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“