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<?php
defined ('_JEXEC') or die();
/**
* KlarnaCalc
*
* PHP Version 5.3
*
* @category Payment
* @package KlarnaAPI
* @author MS Dev <ms.modules@klarna.com>
* @copyright 2012 Klarna AB (http://klarna.com)
* @license http://opensource.org/licenses/BSD-2-Clause BSD-2
* @link http://integration.klarna.com/
*/
/**
* KlarnaCalc provides methods to calculate part payment functions.
*
* All rates are yearly rates, but they are calculated monthly. So
* a rate of 9 % is used 0.75% monthly. The first is the one we specify
* to the customers, and the second one is the one added each month to
* the account. The IRR uses the same notation.
*
* The APR is however calculated by taking the monthly rate and raising
* it to the 12 power. This is according to the EU law, and will give
* very large numbers if the $pval is small compared to the $fee and
* the amount of months you repay is small as well.
*
* All functions work in discrete mode, and the time interval is the
* mythical evenly divided month. There is no way to calculate APR in
* days without using integrals and other hairy math. So don't try.
* The amount of days between actual purchase and the first bill can
* of course vary between 28 and 61 days, but all calculations in this
* class assume this time is exactly and that is ok since this will only
* overestimate the APR and all examples in EU law uses whole months as well.
*
* @category Payment
* @package KlarnaAPI
* @author MS Dev <ms.modules@klarna.com>
* @copyright 2012 Klarna AB (http://klarna.com)
* @license http://opensource.org/licenses/BSD-2-Clause BSD-2
* @link http://integration.klarna.com/
*/
class KlarnaCalc
{
/**
* This constant tells the irr function when to stop.
* If the calculation error is lower than this the calculation is done.
*
* @var float
*/
protected static $accuracy = 0.01;
/**
* Calculates the midpoint between two points. Used by divide and conquer.
*
* @param float $a point a
* @param float $b point b
*
* @return float
*/
private static function _midpoint($a, $b)
{
return (($a+$b)/2);
}
/**
* npv - Net Present Value
* Calculates the difference between the initial loan to the customer
* and the individual payments adjusted for the inverse of the interest
* rate. The variable we are searching for is $rate and if $pval,
* $payarray and $rate is perfectly balanced this function returns 0.0.
*
* @param float $pval initial loan to customer (in any currency)
* @param array $payarray array of monthly payments from the customer
* @param float $rate interest rate per year in %
* @param int $fromdayone count interest from the first day? yes(1)/no(0)
*
* @return float
*/
private static function _npv($pval, $payarray, $rate, $fromdayone)
{
$month = $fromdayone;
foreach ($payarray as $payment) {
$pval -= $payment / pow(1 + $rate/(12*100.0), $month++);
}
return ($pval);
}
/**
* This function uses divide and conquer to numerically find the IRR,
* Internal Rate of Return. It starts of by trying a low of 0% and a
* high of 100%. If this isn't enough it will double the interval up
* to 1000000%. Note that this is insanely high, and if you try to convert
* an IRR that high to an APR you will get even more insane values,
* so feed this function good data.
*
* Return values: float irr if it was possible to find a rate that gets
* npv closer to 0 than $accuracy.
* int -1 The sum of the payarray is less than the lent
* amount, $pval. Hellooooooo. Impossible.
* int -2 the IRR is way to high, giving up.
*
* This algorithm works in logarithmic time no matter what inputs you give
* and it will come to a good answer within ~30 steps.
*
* @param float $pval initial loan to customer (in any currency)
* @param array $payarray array of monthly payments from the customer
* @param int $fromdayone count interest from the first day? yes(1)/no(0)
*
* @return float
*/
private static function _irr($pval, $payarray, $fromdayone)
{
$low = 0.0;
$high = 100.0;
$lowval = self::_npv($pval, $payarray, $low, $fromdayone);
$highval = self::_npv($pval, $payarray, $high, $fromdayone);
// The sum of $payarray is smaller than $pval, impossible!
if ($lowval > 0.0) {
return (-1);
}
// Standard divide and conquer.
do {
$mid = self::_midpoint($low, $high);
$midval = self::_npv($pval, $payarray, $mid, $fromdayone);
if (abs($midval) < self::$accuracy) {
//we are close enough
return ($mid);
}
if ($highval < 0.0) {
// we are not in range, so double it
$low = $high;
$lowval = $highval;
$high *= 2;
$highval = self::_npv($pval, $payarray, $high, $fromdayone);
} else if ($midval >= 0.0) {
// irr is between low and mid
$high = $mid;
$highval = $midval;
} else {
// irr is between mid and high
$low = $mid;
$lowval = $midval;
}
} while ($high < 1000000);
// bad input, insanely high interest. APR will be INSANER!
return (-2);
}
/**
* IRR is not the same thing as APR, Annual Percentage Rate. The
* IRR is per time period, i.e. 1 month, and the APR is per year,
* and note that that you need to raise to the power of 12, not
* mutliply by 12.
*
* This function turns an IRR into an APR.
*
* If you feed it a value of 100%, yes the APR will be millions!
* If you feed it a value of 9%, it will be 9.3806%.
* That is the nature of this math and you can check the wiki
* page for APR for more info.
*
* @param float $irr Internal Rate of Return, expressed yearly, in %
*
* @return float Annual Percentage Rate, in %
*/
private static function _irr2apr($irr)
{
return (100 * (pow(1 + $irr / (12 * 100.0), 12) - 1));
}
/**
* This is a simplified model of how our paccengine works if
* a client always pays their bills. It adds interest and fees
* and checks minimum payments. It will run until the value
* of the account reaches 0, and return an array of all the
* individual payments. Months is the amount of months to run
* the simulation. Important! Don't feed it too few months or
* the whole loan won't be paid off, but the other functions
* should handle this correctly.
*
* Giving it too many months has no bad effects, or negative
* amount of months which means run forever, but it will stop
* as soon as the account is paid in full.
*
* Depending if the account is a base account or not, the
* payment has to be 1/24 of the capital amount.
*
* The payment has to be at least $minpay, unless the capital
* amount + interest + fee is less than $minpay; in that case
* that amount is paid and the function returns since the client
* no longer owes any money.
*
* @param float $pval initial loan to customer (in any currency)
* @param float $rate interest rate per year in %
* @param float $fee monthly invoice fee
* @param float $minpay minimum monthly payment allowed for this country.
* @param float $payment payment the client to pay each month
* @param int $months amount of months to run (-1 => infinity)
* @param boolean $base is it a base account?
*
* @return array An array of monthly payments for the customer.
*/
private static function _fulpacc(
$pval, $rate, $fee, $minpay, $payment, $months, $base
) {
$bal = $pval;
$payarray = array();
while (($months != 0) && ($bal > self::$accuracy)) {
$interest = $bal * $rate / (100.0 * 12);
$newbal = $bal + $interest + $fee;
if ($minpay >= $newbal || $payment >= $newbal) {
$payarray[] = $newbal;
return $payarray;
}
$newpay = max($payment, $minpay);
if ($base) {
$newpay = max($newpay, $bal/24.0 + $fee + $interest);
}
$bal = $newbal - $newpay;
$payarray[] = $newpay;
$months -= 1;
}
return $payarray;
}
/**
* Calculates how much you have to pay each month if you want to
* pay exactly the same amount each month. The interesting input
* is the amount of $months.
*
* It does not include the fee so add that later.
*
* Return value: monthly payment.
*
* @param float $pval principal value
* @param int $months months to pay of in
* @param float $rate interest rate in % as before
*
* @return float monthly payment
*/
private static function _annuity($pval, $months, $rate)
{
if ($months == 0) {
return $pval;
}
if ($rate == 0) {
return $pval/$months;
}
$p = $rate / (100.0*12);
return $pval * $p / (1 - pow((1+$p), -$months));
}
/**
* Calculate the APR for an annuity given the following inputs.
*
* If you give it bad inputs, it will return negative values.
*
* @param float $pval principal value
* @param int $months months to pay off in
* @param float $rate interest rate in % as before
* @param float $fee monthly fee
* @param float $minpay minimum payment per month
*
* @return float APR in %
*/
private static function _aprAnnuity($pval, $months, $rate, $fee, $minpay)
{
$payment = self::_annuity($pval, $months, $rate) + $fee;
if ($payment < 0) {
return $payment;
}
$payarray = self::_fulpacc(
$pval, $rate, $fee, $minpay, $payment, $months, false
);
$apr = self::_irr2apr(self::_irr($pval, $payarray, 1));
return $apr;
}
/**
* Grabs the array of all monthly payments for specified PClass.
*
* <b>Flags can be either</b>:<br>
* {@link KlarnaFlags::CHECKOUT_PAGE}<br>
* {@link KlarnaFlags::PRODUCT_PAGE}<br>
*
* @param float $sum The sum for the order/product.
* @param KlarnaPClass $pclass KlarnaPClass used to calculate the APR.
* @param int $flags Checkout or Product page.
*
* @throws KlarnaException
* @return array An array of monthly payments.
*/
private static function _getPayArray($sum, $pclass, $flags)
{
$monthsfee = 0;
if ($flags === KlarnaFlags::CHECKOUT_PAGE) {
$monthsfee = $pclass->getInvoiceFee();
}
$startfee = 0;
if ($flags === KlarnaFlags::CHECKOUT_PAGE) {
$startfee = $pclass->getStartFee();
}
//Include start fee in sum
$sum += $startfee;
$base = ($pclass->getType() === KlarnaPClass::ACCOUNT);
$lowest = self::get_lowest_payment_for_account($pclass->getCountry());
if ($flags == KlarnaFlags::CHECKOUT_PAGE) {
$minpay = ($pclass->getType() === KlarnaPClass::ACCOUNT) ? $lowest : 0;
} else {
$minpay = 0;
}
$payment = self::_annuity(
$sum,
$pclass->getMonths(),
$pclass->getInterestRate()
);
//Add monthly fee
$payment += $monthsfee;
return self::_fulpacc(
$sum,
$pclass->getInterestRate(),
$monthsfee,
$minpay,
$payment,
$pclass->getMonths(),
$base
);
}
/**
* Calculates APR for the specified values.<br>
* Result is rounded with two decimals.<br>
*
* <b>Flags can be either</b>:<br>
* {@link KlarnaFlags::CHECKOUT_PAGE}<br>
* {@link KlarnaFlags::PRODUCT_PAGE}<br>
*
* @param float $sum The sum for the order/product.
* @param KlarnaPClass $pclass KlarnaPClass used to calculate the APR.
* @param int $flags Checkout or Product page.
* @param int $free Number of free months.
*
* @throws KlarnaException
* @return float APR in %
*/
public static function calc_apr($sum, $pclass, $flags, $free = 0)
{
if (!is_numeric($sum)) {
throw new Klarna_InvalidTypeException('sum', 'numeric');
}
if (is_numeric($sum) && (!is_int($sum) || !is_float($sum))) {
$sum = floatval($sum);
}
if (!($pclass instanceof KlarnaPClass)) {
throw new Klarna_InvalidTypeException('pclass', 'KlarnaPClass');
}
if (!is_numeric($free)) {
throw new Klarna_InvalidTypeException('free', 'integer');
}
if (is_numeric($free) && !is_int($free)) {
$free = intval($free);
}
if ($free < 0) {
throw new KlarnaException(
'Error in ' . __METHOD__ .
': Number of free months must be positive or zero!'
);
}
if (is_numeric($flags) && !is_int($flags)) {
$flags = intval($flags);
}
if (!is_numeric($flags)
|| !in_array(
$flags, array(
KlarnaFlags::CHECKOUT_PAGE, KlarnaFlags::PRODUCT_PAGE
)
)
) {
throw new Klarna_InvalidTypeException(
'flags',
KlarnaFlags::CHECKOUT_PAGE . ' or ' . KlarnaFlags::PRODUCT_PAGE
);
}
$monthsfee = 0;
if ($flags === KlarnaFlags::CHECKOUT_PAGE) {
$monthsfee = $pclass->getInvoiceFee();
}
$startfee = 0;
if ($flags === KlarnaFlags::CHECKOUT_PAGE) {
$startfee = $pclass->getStartFee();
}
//Include start fee in sum
$sum += $startfee;
$lowest = self::get_lowest_payment_for_account($pclass->getCountry());
if ($flags == KlarnaFlags::CHECKOUT_PAGE) {
$minpay = ($pclass->getType() === KlarnaPClass::ACCOUNT) ? $lowest : 0;
} else {
$minpay = 0;
}
//add monthly fee
$payment = self::_annuity(
$sum,
$pclass->getMonths(),
$pclass->getInterestRate()
) + $monthsfee;
$type = $pclass->getType();
switch($type) {
case KlarnaPClass::CAMPAIGN:
case KlarnaPClass::ACCOUNT:
return round(
self::_aprAnnuity(
$sum, $pclass->getMonths(),
$pclass->getInterestRate(),
$pclass->getInvoiceFee(),
$minpay
),
2
);
case KlarnaPClass::SPECIAL:
throw new Klarna_PClassException(
'Method is not available for SPECIAL pclasses'
);
case KlarnaPClass::FIXED:
throw new Klarna_PClassException(
'Method is not available for FIXED pclasses'
);
default:
throw new Klarna_PClassException(
'Unknown PClass type! ('.$type.')'
);
}
}
/**
* Calculates the total credit purchase cost.<br>
* The result is rounded up, depending on the pclass country.<br>
*
* <b>Flags can be either</b>:<br>
* {@link KlarnaFlags::CHECKOUT_PAGE}<br>
* {@link KlarnaFlags::PRODUCT_PAGE}<br>
*
* @param float $sum The sum for the order/product.
* @param KlarnaPClass $pclass PClass used to calculate total credit cost.
* @param int $flags Checkout or Product page.
*
* @throws KlarnaException
* @return float Total credit purchase cost.
*/
public static function total_credit_purchase_cost($sum, $pclass, $flags)
{
if (!is_numeric($sum)) {
throw new Klarna_InvalidTypeException('sum', 'numeric');
}
if (is_numeric($sum) && (!is_int($sum) || !is_float($sum))) {
$sum = floatval($sum);
}
if (!($pclass instanceof KlarnaPClass)) {
throw new Klarna_InvalidTypeException('pclass', 'KlarnaPClass');
}
if (is_numeric($flags) && !is_int($flags)) {
$flags = intval($flags);
}
if (!is_numeric($flags)
|| !in_array(
$flags,
array(
KlarnaFlags::CHECKOUT_PAGE, KlarnaFlags::PRODUCT_PAGE
)
)
) {
throw new Klarna_InvalidTypeException(
'flags',
KlarnaFlags::CHECKOUT_PAGE . ' or ' . KlarnaFlags::PRODUCT_PAGE
);
}
$payarr = self::_getPayArray($sum, $pclass, $flags);
$credit_cost = 0;
foreach ($payarr as $pay) {
$credit_cost += $pay;
}
return self::pRound($credit_cost, $pclass->getCountry());
}
/**
* Calculates the monthly cost for the specified pclass.
* The result is rounded up to the correct value depending on the
* pclass country.<br>
*
* Example:<br>
* <ul>
* <li>In product view, round monthly cost with max 0.5 or 0.1
* depending on currency.<br>
* <ul>
* <li>10.50 SEK rounds to 11 SEK</li>
* <li>10.49 SEK rounds to 10 SEK</li>
* <li> 8.55 EUR rounds to 8.6 EUR</li>
* <li> 8.54 EUR rounds to 8.5 EUR</li>
* </ul></li>
* <li>
* In checkout, round the monthly cost to have 2 decimals.<br>
* For example 10.57 SEK/per månad
* </li>
* </ul>
*
* <b>Flags can be either</b>:<br>
* {@link KlarnaFlags::CHECKOUT_PAGE}<br>
* {@link KlarnaFlags::PRODUCT_PAGE}<br>
*
* @param int $sum The sum for the order/product.
* @param KlarnaPClass $pclass PClass used to calculate monthly cost.
* @param int $flags Checkout or product page.
*
* @throws KlarnaException
* @return float The monthly cost.
*/
public static function calc_monthly_cost($sum, $pclass, $flags)
{
if (!is_numeric($sum)) {
throw new Klarna_InvalidTypeException('sum', 'numeric');
}
if (is_numeric($sum) && (!is_int($sum) || !is_float($sum))) {
$sum = floatval($sum);
}
if (!($pclass instanceof KlarnaPClass)) {
throw new Klarna_InvalidTypeException('pclass', 'KlarnaPClass');
}
if (is_numeric($flags) && !is_int($flags)) {
$flags = intval($flags);
}
if (!is_numeric($flags)
|| !in_array(
$flags,
array(
KlarnaFlags::CHECKOUT_PAGE, KlarnaFlags::PRODUCT_PAGE
)
)
) {
throw new Klarna_InvalidTypeException(
'flags',
KlarnaFlags::CHECKOUT_PAGE . ' or ' . KlarnaFlags::PRODUCT_PAGE
);
}
$payarr = self::_getPayArray($sum, $pclass, $flags);
$value = 0;
if (isset($payarr[0])) {
$value = $payarr[0];
}
if (KlarnaFlags::CHECKOUT_PAGE == $flags) {
return round($value, 2);
}
return self::pRound($value, $pclass->getCountry());
}
/**
* Returns the lowest monthly payment for Klarna Account.
*
* @param int $country KlarnaCountry constant.
*
* @throws KlarnaException
* @return int|float Lowest monthly payment.
*/
public static function get_lowest_payment_for_account($country)
{
$country = KlarnaCountry::getCode($country);
switch (strtoupper($country)) {
case "SE":
return 50.0;
case "NO":
return 95.0;
case "FI":
return 8.95;
case "DK":
return 89.0;
case "DE":
case "AT":
return 6.95;
case "NL":
return 5.0;
default:
throw new KlarnaException("Invalid country {$country}");
}
}
/**
* Rounds a value depending on the specified country.
*
* @param int|float $value The value to be rounded.
* @param int $country KlarnaCountry constant.
*
* @return float|int
*/
public static function pRound($value, $country)
{
$multiply = 1; //Round to closest integer
$country = KlarnaCountry::getCode($country);
switch($country) {
case "FI":
case "DE":
case "NL":
case "AT":
$multiply = 10; //Round to closest decimal
break;
}
return floor(($value*$multiply)+0.5)/$multiply;
}
}
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