discount function

[Bshlomis]

what if the payment occurs in arrear? is there any way to implement this in the discount function?

[zchmielewska]

Hi @Bshlomis,

thanks for the question.

Here's a simple example: there are three payments of 1000. The interest rates are 4%, 5% and 3%.

1. Payments in arrears

# model.py
import numpy as np
from cashflower import discount, variable


@variable(array=True)
def discount_rates():
    return np.array([1, 1/1.04, 1/1.05, 1/1.03])


@variable(array=True)
def payments_in_arrears():
    return np.array([0, 1000, 1000, 1000])


@variable(array=True)
def pv_payments_in_arrears():
    return discount(cash_flows=payments_in_arrears(), discount_rates=discount_rates())

# settings.py
settings = {
    # ...
    "T_MAX_CALCULATION": 3,
    "T_MAX_OUTPUT": 3,
}

2. Payments due

# model.py
import numpy as np
from cashflower import discount, variable


@variable(array=True)
def discount_rates():
    return np.array([1, 1/1.04, 1/1.05, 1/1.03])


@variable(array=True)
def payments_due():
    return np.array([1000, 1000, 1000, 0])


@variable(array=True)
def pv_payments_due():
    return discount(cash_flows=payments_due(), discount_rates=discount_rates())

# settings.py
settings = {
    # ...
    "T_MAX_CALCULATION": 3,
    "T_MAX_OUTPUT": 3,
}

Output

 t  discount_rates  payments_due  payments_in_arrears  pv_payments_due  pv_payments_in_arrears
 0            1.00       1000.00                 0.00          2877.29                 2766.37
 1            0.96       1000.00              1000.00          1952.38                 2877.02
 2            0.95       1000.00              1000.00          1000.00                 1970.87
 3            0.97          0.00              1000.00             0.00                 1000.00