How to compute the valuation of a cash flow in the presence of a wealth tax.

valuation_of_cash_flow_with_wealth_tax.py

import numpy as np
from numpy.linalg import solve

def vmat(n, discount_rate, tax_rate):
    m = np.zeros(shape=(n,n))
    discount = tax_rate*np.exp(-1*discount_rate*np.arange(n))
    for i in range(n):
        m[i, i:n] = discount[0:n-i]
        m[i,i] = 1
    return m

def remaining_cashflow(cash_flow, discount_rate):
    _discount = np.exp(-1*discount_rate*np.arange(len(cash_flow)))
    return np.convolve(cash_flow, _discount[::-1])[len(cash_flow)-1:]

def valuation(cash_flow, discount_rate, tax_rate):
    """
    Returns the valuation of a cash flow, as well as the current NPV of a cash flow, for a given cash flow sequence given as input.
    """
    return solve(vmat(len(cash_flow), discount_rate, tax_rate), remaining_cash_flow(cash_flow, discount_rate))