7 Management Options, Control, and LiquidityChapter 7• Management Options, Control, and Liquidity 229 While Amazon has far more options outstanding as a percent of the outstanding

225

ch

ap

te

r

7Management Options, Control, and Liquidity

O nce you have valued the equity in a firm, it mayappear to be a relatively simple exercise to estimate the valueper share. All it seems you need to do is divide the value of theequity by the number of shares outstanding. But, in the case oftechnology firms, even this simple exercise can become com-plicated by the presence of management and employeeoptions. In this chapter, we begin by considering the magni-tude of this option overhang on valuation and then considerways of incorporating the effect into the value per share.

We also consider two other issues that may be of relevance,especially when valuing smaller technology firms or privatebusinesses. The first issue is the concentration of shares in thehands of the owner/managers of these firms and the conse-quences for stockholder power and control. This effect isintensified when a firm has shares with different voting rights.

The Dark Side of ValuationThe Dark Side of ValuationThe Dark Side of Valuation226

The second issue is the effect of illiquidity. When investors in afirm’s stock or equity cannot easily liquidate their positions,the lack of liquidity can affect value. This can become anissue, not only when you are valuing private firms, but alsowhen valuing small publicly traded firms with relatively fewshares traded.

Management and Employee OptionsFirms use options to reward managers as well as other

employees. These options have two effects on value per share.One is created by options that have already been granted.These options reduce the value of equity per share, since aportion of the existing equity in the firm has to be set aside tomeet these eventual option exercises. The other is the likeli-hood that these firms will continue to use options to rewardemployees or to compensate them. These expected optiongrants reduce the portion of the expected future cash flowsthat accrue to existing stockholders.

The Magnitude of the Option Overhang

The use of options in management compensation packagesis not new to technology firms. Many firms in the 1970s and1980s initiated option-based compensation packages to inducetop managers to think like stockholders in their decision mak-ing. What is different about technology firms? One differenceis that management contracts at these firms are much moreheavily weighted toward options than are those at other firms.The second difference is that the paucity of cash at these firmshas meant that options are granted not just to top managersbut to employees all through the organization, making thetotal option grants much larger. The third difference is thatsome of the smaller firms have used options to meet operatingexpenses and to pay for supplies.

Figure 7–1 summarizes the number of options outstandingas a percent of outstanding stock at technology firms and com-pares them to options outstanding at nontechnology firms.

Chapter 7 • Management Options, Control, and L iquid ity 227

As Figure 7–1 makes clear, the overhang is larger foryounger new technology firms. In Figure 7–2, the number ofoptions as a percent of outstanding stock at Amazon, Ariba,Cisco, Motorola, and Rediff.com are reported.

Rediff.com has no options outstanding, but the other fourfirms have options outstanding. Amazon, in particular, hasoptions on 80.34 million shares, representing more than 22%of the actual shares outstanding at the firm (351.77 million).Motorola, reflecting its status as an older and more maturefirm, has far fewer options outstanding, relative to the numberof outstanding shares.

Firms that use employee options usually restrict when andwhether these options can be exercised. It is standard, forinstance, that the options granted to an employee cannot beexercised until they are vested. For vesting to occur, theemployee usually has to remain for a period that is specified ina contract. Firms do this to keep employee turnover low, but

FIGURE 7–1Options as Percent of Outstanding Stock (Source: Morningstar, www.morningstar.com, June 7, 2000, Morningstar, Inc.)

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

New Technology Old Technology Other Firms


the practice also has implications for option valuation, as weexamine later. Firms that issue options do not face any taxconsequences in the year in which they make the issue. Whenthe options are exercised, however, firms are allowed to treatthe difference between the stock price and the exercise priceas an employee expense. This tax deductibility also has impli-cations for option value.

ILLUSTRATION 7.1

Options Outstanding

Table 7.1 summarizes the number of options outstanding at each of the firms that we arevaluing, with the average exercise price and maturity of the options, as well as the per-cent of the options that are vested in each firm.

FIGURE 7–2Options Outstanding as Percent Shares Outstanding

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

Amazon Ariba Cisco Motorola Rediff.com


While Amazon has far more options outstanding as a percent of the outstanding stock,Ariba’s options have a much lower exercise price, on average. In fact, Ariba’s stock priceof $75 at the time of this analysis was almost eight times the average exercise price of$6.77. The average maturity of the options at all of these firms is also in excess of sixyears for Cisco and Motorola, and in excess of nine years for Amazon and Ariba.1 Thecombination of a low exercise price and long maturity make the options issued by thesefirms very valuable. Fewer of Amazon and Ariba’s options are vested, reflecting the factthat these are younger firms which have granted more of these options recently.

Options in Existence

Given the large number of options outstanding at manytechnology firms, your first task is to consider ways in whichyou can incorporate their effect into value per share. The sec-tion begins by presenting the argument for why these out-standing options matter when computing value per share andthen considers four ways in which you can incorporate theireffect on value.

Why Options Affect Value per Share. Why do existing options affectvalue per share? Note that not all options do. In fact, optionsissued and listed by the options exchanges have no effect onthe value per share of the firms on which they are issued. Theoptions issued by firms do have an effect on value per share,since there is a chance that they will be exercised in the nearor far future. Given that these options offer the right to indi-viduals to buy stock at a fixed price, they will be exercisedonly if the stock price rises above that exercise price. When

TABLE 7.1 Options Outstanding


Number of options outstanding

80.34 20.675 439.00 36.98 0

Average exercise price

$27.76 $6.77 $22.52 $46.00 NA

Average maturity

9.00 9.31 6.80 6.20 NA

% vested 58% 61% 71% 75% NA


they are exercised, the firm has two choices, both of whichhave negative consequences for existing stockholders. Thefirm can issue additional shares to cover the option exercise.But this increases the number of shares outstanding andreduces the value per share to existing stockholders.2 Alterna-tively, the firm can use cash flows from operations to buy backshares in the open market and use these shares to meet theoption exercise. This approach reduces the cash flows avail-able to current equity investors in future periods and makestheir equity less valuable today.

Ways of Incorporating Existing Options into Value. Four approaches areused to incorporate the effect of options that are already out-standing into the value per share. However, the first threeapproaches can lead to misleading estimates of value.

1.1.1.1. Use fully diluted number of shares to estimate per-share value. The simplest way to incorporate the effectof outstanding options on value per share is to dividethe value of equity by the number of shares that will beoutstanding if all options are exercised today—the fullydiluted number of shares. While this approach has thevirtue of simplicity, it will lead to too low an estimate ofvalue per share for two reasons:

� It considers all options outstanding, not just onesthat are in the money and vested. To be fair, thereare variants of this approach where the shares out-standing are adjusted to reflect only in-the-moneyand vested options.

� It does not incorporate the expected proceeds fromexercise, which will comprise a cash inflow to thefirm.

Finally, this approach does not build in the time pre-mium on the options into the valuation either.


ILLUSTRATION 7.2

Fully Diluted Approach to Estimating Value per Share

To apply the fully diluted approach to estimate the per-share value, use the equity valuesestimated in Chapter 6, “Estimating Firm Value,” for each firm in conjunction with thenumber of shares outstanding, including those underlying the options. Table 7.2 summa-rizes the value per share derived from this approach.

The value per share from the fully diluted approach is significantly lower than the valueper share from the primary shares outstanding. This value, however, ignores both the pro-ceeds from the exercise of the options as well as the time value inherent in the options.

2.2.2.2. Estimate expected option exercises in the futureand build in expected dilution. In this approach, youforecast when in the future the options will be exer-cised and build in the expected cash outflows associ-ated with the exercise, by assuming that the firm willbuy back stock to cover the exercise. The biggest limi-tation of this approach is that it requires estimates ofwhat the stock price will be in the future and whenoptions will be exercised on the stock. Given that your

TABLE 7.2 Fully Diluted Approach to Estimating Value per Share


Value of equity

$13,589 $17,941 $318,336 $69,957 $474

Primary shares

351.77 235.8 6890 2152 24.9

Fully diluted shares

432.11 256.475 7329 2188.98 24.9

Value per share (primary)

$38.63 $76.08 $46.20 $32.51 $19.05

Value per share (fully diluted)

$31.45 $69.95 $43.44 $31.96 $19.05


objective is to examine whether the price today is cor-rect, forecasting future prices to estimate the currentvalue per share seems circular. In general, thisapproach is neither practical nor particularly useful forreasonable estimates of value.

3.3.3.3. Adjust for outstanding options, but add proceeds toequity. This approach, called the Treasury Stockapproach, is a variant of the fully diluted approach.Here, the number of shares is adjusted to reflectoptions that are outstanding, but the expected pro-ceeds from the exercise (exercise price × number ofoptions) are added to the value of equity. The limita-tions of this approach are that, like the fully dilutedapproach, it does not consider the time premium onthe options and there is no effective way of dealingwith vesting. Generally, this approach, by underesti-mating the value of options granted, will overestimatethe value of equity per share.

The biggest advantage of this approach is that itdoes not require a value per share (or stock price) toincorporate the option value into per-share value. Asyou will see with the last (and recommended)approach, a circularity is created when the stock priceis input into the estimation of value per share.

ILLUSTRATION 7.3

Treasury Stock Approach

In Table 7.3, we estimate the value per share by using the treasury stock approach forAmazon, Ariba, Cisco, Motorola, and Rediff.com.

Note that the value per share from this approach is higher than the value per share fromthe fully diluted approach for each of the companies with options outstanding. The differ-ence is greatest for Amazon because the options have a higher exercise price, relative tothe current stock price. The estimated value per share still ignores the time value of theoptions.

233

TABL

E 7.

3Va

lue of

Equit

y per

Share

: Trea

sury

Stoc

k App

roach Am

az

on

Ar

iba

Cis

co

Mo

to

ro

la

Re

dif

f.c

om

Nu

mbe

r of

opt

ion

s ou

tsta

ndi

ng

80.3

420

.675

439

36.9

80

Ave

rage

exe

rcis

e pr

ice

$27.

76$6

.77

$22.

52$4

6.00

$0.0

0

Pro

ceed

s fr

om e

xerc

ise

$2,2

29.8

4$1

39.9

7$9

,886

.28

$1,7

01.0

8$0

.00

Val

ue

of e

quit

y$1

3,58

8.61

$17,

940.

64$3

18,3

35.7

8$6

9,95

6.97

$474

.37

+ P

roce

eds

from

exe

rcis

e$2

,229

.84

$139

.97

$9,8

86.2

8$1

,701

.08

$0.0

0

Tota

l val

ue

$15,

818.

45$1

8,08

0.61

$328

,222

.06

$71,

658.

05$4

74.3

7

Fu

lly d

ilu

ted

nu

mbe

r of

sh

ares

432.

1125

6.47

573

2921

88.9

8 2

4.9

Val

ue

per

shar

e $3

6.61

$70.

50$4

4.78

$32.

74 $

19.0

5


4.4.4.4. Value options by using an option pricing model. Thecorrect approach to dealing with options is to estimatethe value of the options today, given today’s value pershare and the time premium on the option. Once thisvalue has been estimated, it is subtracted from theequity value and divided by the number of shares out-standing to arrive at value per share.

Value of Equity per Share = (Value of Equity – Value of Options Outstanding) / Primary Number of Shares Outstanding

In valuing these options, however, you confront fourmeasurement issues.

a.a.a.a. Vesting. Not all of the options outstanding arevested, and some of the nonvested options mightnever be exercised.

b.b.b.b. Stock price. The stock price to use in valuing theseoptions is debatable. The value per share is aninput to the process as well as the output of theprocess.

c.c.c.c. Taxation. Since firms are allowed to deduct a por-tion of the expense associated with option exer-cises, there may be a potential tax savings when theoptions are exercised.

d.d.d.d. Nontraded firms. Key inputs to the option pricingmodel, including the stock price and the variance,cannot be obtained for private firms or firms on theverge of a public offering, like Rediff.com. Theoptions must nevertheless be valued.

These options are discussed in more detail below.

a.a.a.a. Dealing with vesting: Recall that firms grantingemployee options usually require that theemployee receiving the options stay with the firmfor a specified period, for the option to be vested.Consequently, when you examine the options out-standing at a firm, you are looking at a mix ofvested and nonvested options. The nonvestedoptions should be worth less than the vested


options, but the probability of vesting will dependon how in-the-money the options are and theperiod left for an employee to vest. While therehave been attempts3 to develop option pricingmodels that allow for the possibility that employeesmay leave a firm before vesting and forfeit the valueof their options, the likelihood of such an occur-rence when a manager’s holdings are substantialshould be small. Carpenter (1998) developed a sim-ple extension of the standard option pricing modelto allow for early exercise and forfeiture and used itto value executive options.

b.b.b.b. Arriving at a stock price to use: The answer towhich stock price to use may seem obvious. Sincethe stock is traded and you can obtain a stock price,it would seem that you should be using the currentstock price to value options. However, you are valu-ing these options to arrive at a value per share thatyou will then compare to the market price to decidewhether a stock is under- or overvalued. Thus, itseems inconsistent to use the current market priceto arrive at the value of the options and then usethis option value to estimate an entirely differentvalue per share.

There is a solution. You can value the optionsby using the estimated value per share. Doing socreates circular reasoning in your valuation. Inother words, you need the option value to estimatevalue per share and value per share to estimate theoption value. We would recommend that the valueper share be initially estimated by the treasurystock approach and that you then converge on theproper value per share by iterating.4

There is another related issue. When optionsare exercised, they increase the number of sharesoutstanding, and by doing so, they can have aneffect on the stock price. In conventional optionpricing models, the exercise of the option does notaffect the stock price. These models must be


adapted to allow for the dilutive effect of optionexercise. We examine how option-pricing modelscan be modified to allow for dilution in Chapter 11,“Real Options in Valuation.”

c.c.c.c. Taxation: When options are exercised, the firm candeduct the difference between the stock price atthe time and the exercise price as an employeeexpense, for tax purposes. This potential tax bene-fit reduces the drain on value created by havingoptions outstanding. One way in which you couldestimate the tax benefit is to multiply the differ-ence between the stock price today and the exer-cise price by the tax rate; clearly, this would makesense only if the options are in-the-money.Although this approach does not allow for theexpected price appreciation over time, it has thebenefit of simplicity. An alternative way of estimat-ing the tax benefit is to compute the after-tax valueof the options:

After-Tax Value of Options = Value from Option Pricing Model (1 – Tax Rate)

This approach is also straightforward andallows you to consider the tax benefits from optionexercise in valuation. One of the advantages of thisapproach is that you can use it to consider thepotential tax benefit even when options are out-of-the-money.

d.d.d.d. Nontraded firms: A couple of key inputs to theoption pricing model—the current price per shareand the variance in stock prices—cannot beobtained if a firm is not publicly traded. There aretwo choices in this case. One is to revert to thetreasury stock approach to estimate the value ofthe options outstanding and abandon the optionpricing models. The other choice is to stay with theoption pricing models and to estimate the value pershare from the discounted cash flow model. Thevariance of similar firms that are publicly tradedcan be used to estimate the value of the options.


ILLUSTRATION 7.4

Option Value Approach

In Table 7.4, we begin by estimating the value of the options outstanding, using amodified option pricing model that allows for dilution.5 To estimate the value of theoptions, we first estimate the standard deviation in stock prices6 over the previous twoyears. Weekly returns are used to make the estimate, and the estimate is annualized.7

All options, vested as well as nonvested, are valued and there is no adjustment fornonvesting.

In estimating the after-tax value of the options at Amazon and Ariba, we have used theirprospective marginal tax rate of 35%. If the options are exercised prior to these firmsreaching their marginal tax rates, the tax benefit is lower since the expenses are carriedforward and offset against income in future periods.

You can now calculate the value per share by subtracting the value of the options out-standing from the value of equity and dividing by the primary number of shares outstand-ing, as in Table 7.5.

The inconsistency referred to earlier is clear when you compare the value per share esti-mated in Table 7.5 to the price per share used in Table 7.4 to estimate the value of theoptions. For instance, Amazon’s value per share is $32.33, whereas the price per shareused in the option valuation is $49. If you choose to iterate, you would revalue theoptions by using the estimated value of $32.33, which would lower the value of theoptions and increase the value per share, leading to a second iteration and a third one,and so on. The values converge to yield a consistent estimate. The consistent estimates ofvalue are provided in Table 7.6.

For Motorola and Ariba, the difference in value from iterating is negligible, since the valueper share that we estimated for the firms is close to the current stock price. For Cisco, thevalue of the options drops by almost 40%, but the overall effect on value is mutedbecause the number of options outstanding as a percent of outstanding stock is small. Thedifference in values is greatest at Amazon, for two reasons. First, the value per share wassignificantly lower than the current price at the time of the valuation. Second, Amazonhad the highest value for options outstanding as a percent of stock outstanding.

238

TABL

E 7.

4Es

timate

d Valu

e of O

ption

s Outs

tandin

g

Op

tio

n P

ric

ing

Mo

del

Am

azo

nA

rib

aC

isc

oM

oto

ro

la

Re

dif

f.c

om

Nu

mbe

r of

opt

ion

s ou

tsta

ndi

ng

80.3

4

20.6

75 4

3936

.98

0A

vera

ge e

xerc

ise

pric

e$2

7.76

$6

.77

$22.

52$4

6.00

$0.0

0E

stim

ated

sta

nda

rd d

evia

tion

(vo

lati

lity

) 8

5%

80%

40%

34%

80%

Sto

ck p

rice

at

tim

e of

an

alys

is$4

9.00

$7

5.63

$64.

88$3

4.25

$10.

00V

alu

e pe

r op

tion

$42.

44

$72.

92$5

0.13

$11.

75$8

.68

Val

ue

of o

ptio

ns

outs

tan

din

g$3

,409

.67

$1,

508.

00$2

2,00

8.00

$435

.00

$0.0

0Ta

x ra

te35

.00%

3

5.00

%35

.00%

35.0

0%38

.50%

Aft

er-t

ax v

alu

e of

opt

ion

s ou

tsta

ndi

ng

$2,2

16

$98

0.00

$14,

305.

00$2

83.0

0$0

.00

TABL

E 7.

5Va

lue of

Equit

y per

Share

Am

azo

nA

rib

aC

isc

oM

oto

ro

la

Re

dif

f.c

om

Val

ue

of e

quit

y$1

3,58

8.61

$17,

940.

64$3

18,3

35.7

8

$69,

956.

97$4

74.3

7–

Val

ue

of o

ptio

ns

outs

tan

din

g$2

,216

.00

$

980.

00$1

4,30

5.00

$2

83.0

0 $

0.00

Val

ue

of e

quit

y in

sh

ares

ou

tsta

ndi

ng

$11,

372.

32$1

6,96

0.71

$304

,030

.58

$6

9,67

4.46

$474

.37

Pri

mar

y sh

ares

ou

tsta

ndi

ng

351.

7723

5.8

689

021

52

24.9

Val

ue

per

shar

e$3

2.33

$71.

93$4

4.13

$3

2.38

$19

.05

TABL

E 7.

6Co

nsist

ent E

stima

tes of

Value

per S

hare

Am

azo

nA

rib

aC

isc

oM

oto

ro

la

Re

dif

f.c

om

Val

ue

of o

ptio

ns

(wit

h c

urr

ent

stoc

k pr

ice)

$2,2

16.0

0$9

80.0

0 $

14,3

05.0

0$2

82.5

1$0

.00

Val

ue

per

shar

e$3

2.33

$71.

93

$44.

13$3

2.38

$19.

05V

alu

e of

opt

ion

s (w

ith

ite

rate

d va

lue)

$1,5

00.0

0$9

33.0

0

$8,8

61.0

0$2

82.5

1$0

.00

Val

ue

per

shar

e$3

4.37

$72.

13

$44.

92$3

2.38

$19.

05


Future Option Grants

While incorporating options that are already outstanding isfairly straightforward, incorporating the effects of futureoption grants is much more complicated. In this section, weexamine the argument for why these option issues affect valueand discuss how to incorporate these effects into value.

Why Future Options Issues Affect Value. Just as outstanding optionsrepresent potential dilution or cash outflows to existing equityinvestors, expected option grants in the future will affect valueper share by increasing the number of shares outstanding infuture periods. The simplest way of thinking about thisexpected dilution is to consider the terminal value in the dis-counted cash flow model. As constructed in the last chapter,the terminal value is discounted to the present and divided bythe shares outstanding today to arrive at the value per share.However, expected option issues in the future will increase thenumber of shares outstanding in the terminal year and there-fore reduce the portion of the terminal value that belongs toexisting equity investors.

Ways of Incorporating Effect into Value per Share. It is much more diffi-cult to incorporate the effect of expected option issues intovalue than existing options outstanding. The reason is that youhave to forecast not only how many options will be issued by afirm in future periods but also what the terms of these optionswill be. While this forecasting may be possible for a couple ofperiods with proprietary information (the firm lets you knowhow much it plans to issue and at what terms), it will becomemore difficult in circumstances beyond that point. Below, weconsider a way in which to obtain an estimate of the optionvalue and look at two ways of dealing with this estimate, onceobtained.

Estimate Option Value as an Operating or Capital Expense. You can esti-mate the value of options that will be granted in future periodsas a percentage of revenues or operating income. By doing so,you avoid the need to estimate the number and terms of futureoption issues. Estimation will also become easier because you


can draw on the firm’s own history (by looking at the value ofoption grants in previous years as a proportion of revenues)and the experiences of more mature firms in the sector. Gen-erally, as firms become larger, the value of options granted as apercent of revenues should become smaller.

Having estimated the value of expected future optionissues, you are left with another choice. You can consider thisvalue each period as an operating expense and compute theoperating income after the expense. You are assuming, then,that option issues form part of annual compensation. Alterna-tively, you can treat this value as a capital expense and amor-tize it over multiple periods. While the cash flow in eachperiod is unaffected by this distinction, it has consequencesfor the return on capital and reinvestment rates that you mea-sure for a firm.

It is important that you do not double-count future optionissues. The current operating expenses of the firm alreadyinclude the expenses associated with option exercises in thecurrent period. The operating margins and returns on capitalthat you might derive by looking at industry averages reflectthe effects of option exercise in the current period for thefirms in the industry. If the effect on operating income ofoption exercise in the current period is less than the expectedvalue of new option issues, you have to allow for an additionalexpense associated with option issues. Conversely, if a dispro-portionately large number of options were exercised in the lastperiod, you have to reduce the operating expenses to allow forthe fact that the expected effect of option issues in future peri-ods will be smaller.

ILLUSTRATION 7.5

Valuing with Expected Option Issues

In all of the valuations you have seen so far, the current operating income and the indus-try averages were key inputs. The current operating income was used to compute the cur-rent return on capital, margin, and reinvestment rate for the firm. The industry averagemargins or returns on capital were used to estimate the stable growth inputs.


The current operating income reflects the effects of options exercised over the last periodbut not the effect of new options issued. To the extent that the latter is greater (or lower)than the former, the operating income, margins, and returns on capital have been over-stated (or understated). To illustrate the adjustment, we consider the number of optionsissued and the number exercised at Amazon and Cisco during the last year, summarizedin Table 7.7, and the exercise prices of each.

The values of the option grants are estimated with the option pricing model,8 whereas thevalue of the options exercised is the exercise value—the difference between the stockprice and the exercise price. For Amazon, the value of the options granted was signifi-cantly higher than the value of the exercised options. Consequently, its operating losswould have been even greater (by $809 million) than was estimated in Chapter 4 if thedifference between the exercise value and the new options granted is considered an addi-tional employee expense. For Cisco, on the other hand, the value of the options exercisedexceeded the value of the options granted. The difference between the two (of $807 mil-lion) should be added to operating income to arrive at the corrected operating income.Similar adjustments can be made to the operating income at Ariba and Motorola; Ariba’soperating income would have been $246 million lower with the adjustment, and Motor-ola’s would have increased by $14 million.

The industry-average returns on capital and margins are more difficult to adjust. Youwould have to make the adjustment described above to every firm in the industry andcompute returns on capital and margins after the adjustment. For simplicity, the value ofoptions exercised is assumed to be equal to the value of options issued in the currentperiod for the industry.

TABLE 7.7 Options Issued and Exercised: Amazon and Cisco

Amazon Cisco

NumberNumberNumberNumber Exercise Exercise Exercise Exercise PricePricePricePrice

ValueValueValueValue NumberNumberNumberNumber Exercise Exercise Exercise Exercise PricePricePricePrice

ValueValueValueValue

Options granted 31.739 $63.60 $1,273 107 $49.58 $4,589

Options canceled 11.281 $3.86 — 10 $24.66 $0

Options exercised 16.125 $19.70 $472 93 $6.85 $5,396

Effect on operating income

–$809 +$807


Table 7.8 reports on the adjustment to current operating income and the final values pershare that emerge as a result of this adjustment.

The effect of the adjustment is trivial at Motorola. The value per share is lower than theoriginal estimates at Amazon and Ariba, reflecting the drain on value per share thatoptions will continue to be in future years. The value per share is higher at Cisco becauseof the increase in operating income created by the adjustment.

Estimate Expected Stock Price Dilution from Option Issues. The other wayof dealing with expected option grants in the future is to buildin the expected dilution that will result from these optionissues. To do so, you have to make a simplifying assumption.For instance, you could assume that options issued will repre-sent a fixed percent of the outstanding stock each period andbase this estimate on the firm’s history or on the experience ofmore mature firms in the sector. Generally, this approach ismore complicated than the first one and does not lead to amore precise estimate of value. Clearly, it would be inappropri-ate to do both: show option issues as an expense and allow forthe dilution that will occur from the issue. That double-countsthe same cost.

TABLE 7.8 Values per Share with Option Adjustment to Current Operating Income

Amazon Ariba Cisco Motorola

Unadjusted operating income

$(276.00) $(163.70) $3,455.00 $3,216.00

Value per share (no option adjustment)

$32.33 $71.93 $44.13 $32.38

Adjusted operating income

$(1,076.29) $(409.00) $4,262.00 $3,230.00

Value (option grant adjustment)

$26.62 $58.80 $53.04 $32.48


warrants.xls: This spreadsheet enables you to valuethe options outstanding in a firm, allowing for the dilu-tion effect.

Value of ControlWhen you divide the value of the equity by the number of

shares outstanding, you assume that the shares all have thesame voting rights. If different classes of shares have differentvoting rights, the value of equity per share has to reflect thesedifferences, with the shares with more voting rights havinghigher value. Note, though, that the total value of equity is stillunchanged. To illustrate, assume that the value of equity in afirm is $500 million and that 50 million shares are outstand-ing; 25 million of these shares have voting rights and 25 mil-lion do not. Furthermore, assume that the voting shares willhave a value 10% higher than the nonvoting shares. To esti-mate the value per share:

Value per Nonvoting Share = $500 million / (25 million × 1.10 + 25 million)

= $500 million / 52.5 million = $9.52

Value per Voting Share = $9.52 (1.10) = $10.48

The key issue that you face in valuation, then, is determin-ing the discount to apply for nonvoting shares or, alternatively,the premium to attach to voting shares.

Voting Shares versus Nonvoting Shares

What premium should be assigned to the voting shares?You have two choices. One is to look at studies that empiri-cally examine the size of the premium for voting rights and toassign this premium to all voting shares. Lease, McConnell,and Mikkelson (1983) examined 26 firms that had two classesof common stock outstanding, and they concluded that the


voting shares traded at a premium relative to nonvotingshares.9 The premium, on average, amounted to 5.44%, andthe voting shares sold at a higher price in 88% of the monthsfor which data were available.

The other choice is to be more discriminating and vary thepremium depending on the firm. Voting rights have valuebecause they give shareholders a say in the management of thefirm. To the extent that voting shares can make a difference––by removing incumbent management, forcing management tochange policy, or selling to a hostile bidder in a takeover––their price will reflect the possibility of a change in the way thefirm is run.10 Nonvoting shareholders, on the other hand, donot participate in these decisions.

Valuing Control

If the value of control arises from the capacity to changethe way a firm is run, it should be a function of how well orbadly the firm is run. If the firm is well run, the potential gainfrom restructuring is negligible, and the difference in valuesbetween voting and nonvoting shares should be negligible aswell. If the firm is managed badly, the potential gain fromrestructuring is significant, and voting shares should sell at asignificant premium over nonvoting shares.

One way to value control is to value the firm under existingmanagement and policies and then revalue it, assuming thatthe firm is optimally run. The difference between the two val-ues is the value of control:

Value of Control = Value of Firm Optimally Run – Status Quo Valuation of Firm

The key to estimating this value is to come up with theparameters that you would use to value the firm, optimally run.This issue is revisited in Chapter 12, “Value Enhancement.”


Control in Private Businesses

The issue of control also comes up when you are valuingprivate businesses, especially when the stake in the businessthat is being valued is less than a controlling one. For instance,a 49% stake in a private business may sell at a considerablediscount on a 51% stake because the latter provides controlwhereas the former does not. You can estimate the discount,using the same approach that you developed for valuing con-trol, by valuing the private business under the status quo andthen again as an optimally managed business. The discountshould be larger with a 49% stake in a poorly managed privatebusiness than it would be with a well-managed one.

Value of LiquidityOnce a firm has been valued, should there be a discount

for illiquidity if the stake in the firm, whether it takes the formof publicly traded shares or a partnership, cannot be easilysold? Illiquidity falls in a continuum, and even publicly tradedfirms vary in terms of how liquid their holdings are. The illi-quidity discount tends to be most significant when privatebusinesses are up for sale. In practice, the estimation of liquid-ity discounts seems arbitrary, with discounts of 25% to 30%being most commonly used in practice.

Determinants of Illiquidity Discount

The illiquidity discount should vary from firm to firm andshould depend on the following factors:

� Size of the business: As a percent of value, the discountshould be smaller for larger firms; a 30% discount maybe reasonable for a million-dollar firm, but not for a bil-lion-dollar firm.

� Type of assets owned by the firm: Firms with more liq-uid assets should be assigned lower liquidity discounts,since assets can be sold to raise cash. Thus, the discountshould be lower for a private business with real estateand marketable securities as assets than for one withfactories and equipment.


� Health and cash flows of the business: Stable busi-nesses that generate large annual cash flows should seetheir value discounted less than high-growth businesseswhere operating cash flows are either low or negative.

Quantifying the Liquidity Discount

There are two ways of quantifying the liquidity discount.One way is to use the results of studies that have looked atrestricted stock. Restricted securities are securities issued by acompany, but not registered with the SEC, that can be soldthrough private placements to investors. These securities can-not be sold for a two-year holding period, and limited amountscan be sold after that. These restricted stocks trade at dis-counts ranging from 25% to 40%, because they cannot betraded. Silber, in 1991, related the discount to observablecharacteristics of the firms issuing the stock:

Ln(Price of Restricted Stock ÷ Price of Unrestricted Stock) = 4.33 + 0.036 Ln(Revenues) – 0.142 (Restricted Block as a Percent of Total Stock Outstanding) + 0.174 (DERN) + 0.332 (DCUST)

where DERN = 1 if earnings were positive and zero if not, andDCUST = 1 if the investor with whom the stock was placed hada customer relationship with the firm and 0 if not.

The other, and potentially more promising, route is toextend the research on the magnitude of the bid-ask spread.Note that the spread, which measures the difference betweenthe price at which one can buy a stock or sell it in an instant, isa measure of the liquidity discount for publicly traded stocks.Studies of the spread have noted that it tends to be larger forsmaller, more volatile, and lower-priced stocks. You could lookat private firms as very small, nontraded stocks and estimate a“spread” which would also be the liquidity discount.

While you would expect the illiquidity discounts to belarger at privately owned technology firms, the discounts willbe tempered by the option that these firms have to go to themarket. In 1999 and early 2000, for instance, when investors


were attaching huge market values to Internet-based firms,investors in privately held online ventures may have been will-ing to settle for little or no discount because of this potential.

Liquidity Discounts at Publicly Traded Firms

Some publicly traded stocks are lightly traded, and thenumber of shares available for trade (often referred to as thefloat) is small relative to the total number of shares outstand-ing.11 Investors who want to quickly sell their stock in thesecompanies often have a price impact when they sell, and theimpact will increase with the size of the holding.

Investors with longer time horizons and a lesser need toquickly convert their holdings into cash have a smaller prob-lem associated with illiquidity than do investors with shortertime horizons and a greater need for cash. Investors shouldconsider the possibility that they will need to convert theirholdings into cash quickly when they look at lightly tradedstocks as potential investments and should therefore requiremuch larger discounts on value before they take large posi-tions. Assume, for instance, that an investor is looking at Red-iff.com, a stock that was valued at $19.05 per share. The stockwould be underpriced if it were trading at $17, but it might notbe underpriced enough for a short-term investor to take a largeposition in it. In contrast, a long-term investor may find thestock an attractive buy at that price.

ILLUSTRATION 7.6

Float and Bid-Ask Spreads

In Table 7.9, the trading volume, float, and bid-ask spreads are reported for Amazon,Ariba, Cisco, Motorola, and Rediff.com.


Although the bid-ask spreads are between 1/16 and 1/8 for all of the firms, the spreadis a much larger percentage of the stock price for Rediff, which is trading at about $10 pershare, than it is for Cisco or Ariba. In addition, only about 20% of the shares outstandingare available for trading at Rediff and only about a third of the shares at Amazon aretraded.

Summary The existence of options and the possibility of future

option grants makes getting from equity value to value pershare a complicated exercise. To deal with options outstandingat the time of the valuation, there are four approaches.

The simplest is to estimate the value per share by dividingthe value of equity by the fully diluted number of shares out-standing. This approach ignores both the expected proceedsfrom exercising the options and the time value of the options.

The second approach of forecasting expected option exer-cises in the future and estimating the effect on value per shareis not only tedious but unlikely to work.

In the treasury stock approach, you add the expected pro-ceeds from option exercise to the value of equity and thendivide by the fully diluted number of shares outstanding. Whilethis approach does consider the expected proceeds from exer-cise, it still ignores the option time premium.

In the final and preferred approach, you value the optionsby using an option pricing model and subtract the value fromthe value of equity. The resulting estimate is divided by theprimary shares outstanding to arrive at the value of equity pershare.

TABLE 7.9 Liquidity Measures: Amazon, Ariba, Cisco, Motorola, and Rediff

Amazon Ariba Cisco Motorola Rediff

Number of shares 351.77 235.80 6,890.00 2,152.00 24.90

Trading volume 8.22 6.19 42.87 14.1 NA

Float 138.80 134.70 6880.00 1940.00 4.60

Bid-ask spread $0.0625 $0.1250 $0.0625 $0.0625 $0.125


Usually, the current price of the stock is used in optionpricing models, but the value per share estimated from the dis-counted cash flow valuation can be substituted to arrive at amore consistent estimate. To deal with expected option grantsin the future, you must dissect the current operating incometo consider the effect that option exercises in the currentperiod had on operating expenses. If the options granted dur-ing the period had more value than the option expense result-ing from exercise of options granted in prior periods, thecurrent operating income has to be adjusted down to reflectthe difference. Industry-average margins and returns on capi-tal will also have to be adjusted for the same reason.

Once the value per share of equity has been estimated,that value may need to be adjusted for differences in votingrights. Shares with disproportionately high voting rights willsell at a premium relative to shares with low or no votingrights. The difference will be larger for firms that are badlymanaged and smaller for well-managed firms. When valuing aprivate firm, you may also need to discount the estimatedvalue of equity to reflect the lack of liquidity in the shares. Infact, even publicly traded firms can face a discount if theshares that are traded are illiquid.

Endnotes1. Employee options usually have 10-year lives at the time ofissue.

2. This circumstance would be dilution in the true sense of theword, rather than the term that is used to describe any increasein the number of shares outstanding. The reason there is dilutionis that the additional shares are issued only to the option holdersat a price below the current price. In contrast, the dilution thatoccurs in a rights issue where every stockholder gets the right tobuy additional shares at a lower price is value neutral. The shareswill trade at a lower price, but everyone will have more sharesoutstanding.

3. Cuny and Jorion (1995) examine the valuation of optionswhen there is the possibility of forfeiture.


4. The value per share, obtained with the treasury stock ap-proach, will become the stock price in the option pricing model.The option value that results from using this price is used to com-pute a new value per share, that value is fed back into the optionpricing model, and so on.

5. We use the Black-Scholes model, adjusted to reflect dilution.

6. The variance estimate is actually on the natural log of thestock prices, so you can cling to at least the possibility of a normaldistribution. Neither stock prices nor stock returns can be nor-mally distributed because prices cannot fall below zero and re-turns cannot be lower than –100%.

7. All of the inputs to the Black-Scholes model have to be in an-nual terms. To annualize a weekly variance, you multiply by 52.

8. To value these options, the standard deviations reported ear-lier and 10-year lives are used. The maturities of the optionsgranted were obtained from the 10-Ks.

9. The two classes of stock received the same dividend.

10. In some cases, the rights of nonvoting stockholders are pro-tected in the specific instance of a takeover by forcing the bidderto buy the nonvoting shares as well.

11. The float is estimated by subtracting out from the shares out-standing, shares that are owned by insiders, 5% owners, and rule144 shares. (Rule 144 refers to restricted stock that cannot betraded.)

Documents

7 Management Options, Control, and LiquidityChapter 7• Management Options, Control, and Liquidity 229 While Amazon has far more options outstanding as a percent of the outstanding