#!/usr/bin/perl -w

use strict;

# Inputs: 
# ./tax_lien_monte_cristo.pl <number liens> <average lien price> <premium %>
#
# e.g.
# ./tax_lien_monte_cristo 10 1500 7 for 10 liens at a premium of 7% at $1500 each.  
# Price should not include premiums.

if (@ARGV != 4)
{
	print "Usage: <number liens> <average lien price> <premium %> <iterations>\n"; 
	exit;
}
my $num_liens = shift @ARGV;
my $price = shift @ARGV;
my $premium = shift @ARGV;
my $meta_iterations = shift @ARGV;

# print "Using $num_liens liens at an average price of $price; assuming a premium of $premium%\n";
# print "Landing a house assumes a return of 15x on the lien amount.\n\n";

# This is the per-month interest.
my $interest = 0.0083;

# Each bucket is expressed in terms of (month, percentage).  The stimulation picks a percentage 
# and then picks a month that is less than the percentage but not less than the month preceding it.

my $buckets = [
[ 1, 2.6393 ], 
[ 2, 6.039 ], 
[ 3, 9.3749 ], 
[ 4, 12.647 ], 
[ 5, 15.8553 ], 
[ 6, 18.9998 ], 
[ 7, 22.0805 ], 
[ 8, 25.0974 ], 
[ 9, 28.0505 ], 
[ 10, 30.9398 ], 
[ 11, 33.7653 ], 
[ 12, 36.527 ], 
[ 13, 39.2249 ], 
[ 14, 41.859 ], 
[ 15, 44.4293 ], 
[ 16, 46.9358 ], 
[ 17, 49.3785 ], 
[ 18, 51.7574 ], 
[ 19, 54.0725 ], 
[ 20, 56.3238 ], 
[ 21, 58.5113 ], 
[ 22, 60.635 ], 
[ 23, 62.6949 ], 
[ 24, 64.691 ], 
[ 25, 66.6233 ], 
[ 26, 68.4918 ], 
[ 27, 70.2965 ], 
[ 28, 72.0374 ], 
[ 29, 73.7145 ], 
[ 30, 75.3278 ], 
[ 31, 76.8773 ], 
[ 32, 78.363 ], 
[ 33, 79.7849 ], 
[ 34, 81.143 ], 
[ 35, 82.4373 ], 
[ 36, 83.6678 ], 
[ 37, 84.8345 ], 
[ 38, 85.9374 ], 
[ 39, 86.9765 ], 
[ 40, 87.9518 ], 
];

my $results = {};
	
for (my $meta_iter = 0; $meta_iter < $meta_iterations; $meta_iter+=1)
{
	
	my $subtax = 0;
    my $total_profit = 0.0;
    my $iteration = 1;
    my $negative = 0;
    my $premium_amount = $price * ($premium / 100.0);
    my $total_principal = $premium_amount * $num_liens;
    my $houses = 0;
    
    for (my $x = 0; $x < $num_liens; $x+=1)
    {
        my $percent = rand(100);
        my $prior = 0.0;
        my $month = 0;
        foreach my $bucket (@$buckets)
        {
        	$month = $bucket->[0];
        	if ($percent > $prior && $percent <= $bucket->[1])
        	{
        		#print "Iteration $iteration fits month $month; got $percent\n";
        		last;
        	}
        	$prior = $bucket->[1];
        }
        
        my $house = $month == @$buckets;
        
        my $principal = $price;                 # Principal to start with.  This gets added on to every subtax.
        my $total = $price;                     # Running total.
        my $profit = 0.0;
        
        unless ($house)
        {
        	# We don't have a house.  Calculate the profits here.  
        	my $monthly = $principal * $interest;   # Monthly accrual.  Increases with subtax.
        	for (my $i = 0; $i < $month; $i+=1)
        	{
        		# Time to subtax?
        		if ($i >= 10 && (($i - 10)%12)==0)
        		{
					$subtax += 1 if $i < 12;
					
        			# Principal gets the price added on.
        			$principal = $principal + $price;
        			
        			# Total increments by the price.
        			$total = $total + $price;
        			
        			# Monthly gets updated as a function of the total.
        			$monthly = $total * $interest;
        		}
        			
        		# Add onto the monthly.  
        		$total += $monthly; 
        	}
        	
        	# Now calculate the premium.  
        	$profit = $total - $principal - $premium_amount;
        	
        	my $premium_formatted = sprintf "%.2f", $premium_amount;
        	my $total_formatted = sprintf "%.2f", $total;
        	my $profit_formatted = sprintf "%.2f", $profit;
        	my $percent = $profit / $principal * 100;
        	my $percent_formatted = sprintf "%.2f", $percent;
    		$total_principal = $total_principal + $principal;
    		
    		$negative = $negative + 1 if ($profit < 0.0);		
    		$total_profit = $profit + $total_profit;
        
        	# print "Iteration $iteration: Took $month months; accumulated $total_formatted; profit $percent_formatted% after premium of $premium_formatted = $profit_formatted\n"; 
        }
        else
        {
    		$houses = $houses + 1;
        	$principal = $price * 3;
    		$total_principal = $total_principal + $principal;
    		
        	$total = $price * 15;
        	$profit = $price * 15.00;
    		$total_profit = $profit + $total_profit;
        	my $profit_formatted = sprintf "%.2f", $profit;
        	
        		# print "Iteration $iteration: Took 40 months; we foreclosed and got a 15x return of $profit_formatted\n";
        }
    	$iteration = $iteration + 1;
    }
    
    #print "\n";
    
    my $principal_formatted = sprintf "%.2f", $total_principal;
    my $profit_formatted = sprintf "%.2f", $total_profit;
    my $percent = $total_profit / $total_principal * 100;
    my $percent_formatted = sprintf "%.2f", $percent;
	my $result = {};
	$result->{profit} = $total_profit;
	$result->{percent} = $percent;
	$result->{houses} = $houses;
	$result->{negative} = $negative;
	$result->{principal} = $total_principal;
	$result->{subtax} = $subtax;
	$results->{$meta_iter} = $result;
    
    # print "For $num_liens liens, we had $negative liens with a negative return, got $houses houses, total outlay of \$$principal_formatted (including premiums and subtaxations) and made a profit of \$$profit_formatted or $percent_formatted%\n";
  
	#print "$meta_iter,$negative,$houses,$principal_formatted,$profit_formatted,$percent_formatted\n";
}

# Make averages.
my $avg_profit = 0.0;
my $avg_houses = 0.0;
my $avg_negative = 0.0;
my $avg_principal = 0.0;
my $lost_money = 0.0;
my $no_house_avg_profit = 0.0;
my $no_house_avg_principal = 0.0;
my $no_house_iter = 0.0;
my $lost_money_nh = 0.0;
my $avg_subtax = 0.0;

foreach my $result (values %$results)
{
	$lost_money += 1 if $result->{profit} < 0.0;
	
	$avg_profit += $result->{profit};
	$avg_houses += $result->{houses};
	$avg_negative += $result->{negative};
	$avg_principal += $result->{principal};
	$avg_subtax += $result->{subtax};
	
	next if $result->{houses};
	$no_house_iter += 1;
	$lost_money_nh += 1 if $result->{profit} < 0.0;
	$no_house_avg_principal += $result->{principal};
	$no_house_avg_profit += $result->{profit};
}


my $final_subtax = $avg_subtax / $meta_iterations;
my $final_subtax_pct = $final_subtax / $num_liens;
my $final_subtax_formatted = sprintf "%.2f", $final_subtax;
my $final_subtax_pct_formatted = sprintf "%.2f", $final_subtax_pct;


my $final_profit_nh = $no_house_iter > 0 ? $no_house_avg_profit / $no_house_iter : 0.0;
my $final_principal_nh = $no_house_iter > 0 ? $no_house_avg_principal / $no_house_iter : 0.0;
my $final_loss_nh = $no_house_iter > 0 ? $lost_money / $no_house_iter * 100 : 0.0;
my $percent_nh = $no_house_iter > 0 ? $final_profit_nh / $final_principal_nh * 100 : 0.0;

my $final_profit = $avg_profit / $meta_iterations;
my $final_houses = $avg_houses / $meta_iterations;
my $final_negative = $avg_negative / $meta_iterations;
my $final_loss = $lost_money / $meta_iterations * 100;
my $final_principal = $avg_principal / $meta_iterations;
my $no_house_iter_avg = $no_house_iter / $meta_iterations * 100;

my $percent = $final_profit / $final_principal * 100;
my $percent_formatted = sprintf "%.2f", $percent;
my $profit_formatted = sprintf "%.2f", $final_profit;
my $houses_formatted = sprintf "%.2f", $final_houses;
my $negative_formatted = sprintf "%.2f", $final_negative;
my $principal_formatted = sprintf "%.2f", $final_principal;
my $chance_loss = sprintf "%.2f", $final_loss;


my $principal_formatted_nh = sprintf "%.2f", $final_principal_nh;
my $percent_formatted_nh = sprintf "%.2f", $percent_nh;
my $profit_formatted_nh = sprintf "%.2f", $final_profit_nh;
my $chance_no_house = sprintf "%.2f", $no_house_iter_avg;
my $chance_loss_nh = sprintf "%.2f", $final_loss_nh;

print "Over $meta_iterations iterations:\n";
print "  Average outlay: \$$principal_formatted\n";
print "  Subtaxed the next year: $final_subtax_formatted Pct: $final_subtax_pct_formatted%\n";
print "  Average profit: \$$profit_formatted; $percent_formatted%\n";
print "  Number of losing iterations: $lost_money; $chance_loss%\n";
print "  Number of iterations without houses: $no_house_iter; $chance_no_house\%\n";
print "  Average outlay (no house only): \$$principal_formatted_nh\n";
print "  Average profit (no house only): \$$profit_formatted_nh; $percent_formatted_nh%\n";
print "  Number of losing iterations (no house only): $lost_money_nh; $chance_loss_nh%\n";