{ From user Lonnie, Model Pricing_model at Wed, Mar 22, 2006 9:02 AM}
Softwareversion 3.1.1


{ System Variables with non-default values: }
Samplesize := 2
Windows := 2
Usetable := 0
Typechecking := 1
Checking := 1
Graphwindows := 5
Showhier := 1
Saveoptions := 2
Savevalues := 0
Editor := 0
Publishoneval := 1
Webhelper := -1
Allwarnings := 0


{ Non-default Time SysVar value: }
Time := Sequence( 1, Number_of_iterations, 1 )
Title Time: Time
Description Time: Dynamic simulation periods are specified in Time's ~~
definition. This is usually a list of numbers or labels, typically in~~
 some unit of time (days, weeks, months, etc.).  Use the ÒDynamic()Ó ~~
function in your variables to perform dynamic simulation.

Attribute Reference

Attribute Date_bough

Attribute Notes

Attribute Additional

Attribute New_attribute

Askattribute Reference,Function,Yes
Askattribute Notes,Function,Yes
Askattribute New_attribute,Function,Yes
Askattribute Reference,Module,Yes
Askattribute Notes,Module,Yes
Askattribute Value,Variable,Yes
Askattribute Reference,Variable,Yes
Askattribute Notes,Variable,Yes
Model Pricing_model
Title: Pricing Model
Description: The purpose of this model is to determine the amount of ~~
revenue needed on a monthly basis from each subscriber of a service t~~
o just meet the weighted average cost of capital of the firm from the~~
 service release date to the end of the Study Horizon.  In other word~~
s, it calculates the monthly unit revenue rate required from each sub~~
scriber of a service to give a return on investment at the end of the~~
 Study Horizon that is equal to the weighted average cost of capital ~~
of the firm.  This problem is trivial when the net cash flow, as well~~
 as the number of subscribers, is constant over time.  The solution i~~
s merely Net_Cash_Flow/Subscribers.  However, in the general case whe~~
re the number of subscribers and the net cash flow is time variant an~~
d the time value of money is worth consideration, an iterative method~~
 must be employed that begins with an initial estimate and converges ~~
on a solution by the successive addition of residual errors.~
~
As a test case, this model depicts a scenario in which a service is r~~
olled out to a marketplace that generates a perpituity revenue from e~~
ach subscriber (e.g., a cable TV operator charges each subscriber ~$3~~
0.00/Subscriber/Month regardless of how many customers are in the sys~~
tem).  The service penetration ramps up over the Roll Out Time in an ~~
s-curve fashion until 99% of the Rollout Penetration is achieved.  Su~~
bsequently, the number of subscribers grows exponentially until the e~~
xpected Final Penetration is reached at the end of the Study Horizon.~~
~
~
The Expenses are modeled with an initial investment at Month=0 and a ~~
perpituity throughout the life of the model.  For simplicity's sake, ~~
the expenses as a perpituity are intended to include all costs of ser~~
vices sold, tax, and any other cash expenses.~
~
The required revenue rate is determined by an iterative process.  The~~
 initial required revenue rate is assumed to be zero.  Thus, the requ~~
ired revenue rate determined by the first iteration represents the fi~~
rst estimate of how much revenue is required from each subscriber on ~~
a monthly basis to meet the expected ROI over the Study Horizon.  How~~
ever, this estimate may be too high or too low to meet the ROI.  Ther~~
efore, this value added to the original estimate is cycled back throu~~
gh the model to calculate the error of the previous estimate.  Of cou~~
rse, this error estimate also has an error associated with it.  Again~~
 the error is cycled back through with each successive iteration unti~~
l the error is considerably small.  This successive addition of initi~~
al estimate and residual error eventually converges on the Revenue Ra~~
te that gives the expected ROI.  The number of iterations required mu~~
st be determined by trial and error~
~
The solution method is to calculate the present worth of the cash flo~~
ws over the Study Horizon for each iteration.  The present worth is c~~
onverted into an equivalent period perpituity.  The perpituity, repre~~
senting the constant amount of revenue needed each month to meet the ~~
expected ROI, is divided by the number of subscribers to determine th~~
e monthly unit required revenue rate.  However, this result is hyperb~~
olic in shape because the number of Subscribers (the denominator) is ~~
increasing with each month against the equivalent period perpituity (~~
the numerator).  The correct solutiuon, then, is represented by the w~~
eighted average (the centroid) of this curve.  The weighted average d~~
etermined after the first iteration represents the initial required r~~
evenue rate estimate.  Each successive weighted average represents th~~
e residual error of each iteration.~
~
A final note: The index representing time in the model is named "Mont~~
h."  The System Variable "Time" is used as the index for the iteratio~~
ns.
Author: Robert D. Brown, III~
Director of Business Systems Modeling~
Integrated Product Development~
11450 Technology Circle~
Duluth, GA 30097-1504~
678.473.8515~
678.473.2100 fax~
rob.brown@antec.com
Date: Tue, Mar 24, 1998 10:21 AM
Saveauthor: Lonnie
Savedate: Wed, Mar 22, 2006 9:02 AM
Defaultsize: 48,24
Diagstate: 1,79,56,606,391,17
Windstate: 1,72,82
Fileinfo: 0,Model Pricing_model,2,2,0,0,W:\Analytica\ExecDebug\Exampl~~
e Models\Business Examples\Subscriber Pricing Model.ana
Pagesetup: (00030000004800480000000002480300FFF2FFF40256030C034505280~~
3FC00020000004800480000000002D802280001000000640000000100030303000000~~
01270F000100010000000000000000000000006008001901900000000000000000000~~
000000000000100000000000000000000000000000000)

Module Model_details
Title: Model Details
Description: The purpose of this model is to determine the amount of ~~
revenue needed on a monthly basis from each subscriber of a service t~~
o just meet the weighted average cost of capital of the firm from the~~
 service release date to the end of the Study Horizon.  In other word~~
s, it calculates the monthly unit revenue rate required from each sub~~
scriber of a service to give a return on investment at the end of the~~
 Study Horizon that is equal to the weighted average cost of capital ~~
of the firm.
Author: Robert D. Brown, III~
Director of Business Systems Modeling~
Integrated Product Development~
11450 Technology Circle~
Duluth, GA 30097-1504~
678.473.8515~
678.473.2100 fax~
rob.brown@antec.com
Date: Tue, Apr 14, 1998 5:15 PM
Defaultsize: 48,24
Nodelocation: 456,200,0
Nodesize: 62,36
Diagstate: 1,140,47,428,234,17

Module Service_penetration
Title: Service Penetration
Author: rbrown
Date: Mon, Jul 6, 1998 1:03 PM
Defaultsize: 48,24
Nodelocation: 72,88,0
Nodesize: 44,20
Diagstate: 1,120,130,340,294,17

Variable Subscribers
Title: Subscribers
Description: The actual fraction of the market size that adopt the se~~
rvice.  The cumulative distribution in time is represented by an s-cu~~
rve that reaches 99% of the Rollout Penetration by the end of the Rol~~
lout Time.  The distribution then grows exponentially until the end o~~
f the study horizon.
Definition: ((Rollout_penetration*Market_size)*S_curve1(0.01,Month,Ro~~
llout_time))*((1+Growthrate_after_ro)^(Month-Rollout_time))
Nodelocation: 224,88,0
Nodesize: 44,20
Windstate: 1,59,103
Valuestate: 1,8,44,814,570,1,MIDM
Aliases: Alias Subscribers2
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:60~
Yminimum:0~
Ymaximum:60~
Zminimum:0.05~
Zmaximum:0.4~
Xintervals:12~
Yintervals:4~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.05,0.25,0.5,0.75,0.95]~

Reformval: [Month, Final_penetration ]

Decision Rollout_time
Title: Rollout Time
Units: Months
Description: Input the amount of time that takes the Subscriber distr~~
ibution to reach 99% of the Rollout Penetration.
Definition: Choice(Self,0)
Nodelocation: 88,88,0
Nodesize: 44,20
Windstate: 1,280,290
Aliases: Formnode Rollout1
Domain: [12,18,24,30]

Decision Rollout_penetration
Title: Rollout Penetration
Units: % Market Size
Description: Input the expected market penetration of the service at ~~
the Rollout Time.
Definition: Choice(Self,0)
Nodelocation: 88,152,0
Nodesize: 44,20
Windstate: 1,182,281
Aliases: Formnode Potential_penetrati1
Numberformat: 1,%,4,0,0,0
Domain: [0.15,0.2,0.25]

Decision Market_size
Title: Market Size
Units: Potential Subscribers
Description: Input the maximum potential service subscribers.
Definition: 50K
Nodelocation: 88,32,0
Nodesize: 44,20
Windstate: 1,76,53
Valuestate: 1,232,242,416,303,0,MIDM
Aliases: Formnode Serving_area1
Domain: [50K]

Variable Growthrate_after_ro
Title: Growth Rate After Rollout
Units: %
Description: Calculates the compound annual growth rate of the subscr~~
iber distribution from the time Rollout Penetration is achieved to th~~
e Final Penetration at the Study Horizon.
Definition: ((Final_penetration/Rollout_penetration)^(1/(Study_horizo~~
n-Rollout_time)))-1
Nodelocation: 224,152,0
Nodesize: 44,24
Windstate: 1,201,96
Valuestate: 1,8,44,814,570,0,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:0~
Showkey:1~
Xminimum:12~
Xmaximum:30~
Yminimum:0~
Ymaximum:0.04~
Zminimum:0.15~
Zmaximum:0.4~
Xintervals:3~
Yintervals:4~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Rollout_time, Final_penetration ]
Numberformat: 1,%,4,1,0,0

Decision Final_penetration
Title: Final Penetration
Units: % Market Size
Description: Input the expected market penetration at the Study Horiz~~
on.
Definition: Choice(Self,0)
Nodelocation: 88,216,0
Nodesize: 44,20
Windstate: 1,200,210
Aliases: Formnode Final_penetration1
Numberformat: 1,%,4,0,0,0
Domain: [0.15,0.2,0.3,0.4]

Close Service_penetration

Module Revenue_module
Title: Revenue Module
Author: rbrown
Date: Mon, Jul 6, 1998 1:03 PM
Defaultsize: 48,24
Nodelocation: 184,40,0
Nodesize: 44,20
Diagstate: 1,264,274,445,310,17

Variable Required_monthly_rev
Title: Required Monthly Revenue
Units: $/Month
Description: Calculates the equivalent amount of perpetuity revenue ~~
needed for each month in the model to meet the weighted average cost ~~
of capital.
Definition: (-Annuity_prsnt_amoun1(Pw_fcf,Equiv_perd_int_rate1(Wacc1,~~
12),Study_horizon))
Nodelocation: 96,232,0
Nodesize: 44,24
Windstate: 1,157,283
Valuestate: 1,9,44,814,570,0,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:3000~
Xmaximum:4600~
Yminimum:0~
Ymaximum:1~
Zminimum:1~
Zmaximum:1~
Xintervals:8~
Yintervals:4~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Market_size, Rollout_penetration ]
Numberformat: 1,D,4,2,0,1

Variable Wavg_reqd_rev_rate
Title: Wtd Avg Required Monthly Revenue Rate
Units: $/Sub/Month
Description: The output of this calculation represents the weighted a~~
verage (the centroid) of the previous node.  The weighted average det~~
ermined after the first iteration represents the initial required rev~~
enue rate estimate.  Each successive weighted average represents the ~~
residual error of each iteration.
Definition: (Sum((Month*Mo_reqd_rev_rate),Month)/Sum(Month,Month))
Nodelocation: 96,48,1
Nodesize: 48,32
Windstate: 1,76,121
Valuestate: 1,9,56,814,570,0,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:20~
Yminimum:-2~
Ymaximum:0.01~
Zminimum:1~
Zmaximum:1~
Xintervals:3~
Yintervals:5~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Final_penetration, Time ]

Variable Revenue_rate
Title: Revenue Rate
Units: $/Subscriber
Description: The unit revenue rate charged per subscriber.  The outpu~~
t of this calculation represents a convergence in the stable value th~~
at gives the necessary return on investment that meets the weighted a~~
verage cost of capital.~
~
Dynamic(0,(Self[Time-1]+Wavg_reqd_rev_rate[Time-1]))
Definition: Dynamic(0,(Self[Time-1]+Wavg_reqd_rev_rate[Time-1]))
Nodelocation: 216,48
Nodesize: 44,20
Nodeinfo: 1,1,1,1,1,1,0,,0,
Windstate: 1,76,50
Valuestate: 1,175,122,479,414,0,MIDM
Nodecolor: -26215,-13105,-1

Objective Revenue_rate2
Title: Revenue Rate
Units: $/Subscriber
Description: The unit revenue rate charged per subscriber that meets ~~
the weighted cost of capital at the study horizon.
Definition: Revenue_rate[Time=Number_of_iterations]
Nodelocation: 320,48
Nodesize: 44,20
Nodeinfo: 1,1,1,1,1,1,0,,1,
Valuestate: 1,8,44,814,570,1,MIDM
Aliases: Formnode Revenue_rate1
Nodecolor: -1,1,1
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:0.3~
Yminimum:25.2~
Ymaximum:27~
Zminimum:1~
Zmaximum:1~
Xintervals:10~
Yintervals:10~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Rollout_time, Final_penetration ]

Variable Revenue
Title: Revenue
Units: $
Description: The revenue generated from from paying subscribers.
Definition: Revenue_rate*Subscribers
Nodelocation: 216,104
Nodesize: 44,20
Valuestate: 1,136,146,416,303,1,MIDM
Reformval: [Month, Final_penetration ]

Variable Mo_reqd_rev_rate
Title: Monthly Required Revenue Rate
Units: $/Month
Description: Calculates the required revenue from each subscriber eac~~
h month to meet the weighted average cost of capital at the Study Hor~~
izon.~
~
This value is not a constant.  Although Required_monthly_rev remains ~~
constant, Subscribers changes with time.  The shape of the curve is h~~
yperbolic in each iteration.
Definition: Required_monthly_rev/Subscribers
Nodelocation: 96,160,0
Nodesize: 44,24
Valuestate: 1,296,306,416,303,1,MIDM
Reformval: [Time, Undefined ]

Alias Subscribers2
Title: Subscribers
Definition: 1
Nodelocation: 216,160,0
Nodesize: 44,20
Original: Subscribers

Close Revenue_module

Module System_functions
Title: System Functions
Author: rbrown
Date: Mon, Jul 6, 1998 1:03 PM
Defaultsize: 48,24
Nodelocation: 72,160,0
Nodesize: 44,20
Nodeinfo: 1,0,0,1,1,1,0,,0,
Diagstate: 1,161,280,435,186,17

Function Annuity_prsnt_amoun1(P,i,N)
Title: Annuity from a Present Amount
Description: The annuity from a present amount is the period amount w~~
hich can be withdrawn for a definite period of time from a present su~~
m of money at a given rate of interest each compounding period.~
~
P = the present amount~
i = the period interest rate~
N = the period at which the present amount is depleted
Definition: P*(i*(1+i)^N)/(((1+i)^N)-1)
Nodelocation: 240,80,0
Nodesize: 44,24
Windstate: 1,136,146
Paramnames: P,i,N

Function Equiv_perd_int_rate1(APR, N)
Title: Equivalent Period Interest Rate
Description: Calculates the period interest rate of the yearly compou~~
nding interest rate.~
APR = Annual percentage rate~
N = Number of compounding periods in a year
Definition: ((1+APR)^(1/N))-1
Nodelocation: 144,80,0
Nodesize: 44,24
Windstate: 1,124,116
Paramnames: APR,N

Decision Study_horizon
Title: Study Horizon
Units: Months
Description: Enter the total amount of time the study lasts.
Definition: 60
Nodelocation: 144,24
Nodesize: 44,20
Nodeinfo: 1,0,0,1,1,1,0,,0,
Aliases: Formnode Study_horizon2

Index Month
Title: Month
Definition: Sequence( 0, Study_horizon, 1 )
Nodelocation: 240,24,0
Nodesize: 44,20

Decision Number_of_iterations
Title: Number of Iterations
Description: Enter number of iterations
Definition: 15
Nodelocation: 48,24
Nodesize: 44,20
Nodeinfo: 1,1,0,1,1,1,0,,0,
Aliases: Formnode Number_of_iteration1

Library Func_lib
Title: Function Library
Author: Robert Brown
Date: Wed, Oct 16, 1996 4:29 PM
Saveauthor: rbrown
Savedate: Wed, Jun 3, 1998 4:03 PM
Defaultsize: 48,24
Nodelocation: 336,24,0
Nodesize: 44,20
Nodeinfo: 1,1,0,1,1,1,0,,0,
Diagstate: 1,61,62,390,168,17
Nodecolor: 1,-1,-1
Pagesetup: (00030000004800480000000002D80228FFE1FFE202F90246034705280~~
3FC00020000004800480000000002D802280001000000640000000100030303000000~~
01270F00010001000000000000000000000000600800190190000000000000000000~~
0000000000000000000000000000000000000000000000)

Module Financial_functions
Title: Financial Functions
Author: rbrown
Date: Tue, Dec 23, 1997 2:17 PM
Defaultsize: 48,24
Nodelocation: 184,48,0
Nodesize: 44,20
Diagstate: 1,527,20,473,315,17

Function Future_worth(P, i, N)
Title: Future Worth of a Present Amount
Description: The sum at the end of a specific period of time that a ~~
present amount will accumulate to at given rate of interest each comp~~
ounding period.~
~
P = present amount~
i = period interest rate~
N = the period at the end of the compounding sequence
Definition: P*(1+i)^N
Nodelocation: 64,40
Nodesize: 44,24
Paramnames: P,i,N

Function Present_worth(F, i, N)
Title: Present Worth of a Future Amount
Description: The amount of money at the start of a specific period of~~
 time which will accumulate to a known sum at the end of that period ~~
at a given rate of interest each compounding period.~
~
F = the future amount~
i= the period interest rate~
N = the period at which the future amount occurs
Definition: F/(1+i)^N
Nodelocation: 168,40,1
Nodesize: 44,24
Paramnames: F,i,N

Function Annual_depreciation(P,S,N)
Title: Annual Depreciation
Units: $
Description: Calculates the annual straight line depreciation value o~~
f a purchase.  P is the acquisition cost.  S is the salvage cost.  N ~~
is the taxation interval for considering the depreciation.
Definition: (P-S)/N
Nodelocation: 168,176,0
Nodesize: 44,24
Paramnames: P,S,N

Function Period_remaining_bal(L,i,m,N)
Title: Period Remaining Balance
Units: $
Description: Returns the period N remaining balance due on a loan L o~~
btained at N=0.  The loan has a life of m periods paid back at a peri~~
od interest rate of i.
Definition: L*((1+i)^N-((1+i)^N-1)/(1-(1+i)^(-m)))
Nodelocation: 272,176,0
Nodesize: 44,24
Paramnames: L,i,m,N

Function Equiv_perd_int_rate(APR, N)
Title: Equivalent Period Interest Rate
Description: Calculates the period interest rate of the yearly compou~~
nding interest rate.~
APR = Annual percentage rate~
N = Number of compounding periods in a year
Definition: ((1+APR)^(1/N))-1
Nodelocation: 64,176,0
Nodesize: 44,24
Paramnames: APR,N

Function Annuity_future_worth(A,i,N)
Title: Future Worth of an Annuity
Description: The future worth of an annuity for a given period of tim~~
e is the sum at the end of that period of the future worths of all pa~~
yments at a given rate of interest each compounding period.~
~
A = the amount of the annuity~
i = the period interest rate~
N = the period at the end of the compounding
Definition: (A*(1+i)^N-1)/i
Nodelocation: 272,40,1
Nodesize: 44,24
Paramnames: A,i,N

Function Annuity_presnt_worth(A,i,N)
Title: Present Worth of an Annuity
Description: The present worth of an annuity for a given period of ti~~
me is the sum at the start of that period of the present worths of ea~~
ch payment in the series, at a given rate of interest each compoundin~~
g period.
Definition: A*((1+i)^N-1)/(i*(1+i)^N)
Nodelocation: 376,40,0
Nodesize: 44,24
Paramnames: A,i,N

Function Annuity_prsnt_amount(P,i,N)
Title: Annuity from a Present Amount
Description: The annuity from a present amount is the period amount w~~
hich can be withdrawn for a definite period of time from a present su~~
m of money at a given rate of interest each compounding period.~
~
P = the present amount~
i = the period interest rate~
N = the period at which the present amount is depleted
Definition: P*i*(1+i)^N/((1+i)^N-1)
Nodelocation: 272,104,0
Nodesize: 44,24
Paramnames: P,i,N

Function Future_wrth_lin_grad(G,i,N)
Title: Future Worth of a Linear Gradient
Description: The future worth of a linear gradient is the future wort~~
h at the end of the period of the changing portion of an arithmetic p~~
rogression for a given period of time at a given rate of interest eac~~
h componding period.~
~
G = the amount of the arithmetic gradient~
i = the period interest rate~
N = the period at the end of the compounding
Definition: (G/i)*(((1+i)^N-1)/i-N)
Nodelocation: 64,104,0
Nodesize: 44,24
Windstate: 1,120,130
Paramnames: G,i,N

Function Presnt_wrth_lin_grad(G,i,N)
Title: Present Worth of a Linear Gradient
Description: The present worth of a linear gradient is the present wo~~
rth at the start of the period of the changing portion of an arithmet~~
ic progression for a given period of time at a given rate of interest~~
 each compounding period.~
~
G = the amount of the arithmetic gradient~
i = the period interest rate~
N = the period when the compounding ends
Definition: (G/i)*((((1+i)^N-1)/(i*(1+i)^N))-N/(1+i)^N)
Nodelocation: 168,104,1
Nodesize: 44,24
Windstate: 1,136,146
Paramnames: G,i,N

Function Linear_grad_annuity(G,i,N)
Title: Annuity for a Linear Gradient
Description: The annuity for a linear gradient is the annuity over th~~
e total period equivalent to the changing portion of an arithmetic pr~~
ogression for a given period of time at a given rate of interest each~~
 compounding period.~
~
G = the amount of the arithmetic gradient~
i= the period interest rate~
N = the period when the compounding ends
Definition: G*(1/i-N/((1+i)^N-1))
Nodelocation: 376,104,0
Nodesize: 44,24
Windstate: 1,152,162
Paramnames: G,i,N

Module Mortgage_bond
Title: Mortgage Bond
Author: rbrown
Date: Tue, Dec 23, 1997 2:17 PM
Defaultsize: 48,24
Nodelocation: 224,240,0
Nodesize: 44,20
Diagstate: 1,136,146,456,343,17

Decision Face_value
Title: Face Value of Bond
Units: $
Definition: 1000
Nodelocation: 184,24
Nodesize: 44,20

Decision Sale_value
Title: Sale Value of Bond
Units: $
Definition: 900
Nodelocation: 48,88
Nodesize: 44,20

Decision Interest_rate
Title: Bond Interest Rate
Units: %
Definition: .08
Nodelocation: 184,152
Nodesize: 44,20
Valuestate: 1,120,130,416,303,0,MIDM
Numberformat: 1,%,4,2,0,0

Decision Bond_life
Title: Bond Life
Definition: 10
Nodelocation: 312,88
Nodesize: 44,20

Variable Bond_cash_flow
Title: Bond Cash Flow
Units: $
Definition: Bond_cash_flows(Period,Sale_value,Face_value,Bond_life,In~~
terest_rate,Bonds_sold)
Nodelocation: 184,88
Nodesize: 44,20
Windstate: 1,40,50
Valuestate: 1,232,242,416,303,1,MIDM

Index Period
Title: Period
Definition: Sequence(1,Bond_life,1)
Nodelocation: 48,24
Nodesize: 44,20
Valuestate: 1,200,210,416,303,0,MIDM

Function Bond_cash_flows(N,SVB,FVB,M,i,x)
Title: Mortgage Bond Cash Flows
Units: $
Description: Calculates the cash flows for a mortgage bond.~
~
N = the period sequence~
SVB = sale value of the bond~
FVB = face value of the bond~
M = life of the bond~
i = interest rate of the bond~
x = number of bonds sold
Definition: If N=1 Then x*(SVB-i*FVB) Else If N=M Then -x*FVB*(1+i) E~~
lse -x*i*FVB
Nodelocation: 72,152
Nodesize: 44,24
Windstate: 1,133,119
Paramnames: N,SVB,FVB,M,i,x

Decision Bonds_sold
Title: Number of Bonds Sold
Definition: 1000
Nodelocation: 312,32
Nodesize: 44,20

Variable Present_value_of_bon
Title: Present Value of Bond Cash Flow
Definition: Cumulate(Bond_cash_flow/(1+Discount_rate)^(Period-1),Peri~~
od)
Nodelocation: 312,152
Nodesize: 44,24
Valuestate: 1,152,162,416,303,0,MIDM

Constant Discount_rate
Title: Discount Rate
Definition: .10
Nodelocation: 312,216
Nodesize: 44,20

Close Mortgage_bond

Function Wacc(Rt, Ri, Rf, Rcs, Beta, Debt, Equity)
Title: Weighted Average Cost of Capital
Description: Calculates the annual nominal (adjusted for inflation) w~~
eighted average cost of capital of an investment.  ~
~
Rt = Corporate tax rate~
Ri = Interest rate on debt~
Rf = Risk free bond rate~
Rcs = Historical return on common stock~
Beta = Equity beta~
Debt = Outstanding leverage~
Equity = Market value of equity
Definition: ((1-Rt)*Ri*Debt+(Rf+(Beta*Rcs))*Equity)/(Debt+Equity)
Nodelocation: 376,176,0
Nodesize: 44,24
Windstate: 1,223,162
Paramnames: Rt,Ri,Rf,Rcs,Beta,Debt,Equity
Reference: Higgins, R. _Analysis for Financial Management_.  Irwin/Mc~~
Graw-Hill: 1998.  pp. 269-298.
Notes: Rf has typically been 6.4% on government long-term bonds~
~
Rcs has typically been7% (1926-1995)
Additional: This function should only be used when an investment is a~~
 "carbon copy" of an existing asset.~
~
If the rate stated for the risk free bond excludes inflation, the inf~~
lation premium should be included in the calculation.~
~
The risk free bond rate was 6.4% by Oct. 1995.~
~
The historical return on common stock (1926-1995) was 7%

Close Financial_functions

Module Math_functions
Title: Math Functions
Description: Library of Rob Brown's math functions. Note that none of~~
 these are used in this.~
~
[LDC] Eliminated several unused functions that are redundant with fun~~
ctions present in Analytica 3.x.
Author: rbrown
Date: Tue, Dec 23, 1997 2:17 PM
Defaultsize: 48,24
Nodelocation: 64,48
Nodesize: 44,20
Diagstate: 1,368,6,344,231,17

Function Sgrowth(y0,g,t)
Title: Sgrowth
Description: S growth function of time; y0 is initial displacement va~~
lue at t=0; g is exponential growth rate; t is the instantaneous time~~
.  This function asymptotically approaches a maximum amplitude.
Definition: 1/(1+(1/y0-1)*exp(-g*t))
Nodelocation: 48,24
Nodesize: 44,20
Paramnames: y0,g,t

Function Learn_curve_unit(Cost_for_first_unit,Learning_rate:Numeric;N~~
umber_of_units:ArrayType)
Title: Learning Curve: Unit
Units: $
Description: Calculates the descending cost per unit as a function of~~
 the number of units produced.~
~
Cost_for_first_unit: The total cost of the first unit produced ~
Learning_rate: The learning curve rate, expressed as a whole number~
Number_of_units: A sequence of values (stepsize=1) starting with the ~~
first unit ending with the total quanity of units produced.
Definition: Cost_for_first_unit*Number_of_units^(Logten(Learning_rate~~
/100)/Logten(2))
Nodelocation: 160,24
Nodesize: 44,20
Windstate: 1,133,216
Paramnames: Cost_for_first_unit,Learning_rate,Number_of_units

Function Learn_curve_unit_avg(Cost_for_first_unit,Learning_rate:Numer~~
ic;Number_of_units:ArrayType)
Title: Learning Curve: Cumulative Average Cost per Unit
Units: $
Description: Calculates the descending cumulative average cost per u~~
nit as a function of the number of units produced.~
~
Cost_for_first_unit: The total cost of the first unit produced ~
Learning_rate: The learning curve rate, expressed as a whole number~
Number_of_units: A sequence of values (stepsize=1) starting with the ~~
first unit ending with the total quanity of units produced.
Definition: Cumulate(Cost_for_first_unit*Number_of_units^(Logten(Lear~~
ning_rate/100)/Logten(2)),Number_of_units)/Number_of_units
Nodelocation: 160,104
Nodesize: 44,40
Windstate: 1,133,317
Paramnames: Cost_for_first_unit,Learning_rate,Number_of_units

Function Learn_curve_time(Time_for_first_unit,Learning_rate:Numeric;N~~
umber_of_units:ArrayType)
Title: Learning Curve: Time
Units: minutes
Description: Calculates the descending cost in time per unit as a fun~~
ction of the number of units produced.~
~
Time_for_first_unit: The total cost in time of the first unit produce~~
d ~
Learning_rate: The learning curve rate, expressed as a whole number~
Number_of_units: A sequence of values (stepsize=1) starting with the ~~
first unit ending with the total quanity of units produced.
Definition: Time_for_first_unit*Number_of_units^(Logten(Learning_rate~~
/100)/Logten(2))
Nodelocation: 272,24
Nodesize: 44,20
Paramnames: Time_for_first_unit,Learning_rate,Number_of_units

Function Learn_curve_time_avg(Time_for_first_unit,Learning_rate:Numer~~
ic;Number_of_units:ArrayType)
Title: Learning Curve: Cumulative Average Cycle Time
Units: $
Description: Calculates the descending cumulative average cost in tim~~
e per unit as a function of the number of units produced.~
~
Time_for_first_unit: The total cost in time of the first unit produce~~
d ~
Learning_rate: The learning curve rate, expressed as a whole number~
Number_of_units: A sequence of values (stepsize=1) starting with the ~~
first unit ending with the total quanity of units produced.
Definition: Cumulate(Time_for_first_unit*Number_of_units^(Logten(Lear~~
ning_rate/100)/Logten(2)),Number_of_units)/Number_of_units
Nodelocation: 272,104
Nodesize: 44,40
Paramnames: Time_for_first_unit,Learning_rate,Number_of_units

Function S_curve(Yo, T, Tp)
Title: S Curve
Description: The S Curve is a function that asymptotically appraoches~~
 a maximum amplitude of 1.  Yo is the intial value at time T=1.  T is~~
 the time index. Tp is the time to 1-Yo penetration.   If the S Curve~~
 is used to approximate a service roll-out, let Yo=1%. Then Tp is the~~
 time to 99% service penetration.
Definition: 1/(1+(Yo/(1-Yo))^(2*T/Tp-1))
Nodelocation: 56,104,0
Nodesize: 44,20
Windstate: 1,56,66
Paramnames: Yo,T,Tp

Close Math_functions

Close Func_lib

Function S_curve1(Yo, T, Tp)
Title: S Curve
Description: The S Curve is a function that asymptotically appraoches~~
 a maximum amplitude of 1.  Yo is the intial value at time T=1.  T is~~
 the time index. Tp is the time to 1-Yo penetration.   If the S Curve~~
 is used to approximate a service roll-out, let Yo=1%. Then Tp is the~~
 time to 99% service penetration.
Definition: 1/(1+(Yo/(1-Yo))^(2*T/Tp-1))
Nodelocation: 48,80,0
Nodesize: 44,20
Paramnames: Yo,T,Tp

Close System_functions

Module Pro_forma_module
Title: Pro Forma Module
Author: rbrown
Date: Mon, Jul 6, 1998 1:03 PM
Defaultsize: 48,24
Nodelocation: 296,88,0
Nodesize: 44,20
Diagstate: 1,122,50,478,445,17

Variable Pw_fcf
Title: Present Worth of Free Cash Flow
Units: $
Description: Calculates the present worth of the cash flow given the ~~
weighted average cost of capital at the Study Horizon.
Definition: Npv(Equiv_perd_int_rate1(Wacc1,12), Free_cash_flow, Month~~
 )*(1+Equiv_perd_int_rate1(Wacc1,12))
Nodelocation: 280,360,0
Nodesize: 44,24
Windstate: 1,100,164
Valuestate: 1,8,44,814,570,0,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:1~
Yminimum:-180K~
Ymaximum:-120K~
Zminimum:1~
Zmaximum:1~
Xintervals:5~
Yintervals:4~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Final_penetration, Rollout_penetration ]

Decision Wacc1
Title: Weighted Average Cost of Capital
Units: %/Year
Definition: Choice(Self,3)
Nodelocation: 159,358,1
Nodesize: 48,32
Windstate: 1,216,226
Aliases: Formnode Discount_rate2
Numberformat: 1,%,4,0,0,0
Domain: [0.08,0.1,0.12,0.14,0.16,0.18,0.2,0.22,0.24,0.26,0.28]
Reference: Cable Plus

Objective Free_cash_flow1
Title: Free Cash Flow
Units: $
Description: The Free Cash Flow after the last iteration.
Definition: Free_cash_flow[Time=Number_of_iterations]
Nodelocation: 392,288
Nodesize: 44,20
Nodeinfo: 1,1,1,1,1,1,0,,1,
Valuestate: 1,8,44,814,570,1,MIDM
Aliases: Formnode Cash_flow2
Nodecolor: -1,1,1
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:1~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:60~
Yminimum:-200K~
Ymaximum:200K~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:10~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Month, Rollout_time ]

Variable Interest
Title: Interest
Units: $
Description: Interest payment in each period
Definition: -Ipmt( Equiv_perd_int_rate1( Interest_rate1, 12 ), Month,~~
 60, Capital_requirement )
Nodelocation: 56,168
Nodesize: 44,20
Windstate: 1,188,343

Variable Depreciation
Title: Depreciation
Definition: (Capital_requirement/60)
Nodelocation: 164,231
Nodesize: 44,20

Variable Principal
Title: Principal
Units: $
Description: Principal payment in each period
Definition: -Ppmt( Equiv_perd_int_rate1( Interest_rate1, 12 ), Month,~~
 60, Capital_requirement )
Nodelocation: 160,288
Nodesize: 44,20

Constant Tax_rate
Title: Tax Rate
Definition: .38
Nodelocation: 284,39
Nodesize: 44,20
Aliases: Formnode Tax_rate1

Variable Tax_provision
Title: Tax Provision
Units: $
Definition: Tax_rate*Operating_profit
Nodelocation: 284,95
Nodesize: 44,20
Valuestate: 1,8,44,814,570,0,MIDM
Reformval: [Month, Time ]

Variable Gross_profit
Title: Gross Profit
Definition: Revenue-Expenses
Nodelocation: 164,103
Nodesize: 44,20
Reformval: [Month, Time ]

Constant Capital_requirement
Title: Capital Requirement
Units: $
Definition: 1000000
Nodelocation: 56,288
Nodesize: 44,20
Aliases: Formnode Capital_requirement1

Variable Operating_profit
Title: Operating Profit
Units: $
Definition: Gross_profit-Interest-Depreciation
Nodelocation: 164,167
Nodesize: 44,20
Reformval: [Month, Time ]

Variable Nopat
Title: Net Operating Profit After Tax
Units: $
Definition: Operating_profit-Tax_provision
Nodelocation: 284,167
Nodesize: 44,24

Variable Operating_cash_flow
Title: Operating Cash Flow
Definition: Nopat+Depreciation
Nodelocation: 284,231
Nodesize: 44,20

Variable Free_cash_flow
Title: Free Cash Flow
Units: $
Definition: (Operating_cash_flow-Principal)
Nodelocation: 280,288
Nodesize: 44,20
Valuestate: 1,8,44,814,570,0,MIDM
Reformval: [Month, Time ]

Constant Interest_rate1
Title: Interest Rate
Units: %/Year
Definition: 8%
Nodelocation: 56,104,0
Nodesize: 44,20
Aliases: Formnode Interest_rate2

Close Pro_forma_module

Module Expense_module
Title: Expense Module
Author: rbrown
Date: Mon, Jul 6, 1998 1:03 PM
Defaultsize: 48,24
Nodelocation: 188,137,0
Nodesize: 44,20
Diagstate: 1,1,4,293,183,17

Variable Expenses
Title: Expenses
Units: $
Definition: Expense_rate*Subscribers
Nodelocation: 120,96
Nodesize: 44,20
Windstate: 1,310,122
Valuestate: 1,8,44,814,570,1,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:2~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:60~
Yminimum:0~
Ymaximum:300K~
Zminimum:12~
Zmaximum:30~
Xintervals:12~
Yintervals:10~
Includexzero:0~
Includeyzero:1~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Month, Rollout_time ]

Variable Expense_rate
Title: Expense Rate
Units: $/Subscriber
Definition: 20/S_curve1(0.01,Month,Rollout_time)
Nodelocation: 120,40
Nodesize: 44,20
Valuestate: 1,8,44,814,570,1,MIDM
Graphsetup: Graphtool:0~
Distresol:10~
Diststeps:1~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Linestyle:5~
Frame:1~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:0~
Xmaximum:60~
Yminimum:0~
Ymaximum:2000~
Zminimum:12~
Zmaximum:30~
Xintervals:12~
Yintervals:10~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1, 1, 1, 1, 1, 0, 0, 0]~
Probindex:[5%, 25%, 50%, 75%, 95%]~

Reformval: [Month, Rollout_time ]

Close Expense_module

Close Model_details

Decision Please_read
Title: Please Read
Description: The purpose of this model is to determine the amount of ~~
revenue needed on a monthly basis from each subscriber of a service t~~
o just meet the weighted average cost of capital of the firm from the~~
 service release date to the end of the Study Horizon.  In other word~~
s, it calculates the monthly unit revenue rate required from each sub~~
scriber of a service to give a return on investment at the end of the~~
 Study Horizon that is equal to the weighted average cost of capital ~~
of the firm.  This problem is trivial when the net cash flow, as well~~
 as the number of subscribers, is constant over time and the time val~~
ue of money is disregarded.  The solution is merely Net_Cash_Flow/Sub~~
scribers.  However, in the general case where the number of subscribe~~
rs and the net cash flow is time variant and the time value of money ~~
is worth consideration, an iterative method must be employed that beg~~
ins with an initial estimate and converges on a solution by the succe~~
ssive addition of residual errors.~
~
As a test case, this model depicts a scenario in which a service is r~~
olled out to a marketplace that generates a perpetuity revenue from e~~
ach subscriber (e.g., a cable TV operator charges each subscriber ~$3~~
0.00/Subscriber/Month regardless of how many customers are in the sys~~
tem).  The service penetration ramps up over the Roll Out Time in an ~~
s-curve fashion until 99% of the Rollout Penetration is achieved.  Su~~
bsequently, the number of subscribers grows exponentially until the e~~
xpected Final Penetration is reached at the end of the Study Horizon.~~
~
~
The Expenses are modeled with an initial investment at Month=0 and a ~~
perpetuity throughout the life of the model.  For simplicity's sake, ~~
the expenses as a perpetuity are intended to include all costs of ser~~
vices sold, tax, and any other cash expenses.~
~
The required revenue rate is determined by an iterative process.  The~~
 initial required revenue rate is assumed to be zero.  Thus, the requ~~
ired revenue rate determined by the first iteration represents the fi~~
rst estimate of how much revenue is required from each subscriber on ~~
a monthly basis to meet the expected ROI over the Study Horizon.  How~~
ever, this estimate may be too high or too low to meet the ROI.  Ther~~
efore, this value added to the original estimate is cycled back throu~~
gh the model to calculate the error of the previous estimate.  Of cou~~
rse, this error estimate also has an error associated with it.  Again~~
 the error is cycled back through with each successive iteration unti~~
l the error is considerably small.  This successive addition of initi~~
al estimate and residual error eventually converges on the Revenue Ra~~
te that gives the expected ROI.  The number of iterations required mu~~
st be determined by trial and error~
~
The solution method is to calculate the present worth of the cash flo~~
ws over the Study Horizon for each iteration.  The present worth is c~~
onverted into an equivalent period perpetuity.  The perpetuity, repre~~
senting the constant amount of revenue needed each month to meet the ~~
expected ROI, is divided by the number of subscribers to determine th~~
e monthly unit required revenue rate.  However, this result is hyperb~~
olic in shape because the number of Subscribers (the denominator) is ~~
increasing with each month against the equivalent period perpetuity (~~
the numerator).  The correct solutiuon, then, is represented by the w~~
eighted average (the centroid) of this curve.  The weighted average d~~
etermined after the first iteration represents the initial required r~~
evenue rate estimate.  Each successive weighted average represents th~~
e residual error of each iteration.~
~
A final note: The index representing time in the model is named "Mont~~
h."  The System Variable "Time" is used as the index for the iteratio~~
ns.
Definition: 0
Nodelocation: 456,112,1
Nodesize: 48,24
Nodeinfo: 1,1,1,1,1,1,1,,0,
Windstate: 1,8,44
Nodecolor: -1,32766,1
Nodefont: Arial, 13

Formnode Rollout1
Title: Rollout
Definition: 0
Nodelocation: 184,74
Nodesize: 176,14
Original: Rollout_time

Formnode Potential_penetrati1
Title: Potential Penetration
Definition: 0
Nodelocation: 184,129
Nodesize: 176,14
Original: Rollout_penetration

Formnode Serving_area1
Title: Serving Area
Definition: 0
Nodelocation: 184,101
Nodesize: 176,14
Original: Market_size

Formnode Final_penetration1
Title: Final Penetration
Definition: 0
Nodelocation: 184,157
Nodesize: 176,14
Original: Final_penetration

Formnode Discount_rate2
Title: Discount Rate
Definition: 0
Nodelocation: 184,264,1
Nodesize: 176,16
Original: Wacc1

Formnode Study_horizon2
Title: Study Horizon
Definition: 0
Nodelocation: 184,20
Nodesize: 176,14
Original: Study_horizon

Formnode Number_of_iteration1
Title: Number of Iterations
Definition: 0
Nodelocation: 184,47
Nodesize: 176,14
Original: Number_of_iterations

Formnode Revenue_rate1
Title: Revenue Rate
Definition: 1
Nodelocation: 185,321
Nodesize: 176,14
Nodecolor: -1,1,1
Original: Revenue_rate2

Formnode Cash_flow2
Title: Cash Flow
Definition: 1
Nodelocation: 185,294
Nodesize: 176,14
Nodecolor: -1,1,1
Original: Free_cash_flow1

Formnode Capital_requirement1
Title: Capital Requirement
Definition: 0
Nodelocation: 184,239
Nodesize: 176,14
Original: Capital_requirement

Formnode Interest_rate2
Title: Interest Rate
Definition: 0
Nodelocation: 184,212
Nodesize: 176,14
Original: Interest_rate1

Formnode Tax_rate1
Title: Tax Rate
Definition: 0
Nodelocation: 184,185
Nodesize: 176,14
Original: Tax_rate

Close Pricing_model