/**
* @return string
*/
public function getBondFairValue()
{
// we need to get the coupon rate per payment period = c/payment frequency
$couponRateForPeriod = MathFuncs::div($this->bondAnnualCouponRate, $this->bondPaymentFrequency);
// similarly, we need to calculate the VIR per payment period = i/payment frequency
$VIRForPeriod = MathFuncs::div($this->bondVIR, $this->bondPaymentFrequency);
// we also save the bond's number of payments to an auxillary variable
$bondNoOfPayments = $this->getBondNoOfPayments();
// next, we also need the present value of the unit annuity pertaining to the bond, in arrears
$PVofUnitBondAnnuity = MathFuncs::div(MathFuncs::sub(1, Mathfuncs::pow(MathFuncs::div(1, MathFuncs::add(1, $VIRForPeriod)), $bondNoOfPayments)), $VIRForPeriod);
// now we can use the formula to calculate the real value of the bond (i.e., the present value of its payments)
// PV = F*[c*PVofUnitBondAnnuity+1/((1+i)^n)]
$fairValue = MathFuncs::mul($this->bondFaceValue, MathFuncs::add(MathFuncs::mul($couponRateForPeriod, $PVofUnitBondAnnuity), MathFuncs::div(1, MathFuncs::pow(MathFuncs::add(1, $VIRForPeriod), $bondNoOfPayments))));
return $fairValue;
}
public function testPow()
{
$this->assertEquals("53.157376", MathFuncs::pow(3.76, 3));
}
/**
* @return string [Value of a single debt repayment instance as a string]
*/
public function getDebtSingleRepayment()
{
// single repayment 'K = PV/((1-v^n)/i)'
return MathFuncs::div($this->debtPrincipal, MathFuncs::div(MathFuncs::sub(1, MathFuncs::pow($this->getDebtDiscountFactor(), $this->debtNoOfCompoundingPeriods)), $this->debtInterest));
}
/**
* @param AnnuityPaymentTypes $annuityPaymentType
* @param AnnuityValueTypes $annuityValueType
* @return null|string
* @throws Exception
*/
public function getAnnuityValue(AnnuityPaymentTypes $annuityPaymentType = null, AnnuityValueTypes $annuityValueType)
{
// if the number of the annuity's compounding periods
// is set to zero, we're dealing with a perpetuity
if (Helpers::checkIfZero($this->annuityNoOfCompoundingPeriods)) {
// we cannot calculate FV of a perpetuity, we therefore return null
// in case such a value is demanded
if ($annuityValueType->getValue() == AnnuityValueTypes::FUTURE_VALUE) {
return null;
}
// PV of a perpetuity = K/i
return Helpers::roundMoneyForDisplay(MathFuncs::div($this->annuitySinglePaymentAmount, $this->annuityInterest));
}
// when the annuity is not a perpetuity, we first need to check that
// the $annuityPaymentType is not null
if (Helpers::checkIfNotNull($annuityPaymentType)) {
// discount factor 'v = 1/(1+i)'
$discountFactor = MathFuncs::div(1, MathFuncs::add(1, $this->annuityInterest));
if ($annuityValueType->getValue() == AnnuityValueTypes::PRESENT_VALUE) {
// PV numerator = 1-v^n
$numerator = MathFuncs::sub(1, MathFuncs::pow($discountFactor, $this->annuityNoOfCompoundingPeriods));
} elseif ($annuityValueType->getValue() == AnnuityValueTypes::FUTURE_VALUE) {
// FV numerator = (1+i)^n-1
$numerator = MathFuncs::sub(MathFuncs::pow(MathFuncs::add(1, $this->annuityInterest), $this->annuityNoOfCompoundingPeriods), 1);
}
if ($annuityPaymentType->getValue() == AnnuityPaymentTypes::IN_ADVANCE) {
// in advance denom. = 1-v
$denominator = MathFuncs::sub(1, $discountFactor);
} elseif ($annuityPaymentType->getValue() == AnnuityPaymentTypes::IN_ARREARS) {
// in arrears denom. = i
$denominator = $this->annuityInterest;
}
if (isset($numerator) && isset($denominator)) {
return MathFuncs::mul(MathFuncs::div($numerator, $denominator), $this->annuitySinglePaymentAmount);
}
}
return null;
}
/**
* @return array
*/
public function getBondDiscountedCashFlows()
{
// discounted cash flows = nominal cash flows discounted by the means of yield
$discountFactor = MathFuncs::div(1, MathFuncs::add(1, $this->getBondYieldPerPaymentPeriod()));
$nominalCashFlows = $this->getBondNominalCashFlows();
$discountedCashFlows = array();
$i = 1;
foreach ($nominalCashFlows as $nominalCashFlowEntry) {
$discountedCashFlows[] = MathFuncs::mul($nominalCashFlowEntry, MathFuncs::pow($discountFactor, $i++));
}
return $discountedCashFlows;
}