Housing model simulation to help me decide if we should buy or not...

ted_housing_model.R

### Define terms to understand investment potentional
### This function will simulate scenarios to compare renting to buying and allow us to make an informed financial decision
## Parameters of the model (some are hard coded but can still be changed)
## r - Annual appreciation rate
## term - Term you want to own the house for (in months)
## house_cos - cost of the house in dollars
## ir - Interest rate of my mortgage
## closing - total closing costs
## sr - cost of selling the house, expressed as a percentage that will be paid in comission
## aou - Amount over/under for final sale (on top of annual appreciation rate, gets a bit confusing so best to set to 0)
## rinvest - Amount of annual appreciation of an investment expressed as a percentage
## tax_penalty - how much annually will I save in taxes if I buy instead of rent, essentially an annual penalty for renting
housing_comp <- function(r = 0.04, 
                         term = 100,
                         house_cost = 1000000,
                         closing = 13000,
                         ir = 3.375,
                         sr = 0.055,
                         aou = 0,
                         rinvest = 0.05,
                         savings_rate = 0.9,
                         tax_penalty = 10000){
  
  ### Set the property tax rate
  prop_tax_rate <- .0125
  ### Set monthly taxes
  monthly_taxes <- (prop_tax_rate * house_cost) / 12
  ### Loan principal
  principal <- .8*house_cost
  val <- house_cost
  ### My downpayment
  mydp <- .1*house_cost
  
  
  for(x in 1:term){
    val <- val*(1+(r/12))
  }
  
  ### Calculate the amount of principal you have in the home
  mort <- mortgage(principal,ir)
  ## principal paid
  ppaid <- sum(mort$Monthly_Principal[1:term])
  ## interest paid
  ipaid <- sum(mort$Monthly_Interest[1:term])
  
  sold_amount <- (1+aou)*val
  
  ### Calculate the total costs of buying the house (closing and selling costs)
  costs <- ((sold_amount*sr) + closing)
  ### calculate the total profit
  profit <- sold_amount - house_cost
  
  ### Calculate landed cut
  to_landed <- (.1*house_cost)+(.25*profit)
  ### How much the bank takes back
  to_bank <- principal - ppaid
  ### Calculate my profit
  my_profit <- sold_amount - (to_bank + to_landed + costs)
  ### Calculate a simple ROI
  roi <- (my_profit / mydp) - 1
  
  
  ### Add in some benchmarks
  ### What was my rent
  rent<- 3250*term
  
  ### Here I'll calculate how much I'm going to save if I keep renting
  ## Set a savings rate (fraction of the difference between mortage and rent that we'd likely save instead of blowing on travel or amazon)
  savings_rate <- .9
  ### Set what my all in monthly payment would be (taxes, mortagage, insurance)
  monthly_mortgage_pay <- monthly_taxes + mort[1,2] + (.00022* house_cost)
  
  monthly_savings <- (monthly_mortgage_pay - 3250) * savings_rate
  
  ### How much I could theoretically have invented initially
  invest <- mydp + closing
  
  ### Calculate my investment potential savings
  for(x in 1:term){
    invest <- (invest*(1+(rinvest/12)) ) + monthly_savings
  }
  
  cat("costs: ", costs,"\n")
  cat("total profit: ",profit,"\n")
  cat("to bank: ",to_bank,"\n")
  cat("to landed: ",to_landed,"\n")
  cat("my profit: ",my_profit,"\n")
  cat("my house roi: ",roi,"\n")
  cat("my investment: ",invest,"\n")
  #cat("my investment roi: ", (invest / (mydp+closing)) - 1 )
  cat("my rent costs: ", rent,"\n")
  cat("my interest: ", ipaid,"\n")
  ### Term for tax savings thrown in to the rent
  total_cost_living_own <- my_profit - ((monthly_taxes*term) + ipaid)
  total_cost_living_rent <- invest - (rent + ((tax_penalty/12) * term))
  
  cat("Owning total cost of living for ",term,"months: ", total_cost_living_own,"\n")
  cat("Renting total cost of living for ",term,"months: ", total_cost_living_rent,"\n")
  
  ### Now how much money will I have when I walk away?
  cat("If I buy I'll have ", my_profit, " after livining in my own house for ",(term/12), " years \n")
  cat("If I rent I'll have ", invest, " after livining in a rented house for ",(term/12), " years \n")
  
  out <- list("own cost" = total_cost_living_own, "rent cost" = total_cost_living_rent, "my profit" = my_profit, "own roi" = roi)
  
  return(out)
}

### Function to calculate basic mortage payment in the US

## P = principal, the initial amount of the loan
## I = the annual interest rate (from 1 to 100 percent)
## L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.

mortgage <- function(P=500000, I=6, L=30, amort=T) { 
  J <- I/(12 * 100)
  N <- 12 * L
  M <- P*J/(1-(1+J)^(-N))
  monthPay <<- M
  
  # Calculate Amortization for each Month
  if(amort==T) {
    Pt <- P # current principal or amount of the loan
    currP <- NULL
    while(Pt>=0) {
      H <- Pt * J # this is the current monthly interest
      C <- M - H # this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for that month
      Q <- Pt - C # this is the new balance of your principal of your loan
      Pt <- Q # sets P equal to Q and goes back to step 1. The loop continues until the value Q (and hence P) goes to zero
      currP <- c(currP, Pt)
    }
    monthP <- c(P, currP[1:(length(currP)-1)])-currP
    aDFmonth <<- data.frame(
      Amortization=c(P, currP[1:(length(currP)-1)]), 
      Monthly_Payment=monthP+c((monthPay-monthP)[1:(length(monthP)-1)],0),
      Monthly_Principal=monthP, 
      Monthly_Interest=c((monthPay-monthP)[1:(length(monthP)-1)],0), 
      Year=sort(rep(1:ceiling(N/12), 12))[1:length(monthP)]
    )
    aDFyear <- data.frame(
      Amortization=tapply(aDFmonth$Amortization, aDFmonth$Year, max), 
      Annual_Payment=tapply(aDFmonth$Monthly_Payment, aDFmonth$Year, sum), 
      Annual_Principal=tapply(aDFmonth$Monthly_Principal, aDFmonth$Year, sum), 
      Annual_Interest=tapply(aDFmonth$Monthly_Interest, aDFmonth$Year, sum), 
      Year=as.vector(na.omit(unique(aDFmonth$Year)))
    )
    aDFyear <- aDFyear
  }
  
  return(aDFmonth)
}


### Now lets make some plots
library(ggplot2)
term <- 1:100

r = c(.01,.02,.03,.04,.05)
rinvest = c(.02,.04,.06,.08,.1)
out_mat <- matrix(ncol=5, nrow=0)

### buying is flagged as 1
### renting is flagged as 0 just so I can use a matrix
### format is cost, term , r , rinvest, own_flag
for(i in term){
  for(j in 1:length(r)){
    for(k in 1:length(rinvest)){
      
      temp_est <- housing_comp(r=r[j], rinvest= rinvest[k], term = i, house_cost = 750000)
      out_mat <- rbind(out_mat, c(temp_est$`own cost`,r[j],rinvest[k],i,1 ))
      out_mat <- rbind(out_mat, c(temp_est$`rent cost`,r[j],rinvest[k],i,0 ))
      
      
    }
    
  }
  
  
}


out_df <- data.frame(out_mat)
colnames(out_df)<- c('cost', 'r' , 'rinvest', 'term' , 'own_flag')
out_df$own_flag <- replace(out_df$own_flag, out_df$own_flag == 1,"Buy")
out_df$own_flag <- replace(out_df$own_flag, out_df$own_flag == 0,"Rent")

ggplot(out_df,aes(x = term,y=cost, group = own_flag, colour=own_flag)) + facet_grid(r~rinvest)+ geom_path()