Change Excel Circular Dependency into PHP - php

Question

I deleted a question I posted earlier because I oversimplified the example, and got more flak for problems there, so have decided to post the whole problem here instead.
The Task
Much like this question here...Copying Excel's Circular Reference formula in PHP I am trying to change an Excel Circular reference into PHP.
Most of my frustration is not knowing the correct terms to google this for myself.
The Situation
I have converted all logic in the following spreadsheet into PHP below...
<?php
$vat = '1.2';
$mileage = 10;
$price = 6250.00;
$contract_term = 24;
$deposit_months = 6;
$otr_price = 9409.00;
$discount = 0;
$lom_a = 36.08;
$lom_b = 5.14;
$vehicletype = "Car";
$first_reg_fee = 55.00;
$emission_price = 30.00;
$fees = 21.03;
$margin = 50.00;
if (!empty($discount)) {
$discounted_otr_percent = (int)$discount/100;
$discounted_otr_amount = $discounted_otr_percent * $otr_price;
$discounted_otr = $otr_price-$discounted_otr_amount;
} else {
$discounted_otr = $otr_price;
}
$totaltobefunded = ($discounted_otr - $first_reg_fee - 0 /* Emissions */) / $vat;
print '<hr><p>Total to be Funded: <strong>' . $totaltobefunded . '</strong></p>';
$vatbal = $discounted_otr - $first_reg_fee - 0 /* Emissions */ - $totaltobefunded;
print '<p>VAT: <strong>' . $vatbal . '</strong></p>';
if($vehicletype == "Car") {
$balloon = $price / $vat * 0.9;
} else {
$balloon = $price * 0.9;
}
print '<p>CAP 90% price: <strong>' . $balloon . '</strong></p>';
$totalamountborrowed = $totaltobefunded - $balloon;
print '<p>Total Amount Borrowed: <strong>' . $totalamountborrowed . '</strong></p>';
$fundingrental = $totalamountborrowed * $lom_a / 1000;
print '<p>Funding Rental: <strong>' . $fundingrental . '</strong></p>';
$balloonrental = $balloon * $lom_b / 1000;
print '<p>Funding Rental: <strong>' . $balloonrental . '</strong></p>';
$monthlyfinancerental = $fundingrental + $balloonrental;
print '<p>Monthly Finance Rental: <strong>' . $monthlyfinancerental . '</strong></p>';
$monthlyrentalwithfees = $monthlyfinancerental + $fees;
print '<p>Monthly Finance Rental With Fees: <strong>' . $monthlyrentalwithfees . '</strong></p>';
$totalmargin = $margin * $contract_term;
print '<p>Total Margin: <strong>' . $totalmargin . '</strong></p>';
$totalrentalandfees = $monthlyrentalwithfees * ($contract_term + $deposit_months -1);
print '<p>Total Rental and Fees: <strong>' . $totalrentalandfees . '</strong></p>';
$totalcontractcost = $totalmargin + $totalrentalandfees;
print '<p>Total Contract Cost: <strong>' . $totalcontractcost . '</strong></p>';
$actualmonthlyrental = $totalcontractcost / ($contract_term + $deposit_months -1);
print '<p>Actual Monthly Rental: <strong>' . $actualmonthlyrental . '</strong></p>';
$deposit = $actualmonthlyrental * $deposit_months;
print '<p>Deposit: <strong>' . $deposit . '</strong></p>';
In the PHP code above, I have hard coded all of the variables for the time being just to get this working. In the real life example, these will change for each vehicle.
A Circular Reference exists between N19 (Total to be funded) , N34 (Actual Monthly Rental) and N36 (Deposit).
So at some point before, during, or after the FOR statement, there needs to be...
$totaltobefunded = $totaltobefunded - $deposit;
What I have tried
I have tried using the PHP for from the linked question on my example, but it just keeps taking away the deposit from the Total to be funded, and I am left with minus numbers.
In the example in the link, it has the following results...
1410
1211.19
1239.22221
1235.26966839
1235.826976757
1235.7483962773
1235.7594761249
1235.7579138664
1235.7581341448
1235.7581030856
1235.7581074649
1235.7581068474
This refines the number to the best possible outcome, and this is what I am trying to achieve. Just like my Excel document.
At the moment, my PHP prints out....
Total to be Funded: 7795
VAT: 1559
CAP 90% price: 4687.5
Total Amount Borrowed: 3107.5
Funding Rental: 112.1186
Funding Rental: 24.09375
Monthly Finance Rental: 136.21235
Monthly Finance Rental With Fees: 157.24235
Total Margin: 1200
Total Rental and Fees: 4560.02815
Total Contract Cost: 5760.02815
Actual Monthly Rental: 198.62166034483
Deposit: 1191.729962069
What I need help with
Using the PHP code above (which I have over simplified for this question btw), where should I put my "for" statement in order to correctly loop through the 3 numbers in the circular reference to get the result Im after?
As you can see in the Excel Screenshot, the target numbers are...
Total to be Funded: 6815.32
VAT: 2538.68
CAP 90% price: 4687.5
Total Amount Borrowed: 2127.82
Funding Rental: 76.7717456
Funding Rental: 24.09375
Monthly Finance Rental: 100.8654956
Monthly Finance Rental With Fees: 121.8954956
Total Margin: 1200
Total Rental and Fees: 3534.9693724
Total Contract Cost: 4734.9693724
Actual Monthly Rental: 163.27480594483
Deposit: 979.64883566897
I hope this makes sense to someone and they can assist. I'll answer any questions as best as I can.

Answer 1

The solution in PHP is as follows....
<?php
$vat = '1.2';
$mileage = 10;
$price = 6250.00;
$contract_term = 24;
$deposit_months = 6;
$otr_price = 9409.00;
$discount = 0;
$lom_a = 36.08;
$lom_b = 5.14;
$vehicletype = "Car";
$first_reg_fee = 55.00;
$emission_price = 30.00;
$fees = 21.03;
$margin = 50.00;
$deposit = 0;
if (!empty($discount)) {
$discounted_otr_percent = (int)$discount/100;
$discounted_otr_amount = $discounted_otr_percent * $otr_price;
$discounted_otr = $otr_price-$discounted_otr_amount;
} else {
$discounted_otr = $otr_price;
}
$max_iter = 100;
$max_change = 0.001;
$prev_target_val = PHP_INT_MAX;
$totaltobefunded = 0;
$crt_iter = 0;
while(($crt_iter < $max_iter) && (abs($prev_target_val - $totaltobefunded) > $max_change)) {
$crt_iter++;
$prev_target_val = $totaltobefunded;
$totaltobefunded = ($discounted_otr - $first_reg_fee - 0 /* Emissions */) / $vat - $deposit;
$vatbal = $discounted_otr - $first_reg_fee - 0 /* Emissions */ - $totaltobefunded;
if($vehicletype == "Car") {
$balloon = $price / $vat * 0.9;
} else {
$balloon = $price * 0.9;
}
$totalamountborrowed = $totaltobefunded - $balloon;
$fundingrental = $totalamountborrowed * $lom_a / 1000;
$balloonrental = $balloon * $lom_b / 1000;
$monthlyfinancerental = $fundingrental + $balloonrental;
$monthlyrentalwithfees = $monthlyfinancerental + $fees;
$totalmargin = $margin * $contract_term;
$totalrentalandfees = $monthlyrentalwithfees * ($contract_term + $deposit_months -1);
$totalcontractcost = $totalmargin + $totalrentalandfees;
$actualmonthlyrental = $totalcontractcost / ($contract_term + $deposit_months -1);
$deposit = $actualmonthlyrental * $deposit_months;
}
print '<p>Final Number: <strong>' . $actualmonthlyrental . '</strong></p>';
?>