{ From user Fred, Model Rentvsbuy at 18-Jun-2013 6:15:36 AM, encoding="UTF-8" }
SoftwareVersion 4.5.0


{ System Variables with non-default values: }
Time := Sequence(1,Years,1)
DistribSize := 30
TypeChecking := 1
Checking := 1
SaveOptions := 2
SaveValues := 0
{!40000|Att_CatLineStyle Graph_Stats_Valdim: 9}
{!40000|Att_ContLineStyle Graph_Pdf_Valdim: 6}
{!40000|Att_ContLineStyle Graph_Cdf_Valdim: 1}
{!40300|Sys_DomainSelfIndex := 1}
{!40400|Sys_PdfSmoothMethod := 1}


{!-40203|Attribute CloudPlayerStyles}
Attribute Reference
Attribute Date_bough


Model Rentvsbuy
Title: Rent vs. Buy
Description: Financial model comparing the Net Present Value of renting vs. buying a house.~
~
This model uses cash flow conventions:  a node with a negative value means the cash is flowing out (being spent), while a node with a positive value means the cash is flowing in (being received).~
~
The most important variables, to be tailored to your situation, are:~
*  Buying price  ($140,000)~
*  Rate of inflation (normal distribution with mean of 3.5% and standard deviation of 1.3%)~
*  Nominal rate of appreciation (normal distribution with mean of the rate of inflation and standard~
                 deviation of 3%)~
*  Nominal discount rate (6%)~
*  Time horizon (10 years)~
*  Monthly rent ($1200, in the Cost to Rent Module)~
*  Mortgage interest rate (9.5% fixed, in the Cost to Buy Module)~

Author: Max Henrion
Date: Wed, Jun 6, 1990 12:38 AM
SaveAuthor: Fred
SaveDate: Tue, Jun 18, 2013 6:15 AM
DefaultSize: 52,20
DiagState: 2,43,54,576,246,1
NodeColor: -1,-6554,-19660
DiagramColor: 32348,-9825,-8739
FontStyle: Helvetica, 12
FileInfo: 0,Model Rentvsbuy,2,2,0,0,C:\aatemp\Rent.ana
{!40400|Att_clearTypeFonts: -1}

Module Model1
Title: Model
Description: This node contains the detailed structure of the Rent vs. Buy Model.
Author: George Ferguson
Date: Sat, Dec 30, 1995 11:00 PM
DefaultSize: 48,24
NodeLocation: 280,160
NodeSize: 52,20
DiagState: 2,14,12,449,294,17

Decision Price
Title: Buying price
Units: $
Description: Buying price of house.
Definition: 140K
NodeLocation: 72,40
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
Aliases: FormNode Buying_price
NodeColor: -26215,-1,-16110

Variable Years
Title: Time horizon
Units: years
Description: Length of time from buying to selling (or time horizon for this analysis).~
Note this must be an integer.
Definition: 10
NodeLocation: 216,176
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
Aliases: FormNode Time_horizon
NodeColor: 4658,-14548,-1
DisplayOutputs: Variable Pv_rent

Objective Pv_total_cost
Title: Present value of buying and renting
Units: $
Description: This node compares the net present value of the cost of buying to the net present value of the cost of renting.  A negative value denotes a cost.
Definition: Table(Buy_or_rent)(PV_buy,Pv_rent)
NodeLocation: 360,152,1
NodeSize: 56,24
NodeInfo: 1,1,1,1,1,1,0
WindState: 2,413,75,515,300
DefnState: 1,92,149,423,138,0,MIDM
ValueState: 2,139,99,509,354,1,PDFP
Aliases: FormNode Total_cost_of_buying
NodeColor: -1,-25694,-23186
ReformVal: [Buy_or_rent,Buy_or_rent,Undefined,2,1]
DisplayOutputs: Variable Difference

Variable Discount
Title: Discount rate
Units: %/year
Description: Discount rate for converting a future cash flow into a single value (present value). The discount rate represents the values of the buyer at the present time.
Definition: 6
NodeLocation: 72,176
NodeSize: 48,20
NodeInfo: 1,0,1,1,1,1,0
Aliases: Alias Al2, FormNode Nominal_discount_rat
NodeColor: 4658,-14548,-1

Chance Appreciation
Title: Appreciation rate
Units: %/year
Description: Average annual percent rate of appreciation (including inflation) over the ownership period.
Definition: Normal( Inflation, 3 )
NodeLocation: 216,40
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,200,60
ValueState: 1,167,98,420,231,1,PDFP
Aliases: FormNode Nominal_rate_of_appr
NodeColor: 20492,-6282,-1
NumberFormat: 1,D,4,0,0,0

Decision Buy_or_rent
{!40000|Att_PrevIndexValue: ['Buy','Rent']}
Title: Buy or rent
Description: This is the decision to buy or rent.
Definition: ['Buy','Rent']
NodeLocation: 360,40
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,152,162,416,303,0,MIDM
NodeColor: -26215,-1,-16110

Chance Inflation
Title: Rate of inflation
Units: %/year
Description: Average rate of inflation over the ownership period, or time horizon.
Definition: Normal( 3.5, 1.3 )
NodeLocation: 72,104
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,133,151
ValueState: 1,72,82,416,303,1,PDFP
Aliases: FormNode Rate_of_inflation
NodeColor: 20492,-6282,-1

Module Buy
Title: Cost to Buy
Description: This module contains the costs of buying and owning a house over the time period.
Author: korsan
Date: Wed, Feb 8, 1995 11:39 AM
DefaultSize: 48,24
NodeLocation: 216,104
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0,,0,,0
DiagState: 2,71,32,476,311,1
NodeColor: -1,-10283,-21468
{!40400|CloudPlayerStyles: show_object: no}
{!40204-40399|AWP_Attrib:show_object: no}

Variable Downpaymt
Title: Down~
payment
Units: $
Description: Down payment amount at time of purchase.
Definition: (-Percent_down_payment/100)*Price
NodeLocation: 72,176
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0,,0
WindState: 1,59,219
ValueState: 1,40,50,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Mortgage
Title: Mortgage loan amount
Units: $
Description: Total mortgage (loan) amount received.
Definition: Price + DownPaymt
NodeLocation: 72,104
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,136,146,334,256,0,MIDM
NodeColor: 4658,-14548,-1

Module Pv_ownership_cost
Title: Out-of-pocket costs to own
Description: Annual costs, such as mortgage payments, taxes, insurance and maintenance.
Author: M.H.
Date: Wed, Sep 26, 1990 11:30 PM
SaveAuthor: henrion
SaveDate: Tue, Oct 16, 1990 4:04 PM
DefaultSize: 48,24
NodeLocation: 216,104
NodeSize: 52,20
DiagState: 1,42,93,586,294,1
NodeColor: -1,-6554,-19660
FontStyle: Helvetica, 12

Chance Taxrate
Title: Marginal~
tax rate
Units: %
Description: Marginal tax rate including federal and state taxes.  Assumes top brackets, ignoring exclusion of deductions.~
~
Uncertainty about possible changes in Federal and/or state taxes, of plus or minus 2%.
Definition: 33%+9%+Normal(0,2%)
NodeLocation: 72,104
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,136,146,416,303,1,PDFP
NodeColor: 20492,-6282,-1

Variable Payments
Title: Mortgage~
payments
Units: $/year
Description: Annual payments on mortgage (interest plus principal).  Assumes fixed rate mortgage, over 30 years; equal payments at the end of each month.
Definition: 12*Pmt(Mort_rate/1200,360,Mortgage)
NodeLocation: 216,40
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,97,84
ValueState: 1,88,98,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Tax_red
Title: Reduction in income taxes
Units: $/year
Description: Annual reduction in income taxes due to deductibility of interest payments.
Definition: -Taxrate*(Interest_pay+Property_tax)
NodeLocation: 216,104
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,186,479
ValueState: 1,72,82,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Ann_cash_flow
Title: Cash flow of ownership
Units: $
Description: A table of the annual cash flow related to ownership, including mortgage payments, property taxes, maintenance, and insurance, less tax deductions.
Definition: Payments+Property_tax+Insurance+Maintenance+Tax_red
NodeLocation: 360,104,1
NodeSize: 48,24
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,40,50
ValueState: 1,120,130,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Interest_pay
Title: Interest~
payments
Units: $/year
Description: A table of the annual payments of interest, indexed by year.
Definition: For x = Time Do Cumipmt(Mort_rate/1200,360,Mortgage,12*x-11,12*x)
NodeLocation: 72,40
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,92,122
ValueState: 1,152,162,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Property_tax
Title: Property~
taxes
Units: $/year
Description: Annual property taxes.  Assumes state tax of 1%  plus 0.15% local taxes., growing at the rate of inflation.
Definition: -((1+Inflation/100)^Time)*Price*1.5%
NodeLocation: 72,168
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,104,114,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Chance Maintenance
Title: Maintenance
Units: $/year
Description: Annual maintenance costs for the house (no improvements).  Assumes a normal distribution with median at 1% of purchase price, growing with inflation.
Definition: -((1+Inflation/100)^Time)*Normal(1%*Price, .5%*Price)
NodeLocation: 216,232
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,136,146,416,303,0,MIDM
NodeColor: 20492,-6282,-1
DisplayInputs: Chance Maintenance1

Chance Insurance
Title: Insurance
Units: $/year
Description: Annual cost of insuring the house.  Assumes cost of house is 50% of original price, and insurance is 0.3%, growing at the rate of inflation.
Definition: -((1+Inflation/100)^Time)*Price*50%*Lognormal(.3%, 1.5)
NodeLocation: 72,232
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,152,162,416,303,0,MIDM
NodeColor: 20492,-6282,-1
ReformVal: [Time,ProbIndex]

Variable Pv_own
Title: Present value of ownership
Description: Present value of the cash flow stream of ownership costs
Definition: Npv(Discount/100,Ann_cash_flow,Time)
NodeLocation: 512,104,1
NodeSize: 48,24
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,152,162,416,303,0,PDFP
NodeColor: 4658,-14548,-1

Close Pv_ownership_cost

Variable Mort_rate
Title: Mortgage interest rate
Units: %/year
Description: Annual interest rate on mortgage.
Definition: 9.5
NodeLocation: 216,32
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,1325,86
ValueState: 1,88,282,371,190,0,MIDM
Aliases: FormNode Mortgage_interest_ra
NodeColor: 4658,-14548,-1

Module Pv_sales_proceeds
Title: Future sales proceeds
Author: M.H.
Date: Fri, Jan 1, 1904 10:39 AM
SaveAuthor: henrion
SaveDate: Thu, Oct 18, 1990 3:29 PM
DefaultSize: 48,24
NodeLocation: 216,184
NodeSize: 52,20
DiagState: 1,121,136,461,259,1
NodeColor: -1,-6554,-19660
FontStyle: Helvetica, 12

Variable Princ_pay
Title: Principal payments made on mortgage
Units: $/year
Description: A table of the annual payments of principal, indexed by year.
Definition: For x = Time Do Cumprinc(Mort_rate/1200,360,Mortgage,12*x-11,12*x)
NodeLocation: 72,184
NodeSize: 56,28
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,136,146,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Profit
Title: Net sales proceeds
Units: $K
Description: Net proceeds from selling the house at the end of the period of ownership.  Equal to selling price less selling costs and mortgage principal remaining.
Definition: Sell_price+Selling_cost-End_mortgage
NodeLocation: 216,112
NodeSize: 56,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,88,98,416,303,0,PDFP
NodeColor: 4658,-14548,-1

Variable Sell_price
Title: Selling  price
Units: $
Description: Sales price, equal to purchase price times compounded average annual appreciation.
Definition: Price * (1+Appreciation/100)^Years
NodeLocation: 72,112
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,88,98
ValueState: 1,88,98,416,303,1,PDFP
NodeColor: 4658,-14548,-1

Variable End_mortgage
Title: Mortgage principal remaining
Units: $
Description: Outstanding mortgage at selling time.
Definition: Mortgage + Sum(Princ_pay, Time)
NodeLocation: 216,184
NodeSize: 56,28
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,56,66,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Selling_cost
Title: Selling costs
Units: $
Description: Cost of selling the house. Assumes 6% commission to agent + 1% "fix-up" and owner's closing costs.~
~
Note that negative denotes cost.
Definition: -7%  * Sell_price
NodeLocation: 144,40
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,104,114,416,303,1,PDFP
NodeColor: 4658,-14548,-1

Variable Pv_sale
Title: Present value of sale
Units: $
Description: Present value of the sales proceeds.
Definition: Profit/(1+Discount/100)^Years
NodeLocation: 360,112
NodeSize: 56,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,88,98,416,303,0,PDFP
NodeColor: 4658,-14548,-1

Close Pv_sales_proceeds

Module Opportunity_cost
Title: Opportunity cost
Author: korsan
Date: Fri, Feb 3, 1995 4:21 PM
DefaultSize: 48,24
NodeLocation: 216,248
NodeSize: 52,20
DiagState: 1,62,147,473,221,1
NodeColor: -1,-6554,-19660

Variable Foregone_interest
Title: Foregone interest on down payment
Units: $
Description: Foregone posttax interest that could have been earned from investing the down payment and moving costs at the savings interest rate; "opportunity cost".
Definition: (DownPaymt+Moving_costs)*(((1+ Interest_dep/100)^Years)- 1)
NodeLocation: 216,72
NodeSize: 52,28
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,104,114,416,303,1,PDFP
NodeColor: 4658,-14548,-1

Variable Interest_dep
Title: Savings interest rate
Units: %/year
Description: Post-tax interest rate available on the down payment if it were invested elsewhere, e.g. in a CD, or municipal bond.  Assumed equal to the rate of inflation.
Definition: Inflation
NodeLocation: 80,72
NodeSize: 52,28
NodeInfo: 1,1,1,1,1,1,0
NodeColor: 4658,-14548,-1

Variable Pv_forgone_interest
Title: Present value of foregone interest
Description: Present value of the interest that could be earned on the down payment, if it were invested instead.
Definition: Foregone_interest/(1+Discount/100)^Years
NodeLocation: 360,72
NodeSize: 52,28
NodeInfo: 1,1,1,1,1,1,0
WindState: 1,151,196
ValueState: 1,104,114,416,303,1,PDFP
NodeColor: 4658,-14548,-1
NumberFormat: 1,D,3,2,0,0

Alias Al2
Title: Discount rate
Definition: 1
NodeLocation: 216,152
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
NodeColor: 4658,-14548,-1
Original: Discount

Close Opportunity_cost

Variable PV_buy
Title: Present value of buying
Units: $
Description: Total present value of the cash flow related to buying, including the down payment, annual out-of-pocket costs, proceeds of future sale, and forgone interest on the down payment (opportunity cost).
Definition: Pv_own+Pv_sale+Pv_forgone_interest+Downpaymt+Moving_costs
NodeLocation: 360,104,1
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 2,163,91,459,304,1,PDFP
NodeColor: 4658,-14548,-1

Variable Moving_costs
Title: Moving costs
Units: $
Description: Moving, move-in, and cash closing costs.  Assumed to be 1.5% of the Buying price.
Definition: -1.5%*Price
NodeLocation: 360,248
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
ValueState: 1,152,162,416,303,0,MIDM
NodeColor: 4658,-14548,-1

Variable Percent_down_payment
Title: Percent down payment
Units: %
Description: The percent down payment the buyer chooses to make on her house.~
Note units are in percent.
Definition: 20
NodeLocation: 72,248
NodeSize: 52,20
WindState: 1,147,197
Aliases: FormNode Percent_down_paymen1
NodeColor: 0,-13108,-1

Close Buy

Module Renting
Title: Cost to Rent
Description: This module contains the cost of renting over the time period.
Author: korsan
Date: Wed, Feb 8, 1995 11:39 AM
DefaultSize: 52,20
NodeLocation: 216,248
NodeSize: 48,20
NodeInfo: 1,1,1,1,1,1,0
DiagState: 2,60,99,467,144,3
NodeColor: -1,-10283,-21468

Variable Rent
Title: Cash flow of rental costs
Units: $/year
Description: A table of the cost to rent, indexed by time.  Rental cost is assumed to grow over time at the rate of inflation.
Definition: Monthly_rent*12*(1 + Inflation/100)^Time
NodeLocation: 224,64
NodeSize: 52,20
NodeInfo: 1,1,1,1,1,1,0,,0
ValueState: 1,104,114,416,303,1,PDFP
NodeColor: -19660,-9830,-1
DisplayOutputs: Objective Net_diff
{!40400|CloudPlayerStyles: show_object:no}
{!40204-40399|AWP_Attrib:show_object:no}

Variable Pv_rent
Title: Present value to rent
Description: The present value of the cash flow of the monthly rental payments over the time horizon.
Definition: -Npv(Discount/100,Rent,Time)
NodeLocation: 368,64,1
NodeSize: 56,20
WindState: 2,227,319,464,300
ValueState: 1,52,92,432,307,1,PDFP
NodeColor: -19660,-9830,-1

Variable Monthly_rent
Title: Monthly rent
Units: $
Description: Monthly rental cost at the start of the time period.
Definition: 1200
NodeLocation: 80,64
NodeSize: 52,20
ValueState: 1,136,146,416,303,0,MIDM
Aliases: FormNode Monthly_rent1
NodeColor: -19660,-9830,-1

Close Renting

Close Model1

FormNode Nominal_discount_rat
Title: Nominal discount rate
Definition: 0
NodeLocation: 136,48
NodeSize: 136,20
NodeColor: 13107,-13108,-1
Original: Discount

FormNode Rate_of_inflation
Title: Rate of inflation
Definition: 0
NodeLocation: 136,72
NodeSize: 136,20
NodeColor: 13107,-13108,-1
Original: Inflation

FormNode Buying_price
Title: Buying price
Definition: 0
NodeLocation: 424,24
NodeSize: 144,12
NodeColor: 26214,-1,-13108
Original: Price

FormNode Time_horizon
Title: Time horizon
Definition: 0
NodeLocation: 136,24
NodeSize: 136,12
NodeColor: 4658,-14548,-1
Original: Years

FormNode Nominal_rate_of_appr
Title: Nominal rate of appreciation
Definition: 0
NodeLocation: 424,112
NodeSize: 144,20
NodeColor: 26214,-1,-13108
Original: Appreciation

FormNode Total_cost_of_buying
Title: Total cost of buying or renting
Definition: 1
NodeLocation: 296,204,1
NodeSize: 168,12
NodeColor: -1,-25694,-23186
Original: Pv_total_cost

FormNode Mortgage_interest_ra
Title: Mortgage interest rate
Definition: 0
NodeLocation: 424,72
NodeSize: 144,20
NodeColor: 26214,-1,-13108
Original: Mort_rate

FormNode Monthly_rent1
Title: Monthly Rent
Definition: 0
NodeLocation: 136,112
NodeSize: 136,20
NodeColor: -19660,-9830,-1
Original: Monthly_rent

FormNode Percent_down_paymen1
Title: Percent Down Payment
Definition: 0
NodeLocation: 424,48
NodeSize: 144,20
NodeColor: 26214,-1,-13108
Original: Percent_down_payment

Close Rentvsbuy