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<?php |
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namespace Common\Tool; |
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class Financial |
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{ |
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private const FINANCIAL_ACCURACY = 1.0e-6; |
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private const FINANCIAL_MAX_ITERATIONS = 100; |
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private static $isInitialized = false; |
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private static function init() |
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{ |
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if (!self::$isInitialized) { |
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// forces the precision for calculations |
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ini_set('precision', '14'); |
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self::$isInitialized = true; |
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} |
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} |
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/** |
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* Present value interest factor |
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* |
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* nper |
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* PVIF = (1 + rate) |
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* |
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* @param float $rate is the interest rate per period. |
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* @param integer $nper is the total number of periods. |
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* |
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* @return float the present value interest factor |
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*/ |
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private static function PVIF($rate, $nper) |
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{ |
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self::init(); |
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return ((1 + $rate) ** $nper); |
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} |
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/** |
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* Future value interest factor of annuities |
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* |
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* nper |
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* (1 + rate) - 1 |
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* FVIFA = ------------------- |
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* rate |
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* |
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* @param float $rate is the interest rate per period. |
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* @param integer $nper is the total number of periods. |
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* |
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* @return float the present value interest factor of annuities |
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*/ |
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private static function FVIFA($rate, $nper) |
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{ |
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self::init(); |
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// Removable singularity at rate == 0 |
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if ($rate == 0) { |
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return $nper; |
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} |
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return (((1 + $rate) ** $nper) - 1) / $rate; |
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} |
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/** |
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* @param $pv |
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* @param $pmt |
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* @param $rate |
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* @param $period |
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* |
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* @return mixed |
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*/ |
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private static function interestPart($pv, $pmt, $rate, $period) |
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{ |
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self::init(); |
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return -($pv * ((1 + $rate) ** $period) * $rate + $pmt * (((1 + $rate) ** $period) - 1)); |
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} |
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public static function PMT($rate, $nper, $pv, $fv, $type = 0) |
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{ |
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self::init(); |
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// Calculate the PVIF and FVIFA |
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$pvif = self::PVIF($rate, $nper); |
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$fvifa = self::FVIFA($rate, $nper); |
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return ((-$pv * $pvif - $fv) / ((1.0 + $rate * $type) * $fvifa)); |
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} |
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/** |
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* IPMT |
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* Returns the interest payment for a given period for an investment based |
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* on periodic, constant payments and a constant interest rate. |
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* |
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* For a more complete description of the arguments in IPMT, see the PV function. |
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* |
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* |
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* Make sure that you are consistent about the units you use for specifying rate and nper. If you make monthly payments on a four-year loan at 12 percent annual interest, use 12%/12 for rate and 4*12 for nper. If you make annual payments on the same loan, use 12% for rate and 4 for nper. |
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* For all the arguments, cash you pay out, such as deposits to savings, is represented by negative numbers; cash you receive, such as dividend checks, is represented by positive numbers. |
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* |
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* @param $rate // The interest rate per period. |
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* @param $per // The period for which you want to find the interest and must be in the range 1 to nper. |
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* @param $nper // The total number of payment periods in an annuity. |
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* @param $pv // The present value, or the lump-sum amount that a series of future payments is worth right now. |
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* @param float $fv // The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). |
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* @param int $type // The number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0. |
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* |
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* @return mixed|null |
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*/ |
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public static function IPMT($rate, $per, $nper, $pv, $fv = 0.0, $type = 0) |
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{ |
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self::init(); |
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if (($per < 1) || ($per >= ($nper + 1))) { |
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return null; |
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} |
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$pmt = self::PMT($rate, $nper, $pv, $fv, $type); |
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$ipmt = self::interestPart($pv, $pmt, $rate, $per - 1); |
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if (!is_finite($ipmt)) { |
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return null; |
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} |
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return $ipmt; |
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} |
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/** |
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* PPMT |
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* Returns the payment on the principal for a given period for an |
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* investment based on periodic, constant payments and a constant |
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* interest rate. |
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* |
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* @param $rate //Required. The interest rate per period. |
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* @param $per //Required. The period for which you want to find the interest and must be in the range 1 to nper. |
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* @param $nper //Required. The total number of payment periods in an annuity. |
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* @param $pv //Required. The present value, or the lump-sum amount that a series of future payments is worth right now. |
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* @param float $fv //Optional. The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). |
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* @param int $type //Optional. The number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0. |
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* |
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* @return float|null |
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*/ |
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public static function PPMT($rate, $per, $nper, $pv, $fv = 0.0, $type = 0) |
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{ |
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self::init(); |
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if (($per < 1) || ($per >= ($nper + 1))) { |
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return null; |
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} |
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$pmt = self::PMT($rate, $nper, $pv, $fv, $type); |
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$ipmt = self::interestPart($pv, $pmt, $rate, $per - 1); |
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return ((is_finite($pmt) && is_finite($ipmt)) ? $pmt - $ipmt : null); |
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} |
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/** |
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* NPV |
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* Calculates the net present value of an investment by using a |
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* discount rate and a series of future payments (negative values) |
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* and income (positive values). |
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* |
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* n / values(i) \ |
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* NPV = SUM | -------------- | |
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* i=1 | i | |
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* \ (1 + rate) / |
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* |
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* @param float $rate |
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* @param float[] $values |
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* |
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* @return float|int|null |
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*/ |
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private static function NPV($rate, $values) |
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{ |
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self::init(); |
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if (!is_array($values)) { |
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return null; |
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} |
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$npv = 0.0; |
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foreach ($values as $i => $iValue) { |
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$npv += $iValue / ((1 + $rate) ** ($i + 1)); |
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} |
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return (is_finite($npv) ? $npv : null); |
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} |
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/** |
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* IRR |
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* Returns the internal rate of return for a series of cash flows |
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* represented by the numbers in values. These cash flows do not |
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* have to be even, as they would be for an annuity. However, the |
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* cash flows must occur at regular intervals, such as monthly or |
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* annually. The internal rate of return is the interest rate |
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* received for an investment consisting of payments (negative |
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* values) and income (positive values) that occur at regular periods. |
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* |
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* @param float[] $values |
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* @param float $guess |
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* |
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* @return float|null |
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*/ |
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public static function IRR($values, $guess = 0.1) |
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{ |
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self::init(); |
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if (!is_array($values)) { |
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return null; |
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} |
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// create an initial bracket, with a root somewhere between bot and top |
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$x1 = 0.0; |
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$x2 = $guess; |
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$f1 = self::NPV($x1, $values); |
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$f2 = self::NPV($x2, $values); |
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for ($i = 0; $i < self::FINANCIAL_MAX_ITERATIONS; $i++) { |
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if (($f1 * $f2) < 0.0) { |
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break; |
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} |
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if (abs($f1) < abs($f2)) { |
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$f1 = self::NPV($x1 += 1.6 * ($x1 - $x2), $values); |
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} else { |
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$f2 = self::NPV($x2 += 1.6 * ($x2 - $x1), $values); |
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} |
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} |
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if (($f1 * $f2) > 0.0) { |
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return null; |
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} |
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$f = self::NPV($x1, $values); |
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if ($f < 0.0) { |
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$rtb = $x1; |
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$dx = $x2 - $x1; |
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} else { |
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$rtb = $x2; |
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$dx = $x1 - $x2; |
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} |
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for ($i = 0; $i < self::FINANCIAL_MAX_ITERATIONS; $i++) { |
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$dx *= 0.5; |
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$x_mid = $rtb + $dx; |
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$f_mid = self::NPV($x_mid, $values); |
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if ($f_mid <= 0.0) { |
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$rtb = $x_mid; |
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} |
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if ((abs($f_mid) < self::FINANCIAL_ACCURACY) || (abs($dx) < self::FINANCIAL_ACCURACY)) { |
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return $x_mid; |
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} |
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} |
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return null; |
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} |
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/** |
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* @param float[] $values |
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* @param int[] $timestamps |
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* @param float $guess |
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* |
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* @return float|null |
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*/ |
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public static function XIRR($values, $timestamps, $guess = 0.1) |
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{ |
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self::init(); |
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// Initialize dates and check that values contains at least one positive value and one negative value |
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$positive = false; |
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$negative = false; |
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//XIRR Return error if number of values does not equal to number of timestamps |
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if (count($values) != count($timestamps)) { |
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return null; |
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} |
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//XIRR sort array on key (not sure whether it is needed, but just to be sure :-)) |
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array_multisort($timestamps, $values); |
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//XIRR determine first timestamp |
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$lowestTimestamp = new \DateTime('@' . min($timestamps)); |
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$dates = []; |
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foreach ($values as $key => $value) { |
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//XIRR Calculate the number of days between the given timestamp and the lowest timestamp |
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$dates[] = date_diff($lowestTimestamp, date_create('@' . $timestamps[$key]))->days; |
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if ($value > 0) { |
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$positive = true; |
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} |
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if ($value < 0) { |
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$negative = true; |
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} |
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} |
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//XIRR remove all keys from the input array (which are the timestamps) |
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$values = array_values($values); |
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// Return error if values does not contain at least one positive value and one negative value |
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if (!$positive || !$negative) { |
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return null; |
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} |
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// Initialize guess and resultRate |
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$resultRate = $guess; |
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// Implement Newton's method |
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$iteration = 0; |
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$contLoop = true; |
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while ($contLoop && (++$iteration < self::FINANCIAL_MAX_ITERATIONS)) { |
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$resultValue = self::irrResult($values, $dates, $resultRate); |
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$newRate = $resultRate - $resultValue / self::irrResultDeriv($values, $dates, $resultRate); |
|
315
|
|
|
$epsRate = abs($newRate - $resultRate); |
|
316
|
|
|
$resultRate = $newRate; |
|
317
|
|
|
$contLoop = ($epsRate > self::FINANCIAL_ACCURACY) && (abs($resultValue) > self::FINANCIAL_ACCURACY); |
|
318
|
|
|
} |
|
319
|
|
|
|
|
320
|
|
|
if ($contLoop) { |
|
321
|
|
|
return null; |
|
322
|
|
|
} |
|
323
|
|
|
|
|
324
|
|
|
// Return internal rate of return |
|
325
|
|
|
return $resultRate; |
|
326
|
|
|
} |
|
327
|
|
|
|
|
328
|
|
|
// Calculates the resulting amount |
|
329
|
|
|
private static function irrResult($values, $dates, $rate) |
|
330
|
|
|
{ |
|
331
|
|
|
self::init(); |
|
332
|
|
|
|
|
333
|
|
|
$r = $rate + 1; |
|
334
|
|
|
$result = $values[0]; |
|
335
|
|
|
for ($i = 1, $iMax = count($values); $i < $iMax; $i++) { |
|
336
|
|
|
$result += $values[$i] / ($r ** (($dates[$i] - $dates[0]) / 365)); |
|
337
|
|
|
} |
|
338
|
|
|
|
|
339
|
|
|
return $result; |
|
340
|
|
|
} |
|
341
|
|
|
|
|
342
|
|
|
// Calculates the first derivation |
|
343
|
|
|
private static function irrResultDeriv($values, $dates, $rate) |
|
344
|
|
|
{ |
|
345
|
|
|
self::init(); |
|
346
|
|
|
|
|
347
|
|
|
$r = $rate + 1; |
|
348
|
|
|
$result = 0; |
|
349
|
|
|
for ($i = 1, $iMax = count($values); $i < $iMax; $i++) { |
|
350
|
|
|
$frac = ($dates[$i] - $dates[0]) / 365; |
|
351
|
|
|
$result -= $frac * $values[$i] / ($r ** ($frac + 1)); |
|
352
|
|
|
} |
|
353
|
|
|
|
|
354
|
|
|
return $result; |
|
355
|
|
|
} |
|
356
|
|
|
|
|
357
|
|
|
|
|
358
|
|
|
/** |
|
359
|
|
|
* @param float $apr Interest rate. |
|
360
|
|
|
* @param integer $term Loan length in years. |
|
361
|
|
|
* @param float $loan The loan amount. |
|
362
|
|
|
* |
|
363
|
|
|
* @return float |
|
364
|
|
|
*/ |
|
365
|
|
|
public function calculatePMT($apr, int $term, $loan): float |
|
366
|
|
|
{ |
|
367
|
|
|
$term = $term * 12; |
|
368
|
|
|
$apr = $apr / 1200; |
|
369
|
|
|
$amount = $apr * -$loan * ((1 + $apr) ** $term) / (1 - ((1 + $apr) ** $term)); |
|
370
|
|
|
|
|
371
|
|
|
return round($amount); |
|
372
|
|
|
|
|
373
|
|
|
} |
|
374
|
|
|
} |
|
375
|
|
|
|