y=mx+b: Understanding Algorithmic
Approaches to Stock Comp Expense
October 24, 2013
Dan Moody – Sr. Product Manager,
E*TRADE Corporate Services
E*TRADE Financial Corporate Services, Inc. and its affiliates do not provide legal, accounting or tax advice. Always consult your own legal, accounting and tax advisers.
The E*TRADE FINANCIAL family of companies provides financial services that
include trading, investing, related banking product and services to retail
investors, and managing employee stock plans.
Employee stock plan solutions are offered by E*TRADE Financial Corporate
Services, Inc.
Securities products and services offered by E*TRADE Securities LLC, Member
FINRA/SIPC.
E*TRADE Financial Corporate Services, Inc. and E*TRADE Securities are
separate but affiliated companies.
The laws, regulations and rulings addressed in this presentation and by the
products, services and publications offered by E*TRADE Financial Corporate
Services, Inc. are subject to various interpretation and frequent change.
Product descriptions and instructions in this presentation are general in nature
and are not intended to replace documentation and instructional materials
distributed by E*TRADE Financial Corporate Services, Inc.
Define/understand the lifecycle of
a grant
Discuss ASC 718 (fka FAS 123R)
guidance on applicable to each
stage of a grant’s lifecycle.
Understand what tasks are
performed and reports run in
EE/EEO at each stage of a grant’s
lifecycle.
Compensation Expense
Over the Requisite Service Period (ASC 718-10-35-2)
The compensation cost for an award of share-based
employee compensation classified as equity shall be
recognized over the requisite service period…. The
requisite service period is the period during which an
employee is required to provide service in exchange
for an award, which is often the vesting period.
Final Cost Recognized (ASC 718-10-35-3)
The total amount of compensation cost recognized at
the end of the requisite service period for an award of
share-based compensation shall be based on the
number of instruments for which the requisite service
has been rendered (that is, for which the requisite
service period has been completed).
Variable Legend
,
Algorithm Basics
Establishing a Framework
 When does expense begin?

Is the Grant Date a day of expense?
• If it is, then Vest Date – Grant Date + 1
• If it is not, then Vest Date – Grant Date
– Vest Date = Grant Date becomes a Special Case
 When does expense end?


On the Vest Date?
The day before the Vest Date?
Establishing a Framework (CONTINUED)
 What happens first, vesting or cancellation?

If the Cancel Date = Vest Date, are the shares earned or should
the shares be forfeited and the expense reversed?
• Guiding principle: “Good things happen in the morning, and bad things
happen at night”
• By this principle, the shares are earned before they are cancelled when
Cancel Date = Vest Date
 If you answered that the shares are already earned on
the vest date, did you answer that expense ends the
day prior to the Vest Date?

If not, are you being consistent?
Similarities Among Most Algorithms

Total Expense is recognized by the final Vest Date

When Cancel Date = Vest Date, shares are considered vested
and expense is not reversed

When using Multiple, aka FIN 28, amortization of expense
before applying forfeiture rates
Minor Algorithmic Differences

Grant Date counted as a day of expense

Vest Date counted as a day of expense

Cumulative catch-up when vesting begins prior to grant date

Expense acceleration booked in a single period or amortized
evenly over time
Fundamental Algorithmic Differences

Implementation of “Straight-Line”

Application of Forfeiture Rates
Because these are the two largest drivers of differences in
expense algorithms, we will focus our attention primarily on
these two topics.
Math Refresher
Special Properties of Right Triangles
 Tangent of an angle is equal to the opposite
leg divided by the adjacent leg
Cartesian Plane
 A line may be
expressed as
below:
Using Integrals
 Integrals calculate the
area under a function
A
The Cartesian Plane
Looking at Comp Expense in the Cartesian Plane
 Working in the Cartesian
Plane:


•
allows us to evaluate
expense visually
Lends useful tools to
simplify calculations
In order to use the
Cartesian Plane:
– Plot time on the xaxis
– Plot total expense on
the y-axis
Degenerate Case of Straight Line Starting at Origin
:
Piecewise Analysis
Because “Straight Line” is Never Straight
 ASC 718 requires the use
of forfeiture estimates
m = .81 ∙
88.11
67.75
46.31
 As soon as you introduce
forfeiture rates into “straight
line” expense, it’s no longer
straight
m = .86 ∙
m = .90 ∙
NOTE: even though straightline isn’t straight, we are
going to consider it straight for
simplicity’s sake in some
examples that follow
throughout this presentation.
23.75
m = .95 ∙
1
2
3
4
Because…. “Life” Happens
 LOAs can cause gaps in
expense
 These gaps force the line
to be broken into pieces,
requiring a separate y = mx
+ b formula to represent
each piece of the line.
Because Performance Service Period End Dates Move
Prospective
Change Slope
 Moving the Service Period
End Date can cause “kinks”
in the line
 These kinks force the line
to be broken into pieces,
requiring a separate y = mx
+ b formula to represent
each piece of the line.
Original Slope
Effect of Piecewise Analysis on an Expense Algorithm
 Piecewise functions are typically represented in
programming language using nested “if”/“then” statements
 An effective general solution to the problem can bypass
the need for if/then statements
 Evaluating expense as a series of piecewise functions
adds the ultimate power and flexibility in performing
compensation expense calculations
Implementing Straight‐Line
Challenges of the “Double Floor” Provision
The “Double Floor” Provision (ASC 718-10-35-8)
An entity shall make a policy decision about whether to recognize compensation cost for an award with only service conditions that has a graded vesting schedule in either of the following ways:
a. On a straight‐line basis over the requisite service period for each separately vesting portion of the award as if the award was, in‐
substance, multiple awards
b. On a straight‐line basis over the requisite service period for the entire award (that is, over the requisite service period of the last separately vesting portion of the award). However, the amount of compensation cost recognized at any date must at least equal the portion of the grant‐date value of the award that is vested at that date.
Double Floor with a 10-20-30-40 Grant (Back-Loaded)
100%
60%
30%
10%
1
2
3
4
Double Floor with a 40-30-20-10 Grant (Front-Loaded)
100%
90%
70%
40%
1
2
3
4
Double Floor - Violating Both Floors
100%
70%
50%
30%
1
2
3
4
Possible Solution Path 1
100%
70%
50%
30%
1
2
3
4
Possible Solution Path 2
100%
70%
50%
30%
1
2
3
4
Possible Solution Path 2
100%
70%
50%
30%
1
2
3
4
Possible Solution Path 2
100%
%
70%
%
50%
%
30%
%
1
2
3
4
Possible Solution Path 2
100%
%
70%
%
50%
%
30%
%
1
2
3
4
Possible Solution Path 2
100%
70%
50%
30%
1
2
3
4
Double Floor & Weighted Average Forfeiture Percentage
Assume a grant of 4 shares, vesting 1 share per year over 4 years worth $1 per share
YEAR
1
Forfeiture
Percentage Per
Tranche
5%
Expense Per
Tranche
Cumulative
Expense
.95
2
9.75%
.90
1.85
3
14.2625%
.86
2.71
18.5494%
.81
3.52
4
Double Floor & Weighted Average Forfeiture Percentage
3.52
88.11
m = .81
67.75
2.71
m = .86
46.31
1.85
m = .90
m = .8811
0.95
23.75
m = .95
%
1
2
3
4
%
Double Floor & Weighted Average Forfeiture Percentage
3.52
88.11
2.71
67.75
1.85
46.31
0.95
23.75
%
1
2
3
4
%
Double Floor & Weighted Average Forfeiture Percentage
3.52
88.11
2.71
67.75
1.85
46.31
0.95
23.75
%
1
2
3
4
%
Double Floor & Weighted Average Forfeiture Percentage
3.52
88.11
2.71
67.75
1.85
46.31
0.95
23.75
%
1
2
3
4
%
Double Floor & Weighted Average Forfeiture Percentage
m = .8811
88.11
3.52
2.71
m = .81
m = .8811
m = .86
1.85
67.75
46.31
m = .90
m = .8811
0.95
23.75
m = .95
%
m = .8811
1
2
3
4
%
Forfeiture Rates & Expense
Algorithmic Approaches
Forfeiture Estimate (ASC 718-10-35-3)
An entity shall base initial accruals of compensation
cost on the estimated number of instruments for
which the requisite service is expected to be
rendered. That estimate shall be revised if
subsequent information indicates that the actual
number of instruments is likely to differ from previous
estimates.
Forfeiture Rate vs. Forfeiture & Expense Percentage
Forfeiture Rate
Forfeiture Percentage
Expense Percentage
Conversions
CONVERT
→
1
1
.05
1
1
e.g. 5% forfeiture rate over 4 years
e.g. 5% forfeiture rate over 4 years
1
→
1
18.55%
.05
81.45%
CONVERT
→
1
1
.1855
→
1
1
e.g. 18.55 forfeiture % over 4 years
1
5%
e.g. 81.45 expense % over 4 years
1
.8145
5%
Systematic Approaches to Expense & FR
Forfeiture Reversal at Vest Date
•
Can give smooth expense through vest date
Forfeiture Reversal at Forfeiture Date, Dynamic Expense Percentage
•
Can give smooth expense through vest date
Forfeiture Reversal at Vest Date, Back Out Expense Manually
•
Double Dipping
Forfeiture Reversal at Forfeiture Date, Static Expense Percentage
•
Double Dipping
Forfeiture Reversal at Vest Date (Static Expense %)
Expense Percentage
formula
•
Uses a forfeiture rate to arrive at an expense percentage •
Applies expense deflator to each individual grant.
•
Deflator computed from the time of grant “static”
•
If a new rate is entered, a new deflator is computed from the time of grant and a cumulative catch‐up is applied. Forfeiture Reversal at Vest Date (CONTINUED)
•
Mirrors the FAS 123R Illustration •
Proper implementation requires the user to estimate and track forfeitures on a pool‐by‐pool basis
• On the Vest Date: estimated expense compared to actuals, trued‐up
Forfeiture Reversal at Forfeiture Date (Dynamic Expense %)
Expense Percentage
formula
• Uses a forfeiture rate to arrive at an expense percentage
•
•
•
Applies expense percentage to each individual grant.
Expense Percentage compounds rate from the end of each reporting period, hence “dynamic”
If a new rate is entered, a new deflator is computed from the time of grant and a cumulative catch‐up is applied
Forfeiture Reversal at Forfeiture Date (CONTINUED)
•
Every grant remaining recognizes slightly more expense each period
until it vests
•
•
Increase in expense offsets reversals of expense for forfeited grants
On Vest Date: only grants that have not been forfeited remain
lim 1
→
1
The Stair Step Effect of “Double Dipping”
The Stair Step Effect Assuming 5% Forfeiture Rate
m = .81 ∙
88.11
67.75
m = .86 ∙
46.31
m = .90 ∙
23.75
m = .95 ∙
1
2
3
4
FR at Vest: Cliff-Vest Grant/Tranche-Level View
 1 Forfeiture deflated expense
.
2
accrued evenly over time
through the vest date
 2 On vest date, if grant did
not forfeit, additional
expense recognized
immediately
1
3
 3 On vest date, if grant did
forfeit, full expense accrued
to date is reversed
immediately
 If the forfeiture percentage is
correct, the sum of 2 for all
grants remaining is equal to
3 for all grants forfeited
Forfeiture Reversal at Forfeiture Date
Cliff‐Vest Grant / Tranche‐Level View
 1 Forfeiture deflated expense
.
accrued exponentially over
time through the vest date
 On vest date, if grant did not
forfeit, no additional expense
recognized
2
 2 During each reporting
period, slightly more
expense is recognized for
each grant to reflect that the
grant has less time to forfeit
 3 Expense accrued for
1
3
grants that forfeit is reversed
in the period in which the
grant forfeits
 If the forfeiture rate is
correct, the sum of 2 for all
grants remaining is equal to
3 for all grants forfeited
At Forfeiture vs. At Vest
Cliff‐Vest Grant / Tranche‐Level View
.
At Forfeiture vs. At Vest
Graded Vesting Assuming 5% Forfeiture Rate
100.00
88.11
75.00
m = .81 ∙
67.75
m = .86 ∙
50.00
46.31
m = .90 ∙
25.00
23.75
m = .95 ∙
1
2
3
4
At Forfeiture vs. At Vest
Graded Vesting with True‐Ups for At Vest Assuming 5% Forfeiture Rate
100.00
88.11
m = .81 ∙
75.00
67.75
m = .86 ∙
50.00
46.31
m = .90 ∙
25.00
23.75
m = .95 ∙
1
2
3
4
At Forfeiture vs. At Vest
Pool‐Level View
.
 In a perfect world:
 assuming that a
company pegs its
forfeiture rate or
percentage to the
decimal and
forfeitures occur
uniformly over time
 both True-Up at
Forfeiture and TrueUp at Vest produce a
deflated expense
matching the final
actual expense and
accrue that expense
evenly over the
service period
Calculating Forfeiture Rates for Each Method
Assumptions for Examples
Two Identical Pools (Year 1 Pool, Year 2 Pool)
Year 1 Pool
Year 2 Pool
10,000 Shares (100 grants with 100 shares)
10,000 Shares (100 grants with 100 shares)
Value $1.00 Value $1.00 per share
per share
Cliff Vest in 4 Years
Cliff Vest in 4 Years
Forfeiture Rates for Examples
Company believes it has a long‐term share‐weighted employee turnover rate of 10% and does not expect to change this estimate for several years
YEAR
1
Actual Experience for Each Pool by Year
POOL 1
POOL 2
5%
15%
2
9.75%
27.75%
3
14.2625%
38.5875%
18.5494%
47.7994%
4
Forfeiture Reversal at Vest Date - Example
Apply the 10% forfeiture rate to both pools
• On a weighted average basis, 10% is correct (10K shares @ 5%, 10K shares @ 15%)
• Do not make any adjustments to rate estimate
At Vest
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
Year
1
2
3
4
$ 1,640.25 $ 1,640.25 $ 1,640.25 $ 1,640.25 1,584.06
1,640.25 1,640.25 1,640.25 3,224.31 1,640.25 3,280.50 4,920.75 8,145.06 1,640.25 1,640.25 1,640.25 1,640.25 1,640.25 1,640.25 3,280.50 1,640.25 4,920.75 5
1,640.25 (1,340.94)
299.31 5,220.06 Year Total
$ 1,640.25 $ 3,280.50 $ 3,280.50 $ 4,864.56 $ 299.31
Running Total
$ 1,640.25 $ 4,920.75 $ 8,201.25 $ 13,065.81 $ 13,365.12 Forfeiture Reversal at Forfeiture Date - Example
Apply the 10% forfeiture rate to both pools
• On a weighted average basis, 10% is correct (10K shares @ 5%, 10K shares @ 15%)
• Do no make any adjustments to rate estimate
At Forfeiture
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
Year
1
2
3
4
$ 1,822.50 $ 2,010.32 $ 2,653.47 $ 3,431.29 (177.69)
(521.31)
(1,073.50)
1,822.50 1,832.63 2,132.16 2,357.79 1,822.50 3,655.13 5,787.29 8,145.08 1,822.50 1,822.50 1,822.50 1,609.37 (505.74)
1,103.63 2,926.13 2,348.34 (1,129.12)
1,219.22 4,145.35 5
3,056.17 (1,981.45)
1,074.72 5,220.07 Year Total
$ 1,822.50 $ 3,655.13 $ 3,235.79 $ 3,577.01 $ 1,074.72 Running Total
$ 1,822.50 $ 5,477.63 $ 8,713.42 $ 12,290.43 $ 13,365.15 Forfeiture Reversal: at Forfeiture vs. at Vest
At Vest
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
1
Year
3
2
4
5
$ 1,640.25 $ 1,640.25 $ 1,640.25 1,640.25 1,640.25 1,640.25 3,280.50 1,640.25 4,920.75 $ 1,640.25 1,584.06
3,224.31 8,145.06 1,640.25 1,640.25 1,640.25 1,640.25 1,640.25 1,640.25 3,280.50 1,640.25 4,920.75 1,640.25 (1,340.94)
299.31 5,220.06 Year Total
$ 1,640.25 $ 3,280.50 $ 3,280.50 $ 4,864.56 $ 299.31
Running Total
$ 1,640.25 $ 4,920.75 $ 8,201.25 $ 13,065.81 $ 13,365.12 At Forfeiture
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
1
$ 1,822.50 1,822.50 1,822.50 2
Year
3
4
$ 2,010.32 (177.69)
1,832.63 3,655.13 $ 2,653.47 (521.31)
2,132.16 5,787.29 $ 3,431.29 (1,073.50)
2,357.79 8,145.08 1,822.50 1,822.50 1,822.50 1,609.37 (505.74)
1,103.63 2,926.13 2,348.34 (1,129.12)
1,219.22 4,145.35 5
3,056.17 (1,981.45)
1,074.72 5,220.07 Year Total
$ 1,822.50 $ 3,655.13 $ 3,235.79 $ 3,577.01 $ 1,074.72 Running Total
$ 1,822.50 $ 5,477.63 $ 8,713.42 $ 12,290.43 $ 13,365.15 Forfeiture Reversal at Vest Date – Revisited
The Pool-by-Pool Approach
Let’s revisit the Forfeiture Reversal at Vest Date method. This time, we’re going to make some changes:
• We’re going to implement the pool‐by‐pool analysis, still under the assumption of a forward‐looking forfeiture rate of 10% for both Pools
• We’ll analyze historical forfeiture experience, then add our forward looking estimate to the historical forfeiture percentage
Forfeiture Reversal at Forfeiture Date
Dynamic Percentage
•
Because only non‐forfeited grants remain in the expense over the service period: •
•
True‐Up at Forfeiture requires an answer to the question “What percentage of shares do I expect to forfeit on an annual basis”
i.e. the algorithm needs the forfeiture rate
formula
1
Forfeiture Reversal at Vest Date
•
Because ALL grants (forfeited or not) remain in the expense from grant to vest: •
•
•
True‐Up at Vest requires an answer to the question “How many shares do I expect to vest”
i.e. First find the forfeiture percentage, then back into the rate
“Look forward and reason back”
1
formulas
1
1
Forfeiture Reversal at Vest Date
Pool-by-Pool Estimate Process
: 1
For
EACH
Pool
Compute Forfeiture %
1.
2.
3.
Estimate Future Forfeiture%
Compute Forfeiture Rate
∙ 1
%
1
1
Compute the current percentage of shares forfeited
Estimate how many additional shares are expected to forfeit on top of those already forfeited
Back into the rate that yields the appropriate percentage
Forfeiture Reversal at Vest Date – Revisited
The Pool-by-Pool Approach
After Year 1, we notice that only 5% of Pool 1 have actually forfeited, but we still expect at 10% turnover rate. What rate should we input into an expense algorithm to more closely reflect our expectations?
:1
5%
Compute Forfeiture %
Estimate Future Forfeiture%
: 9500 ∙ 1
: 5%
1
25.745%
.30745
Compute Forfeiture Rate
1
.10
.
%
2574.5
.
%
Forfeiture Reversal at Vest Date – Revisited
The Pool-by-Pool Approach
Using the same methodology, we can find rates to use for Pools 1 & 2 in Years 2 through 4. (Year 1 is a given and the same for both.)
Forfeiture Rates Used for Each Pool by Year
YEAR
POOL 1
POOL 2
1
10%
2
8.77%
11.28%
3
7.53%
12.54%
6.27%
13.78%
4
10%
Forfeiture Reversal at Vest Date ‐ Example
Changing our forfeiture rate by pool, backing into the rate from the expected percentage based on history of the pool significantly improves Forfeiture Reversal at Vest Date
At Vest – New Method
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
Year
1
2
3
4
$ 1,640.25 $ 1,822.50 $ 2,019.94 $ 2,233.69 428.69 1,640.45 1,822.50 2,019.94 2,662.38 1,640.45 3,462.75 5,482.69 8,145.06 1,640.25 1,458.00 1,290.94 1,640.25 1,640.25 1,458.00 3,098.25 1,290.94 4,389.19 5
1,137.94 (307.06)
830.87 5,220.06 Year Total
$ 1,640.45 $ 3,462.75 $ 3,477.94 $ 3,953.32 $ 830.87 Running Total
$ 1,640.45 $ 5,103.00 $ 8,580.94 $ 12,534.25 $ 13,365.12 Forfeiture Reversal: at Vest Old vs. at Vest New
At Vest
Accrual
True‐Up
Pool 1
Year Total
Running Total
Pool 2
1
2
Year
3
4
5
$ 1,640.25 $ 1,640.25 $ 1,640.25 $ 1,640.25 1,584.06
1,640.25 1,640.25 1,640.25 3,280.50 1,640.25 4,920.75 3,224.31 8,145.06 1,640.25 1,640.25 1,640.25 Accrual
True‐Up
Year Total
1,640.25 1,640.25 1,640.25 1,640.25 (1,340.94)
299.31 Running Total
1,640.25 3,280.50 4,920.75 5,220.06 Year Total
$ 1,640.25 $ 3,280.50 $ 3,280.50 $ 4,864.56 $ 299.31
Running Total
$ 1,640.25 $ 4,920.75 $ 8,201.25 $ 13,065.81 $ 13,365.12 At Vest – New Method
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
NEW
OLD
1
$ 1,640.25 2
$ 1,822.50 Year
3
$ 2,019.94 1,640.45 1,640.45 1,822.50 3,462.75 2,019.94 5,482.69 4
$ 2,233.69 428.69 2,662.38 8,145.06 1,640.25 1,458.00 1,290.94 1,640.25 1,640.25 1,458.00 3,098.25 1,290.94 4,389.19 1,137.94 (307.06)
830.87 5,220.06 $ 830.87 5
Year Total
$ 1,640.45 $ 3,462.75 $ 3,477.94 $ 3,953.32 Running Total
$ 1,640.45 $ 5,103.00 $ 8,580.94 $ 12,534.25 $ 13,365.12 Forfeiture Reversal: at Forfeiture vs. at Vest New
At Vest – New Method
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
1
$ 1,640.25 2
$ 1,822.50 Year
3
$ 2,019.94 1,640.45 1,640.45 1,822.50 3,462.75 2,019.94 5,482.69 4
$ 2,233.69 428.69 2,662.38 8,145.06 1,640.25 1,458.00 1,290.94 1,640.25 1,640.25 1,458.00 3,098.25 1,290.94 4,389.19 1,137.94 (307.06)
830.87 5,220.06 $ 830.87 5
Year Total
$ 1,640.45 $ 3,462.75 $ 3,477.94 $ 3,953.32 Running Total
$ 1,640.45 $ 5,103.00 $ 8,580.94 $ 12,534.25 $ 13,365.12 At Forfeiture
Pool 1
Accrual
True‐Up
Year Total
Running Total
Pool 2
Accrual
True‐Up
Year Total
Running Total
1
$ 1,822.50 1,822.50 1,822.50 2
Year
3
4
$ 2,010.32 (177.69)
1,832.63 3,655.13 $ 2,653.47 (521.31)
2,132.16 5,787.29 $ 3,431.29 (1,073.50)
2,357.79 8,145.08 1,822.50 1,822.50 1,822.50 1,609.37 (505.74)
1,103.63 2,926.13 2,348.34 (1,129.12)
1,219.22 4,145.35 5
3,056.17 (1,981.45)
1,074.72 5,220.07 Year Total
$ 1,822.50 $ 3,655.13 $ 3,235.79 $ 3,577.01 $ 1,074.72 Running Total
$ 1,822.50 $ 5,477.63 $ 8,713.42 $ 12,290.43 $ 13,365.15 Forfeiture Reversal – @ Vest vs. @ Forfeiture
Forfeiture Reversal on Vest Date
Forfeiture Reversal on Forfeiture Date
Easy in Spreadsheets
Difficult in Spreadsheets
Can smooth expense in certain circumstances
Smooths expense with automatic “reassessments”
Potential for large upward swings on Vest
By Design, no large upward swings on Vest
Requires rate by pool & demographic groups
Requires single rate by demographic group
Weighted Unamortized Expense
Unamortized Expense
Calculation Details
2
Unamortized Expense
A Moving Target
100%
100%
Calculating Wgt Avg Unamortized Expense
Daily Weighted Basis
1. Sum the Unamortized Expense from each day
2. Sum the total number of days in the period
3. Calculate:
∑
1
Wgt Avg Unamortized Expense
Simplistic Approach – Daily Weighted
Assume a grant worth $730.00 with a daily expense of $2.00 (vests
over 365 days). Let’s find Wgt. Unamortized Expense for a period of 5
days, starting from the grant date.
728
726
724
5
722
720
Wgt Avg Unamortized Expense
An Arithmetic Sequence
You may notice that summing the Unamortized Expense is simply an
arithmetic sequence of the days remaining times the daily expense….
2 ∙ 364
2 ∙ 363
2 ∙ 364
:
5
360
2
2
364
1810
: 2 ∙ 1810
2 ∙ 362
363
362
2 ∙ 361
361
2 ∙ 360
360
3620
5
Wgt Avg Unamortized Expense
An Integral
∙
730.00
∙
2
2
A
0
2
2
5
∙
∙
730
730
Wgt Avg Unamortized Expense
An Integral
2
5
2
730.00
2
0
2
730 ∙ 5 730 ∙ 0 3650 25
0 0
A
3625
0
0
5
Wgt Avg Unamortized Expense
An Integral
3625
730.00
A
0
5
Q&A
Contact
Dan Moody
Sr. Product Manager,
E*TRADE Corporate Services
[email protected]