RA
ADFORD RE
EVIEW:
Ex
xpected Life Analysis – Practic
cal Cons
sideratio
ons
Com
mpanies issuiing options to
o employees g
generally upd
date their assu
umptions oncce per year
for purposes of complying
c
witth ASC Topic 718. This is n
not always a straight-forwa
ard
exe
ercise even with an establis
shed processs. Professiona
al advice of in
ndependent va
aluation
exp
perts is freque
ently needed. However, m
many companiies continue tto develop the
ese
ass
sumptions using internal re
esources.
In th
his Radford Review,
R
we highlight one o
of the most da
ata intensive a
assumptions – the
exp
pected life – and
a provide an
n overview off important co
onsiderations.. Specifically, we focus
on methodologie
m
es to adjust hiistorical data to accommod
date the terms of new awa
ards.
When a compan
ny grants optio
ons with vario
ous vesting scchedules and contractual tterms, the
acc
curacy and rep
presentativen
ness of all histtorical data comes into question. An ad
djustment
to historical
h
beha
avior should be
b applied wh
hen such situa
ations arise.
Com
mpanies often
n develop the
eir expected liffe via a simplle automated report outputtted from
the administratio
on system bas
sed on a speccified datasett. However, R
Radford is una
aware of
any
y administrativ
ve systems th
hat have the ccapability to a
adjust historical data to refllect for
exp
pected behaviior under revised terms an
nd conditions of new award
ds (i.e. vesting
g or term).
The
erefore, comp
panies relying on administrrative databasses would be forced to carrve out
larg
ge subsection
ns of data with
h the potentia
al to be left witth a statistica
ally insignificant amount
of data
d
on which
h to place any
y credibility.
er the next se
everal pages, a methodolog
gy used to pe
erform these a
adjustments w
will be
Ove
illus
strated. We will
w also show the magnitud
de of the adjusstments on th
he individual
ass
sumption as well
w as the imp
pact on a “sta
andard” option
n valuation ussing Black-Sccholes. In
the process, we will point to several
s
regula
atory referencces including:
>
>
>
Radfo
ord is an Aon
Hewittt Company
Financia
al Accounting Standards B oard (FASB),, ASC Topic 7
718
PCAOB,, “Auditing the
e Fair Value o
of Share Optiions Granted to Employeess”
Securitie
es & Exchang
ge Commissio
on (SEC), Sta
aff Accounting
g Bulletin #10
07
Radforrd Review: Expec
cted Life Analysis – Practical Con
nsiderations
Date 08/11
0
1
Regulatory Guidance
ASC Topic 718-10-55-24 states that historical experience is generally the starting point for
developing expectations about the future. Since estimated expected term is the period of time for
which the option is expected to remain outstanding, companies may start by calculating a
historical weighted average period of time for which previous grants of share options were
outstanding. However, Topic 718-10-55-24 goes on to state that “historical experience should be
modified to reflect ways in which currently available information indicates that the future is
reasonably expected to differ from the past.”
ASC Topic 718:
The SEC concurs in Question 5 of SAB 107:
“Historical
experience should
be modified to
reflect ways in
which currently
available
information
indicates that the
future is
reasonably
expected to differ
from the past.”
A company may also conclude that its historical share option exercise experience does not
provide a reasonable basis upon which to estimate expected term. This may be the case for
a variety of reasons, including, but not limited to, the life of the company and its relative
stage of development, past or expected structural changes in the business, differences in
terms of past equity-based share option grants, or a lack of variety of price paths that
the company may have experienced.
In Q&A 10, the PCAOB warns:
The auditor should evaluate whether the company's rationale for adjustments to historical
exercise behavior are reasonable and supportable. The auditor also should evaluate
whether the company failed to make a necessary adjustment. For example, if the
historical experience is based on grants with one-year vesting, an adjustment would be
appropriate if current grants have 4-year vesting.
The PCAOB identifies that compensation cost from the fair value of stock options “often will have
a high inherent risk.” Further, one area of increased risk and indication for risk of fraud is with
regard to when “adjustments to historical exercise behavior or historical share price volatility are
not applied consistently to each option grant in circumstances in which they should have been
consistently applied.”
It is clear that an adjustment may be necessary in order to develop the best estimate of an
expected life. There are several accepted approaches we’ve observed in practice including
truncation, time-after-vest, and other approaches1.
Below is the summary of an objective, reasonable, and supportable algorithm for adjusting
historical behavior to accommodate new plan terms, which we also believe to be best practice in
the industry. Note that this approach will have the effect of decreasing the expected life when
new vesting or terms are shorter than historical vesting or terms, and vice versa.
A Simple Example of a Ratio Adjustment
Consider a situation when an individual exercises an option at year 6.50, and the award was
granted with 4-year annual vesting and a 10-year contractual term. On a prospective basis, the
company decides to now grant options with 3-year annual vesting and a 7-year contractual term.
Since the historical option grant under consideration has a 4-year annual vesting schedule, the
average time to vest for this option is 2.50 years2. The exercisable period for this option is:
10.00 (term length) – 2.50 (average time to vest) = 7.50 (exercisable period)
Since the option was exercised at time 6.50, the exercise activity occurred 4.00 (6.50 - 2.50) years
into the 7.50 year exercisable period, or 53.33% of the way through the exercisable period.
1
See Radford Review, When Expected Life Isn’t Expected: Transitioning from Topic 718 to IFRS 2 and Multiple
Tranche Expected Life
2
The average of the four vesting tranches (1+2+3+4)/4 = 2.50 years
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
2
Using this ratio, we can now map a 4-year annual vesting option with 10-year term to a 3-year
vesting schedule with 7-year term option by applying the 53.33% ratio to the new exercisable
period calculated as follows:
7.00 (new term length) – 2.00 (new average time to vest) = 5.00 (new exercisable period)
Now we can calculate the expected time during the new exercisable period using the calculation
below:
53.33%  5.00 (current exercisabl e period)  2.67 years
This example
illustrates how an
exercise at year
6.50 of a 10-year
term with a 4-year
graded vesting
schedule is
equated to an
exercise at year
4.67 of a 7-year
term with 3-year
graded vesting
schedule.
Finally, to calculate the adjusted expected life of the current option grants, we simply add the
exercisable life calculated above to the average time to vest of the current awards (two years).
The calculation is shown below:
2.67 years  2.00 (new average time to vest)  4.67 adjusted expected term
Therefore, this example illustrates how an exercise at year 6.50 of a 10-year term with a 4-year
graded vesting schedule is equated to an exercise at year 4.67 of a 7-year term with 3-year
graded vesting schedule.
The following chart illustrates the difference between the actual and adjusted expected lives for
this sample activity.
Actual and Adjusted Activity
0
1
2
3
4
Actual
Adjusted
5
6
7
8
9
10
6.50 years
4.67 years
Mandatory Holding Period
Voluntary Holding Period
Unrecognized Holding Period
In practice, the above technique would be applied to each vesting tranche rather than be
compared to the grant’s weighted average time to vest. This creates the need to split activity by
vesting tranche, which can be complicated, time consuming, and may require ad hoc reports.
Radford maintains that the most reasonable and meaningful results will come from this
additional analysis.
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
3
Company A Illustration
In this example, we show expected life calculations based on different datasets for Company A,
which has been granting stock options for over 20 years. Historically, various types of vesting
schedules have been applied, with the most common being various forms of 4-year graded
(monthly, annually, starting at year 2 etc.) and 10-year contractual term. The company recently
revised the terms and conditions to 3-year annual vesting and 7-year contractual terms.
Using an administrative system based on all actual data of 55.3M options, the resulting expected
life is 4.45 years. Since the system is unable to apply ratio adjustment to specific awards, the
company is forced to exclude all grants that do not have the new vesting schedule and terms
when calculating expected life for the future grants. However, since options with the current
terms are granted starting in 2010, only 0.3M options are left for analysis.
A recommended solution is to use the ratio adjustment, which is applied to each grant that does
not have the current vesting and term. This solves the problem of having an insignificant amount
of data while taking into account the various vesting schedules and terms.
Please refer to Appendix A for a detailed comparison of the actual historical data and the
adjusted data. The following results highlight the differences in expected life as well as fair
value:
Total Options Weighted Average Weighted Average Expected Black Scholes
Analyzed
Vesting
Contractual Term
Life
Fair Value 1
Actual Data - No Adjustment
Current Vesting/Term Only
Actual Data - Ratio Adjustment
55,337,452
2.58
8.79
4.45
38.5%
340,614
2.00
7.00
4.43
38.4%
55,337,452
2.00
7.00
3.62
34.9%
(18.7%)
(9.2%)
Percent Change (Ratio Adjustment - No Adjustment)
1
Assumed fair value inputs: annual volatility of 45%, risk-free rate of 2.5%, dividend yield of 0.5%.
The above example shows a 19% reduction in the expected life between the data with no
adjustment and the ratio adjustment, which translates to approximately a 9% reduction in the fair
value recognized, simply by adjusting the historical experience to more accurately reflect the new
terms of the awards. Each company will have to analyze the benefits and risks associated with
various types of plan design changes.
As mentioned before, companies using an administrative database to calculate expected life
would be forced to carve out the data that does not match the current vesting schedule and
contractual terms. In the example above, this would leave us with only 0.6% of the total options
analyzed, causing the data to be unreliable. The ratio adjustment provides a reasonable and
appropriate alternative.
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
4
Company B Illustration
Company B has been granting stock options with 4-year annual vesting and 10-year term to its
US-based employee. The company decides to issue options with 4-year cliff vesting and 10-year
term to Europe-based employees. The expected life using exercise at midpoint is 6.28 years
based on US data as shown in Appendix B. Though this assumption can be used for both groups
of employees, it may be more reasonable to calculate separate expected lives as future grants
will have distinct vesting schedules. To develop the expected life for the Europe-based
employees, we apply ratio adjustment, and the resulting expected life is 7.02 years. As more
exercise experience becomes available, Company B may consider calculating the assumptions
based on two separate sets of data.
Total Options Weighted Average Weighted Average Expected Black Scholes
Analyzed
Vesting
Contractual Term
Life
Fair Value 1
US-Based Employees
Europe-Based Employees
1
20,175,991
2.50
10.00
6.28
44.9%
0
4.00
10.00
7.02
47.1%
Assumed fair value inputs: annual volatility of 45%, risk-free rate of 2.5%, dividend yield of 0.5%.
Considerations When Applying the Ratio Adjustment
When the vesting and term changes are significant, greater care must be taken when adjusting the
data. Consider a scenario where a short exercise window follows a lengthy vesting schedule, such
as an option with 4-year cliff vesting and 5-year contractual term that is exercised at year 5. The
company revises the vesting and term to 1 year and 10 years, respectively. The adjusted expected
life for the new option would be 10 years when it is unlikely that an option with 1 year vesting
would be held to the end of a 10-year contractual term. Valuation requires the application of
professional judgment. In situations like this, it is likely that the ratio adjustment would create a
skewed or biased result and would not be the best approach.
Conclusions
Even though many administrative systems include a historical expected life report in their standard
offering, companies should carefully consider the results before applying it to their option
valuations. It is crucial to understand the data used in the calculation and determine its reliability
based on each company’s unique circumstance. As the illustrations in this Radford Review have
shown, not applying adjustments or exclusions could have significant impact on the expense.
While the ratio adjustment approach outlined is one solution, it is critical to remember that with all
valuation assumptions, professional judgment and critique should be applied.
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
5
Contact Us
For more
information, please
contact us at:
Jacob Peters
+1 (215) 255-1874
jpeters@radford.com
Harmony Chi
+1 (415) 486-7133
hchi@radford.com
Jacob Peters, CEP
Senior Consultant
Jacob Peters is a senior consultant based in Philadelphia with Radford Valuation Services (RVS),
the equity valuation group of Radford. He has more than five years of benefits and compensation
consulting experience. Jacob consults on a variety of employee benefits and compensation issues,
including valuation and accounting for employee stock option (ESO) plans, Employee Stock
Purchase Plans (ESPP), and other equity-based compensation under Topic 718; valuation of
compensatory arrangements for purposes of a change in control under IRC 280G; and valuation
and accounting for equity programs in mergers, acquisitions, and divestitures under Topic 805.
Jacob graduated from the Pennsylvania State University where he obtained a bachelor of science
degree in actuarial science with minors in statistics and economics. Jacob has attained the
Certified Equity Professional (CEP) designation.
Harmony Chi, ASA
Analyst
Harmony Chi is an analyst with Radford Valuation Services, the equity valuation group of Radford.
She has consulted on a variety of employee equity compensation issues, including the valuation
and financial reporting of employee stock options and ESPPs under Topic 718, design and
valuation of underwater stock option exchanges, and complex valuations of performance-based
awards. Harmony graduated from University of California at Berkeley with a bachelor of science
degree in mathematics. She is an Associate of the Society of Actuaries. Harmony is based in San
Francisco, California.
About Radford
Radford is the industry leader, providing advice and benchmarking to technology and life sciences
companies to address their toughest HR and rewards challenges: attracting, engaging and
retaining talent. Our advisors provide industry-specific expertise, applying an analytical approach
that integrates market data, trends and our experience in working with nearly 2,000 companies –
from Global 1000 firms to start-ups – to balance the needs of executives, employees and
shareholders. Our advice is customized to a client’s unique situation to ensure your rewards
programs are not just competitive - but can be a competitive advantage.
Radford’s uniquely data-driven perspective is why more technology and life sciences companies,
and their Board of Directors and Compensation Committee, trust Radford for compensation data
and advice than any other firm. Radford clients rely upon our global survey databases of more than
four million incumbents for real-time insight on total compensation levels, practices and emerging
trends to inform their HR and reward strategies.
Headquartered in San Jose, CA, we have professionals in Austin, Bangalore, Beijing, Boston,
Chicago, Hong Kong, London, New York, Philadelphia, San Francisco, Shanghai and Singapore.
Radford is an Aon Hewitt company.
Visit www.radford.com, or for more information, contact info.rad@radford.com.
Locations
Austin, Bangalore,
Beijing, Boston,
Chicago, Hong
Kong, London,
New York,
Philadelphia,
San Francisco,
San Jose,
Shanghai
and Singapore
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
6
Appendix A
Actual Historical Data Analysis - Company A
Grant Year
Options
Options
Options Remaining
Exercise Life
Exercised Cancelled
Remaining
Life
Total
Exercise at Exercise at Exercise at
Full Vesting Midpoint
Full Term
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
41,600
24,000
1,064,880
1,783,040
1,609,396
2,726,660
128,240
101,600
1,731,540
2,423,458
3,259,168
4,939,472
3,388,096
3,442,825
3,523,485
2,327,814
2,787,908
1,797,835
302,858
24,579
-
6,960
960
40,760
9,440
98,076
707,508
375,665
114,680
707,246
315,970
255,097
42,380
20,180
11,766
34,783
59,212
104,846
14,648
20,611
2,330
-
5.18
7.49
3.05
4.57
3.94
5.26
4.11
6.02
4.38
4.43
3.79
4.47
4.43
3.74
2.62
2.71
1.85
0.66
0.82
1.17
0.00
31,976
467,980
615,310
1,076,543
509,249
1,475,158
1,865,470
2,351,824
3,737,102
2,835,268
392,461
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.09
0.84
1.91
2.93
3.85
4.79
5.48
6.72
5.12
6.00
6.59
48,560
24,960
1,105,640
1,792,480
1,707,472
3,434,168
503,905
216,280
2,438,786
2,739,428
3,546,241
5,449,832
4,023,586
4,531,134
4,067,517
3,862,184
4,758,224
4,164,307
4,060,571
2,862,177
392,461
5.18
7.49
3.05
4.57
3.94
5.26
4.11
6.02
4.38
4.43
3.85
4.87
4.99
4.53
3.06
3.70
2.89
2.15
2.79
2.83
2.00
5.18
7.49
3.05
4.57
3.94
5.26
4.11
6.02
4.38
4.43
3.85
4.90
5.14
4.88
3.30
4.60
3.97
4.04
4.76
4.89
4.50
5.18
7.49
3.05
4.57
3.94
5.26
4.11
6.02
4.38
4.43
3.85
4.94
5.28
5.22
3.55
5.49
5.04
5.94
6.72
6.95
7.00
Total / Weighted
Average
37,428,454
2,943,118
3.70
14,965,880
5.07
55,337,452
3.84
4.45
5.06
Options granted in 2010 not analyzed as there is no associated activity on which to place any significance.
Actual Historical Data Analysis (Current Vesting and Term Only) - Company A
Grant Year
Options
Options
Options Remaining
Exercise Life
Exercised Cancelled
Remaining
Life
Total
Exercise at Exercise at Exercise at
Full Vesting Midpoint
Full Term
2009
2010
5,698
-
2,330
-
1.37
0.00
332,586
392,461
5.51
6.59
340,614
392,461
1.99
2.00
4.43
4.50
6.87
7.00
Total / Weighted
Average
5,698
2,330
1.37
332,586
5.51
340,614
1.99
4.43
6.87
Options granted in 2010 not analyzed as there is no associated activity on which to place any significance.
Adjusted Historical Data Analysis - Company A
Grant Year
Options
Options
Options Remaining
Exercise Life
Exercised Cancelled
Remaining
Life
Total
Exercise at Exercise at Exercise at
Full Vesting Midpoint Full Term
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
41,600
24,000
1,064,880
1,783,040
1,609,396
2,726,660
128,240
101,600
1,731,540
2,423,458
3,259,168
4,939,472
3,388,096
3,442,825
3,523,485
2,327,814
2,787,908
1,797,835
302,858
24,579
-
6,960
960
40,760
9,440
98,076
707,508
375,665
114,680
707,246
315,970
255,097
42,380
20,180
11,766
34,783
59,212
104,846
14,648
20,611
2,330
-
3.67
5.67
2.60
3.45
3.25
4.00
3.92
4.50
3.23
3.37
3.22
3.53
3.35
2.90
2.78
2.41
1.83
0.75
0.82
1.83
0.00
31,976
467,980
615,310
1,076,543
509,249
1,475,158
1,865,470
2,351,824
3,737,102
2,835,268
392,461
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.05
0.49
1.27
1.96
2.46
2.92
3.76
4.34
4.89
5.97
6.59
48,560
24,960
1,105,640
1,792,480
1,707,472
3,434,168
503,905
216,280
2,438,786
2,739,428
3,546,241
5,449,832
4,023,586
4,531,134
4,067,517
3,862,184
4,758,224
4,164,307
4,060,571
2,862,177
392,461
3.67
5.67
2.60
3.45
3.25
4.00
3.92
4.50
3.23
3.37
3.26
3.79
3.72
3.41
3.00
3.08
2.40
1.85
2.79
2.86
2.00
3.67
5.67
2.60
3.45
3.25
4.00
3.92
4.50
3.23
3.37
3.26
3.81
3.81
3.64
3.15
3.62
3.13
3.07
4.65
4.91
4.50
3.67
5.67
2.60
3.45
3.25
4.00
3.92
4.50
3.23
3.37
3.26
3.83
3.91
3.87
3.31
4.16
3.86
4.28
6.51
6.95
7.00
Total / Weighted
Average
37,428,454
2,943,118
3.02
14,965,880
4.08
55,337,452
3.15
3.62
4.09
Options granted in 2010 not analyzed as there is no associated activity on which to place any significance.
Appendix B
US-Based Employee Historical Data Analysis - Company B
Grant Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total / Weighted
Average
Options
Exercised
Options
Cancelled
Exercise
Life
4,132
185,250
977,520
697,335
33,363
38,642
23,255
15,334
-
468,000
541,652
269,137
72,556
212,665
68,750
496,936
145,593
103,277
23,700
-
6.61
3.95
3.77
3.16
2.88
2.99
2.93
1.98
1.54
1.19
0.00
1,974,831
2,402,266
3.50
Options
Remaining
Remaining
Life
Total
Exercise at
Full Vesting
Exercise at
Midpoint
Exercise at
Full Term
424,432
361,032
848,461
2,326,476
296,739
2,583,793
2,177,623
2,324,820
4,455,518
2,754,014
0.00
0.54
1.50
2.54
3.80
4.54
5.50
6.39
7.41
8.53
9.44
468,000
970,216
815,419
1,898,537
3,236,476
398,852
3,119,371
2,346,471
2,428,097
4,494,552
2,754,014
6.61
6.36
5.87
5.09
5.26
4.83
4.23
3.49
2.55
2.21
2.22
6.61
6.48
6.20
5.65
6.63
6.52
6.51
6.46
6.10
6.07
6.11
6.61
6.59
6.53
6.22
8.00
8.21
8.79
9.42
9.64
9.92
10.00
15,798,894
5.82
20,175,991
3.97
6.28
8.59
Radford Review: Expected Life Analysis – Practical Considerations
Date 08/11
8