future year f

Ae k(t f), for all t greater than or equal to f, where sales growth rate declines after future year f and
29 Sales growth rate G
30 the peak sales growth (P) occurs in year f. Growth through year f is to be speci¬ed by model user. The following is an
31 example with year f 4, and decay rate k 0.5

33 Year 1 2 3 4 5 6 7 8 9 10

34 Growth N/A 100% 200% 300% 184% 114% 72% 46% 30% 21%
35 Sales 100 200 600 2,400 6,824 14,613 25,077 36,559 47,575 57,393

Formula in Cell C17: G A*EXP( k*(C16 2))




F I G U R E 12-3

Sales Forecast (Decay Rate 0.5)

40,000
35,000
30,000
25,000
Sales




20,000
15,000
10,000
5,000
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Year

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