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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




PART 5 Special Topics
430
F I G U R E 12-3A

Sales Forecast (Decay Rate 0.3)

450,000
400,000
350,000
300,000
Sales




250,000
200,000
150,000
100,000
50,000
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Year




have chosen the future year to be Year 4. The model user speci¬es the
growth rates prior to Year f (we have chosen 100% and 200% in Years 2
and 3, respectively). The growth rates for year f and later are G Ae k(t f).
As you can see, the growth rates from Years 4 through 10 in this example
are identical to the growth rates from Years 2 through 8 in example #1.
Figures 12-3 and 12-3A are graphs that show the sales forecasts from
examples #1 and #1A extended to 28 years. The slower decay rate of 0.3
in Figure 12-3A (versus 0.5 in Figure 12-3) leads to much faster growth.
After 28 years, sales are close to $450,000 versus $38,000. Changing one
single parameter can give the analyst a great deal of control over the sales
forecast. When sensitivity analysis is important, we can control the de-
cline in sales growth simply by using different numbers in cell E9, the
decay rate. This is not only a nice time saver, but it can lead to more
accurate forecasts, as many phenomena in life have exponential decay (or
growth), e.g., the decay of radiation, population of bacteria, etc.


BIBLIOGRAPHY
Fowler, Bradley A. 1989. ˜˜What Do Venture Capital Pricing Methods Tell About Valuation
of Closely Held Firms?™™ Business Valuation Review (June): 73“79.
” ”. 1990. ˜˜Valuation of Venture Capital Portfolio Companies”and Other Moving Tar-

gets.™™ Business Valuation Review (March): 13“17.
” ”. 1996. ˜˜Venture Capital Rates of Return Revisited.™™ Business Valuation Review

(March): 13“16.
Golder, Stanley C. 1986. ˜˜Structuring and Pricing the Financing.™™ In Pratt™s Guide to Venture
Capital Sources, 10th ed., ed. Stanley E. Pratt and Jane K. Morris. Wellesley Hills,
Mass.: Venture Economics.
Morris, Jane K. 1988. In Pratt™s Guide to Venture Capital Sources, 12th ed., ed. Jane K. Morris.
Wellesley Hills, Mass.: Venture Economics.
Pacelle, Mitchell. 1999. ˜˜Venture Firms Dethroning Buyout Kings.™™ Wall Street Journal, 7,
June 1999. p, C1.
Plummer, James L. 1987. QED Report on Venture Capital Financial Analysis. Palo Alto, Calif.:
QED Research, Inc. [See especially 2-7“2-10 and 6-2“6-13.]
Pratt, Stanley E. and Jane K. Morris, Guide to Venture Capital Sources, Venture Economics,
1986.




CHAPTER 12 Valuing Startups 431
CHAPTER 13


ESOPs: Measuring and
Apportioning Dilution1




INTRODUCTION
What Can Be Skipped
DEFINITIONS OF DILUTION
Dilution to the ESOP (Type 1 Dilution)
Dilution to the Selling Owner (Type 2 Dilution)
De¬ning Terms
TABLE 13-1: CALCULATION OF LIFETIME ESOP COSTS
THE DIRECT APPROACH
FMV Equations”All Dilution to the ESOP (Type 1 Dilution; No Type
2 Dilution)
Table 13-2, Sections 1 and 2: Post-transaction FMV with All Dilution
to the ESOP
The Post-transaction Value Is a Parabola
FMV Equations”All Dilution to the Owner (Type 2 Dilution)
Table 13-2, Section 3: FMV Calculations”All Dilution to the Seller
Sharing the Dilution
Equation to Calculate Type 2 Dilution
Tables 13-3 and 13-3A: Adjusting Dilution to Desired Levels
Table 13-3B: Summary of Dilution Tradeoffs
THE ITERATIVE APPROACH
Iteration #1
Iteration #2
Iteration #3
Iteration #n
SUMMARY


1. Adapted and reprinted with permission from Valuation (June 1997): 3“25 and (January 1993): 76“

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